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University Microfilms International 300 North Zeeb Road Ann Arbor, Michigan 48106 USA St. John's Road, Tyler's Green High Wycombe, Bucks, England HP10 8HR 1 I
77-31,975
SHESKIN, Ira Martin, 1950- A PLANNING MODEL OF THE NATURAL GAS PIPELINE NETWORK.
The Ohio State University, Ph.D., 1977 Transportation
University Microfilms International, Ann Arbor, Michigan 4 bim
@ 1977
IRA MARTIN SHESKIN
ALL RIGHTS RESERVED A PLANNING MODEL OF THE NATURAL GAS PIPELINE NETWORK
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
•By
Ira M. Sheskin, B.A., M.A.
* * * #
The Ohio State University
1977
Reading Committee Approved by
Dr. Jeffrey P. Osleeb Dr. Howard L. Gauthier Dr. Edward J. Taaffe
Department of Geography ACKNOWLEDGMENTS
Although a dissertation is theoretically the work of one man, this is rarely the case in reality. A large number of people contributed to the fruition of this project. Acknowledgments are most gratefully extended to
Jeffrey P. Osleeb, my adviser, for his most percep tive suggestion of a research topic and his continual guidance and advice. On a personal level, Jeff generated a warm, personal friendship that was itself an inspiration to the successful completion* of this dissertation.
Howard L. Gauthier, my "in-house" adviser, who gave me his time well beyond the call of duty as a committee member. Thanks are also due for his loan of the OKA computer program.
Edward J. Taaffe, for his helpful comments at various stages of the project.
the Reading Committee as a whole for their most expedient "turn-around".
Barry Lentnek (who begat Jeff) without whom 1 never would have had the confidence to get into this mess in the first place.
ii the faculty at SUNY at Buffalo and Ohio State. A
dissertation is the culmination of one’s total graduate
training.
the graduate students at Ohio State, particularly
Robert Cromley and Charles Morrow-Jones, who had many ideas
"bounced" off them.
Robert Brooks for his most helpful suggestions.
Ellis Boyd of the Federal Power Commission who is
the most helpful and cooperative public servant I found in
any agency.
Bill Monroe of the Federal Power Commission for his
help on the pipeline flow diagrams.
David Sweet of the Public Utility Commission of Ohio
for his information on Ohio natural gas,
Lowell Elder of Columbia Gas for his assistance.
my Parents who have always wanted to say, "My son,
the doctor", but geographyl who instilled in me the need
to know and the will to succeed.
Karen, my wife, who offered the type of comfort
during some of the "darkest" moments of the research that
none of the above persons could.
Nef, who is the best listener of them all.
iii
« VITA
June 10, 1950 ...... Born - Brooklyn, New York * 1972...... B.A. Magna Cuih Laude, Geography, State University of New York at Buffalo, Buffalo, New York
1972-1974 ...... Teaching and Research Assistant, Department of Geography, State University of New York at Buffalo, Buffalo, New York
197 4 ...... M.A., Geography, State University of New York at Buffalo, Buffalo, New York
1974-1975 , ...... Teaching Assistant, Department of Geography, The Ohio State Univer sity, Columbus, Ohio
197 5 ...... Research Assistant, Department of Geography, The Ohio State Univer sity, Columbus, Ohio
1975-1977 ...... Teaching Associate, Department of Geography,. The Ohio State Univer sity, Columbus, Ohio
PUBLICATIONS
"Consumer Behavior in Different Areas", with Barry Lentnek and Stanley R. Lieber, Annals of the Association of Ameri can Geographers, Vol. 65 (December7 1975? pp* 538 -5*4-5 .
"Natural Gas* A Geographical Perspective”, with Jeffrey P. Osleeb, Geographical Review, Vol. 66 (January, 1977) PP* 71-85*
"Consumer Behavior and Urban Spatial Structure in Mexico", with Barry Lentnek and Stanley R. Lieber, in Latin Amerioai Search for Geographic Explanations, Proceedings of the Con ference of Latin Americanist Geographers. Robert Tata, Editor, Vol. V (±976) PP* 57-^* iv "Current and Future Prospects for Canadian-U.S. Natural Gas Trade", with Jeffrey P. Osleeb, Proceedings of the Middle States Division. Association of American Geograph ers, John B. Garver, Jr. and John H. Munson, Editors, VoT. IX (1975) PP. 76-79. "A Selection of Exercises for Introductory Human Geography Courses with Comments for Instructors", with Marylin A. Brown, Ohio State University, Department of Geography, Discussion Paper No. (January, 1977)*
"A Selection of Exercises for Introductory Human Geography Courses", with Marylin A. Brown, Ohio State University, Department of Geography, Discussion Paper No. (January, 1977) (Available in Bulk).
"The Reconstitution of Regression Coefficients in Principal Components Regression Analysis", Ohio State University, Department of Geography, Discussion Paper No. 55 (May, 1977).
Review of Urban Transportation Modeling and Planning, by Peter R. Stopher and Arnim H. Me.vburg and Urban Travel Demand, A Behavioral Analysis, by Thomas A. Domencich and . Daniel McFadden in Geographical Analysis (forthcoming).
AWARDS
Phi Beta Kappa, State University of New York at Buffalo
Alumni Awards for Graduate Student Research.and Creative Achievement, Finalist, The Ohio State University, 1976
FIELDS OF STUDY
Studies in Transportation Geography. Professors Howard L. Gauthier and Edward J. Taaffe
Studies in Urban Transportation Planning. Professors Howard L. Gauthier and Michael Godfrey
Studies in Quantitative and Urban Geography. Professor Jeffrey P . Osleeb
v TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS ...... ii
VITA...... iv
LIST OF TABLES...... x
LIST OF FIGURES ...... xii
LIST OF ABBREVIATIONS...... xv
Chapter
1. INTRODUCTION ...... 1
2. NORMATIVE COMMODITY FLOW STUDY IN GEOGRAPHYt A LITERATURE REVIEW...... 9
2.1 The Transportation Problem ...... 11
2.2 The Out-of-Kilter Algorithm...... 18
2.3 Other Mathematical Programming Approaches ...... 2k
Z.k Conclusions...... 2?
3. A SPATIAL ANALYSIS OF NATURAL GAS DEMAND, SUPPLY, FLOW, AND THE NATURAL GAS PIPELINE NETWORK...... 28
3*1 Introduction ...... 28
3*2 The Spatial Pattern of Natural Gas D e m a n d ...... , ...... 29
' The Importance of Natural Gas to Each State's Energy Budget. . . . 40 Total Natural Gas Consumption.. . 41 Residential Consumption ...... 41
vi Chapter Page
Industrial Consumption...... 41 Commercial Consumption...... 42 Electrical Utility Industry Consumption...... 43
3*3 The Spatial Pattern of Natural Gas S u p p l y ...... 45
3.4 The Natural Gas Pipeline Network and the Plow of Natural Gas ...... 52
4. THE OUT-OF-KILTER ALGORITHM...... 59
4.1 A Conceptual Introduction to the Out-of-Kilter Algorithm...... 59
4.2 The Utility of the OKA for Modeling the Natural Gas Pipeline Network . . 65
5. THE DEMAND SUBMODEL...... 72
5.1 The Definition of Demand Regions . . 72
Step 1 ...... 77 Step 2 ...... 79 Step 3 ...... 81
5.2 The Determination of Future Demand and Consumption in Each Demand R e g i o n ...... ,...... 83
Selecting State-Level Demand Data...... 84 Econometric Models ...... 84 Survey Estimates ...... 87 Selecting Variables to Apportion State-Level Demand to the 177 Demand Regions...... 92
5 .3 Additional Demand Areas...... 99
6 . THE SUPPLY SUBMODEL...... 100
6.1 The Identification of Supply Regions 100
6.2 The Determination of Future Produc tion in Each Supply Re g i o n ...... 108
vii Chapter Page
Selection of Future Production Es t i mat es...... 109 Econometric Estimates of Natural Gas Supply ...... 109 Mathematical and Geological Estimates of Natural Gas S u p p l y ...... 113 FPC Production Estimates . . . 114- Estimating Future Production for the Sixty Supply Regions......
6 .3 Supplementary Sources of Supply.. . . . 121
Atlantic Offshore ...... 121 Alaska...... 122 Mexico...... 122 Canada...... 123 LNG S i t e s ...... 128 SNG S i t e s ...... 128
7. THE PIPELINE NETWORK SUBMODEL...... 129
7*1 The Abstraction of the Natural Gas Pipeline Network as a Graph...... 129
7.2 The Determination of Pipeline Capacities...... 13**
Weymouth Formula...... 138 Disaggregating Border Capacities on the Basis of Pipeline Diameter. . . 138 Disaggregating Border Capacities on the Basis of Flow Volumes’...... 138 Development of Company Flow Diagrams ...... 139 Disaggregating Border Capacities 146 Capacities of Links that do not Cross State Borders...... 151
7*3 The Determination of Shipping Costs. . 155
Method 1 ...... 156 Method 2...... 157 Method 3* * * . . • ■ • ...... l60 Development of the MOKA Algorithm . 162 Scenario 1...... 168 Scenario 2...... 1?1 Determination of Link Mileages. . .-172
viii Chapter Page
7.4 The Intrastate Pipeline Network ...... 179
7 .5 S u m m a r y ...... 181
8 . RESULTS OP THE MODEL...... 182
8.1 Presentation of Results for a Hypothetical Network...... I83
8.2 Selected Results of the Actual Model ...... 197
Selection of a Route for the Alaskan Gas Transportation S y s t e m ...... 197 Other Selected Results .... 211 Summary...... 216
9. ADVANTAGES, LIMITATIONS, AND EXTENSIONS OF THE MO D E L ...... 21?
APPENDIX A ...... 228
B ...... 244-
LIST OF REFERENCES ...... 249 LIST OP TABLES
Table Page t 1. United States Natural Gas Consumption in 1975 ...... 32-33 2. Production and Proved Reserves of Natural Gas in the United States in 1975 ...... ^7
3. Test of Demand Submodel Employing Ohio County D a t a ...... 97
4. FPC Projections of Canadian Exports to the U.S. 124
5. Disaggregating the Capacity of Border X to Obtain Capacities of Border-Crossing Network Links...... 149
6 . Deriving Capacities of Non-Border-Crossing Links...... 151
7 . Shipping Rates of Eight Large Natural Gas Transmission Companies ...... 152
8 . Behavior of the MOKA M o d e l ...... 170
9. The Measurement of-Link Distance to a Region Served by Pipelines Entering from One Other Region ...... 176
10. MOKA Output...... 188
11. Use of the Lower Bound to Assure Minimum Deliveries to a Given Demand Ar e a ’...... 188
12. Determining Optimum Production Levels in Each Supply Area of Hypothetical Network...... 191
1 3 . Use of MOKA as a Link-Addition Algorithm Company A P r o p o s a l ...... 193
14. Use of MOKA as a Link-Addition Algorithm Company B Proposal ...... 193 Table Page
15• 1985 FPC Case II MOKA Results for Alaskan Gas Transport Proposals ...... 203
16. Results for Proposed Routes to Link the Permian Basin to the Eastern U.S...... 207
1 7 . Selected Portions of MOKA Output from Alaska to Montana Proposal...... 212-213
xi . LIST OF FIGURES
Figure Page
1. Growth in U.S. Natural Gas Consumption 1920- 1 9 7 4 ...... 30
2. Natural Gas as a Percentage of Each State’s Energy Consumption...... 34
3. Total Natural Gas Consumption in the United States in 1975 ...... 35 4. Residential Consumption of Natural Gas in ,the United States in 1975...... J6
5* Industrial Consumption of Natural Gas .in the United States in 1975...... 37
6 . Commercial Consumption of Natural Gas in the United States in 1975...... 38 7. Consumption of Natural Gas by the Electrical Utility Industry ...... 39
8 . United States Natural Gas Reserves ...... 46
9* Production of Natural Gas in the United States in 1975...... 48 10. Proved Reserves of Natural Gas in the United States in 1975 ...... • • • • 50
11. Gas Utility Industry Miles of Pipeline and Main. 53
12. The Natural Gas Pipeline Network of the United S t a t e s ...... 55
13* The Conceptual Framework of the Out-of-Kilter Algorithm...... 62
14. Conceptualization of a Regional Approach to Determine "Present or Future Public Convenience or Necessity for Flow Contract and Pipeline Construction Approval" by the FPC...... 68 Xll• • * Figure Page
15. The Out-of-Kilter Algorithm as a Vehicle for Evaluating the System-Wide Implications of ■ Various Proposed Pipeline Routes ...... 70
16. Principal Natural Gas Pipelines of South Dakota ...... 78
17. Demand Regions Based Upon the Structure of the Pipeline Network ...... 80
18. U.S. Gas Consumption and Requirements, 1966- 1995 ...... 90 19• U.S. National Petroleum Council and Canadian National Energy Board Supply Regions ...... 104
20. Supply Regions Employed in this Dissertation . 106
21. Alternative Estimates of U.S. Undiscovered Natural Gas Resources...... 110
22. Dedicated Gas Reserves and Production by FPC Gas Areas, All Interstate Pipeline Companies . 119
23. Exports of Canadian Gas to the U.S...... 126
24. Network of Hypothetical Pipeline Company A . . 132
25. Load Factors of U.S. Natural Gas Pipelines . . 137
26. Disaggregating Deliveries of Each Pipeline Company to Demand Regions within a State . . . 142
27. Flow Diagram for Company X ...... 144
28. The Simplification of the Pipeline Company D i a g r a m s ...... 147
2 9 . Flow Diagram for Two Companies Illustrating the Procedure for Estimating Capacities for Non-Border-Crossing Links...... 152
30. Relationship Between Shipping Cost, Pipeline Capacity, and Load Factor...... 164
31. The Effect of MOKA on Flow P a t t e r n ...... 169
xiii Figure Page
32. The Measurement of Link Distance to a Region served by Pipeline Entering from Two Other R e g i o n s ...... 17k 33. The Measurement of Link Distance to a Region Served by Pipelines Entering from One Other Region...... 175 3*f. The Measurement of Link Distance when Supply and Demand Regions are Coterminous...... 178 35* Hypothetical Network for. MOKA ...... 18k 3 6 . Hypothetical Network with Proposed Company A Link...... I85 37- Hypothetical Network with Proposed Company B Link...... 196
3 8 . Alaskan Gas Pipeline Alternatives ...... 199 39. LNG and Pipeline to California Proposals for the Alaskan Gas Transportation System . . . . 20*1 4-0. Montana Proposal for the Alaskan Gas Transpor tation System ...... 205 kl. Minnesota Proposal for the Alaskan Gas Trans portation System...... 206 kZ. Route 1 Proposal to Deliver Permian Basin Supplies to the East...... 208 4 3 . Route 2 Proposal to Deliver Permian Basin Supplies to the East...... 209
kk. Pipelines From the Atlantic Offshore...... 215 4 5 . Introduction of Storage Capacity to the MOKA Framework ...... 221 k6. Introduction of Sectoral Allocation to the MOKA Framework...... 223
xiv LIST OP ABBREVIATIONS
AGA American Gas Association
BC links Network links that cross state borders
Bcf Billions of cubic feet
BTU British thermal unit
FEA Federal Energy Administration
FPC Federal Power Commission
GRC Gas Requirements Committee
LF Load Factor
LNG Liquefied natural gas
Mcf Thousands of cubic feet
MMcf Millions of cubic feet
MOKA A version of the Out-of-Kilter Algorithm Modified to handle the nonlinear cost-flow relationship
NBC links Network links that do not cross
NEB National Energy Board (Canada)
NPC . National Petroleum Council
OKA Out-of-Kilter Algorithm
P/A Pipeline psi Pounds per square inch
Quads Quadrillions of BTU's
SIC Standard Industrial Classification Synthetic natural gas
Trillions of cubic feet
Value-added in manufacturing
xvi CHAPTER 1
INTRODUCTION
The purpose of this dissertation is to develop a planning model of the U.S. natural gas pipeline network
that is capable of treating policy-related questions. To meet this objective, a number of goals are established.
First, sufficient geographic detail is needed in terms of
the location of natural gas supply and demand such that
specific recommendations can be made. Second, the pipe
line network itself must be modeled in detail, including
accurate estimates of pipeline capacity and shipping cost.
Of particular importance is the ability to account for
the nonlinear relationship between shipping cost and
flow. Third, the model should provide for flexibility
in terms of the ability to vary the input parameters and
assumptions.
These goals are accomplished through the development
of demand, supply, and pipeline network submodels which
provide the data input to a modified version of the out-
of-kilter algorithm, a normative model that yields a
least-cost flow pattern subject to demand, supply, and
pipeline capacity constraints and which attempts to
account for the nonlinear cost-flow relationship. The
1 . utility of the model for treating policy-related, questions is illustrated with particular reference to the routing of the Alaskan gas transportation system.
The need for such a model is emphasized by the t * importance of natural gas to the U.S. economy as a whole, to each sector of the economy and to most regions of the country. The necessity to make certain that available supplies are transferable to areas of demand, the impor tance of transport costs in the natural gas market, the energy-consuming nature of pipeline transportation and the environmentally disruptive nature of pipeline con struction point to the usefulness of the least-cost criterion employed by the model.
* The U.S. utilizes more energy per capita than any
other major industrial country. With only 6 per cent of
the world population, Americans account for 30 Per cent
of the world's energy consumption. Exhaustible fossil
fuels— coal, petroleum, and natural gas— provide 95 per cent of U.S. energy consumption. Natural gas alone,
constitutes approximately 30 per cent of the energy
budget. Approximately 50 per cent of the residential
and industrial sectors, kO per cent of the commercial
sector, and 2*4- per cent of the electrical utility
industry rely upon natural gas to satisfy energy require
ments. In addition, natural gas comprises an important part of the energy budget in all states, with the excep
tion of some New England states and Hawaii. Twelve states
» depend on natural gas for more than 40 per cent of their needs.
Although natural gas usage increased at an annual rate of approximately ? per cent between 194? and 1 9 7 1 ,• consumption is expected to increase at only one-tenth
that rate between 1971 and 1990. Usage had increased rapidly as natural gas is relatively inexpensive, clean, and entails neither consumer handling, storage, nor dis posal problems. Only small increases in future consump
tion are expected due to the inability of supply to keep pace with demand. "Conservative-realistic" estimates of
North American supply indicate that approximately SO.per cent of potential U.S. demand may remain unsatisfied in
1 9 9 0 t even the most optimistic supply projections would result in a 25 per cent deficit. Therefore, consumers, particularly in the industrial and commercial sectors, either will need to employ an alternative energy source,
or massive imports of liquefied natural gas (LNG) and the development of synthetic natural gas (SNG) will be required, even with the development of marginal (Alaskan
and northern Canadian) and offshore areas. All of these
alternatives for supplementing gas supply necessitate
adjustments in the pipeline network. « 4 The natural gas pipeline network, which extends into all Lower 48 states, represents a $27 billion transporta tion system, exceeded in mileage only by the U.S. highway n'etwork. Given the importance of natural gas to all economic sectors and geographic regions of the country, and the extent of the pipeline network, the paucity of data available to researchers concerning the pipeline net work as a whole is surprising. The need for research into the pipeline network has been emphasized by Resources for the Future:
With respect to the natural gas pipeline network, a study could usefully be made of the means of improving the cost- efficiency of the system. Heretofore, pipeline certification has proceeded on • a case-by-case approach, which leads to duplication and cross-hauls. A regional approach to certification needs to be examined, to determine feasibility and possible economics to be derived from pooling or coordinated use of pipeline facilities. Possibly the outer conti nental shelf offers a special field for advance planning in this respect (1968,62).
The importance of advance planning of the pipeline t network is further emphasized by the following consider ations :
1) The importance of natural gas and the projected shortages emphasize the necessity to make certain that
those supplies which do exist are linked by pipeline to areas of deficit, i.e. complementarity and transferability are both prerequisites for movement. The recent example of the Alaskan oil transportation system, which is designed to deliver oil to a region with insufficient demand (California), instead of.an area of significant energy supply deficit (the American Manufacturing Belt) is a situation to be avoided.
2) Transportation costs increase the delivered price of natural gas. Lawrence (1973) suggests that transport costs are a significant proportion of wholesale delivered price. This proportion may be expected to increase over time since the resources of the earth's surface are not only finite, but also are depleted at varying rates geographically.' Supplies close to market are developed and depleted first. Distant sources are developed last, incur greater transportation costs, and require the construction of long-distance network, links.
3) The transportation of natural gas is itself an energy consuming process. More than 3 per cent of nat ural gas produced is used for pipeline fuel.
4) The construction of pipelines is often environ mentally disruptive.
This dissertation strives to provide a framework within which to plan the natural gas pipeline network so
as to service a set of "optimal" flows— "optimal" in that
system-wide minimisation of wholesale delivered price is
sought. 6
Chapter 2 discusses normative commodity flow studies in geography. These studies are catagorized into those employing the transportation problem, the out-of-kilter algorithm and other mathematical programming approaches.
A major conclusion of this review is that most of this work has ignored link capacity constraints and the non- * linear relationship between transport cost and flow.
This review also shows that past researchers have stressed the need for the normative analyst to pay particular attention to the form of the data input.
Chapter 3 describes the spatial pattern of. natural gas supply and demand in the U.S. which has led to the complementarity that produces flow and has resulted in the construction of the natural gas pipeline network.
The spatial pattern of the various types of consumption are of particular interest, in view of the projected disparities in supply and demand and the fact that the market behaves so as to produce deficits that are regional in nature. Included also are descriptions of the pipe line network and the flow of natural gas.
Chapter 4 provides a conceptualization of the out- of-kilter algorithm (OKA), the major analytical tool employed in this research, with particular reference, to its utility for modeling the natural gas delivery system. Chapter 5 defines 177 demand regions in the Lower **8
on the basis of pipeline network structure and develops a procedure for apportioning state-level demand data to
these regions using population and value-added in manu
facturing.
Chapter 6 develops 77 supply regions including
onshore, offshore, Alaskan, Canadian, Mexican, and LNG
and SNG sites and discusses the methodology employed to
derive estimates of future production in each supply area.
Reserve volumes are used to apportion future production
estimates, made by the Federal Power Commission for the
large National Petroleum Council regions, to sixty
onshore supply areas.
Chapter 7 discusses the procedures employed to
model the pipeline network, including the abstraction of
the network as a graph, and the development of capacities
and shipping costs for the network links. Capacities are
derived by using flow volumes to apportion aggregate pipe
line capacity data from the Federal Power Commission (197*0
to the individual network links. A modified version of
the out-of-kilter algorithm (called MOKA) is developed
so as to account for the nonlinear relationship between
transport cost and flow volume.
Chapter 8 illustrates the utility of the MOKA model
using a small sample network. (The size of the actual network precludes its graphic display and full interpre tation within this format.) Included also.are some of the more salient results from various runs of the model using the data developed by the demand, supply, and pipe line network submodels. These results identify bottle necks, suggest routes for the Alaskan Gas Transportation
System and from the offshore Atlantic, and identify probable deficit areas.
Chapter 9 provides a summary of this dissertation and makes suggestions for the further development of the model. CHAPTER 2 NORMATIVE COMMODITY PLOW STUDY IN GEOGRAPHY
A LITERATURE REVIEW
The goal of normative commodity flow models is the derivation of a set of flows satisfying some efficiency criterion, usually the system-wide minimiza tion of transport costs. The technique employed in normative flow modeling is mathematical programming.
Such models involve the minimization (or maximization) of an objective function subject to a set of constraints*
MINIMIZE f (x) (3a)
Subject to* g (x)2 0 (3b)
h (x)= 0 (3c)
X £ S (3d) where,
f (x) is the objective function to be minimized
g (x) is the set of inequality constraints
h (x) is the set of equality constraints
x are the values sought (X^,X2 , X y • • Xn )
S = some set of numbers, usually defined as the set of real numbers, R
With a few exceptions, geographers have assumed the
linearity of both the objective function and the con
straints . The review below is divided into studies that 9 employ the transportation problem, the out-of-kilter algorithm and other mathematical programming formula tions . 2.1 The Transportation Problem
This linear programming formulation has received considerable attention for the modeling of both commodity and passenger flow. Garrison’s (1959) treatment is the seminal work in geography and Scott (1971) provides a general description of the algorithm and some of its extensions. The objective function is to minimize trans portation costs while meeting a set of supply and demand constraints. The model assumes that transport rates are independent of flow volume, and that production and consumption occur at a set of points in space.
The formulation is* M N MINIMIZE F £ ij ij■? ( ^a ) i=l N Subject to* X! = ai (^k)
ii
N Y “ ‘ C^°) 13■; J J A
= 0 (4d)*
xij = 0 <*•>
where,
^ij = 'fcran3P0r'*: cost between i and j Xij = the flow from i to j 11 12
= the total supply at i
b. = the total demand at j J M = the number of supply regions
N = the number of demand regions.
Cox (1965) employs this model to examine interstate
flows of aluminum bars based on a 1 per cent sample of
Waybills taken by the Interstate Commerce Commission for
I960. The rail network (on which most aluminum is trans ported) is not modeled and freight rates were not avail
able for origin-destination pairs between which actual
flow does not occur. Thus, Cox minimizes total distance
rather than cost, although he recognizes that cost is not
a linear function of distance for rail transport (cost
and distance are linearly related in pipeline transport).
Using a chi-square test, Cox shows a significant differ
ence between actual and optimal flows at the 99 per cent
confidence level. A regression analysis produces an o R of .lb, which is significant, but does indicate that
•a great deal of inefficiency exists. Examination of
residuals from this regression shows that high positive
residuals occur over long-distance routes, while high negative residuals occur over short routes, illustrating
the effect of ignoring the nonlinear cost-distance
relationship. After estimating revenue per ton-mile for nine of the 4-1 origin-destination pairs for which no 13 2 current flow occurs, a new R of .28 is found, doubling the explanation of the distance model. Cox makes note of two problems with linear program ming techniques which are of particular interest in the present context. First, the data for such problems are often extremely fragmentary in nature. Second, linear programming techniques treat places of supply and demand as points, rather than areas, this being a particularly acute problem when the supply or demand is eccentrically located within a region. Developing a spatial data set with particular reference to the ability to legitimately- represent an area with a point is stressed in this dissertation. Barr (1970) derives a set of optimal flows for round- wood in the Soviet Union, estimating that a 20 per cent savings could be. realized if the optimal pattern were adopted. He notes that the correspondence between actual and optimal flows is greater for large volume shipments, since small volume flows are more likely to be cross hauled or backhauled, phenomenae the.transportation problem ignores. Barr also indicates that another reason for a discrepancy between actual and optimal shipments is product heterogeneity. Some types of roundwood move only to specialized processing centers in certain demand regions. Such specialized shipments are usually of small 1^ magnitude. This problem of Barr's emphasizes that the transportation problem is a single-commodity algorithm
(as is the out-of-kilter algorithm). Fortunately, natural gas is an almost uniform commodity such that this problem does not arise.
Henderson (1958) uses the transportation problem to examine the efficiency of the U.S. coal industry. He divided the United States into fourteen districts, eleven of which produce significant volumes of coal. Since costs vary between underground and strip mining opera tions, Henderson treats these activities separately and identifies twenty-two coal supplying areas. Since all fourteen districts consume coal, there are fourteen demand regions in the problem. A comparison of actual and optimal flows for 19 ^7 * 19 ^9 , and 1951 permits the identification of "imperfections" in the flow pattern.
Henderson points out that the flow pattern determined by the model is that which would exist under conditions of perfect competition. A more interesting observation in
the present context is that the chief problem for the analyst is the arrangement of the data so that the results are meaningful. As will be seen in Chapters 5-7* this dissertation concerns itself to a great extent with
"arrangement of data" such that the results are more meaningful than have been obtained by past researchers. A study by Gould and Leinbach (1966 ), while concerned with the movement of hospital patients and not commodity flow, is of interest in' that it shows the manner in which a national government, planning additions to the trans portation system, can simulate network development and analyze the effects on travel patters.while revising decisions with regard to hospital location. They illus trate this procedure for the case of western Guatemala in which the problem is to decide the location and capacities of three hospitals (given ten potential sites) and of transport network improvement.
Other examples of the use of the transportation problem include studies of Indian wheat movements by
Dickason and Wheeler (196?), Indian cement flows by Gosh
(1965), cement movements in New Zealand by-Rimmer (1968 ), and Australian wool shipments by Dent (1966). Three studies, one by Waverman (1972) and two by Osleeb and
Sheskin (1975, 1977) relate' directly to the topic of this dissertation. Many of the details of these works are discussed in Chapters 5-7* Brief reviews are pro vided below*
Waverman (1972) employs the simple transportation problem to examine the effects of Canadian government policy on the cost-efficiency of the North American natural gas delivery system. His results indicate that I
16
Canada's insistence upon supplying the Ontario-Quebec market with Albertan gas, via the construction of a
Trans-Canada pipeline (an all-Canadian pipeline),has led to inefficiencies in the system. His failure to consider the existing pipeline network and its capacities, however, leads him to spurious results.
Osleeb and Sheskin (1975) employ the transportation problem to derive the probable U.S. market areas for
Canadian natural gas in 1990 under varying sets of supply assumptions. Assuming that the Canadians are willing to ship excess production, Alberta is shown to supply large portions of the western and midwestern parts of the country.
Osleeb and Sheskin (1977) also employ the transpor tation problem to derive optimal flows and as a predic tive tool for natural gas flows in North America. The high correlations between optimal and actual flows (.80 -
.9 3 ) indicate that the current market place has been operating so as to minimize transport costs. Given that the model satisfactorily replicates current behavior, the assumption is made that such behavior will continue in the future. Future (1980-1990) production and consump tion levels in seventeen North American supply regions and fifty-six demand regions, are used to derive a set 17 of future flows. Since there exists excess demand in the system, a dummy supply area is established such that areas of probable deficit may be identified and suggestions offered as to where to provide facilities to produce supplemental supplies. 2.2 The Out-of-Kilter Algorithm
An extension of the transportation problem, the out- of-kilter algorithm (OKA), also has been employed as a normative commodity flow model. The objective is to maximize flow through a network at a minimum cost subject to lower and upper capacity constraints on each network link. A set of intermediate nodes, at which flow may
"switch" from one route to another may be defined, and demand and supply constraints introduced. Explanations of the algorithmic procedure may be found in Ford and
Fulkerson (1962) and Potts and Oliver (1972). A concep tualization is found in Taaffe and Gauthier (1973)•
Gauthier (1968 ) employs the OKA to identify the system-wide impacts of link improvements and to identify bottlenecks in the highway network of Sao Paulo, Brazil.
By omitting demand and supply constraints, the flow level in the system is determined by the capacities on the net work links. All lower capacities are set equal to zero as there is not reason to assume any given highway will be included in the solution of the maximum flow-minimum cost problem. Estimates of the upper capacity of each link are based upon formulations of the Departmento 18 Estrados de Rodagem do Estado do Sao Paulo (DER) which are similar to those employed by the Highway Research
Board in the United States. The "practical daily capaci ty" in vehicles per day is a function of such factors as speed, spacing intervals, surface type, driver character istics, essential vehicle maintenance en route, unforseen operational developments, surface conditions, lane and shoulder width, and curves and gradients. Gauthier then derives a capacity in short tons per day by assuming the use of five ton trucks hauling average three ton loads.
Link costs are derived based upon average operating cost data from the DER. The Ferreira procedure employed by the Brazilian transport economists is used to estimate transfer costs as a function of distance and road type.
Three subnetworks of the Sao Paulo highway network are defined, considering Sao Paulo and the two regional centers of Riberao Preto and Bauru as sources and sinks.
To eliminate obviously uneconomic paths, the subnetworks are defined to include only those links within an ellipse with the source and sink as foci. A major result of this study is that while the Brizilian program of highway improvement, which is aimed at increasing the attractive- > ness of the regional centers for capital investment, has increased flow between the regional centers and reduced transportation costs, the transportation costs between
Sao Paulo and the regional centers have been reduced even more, giving Sao Paulo even further locational advantage.
Gauthier also notes the existence of, bottlenecks in the system that restrict the utilization of some high capa city links (such as the Via Anghanguera), He also examines the effect of link improvement upon cost and flow in the various subnetworks. Gauthier stresses the
"necessity of considering improvements in a transportation linkage in terms of their system-wide impact and not just of the two centers at the end points" (p. 18 6 ).
Abler, Adams and Gould (1971) employ the simplex method (rather than the OKA) to solve a capacitated transportation problem containing intermediate nodes for a hypothetical network with five surplus and ten deficit regions. They examine the effects of either the addition of new gravel roads or the upgrading of existing links upon flow in the system. They note’ which alternative will most lower transport costs. In addition, examination of the optimal flow pattern with the proposed additions shows that "the decision to upgrade a portion of a transportation network, and thereby radically lowering the costs over the improved section, sends ripples of 21
benefits throughout the whole system rather than .just the
areas receiving the improvements" (p. .
King, Casetti, Odlund, and Semple (1971) use the out-of-kilter algorithm to determine the optimal trans
portation pattern of bituminous coal in the Great Lakes
region. Nineteen major coal receiving centers are defined
as aggregates of electric-generating plants and coking
oven centers which together account for 75 per cent of
demand. Fifteen composite nodes representing coal-mining
districts are defined. Each node represents a group of
coal producing counties. The productive capacity of each
supply node is defined as the sum of the bituminous coal
shipments for 1963 (probably leading to an underestima
tion). For transport rates, this study uses volume and
trainload rates which apply to most major coal shipments.
These rates, the authors note, are related to competition
and not simply to the distance of haul and are consistent
with the marketing strategy of the companies involved.
What they fail to note is that the use of actual shipping
rates rather than costs biases their solution toward the
actual flow pattern. No capacities are employed on the
network links.
An interesting facet of the work of King, et al. is
the inclusion of a temporal dimension such that the
phenomenon of shipping coal via less expensive water routes in the summer with storage at the demand site for use in the winter when the water routes are frozen may be taken into account. Thus, they set up the QKA as an intertemporal transportation problem. Each demand node is divided into winter and summer nodes and demand is divided equally between them. Storage is accounted for by use of a link connecting summer and winter nodes. The parameters of this link are the storage costs and capa cities at each destination. This analysis shows that supply nodes should ship to differing demand nodes in different seasons. Some sensitivity analysis is under taken by allowing storage costs to vary.
Sinclair and Kissling (1971) employ the OKA in an analysis of the fruit distribution network of New Zealand.
Their network is designed to allow for the seasonal move ment of fruit from a set of inspection points to a set of ''cool store" locations and then to local markets or ports. The model is formulated to obtain weekly optimal flows. They admit that such a set of weekly solutions does not necessarily imply a yearly minimum, but suffi cient computer storage was not available to model the entire year. They state that "it proved impossible to obtain data as to routeway upper capacity values" (p. 1 3 5 )*
Although they worked with a highway network for which . capacity manuals exist, they dealt with a seasonal product 23 and a "dynamic capacity" was required, i.e., a capacity that changed with seasonal conditions. In addition, since fruit trucks form a very small percentage of total traffic, capacity is somewhat irrelevant. 2.3 Other Mathematical Programming Models
A number of other commodity flow studies employing programming techniques have appeared in the literature.
All employ algorithms* which build upon the basic struc
tures presented above.
Goldman (1958) formulates a linear program for the
efficient transportation of several goods when one good may be hauled as a backhaul. He proposes a hypothetical . * situation in which one island has coal, another has iron
ore, a third has limestone, and all demand steel. The question addressed is where production should be located
and flows oriented so as to minimize transportation costs.
Casetti (1966) uses the algorithm to attempt to analyse
the impact upon location of steel mills supplying the
Canadian market, of the flow of iron ore from Seven
Islands through the St. Lawrence Seaway to the Great
Lakes steel centers and of the increase in. Canadian con
sumption. He attempts to determine the optimum pattern
of steel production and transport, raw material trans port, and empty-carrier movement that minimizes cost and
satisfies both the steel requirements of the Canadian markets and the ore requirements of the U.S., market,
Casetti regards his study as exploratory in nature due Zk to both the quality of his data and certain assumptions of his model. Since the "backhaul"concept is inappropriate to pipeline transportation, the Goldman algorithm is rejected for use in this dissertation.
i Osleeb and Cromley (1977» 1978) describe a.nonlinear mathematical programming technique to determine optimal plant locations, sizes, and market areas through the trade off of internal economies of scale with transporta tion costs incurred, due to spatial price equalization
(uniform-delivered price). The strength of the algorithm for planning purposes is illustrated via application to.
Coca Cola bottling plants in southern Ontario. Particular attention is paid to estimating link travel cost as a function of travel time, which is shown to be a function of vehicle speed, which, in turn, is a function of link capacity. Two studies (completed by non-geographers) have employed mathematical programming to examine natural gas flows. Many of the details of these works are discussed in Chapters 5-7* A brief review is provided below.
1) Lawrence (1973) employs a programming approach to derive a set of optimal natural gas flows and prices and identifies when additional capacity will be needed in a given pipeline corridor. Unfortunately, the quality of his data and its level of aggreation represent serious drawbacks to his conclusions, which he readily admits.
2) Brooks (1975) employs mathematical programming to examine the effects of various regulatory policies upon the natural gas industry. This dissertation is based partly upon conversations with Brooks (at the FEA) as
to where improvements in his model might be made. 2.*f Conclusions
Henderson's (1958) statement concerning the import ance of the form of data input in producing meaningful results is stressed in this dissertation. Thus, particu- 4 lar attention is to he paid to the definition of demand and supply regions which are consistent with network structure. Except for the work of Gauthier (197*01 no empirical geographic study has employed capacity constra ints, a necessary inclusion if one is to properly assess network capabilities. In addition, all geographic studies have treated transport costs as being independent of flow volume, which is not the case for most commodities.
An attempt is made to account for this relationship in this research.
2? CHAPTER 3
A SPATIAL ANALYSIS OF NATURAL GAS
DEMAND, SUPPLY, FLOW, AND THE
NATURAL GAS PIPELINE NETWORK
3*1 Introduction
•
The natural gas industry is comprised of production, transmission, and distribution sectors. Although this dissertation is concerned chiefly with transmission, all three sectors are highly interconnected. The purpose of. this chapter is to examine the spatial aspects of natural gas demand (Section 3*2), supply (Section 3.3), and the pipeline network and flow of natural gas (Section
3.*0. Emphasis is given to those aspects which provide necessary background for the interpretation of results from the modified out-of-kilter algorithm (MOKA) which 0 forms the major analytical tool of this dissertation.
This chapter describes the current situation; descriptive material related to probable future conditions is provided in chapters 5**?»
28 3*2 The1 Spatial Pattern of Natural Gas Demand
Natural gas demand has increased steadily because of its clean-burning properties, lack of consumer storage and.disposal problems, and, until recently, its spatial availability and relatively low cost. Particularly after World War II, the availability of large volumes of natural gas found while searching for oil and the devel opment of long-distance, high-pressure pipelines, per mitted the rapid expansion of the industry. Thus, natural gas increased from a 4 per cent share of the 20 quadrillion BTU's consumed in the U.S. in 1920, to 18 per cent of the 35 quads consumed in 1950 , to 30 per cent of the 73 quads consumed in 1974 (Figure 1) (FEA, 1975)-
If transportation uses are not considered, natural gas provides approximately 50 per cent of the energy consumed, twice that of oil or coal. Natural gas is employed by some 40 million residences, 3*4 million commercial users and over 200,000 industrial firms (American Gas Associa tion, 1975)*
Of the natural gas produced in the U.S., 46.2 per cent is consumed to meet 50 per cent of the energy requirements of industry. Of this volume, 24 per cent
29 • Q uadrillion B1U %
Other
f W
. 1920 1950 1974 Figure 1.— Growth in U.S. Natural Gas Consumption 1920-197^ w Source* Federal Energy Administration, 1975, o 31 is consumed by chemicals and allied products, 16 per cent by petroleum and coal products, and 13 per cent by the primary metal industry. Almost 40 per cent of the 8 .7
Tcf consumed in industry is used as boiler fuel in the chemical, petroleum, food, and paper industries. Gas forms an important feed-stock and process fuel in the manufacture of ammonia, fertilizer, and methanol.
Of the natural gas produced in the U.S., 24.5 per cent is used as fuel for about 50 per cent of the resi dential sector. Of this gas, 70 per cent is used for space heating and approximately 20 per cent for water heaters. Approximately 12 per cent of marketed natural gas is used to fuel almost 40 per cent of commercial establishments and close to 1? per cent is used to pro duce 25 per cent of the electricity consumed in the
U.S. (FEA, 1975).
The spatial pattern of 1975 natural gas consumption is illustrated by Table 1 and Figures 2-7. Although these data have appeared previously in Bureau of Mines
(1976) and Gas Requirements Committee (1975) publications, these sources have not undertaken the examination of the spatial patterns revealed by this information. TABLE 1 1975 NATURAL GAS CONSUMPTION CHHCfl M>- aa as C u. V c u. * C .j V a m * -mmt Ns * - »«.'i «j j( i« N m w ! » m 'iin . « i» w a » m m o m o r-m i* a a sm iN tm m s-sm a m a m M 3 *-i a u ► c ? l(IIIMl(llllllf I mE>ammNNfmf “®*■ f\i® m - S m C # - 0 0 ■ * ® f“ m N fN f-m N N m m a > E m « O A IN « ! 5553*2 4 «£ titiiiit»*»*itil******(t««<* *»-< * x w o l f n + H N H O N a i n n N S M t r 5S3 8? __ ammtfaa a > o « a *i «>•#« «>•#« S3£5& *i a « K5?a o > ^ L*-"5 a ammtfaa n m ■ «c*u i - m.o7. N;3B*»4ai'' ;i34B fN .jon7i.N am s-T im * j m m z n r m z r ^ i . s x r r - * hiv 2*00 3 2*00 C -ITKtU t K T I - « 5 JOO<| n 4 *« « na IN m 9 « c * *n * * n c i O* m^.Nmrn o o n o n K J 3iaNO . m IN *• o 32 I TABLE 1-CONTlNUfcO 197b NATURAL GAS CONSUMPTION 1MHCF) ELECTRIC STATE INDUSTRIAL T OF us : O* STATF UTILITY * OF US *_ flF STATF ALABAMA 154180 2 . 1 9 59.31 5 9 8 5 0 . 2 0 2 . 3 0 ARI2UNA •.8533 0 . 6 9 2 9 . 4 7 1 6 652 0.61 11.32 ARKANSAS 1 3 7 4 3 0 1.95 5 7 . 3 7 51462 1.03 1 3 .14 CALIFORNIA 5 6 * 8 5 9 B.01 31. 2 5 2 7 9 3 6 5 9 . 1 6 15.46 . COLORADO A 63 32 C . 6 6 1 5 . 9 3 5 6 6 9 5 1.86 1 9 .50 CONNECTICUT lSCAG 0.21 ■73.33 369 0.01 0 . 5 7 OtLA WARE 67 ST 0 . 1 U 3 7 . 3 7 2 6 5 0.01 2 . 0 ? FLORIDA 7 2 1 5 3 1.02 2 3 . 6 6 131215 4 . 3 0 5 1 . 0 2 GEORGIA 1 7 5 9 0 0 2 . 4 9 5 1 . 2 3 11383 0 . 3 7 3 .32 IDAHO 3 1 * 5 0 0 . 4 5 6 1 . HI 0 0 . 0 O.G ILLINOIS 345160 4.39 30.55 32688 1.07 2 . 8 9 INDIANA 22152b 3 . 1 4 4 5 . 3 6 10321 0 . 3 4 2.11 IOWA 1 M 5 9 6 0 1.55 3 2 . 2 7 * 7 2 7 1 1.55 14. 0 0 KANSAS 1 1 9 9 5 5 1.7b 24.H5 - 1 2 5 3 9 2 *.11 2 5 . 9 7 Kf-H 1LiCKY 5vC»o7 0 . 6 * 7 6 . 4 0 61 0 0. 03 0 . 3 9 LOUISIANA 7 1 6 0 9 1 1 0 . 1 5 52.02 365663 11.99 26.57 MAINE 66U 0.01 2 9 . 4 2 0 0. 0 0. 0 MARYLAND 4 3 U 3 5 C.62 25.54 19 0.00 0.01 MASSACHUSETTS 1 9 3 1 5 0 . 2 7 1 2 .65 2 8 9 0 0 . 0 9 1.89 MICHIGAN 3 0 4 * 6 4 * . 3 7 3 3 . 7 5 22801 0 . 7 5 2.53 MINNESOTA 9 4 0 2 5 1 . 3 3 2 9 . 5 4 2 8 2 5 6 0.93 6.88 MISSISSIPPI 9 2 5 7 7 1.31 * 4 . 4 9 21469 0.70 10.33 MISSOURI 75b*l 1.00 21.41 2 7 4 6 3 0 . 9 0 7.75 MONTANA 34067 U.4E 41.83 1C60 0.03 1.30 NEbRASKA 5 0 0 9 2 C . 7 2 25.81 36716 1.20 18.6* NEVADA 10326 0 . 1 5 1 7 . 0 0 0 . 4 8 4 4 . 4 9 N E W HAMPSHIRE 1190 0 . 0 2 1 4 . 9 3 0.01 2.22 N E W JERSEY 5 3 6 C 4 0 . 7 6 19.22 8815 0 . 2 9 3 . 1 6 N E W MEXICO 2 9 9 7 2 0 . 4 2 17.92 43340 I.S3 2 8 .91 N E W YORK 8 9 * 5 7 1.27 1 5 . 6 5 1 6 2 7 4 0 . 5 3 2. 05 NURTH CAROLINA 5 6 2 9 5 C. EC 4 9 . 7 6 0 0 . 0 0 . 0 NORTH DAKOTA 1*39 0 . 0 2 5 . 5 6 155 0.01 0 . 6 0 OHIO 3 D 9 7 J 9 4.29 32.58 2799 0 . 0 9 0 . 2 9 OKLAHOMA 1 * 5 * 2 9 2 . 0 6 2 2 . 7 4 332850 10.41 52.0* DKLGUN *«b665 0 . 6 9 54 .91 0 0 . 0 0 . 0 PCNilS YLVAFll A 2 5 6 0 9 8 3 . 6 6 3 6 . 9 9 1343 0 . 0 4 0 . 1 9 RHODE ISLAND 5 5 9 9 O . O o 2 5 . 0 4 0 0 . 0 0 . 0 SOUTH CAROLINA 6B150 0 . 9 7 4 9 . 3 0 1 4 9 3 7 0.49 10. 9 2 SOUTH DAKOTA 6 * 9 9 0 . 0 9 19.55 3 2 0 5 0.11 9 . 6 * TENNESSEE 1 0 6 6 0 0 1.51 4 7 . 3 4 0 0. 0 C. C TEXAS 192*,2C6 2 7 . 2 0 * 9 . 2 0 1 3 1 2 5 0 9 4 3 . 0 3 3 3 . 5 6 UTAH 4 0 7 6 5 0.5b 33.12 2820 0.09 2.29 VERMONT 1251 0.02 27. B* £67 0.02 1 2 . 6 2 VIRGINIA 3 1 7 9 9 0 . 4 5 2 5 . 9 2 4 5 7 0.01 0 . 3 7 ' WASHINGTON 8 5 0 3 2 1.21 5 2 . 6 0 0 0 . 0 0 . 0 WEST VIRGINIA 6 1 0 1 6 0 . 3 7 3 5 . 3 9 39 0 . 0 0 0.02 WISCONSIN 13 8 2 2 2 1.96 '37.66 19923 0.65 5 . 4 3 WYOMING 3 9 9 5 9 0 . 5 7 6 0 . B2 0 0 . 0 0.0 US TOTAL 7 0 5 2 3 7 2 ICO.00 305C472 100.00 SOURCES GAS REQUIREMENTS COMMITTEE, 1 9 7 5 : BUREAU OP MINES, 1974! AUTHOR 9419 9 "figure ^.‘"^KaTurai1 Gas as a Percentage of Each State’s Energy Consumption \s- .Classes: (1) 0-15. (2) 15^30, (3) 30-45, (4) 45-60, (5) 60-7 5 . (6) ?5-2 % -p 77 Cas consumption in the Onitec states in 19?5 (in 3cf) Classes: (1) 2-10,(£) 10-70,(3) 70-170, (*0 170-260,(5) 260-700,(6) 600-1500,(7) 1500-3950 4529999994 figure 4\- kesiifenlfral Consumption ot Natural Gas in tne United States in iy?^ (lh Bdf )'KjJ Classes: (1) .8-4,(2) 4-13,(3) 13-35,(4) 35-60,(5) 60-100,(6) 100-300,(7) 300-670 on 62 Figure $ 7 ‘"industrial' Consumption of Natural Gas in the United States in 1975 (in Bcf) Classes: (1).6-1-5.(2)2.5-35.(3)35-80,(4)80-120,(5)120-200(6)200-300(7)300-350,(8)350-2000 3634 Consumption of Natural ‘ Gas 'in'the United-States in 1975 (in Bcf) Sd Classes: (1) .5-10,(2) 10-23,(3) 23-33,(4) 33-50,(5) 50-100,(6) 100-175.(7) 175-2^3 1467 875 rgOTe'*7^'“^ 0TTSLHipET0n- of Natural das' by the Electrical Utility Industry ’ (in BcTT Classes: (1) 0-.04,(2) .04-10,(3) 10-37,(4) 37-60,(5) 60-140,(6) 140-400,(7) 400-1312 ZfO The Importance of Natural Gas to Each State’s Energy Budget. Figure 2 and Table 1 display the spatial pattern of natural gas consumption as a percentage of each state's energy budget. Nineteen states depend on natural gas for more than 30 per cent of their total energy consumption; another seventeen states, for 15-29 per cent. Natural gas forms a major proportion of the total energy consumed in the principal producing states of Louisiana (75*2 per cent), Texas (66.k per cent), Kansas (6 5 .6 per cent), and Oklahoma (6 5 .I per cent) and also in Arkansas (53*8 per cent) and New Mexico (49..? per cent). High values also are evident in states of moderate production, but within which energy consumption itself is not high (Nebrask'a, « Mississippi, Wyoming, Colorado, and Utah). Pipeline network structure explains the rather high values found in Mississippi, Arizona, New Mexico, Nebraska, Missouri, Illinois, and Iowa, which benefit from the passage through their territory of large-diameter (and consequently low- shipping Cost) pipes connecting the major supply areas in the West South Central with the northeast and Califor nia. In contrast, other areas of relatively low pnergy demand, such as New England, do not benefit from location • and consequently have few pipelines.. Thus, natural gas forms a minimal portion of energy consumption in these areas. Total Natural Gas Consumption. Figure 3 displays the 1975 pattern of natural gas consumption. Texas and Louisiana, due to their status as large producers, and California, because of environmental constraints, con sume the largest quantities. The states in the American Manufacturing Belt also consume large quantities. The areas of lowest consumption (the Rocky Mountain states and New England) are also areas of low population. Residential Consumption. ■ The pattern of residential use (Figure 4) shows the influence of both population and climate. Texas and Louisiana consume somewhat less in comparison to a number of highly-populated northern states (New York, Ohio, Michigan, and Illinois). Cali- * . fornia leads the nation, with Illinois a distant secondj northern New England consumes only small volumes in spite of its climate, due to small population and lack of a well-developed pipeline network. Industrial Consumption. Industrial usage (Figure 5) is highest in Texas and Louisiana, with chemicals and allied products ^Standard Industrial Classification (SIC) 28 J , and coal and petroleum products (SIC 29) industries, accounting for some 51 per cent of this usage in the two state area. Consumption by the chemical industry is mostly as a feed-stock. This industry located on the Gulf Coast to take advantage of, the inexpensive natural 42 gaa available there prior to the development of long- . distance pipeline transportation. Primary metals (SIC 33) industries also consume large volumes in Texas and Louisiana. California consumes large quantities of gas for industrial use, particularly for petroleum and coal products (SIC 29)» stone, glass and clay products (SIC 32), and food and kindred products (SIC 20). The large volumes consumed in the industrial heartland of the country include consumption by chemicals and allied products (SIC 32), primary metals (SIC 33)» stone, glass, clay, and concrete products (SIC 32) and transportation equipment (SIC 37— in Michigan) industries. A number of western states use considerable amounts of gas in mining operations (SIC 10-14)1 California, Florida, Washington and a number of midwestern states, for food and kindred products (SIC 20); and Idaho, Washington, Oregon, Wisconsin, and a number of south eastern states for paper and allied products (SIC 26) (Gas Requirements Committee, 1975)* Commercial Consumption. The pattern of commercial con sumption (Figure 6) resembles industrial consumption since "many consumers classified in the commercial catagory serve a supportive role to industry" (Gas Requirements Committee, 1975» 3)* A noteworthy exception is Louisiana, which uses relatively little gas for com mercial activities. Retail outlets and some centrally- metered apartment buildings (which are classified commer cial) in some northern states, use considerable quantities for space heating. Electrical Utility Industry Consumption. Consumption of gas by the electrical utility industry is greatest in Texas and the other large producing states in the South Central and in California and Florida (Figure 7)* Table 1 provides further insight into the pattern of consumption in the Lower 48 states. The proportion of each natural gas usage that occurs in each state is shown. Thus, 21 per cent of the natural gas consumed in the Lower 48 states is consumed in Texas. In addition, the proportion of the total gas consumed by each economic sector in each state is presented. In Ohio, for example, 45 per cent of the 950,84? MMcf' is consumed by the residential sector, 18 per cent by the commercial sector, 33 per cent by the industrial sector, and .3 per cent by the electrical utility industry. The purpose of this examination of the spatial pattern of natural gas consumption has been to summarize the importance of various types of natural gas end uses to different parts of the country. With this information, ifif if an analysis of natural gas delivery were to indicate 4 a deficit in a given state, then an identification could he made of the types of end uses which may be affected. 3*3 The Spatial Pattern of Natural Gas Supply While demand for natural gas has been increasing steadily, proved reserves have been decreasing fpr the past eight years, as production has been exceeding re serve additions. Proved reserves are now at their lowest level since 1952, with the north slope of Alaska as the only major reserve addition in recent years. Natural gas production peaked in 1973 at 22.5 Tcf, declined by 6 per cent to 21.1 Tcf in 1974, and by another 7 per cent to 19*7 Tcf in 1975 (Figure 8) (FEA, 1975)• The spatial pattern of 1975 production by state is shown in Table 2 and Figure 9* Texas and Louisiana alone account for approximately 73 per cent of production, Oklahoma and New Mexico, for another 14 per cent, and Kansas, for an additional 4 per cent. No other state contributes more than 2 per cent of total production. Thus, five states account for 91 per cent of the Lower 48 production (Independent Petroleum Association of America, 1976). . ^5 Tril 3n Cubic Feet 320 m 4 300 • Proved Reserves 2B0 260 240 270 200 ISO 160 4 40 35 30 75 - Additions 20 .15 10 5 0 5 II) 15 * Production 20 25 1947 1950 1955 I960 1965 1970 1973 Figure 8 .— U.S. Natural Gas Reserves ourcei Federal Energy Administration, 19?5, 5. 47 TABLE 2 1975 PRODUCTION AND PROVED RESERVES BY STATE (MMCFI PROVED . 1 PRODUCTION 2. ALABAMA 770961 0.36 20825 0.11 ALASKA 6050749 2.99 155232 0.79 ARIZONA 40729 0.02 0.00 ARKANSAS 1993273 0.99 U B 3 5 3 0.60 CALIFORNIA 5464027 2.71 331945 1.63 COLORADO 1893017 0.94 165303 0.84 CONNECTICUT 0 0.0 0 0.0 DELAWARE 0 G.C c 0.0 FLORIDA 266904 0.13 43645 0.22 GEORGIA P 0.0 0 0.0 IDAHO 0 0.0 0 0.0 ILLINOIS 380804 0.19 1304 0.01 IND1ANA 59 839 0.03 143 0.00 IOWA 0 0.0 0 0.0 KANSAS 12661181 6.26 846936 4.30 KENTUCKY 61263G G.40 59762 0.30 LOUISIANA 61309424 30.32 7130742 36.42 MAINE 0 0.0 0 0.0 MARYLAND 140374 0.07 255 0.00 MASSACHUSETTS 0 0.0 0 0.0 MICHIGAN 1606749 0.79 105703 0.54 MINNESOTA 0 C.U 0 0.0 MISSISSIPPI 1207627 0.60 79805 0.40 MISSOURI 1516 0.00 0 0.0 MONTANA 9299T6 0.46 52424 0.27 NEBRASKA 55618 C .03 4050 0.02 NEVADA 0 0.0 0 0.0 NEW HAMPSHIRE 0 0.0 0 0.0 NEW JERSEY 0 0.0 0 0.0 NEW MEXICO 11759244 5.82 1120615 5.68 NEW YORK 215843 0.11 6632 0.03 NORTH CAROLINA 0 0.0 0 0.0 NORTH OAKOlA 416848 0.21 28051 0.14 OHIO 135401C 0.67. 85622 0.44 OKLAHOMA 13063028 6.47 1672408 '8.48 OREGON 0 0.0 c 0.0 PENNSYLVANIA 16112460 0.83 04 772 0.43 RHODE ISLAND 0 0.0 0 0.0 SOUTH CAROLINA G 0.0 0 0.0 SOU1H DAKOTA 189 0.00 o 0.0 TENNESSEE 6630 0.00 153 0.00 TEXAS 71036848 35.13 7041856 35.71 UT AH 917433 0.45 58583 0.30 VERMONT G 0.0 0 0.0 VIRGINIA 47465 0.02 6092 0.03 WASHINGTON U 0.0 0 0.0 WEST VIRGINIA 231133o 1.14 147789 0.75 WISCONSIN 0 0.0 0 0.0 WYOMING .3703159 1.83 299144 1.52 U.S. TOTAL 202149984 100.00 19718512 100.00 , SOURCE: AMERICAN GAS ASSOCIATION♦ 1975* 4-5 98624241^^ 7653 32 9896 Ti'gure'^V J £roducTian of Natural Gas in tlie United States in 1^75 : ' Ciri Bcf) Classes: (1) 0-.005, (2) .005-100, (3) 100-400, (4) 400-5000, (5) 5000-7200 The pattern'of proved reserves is, of course, similar to that of production, although slightly less spatially concentrated; the five South Central states contain 85 per cent of Lower 48 reserves. Also, California, Wyoming, West Virginia, and Arkansas each contain more than 1 per cent of reserves (Table 2 and Figure 10). The implication of this analysis is that current natural gas production and proved reserves (which are related to future production levels) are spatially concen trated, in contrast to demand, which has been shown above to be spatially dispersed. This leads to high transport costs for delivered natural gas in most sections of the country. While current Canadian and Mexican import and export levels are discussed in Sections 5*3 and 6.3» two alter native supply sources are introduced here— liquefied natural gas (LNG) and synthetic natural gas (SNG). These represent supplemental (in contrast to "tradition al") gas supplies. Contributions from both of these sources are currently minor. Liquefied natural gas is formed by liquefying natural gas by cooling to -260°F. so that its volume is reduced by a factor of 600. Presently, most LNG opera-, tions are for storage and peak-shaving. In the future, imported LNG is expected to contribute significant « quantities to the U.S. market. 3 TXprfc W : ^ovefi Reiserves of Natural G as‘in the United States in 1975 (in Tcf) ^ Classes: (l)O-.Ol, (2 ).01-.1 5 ,(3 ).15-1 .0 ,(4)1.1-2 .0 ,(5 )2 .1-1 0 .0 ,(6)10.1-15.0,(7 )6 0 .0-7 2 .0 0 51 . SNG (chiefly the gasification of coal, naptha, and natural gas liquids) is a process which holds great promise given current U.S. coal reserves, dwindling gas supplies, and the emphasis by President Carter upon the use of coal (1977» The National Energy Plan, Executive Office of the President, Policy and. Planning), While a number of facilities using naptha and natural gas liquids are already in operation, the economic feasibility of coal gasification is still being improved. Coal gas ification depends not only upon the further development of process technology, but also upon the availability of capital ($175-305 million per site) 'and water, and the productivity of the coal mining industry (6-9 million tons of coal per year are required for a commercial gas ification facility) (FPC, 1975)• 3.4 The Natural Gas Pipeline Network and the Flow of Natural Gas Historically, the evanescent nature of natural gas made it difficult to store and transport. As recently as 1930, the lack of long-distance pipeline technology required that gas be "flared off" or sold very inexpen sively to local markets. In the 1930's, a number of technological innovations, including the development of high-strength products and methods for the manufacture of large-diameter, welded, thin-walled pipe, made it possible to deliver large volumes of gas to distant markets in sixteen inch pipe. Thus, it became possible to link the large natural gas fields of Oklahoma, Texas, Louisiana, Kansas, and New Mexico, to the intraurban manufactured gas pipeline networks that existed in north ern cities. Most lines were under thrqe hundred miles until, in 1931» Chicago was linked to the Texas Panhandle by a one-thousand mile, twenty-four inch pipe by the Natural Gas Pipeline Company of America. By 1950» this network had grown to close to 400,000 miles of pipe, in cluding over 113»000 miles of transmission line (Figure 11) (FPC, 1975)* Since 1950, the number of miles of pipe 52 . 53 GAS UTILITY INDUSTRY MILES OF PIPELINE AND MAIN THOUSANDS Of MILES EH Field I. Gathering [|3 Transmission Distribution 1100 1000 900 800 700 600 ss* 500 I 400 300 m 200 100 1950 55 60 65 Figure 11.— Gas Utility Industry Miles of Pipeline and Main Sources American (las Association, 1975, 4-B, & had been increasing at a decreasing rate, until in 1975* the system had grown to 980,044 miles, of which 68,500 is field and gathering lines, 262,000 is transmission lines, and 648,000 is distribution main. Since 19<>9* this network has grown at an average annual rate of 1,8 per cent; 16,908 miles were added in 1975 (American Gas Association, 1975)* By 1990, the industry plans to increase network mileage to 1,220,000, close to a 25 per cent increase* the large-diameter transmission network alone will add over 50,000 miles (AGA Monthly. September, 1976, p. S-6). Since gas is moved through the pipelines under pressure, the increase in mileage has been accom panied by an increase in installed horsepower, from over 5.5 million in 1950 to over 15*4 million in 1975 (American Gas Association, 1975)* Natural gas service expanded geographically since the 1920's with service reaching all of the Lower 48 by 1966 . Today, the pipeline network is spatially extensive* serving most populated areas of the country (Figure 12— Note that many smaller branch lines are not shown on this map). The network is densest in the producing regions of the Gulf Coast, west Texas, Oklahoma, and Kansas and also in.the area around the West Virginia Panhandle, In much of the eastern half of the country, many small towns urn raiKKAL IHIWKK COMMISSION Figure 12.— The Natural Gas Pipeline Network of the United States 56 * receive service, while in some western states only the major metropolitan areas (such as the cities of the Snake River Valley and the Salt Lake.City area) are served. Seven major pipeline corridors may be identified: Corridor 1: from the Gulf Coast to Florida and the Eastern Seaboard Corridor 2: from the Gulf Coast and northern Louisiana to Ohio, Pennsylvania, New York, andi New England Corridor 3: from western Texas, Oklahoma, and Kansas to the area between the eastern Dakotas and Michigan Corridor 4: from Texas, New Mexico, and Oklahoma to the upper midwest Corridor 5: from western Texas to California Corridor 6: from Alberta to the Pacific Northwest Corridor 7: from Alberta into northern Minnesota Thus, the major pipeline companies transport gas from the major producing areas in the south central U.S. and Alberta to the major eastern and Californian markets. The FPC (197*0 has estimated the capacity and .actual annual flow for all pipes crossing state and national borders in 1970. From these data, it is possi ble to compute load factors for each border crossing: LF = AF / CAP (5) where, LP = the average annual load factor AP = the actual annual flow CAP = the capacity at the border crossing. Examination of these data shows that pipelines in corridors 1,2,3. and 5 are of the highest capacity and form the major routeways for gas. Pipelines closer to the source of the gas have greater capacity than pipe lines further "down-line". Pipelines in areas of low demand, and out of areas of small supply are also of low capacity, leading to low capacity lines in much of the Rocky Mountain and New England states. Examination of load factors for the various border crossings indicates great spatial variation. The high capacity corridors (1,2,3. and 5) also operate at high load factors (over 85 per cent for most routes), while pipelines in New England operate at between 50 and 60 per cent of capacity, and many western lines at below ■ 50 per cent. The major flows of natural gas occur from the Gulf Coast to the southeast and Middle Atlantic, from western Texas to California and the west, from north Texas- Oklahoma to the midwest, and from Alberta to California. Very detailed flow data have become available from the PPC (See Section 7.2). Structure and flow are inextricably related since the flow of natural gas (except for a small number of truck shipments) requires pipelines and related facil ities. Thus, construction of pipelines is approved by the FPC if sufficient natural gas supply (usually enough for twenty years) is available and sufficient demand can be shown. Since the cost of pipeline construction is high [averaging $227,000 per mile in 1973 with recent costs as high as one million dollars per mile (Osleeb and Sheskin, 1977)]. and. once in place, there is little recovery value if the pipeline is misplaced, the routing of these lines is of great importance. The spatial patterns of supply and demand shown in this chapter have led to the development of an expensive and extensive' pipeline network to accommodate the resultant flows. This dissertation strives to provide a model which may be i used to develop a regional plan for the adjustment of this network, given the spatial separation of supply and demand. CHAPTER 4- i THE OUT-OF-KILTER ALGORITHM 4.1 A Conceptual Introduction to the Out-of-Kilter Algorithm Linear programming models involve the maximization or minimization of some objective function subject to a set of linear constraints. The out-of-kilter algorithm (OKA) can be expressed as a linear program, although it is usually solved via an efficient network algorithm which, unlike the transportation problem, may begin with an infeasible solution. It then employs the dual varia bles (node prices) to identify suboptimal conditions so as to move toward optimality. Explanations of the algor ithmic procedure may be found in detail in Ford and Fulkerson (1962) and Potts and Oliver (1972). A concep tual introduction to the algorithm is presented in this chapter as well as a discussion of the suitability of this particular modeling format for examining the natural gas pipeline network. 59 The OKA may he expressed as the following linear programi • M N MINIMIZE V V (C. + t. .) X. , (6a) i=l M 1 1J 1J Subject toi (6b) £ v . . (6c) 13 X- 0 (6d) 10 Vi J (6e) l / i j ■ ai Vi (6f) l i xi i ‘ y v j M N V a< - y b . - 0 (6g) ffl 1 3=1 3 Constraints (6e), (6f), and (6g) are non-bindingj where, M ‘ = the number of supply regions N = the number of demand regions t. • = the per unit transport cost from i to j a^ = the supply in supply region i b. = the demand in demand region j J the flow from i to j 1* . s the lower limit on capacity of link (i,j) ^ J 61 u. . - the upper limit on capacity of link (i,j) A J ■» the production cost in supply region i The above states that the objective function of the model is the system-wide minimization of delivered price subject to the binding constraint that all flows fall within upper and lower capacities on the network links and the non-binding constraints that all supply is shipped and all demand is met. The output from such a model includes the minimum cost flow pattern, the cost of this solution, and, via the dual variables, the relative "value" of the commod ity at each location. If demand exceeds supply, the identification of deficit regions is possible; if .supply exceeds demand, regions at which production may be reduced can be identified. In addition, the impact of various proposed network additions may be assessed and "bottlenecks" in the network may be identified. The model makes the following assumptionst 1) Supply is located at a set of supply nodes (a^) 2) Demand is located at a set of demand nodes (b^) J 3) Transportation costs are a linear function of flow, i.e., if it costs X units to ship Y units, it costs 2X to ship 2Y units. Figure 13 is helpful in conceptualizing the algor ithm. In this simple problem, there are three supply DUMMY DUMMY SUPPLY NODE DEMAND NODE Pisrure 1 3 .— The Conceptual Framework of the Out-of-Kilter Algorithm o\ 63 nodes (a^,a2 »a^), three demand nodes (b^,) , and two intermediate nodes (c^,c2 ). Each link has three para meters associated with it* a transport cost (t. • ); a X J lower capacity for flow (1 ^ ) 1 and an upper capacity (u. .). In addition, a dummy supply node (A) and a X J dummy demand node (B) are.provided. These nodes, and the dummy links between them and the other network nodes, are necessary to satisfy equation 6b. The term "dummy" implies that no such nodes or links actually exist in the system being modeled, but are introduced to satisfy the algorithmic procedure. The transport costs on the (A,a^) links may be set equal to the production costs at ai (=ci)* l°wer capacity may be set to zero or some minimum production level; and the upper capacity to the maximum production level at a^. The transport costs on the (b.,B) links are generally set to zero, although they J may be set to some cost incurred at the demand sites; the lower capacities may be set equal to some minimum volume that must be delivered to b.j and the upper capacities J to the total demand at b.. The algorithm will then pro- J ceed until, subject to capacity constraints, flow through the network is maximized at a minimum cost. Section k,2 discusses the applicability of the OKA for the natural gas pipeline network. It will be shown 6k that the algorithm is adaptable so that it can handle a number of the special characteristics of this system. « 4.2 The Utility of the OKA for Modeling the Natural Gas Pipeline Network % The OKA represents an efficient framework within which to couch the natural gas delivery system. It must be recognized that any model of such a system will involve a considerable number of assumptions to meet the require ments of the model itself and to mold the usually imper fect data set into the required model format. While the details of this procedure form the subject of Chapters 5-7. this section presents a general discussion of the goals and assumptions of the OKA and its adaptability to the problem addressed by this dissertation. The goal of the OKA is a system-wide minimization of transport costs (or delivered prices). In Chapter 1, the importance of developing a plan for the natural gas pipe line network based upon minimizing transport cost has been discussed. Thus, the major criterion for forming the basis for a regional plan for the pipeline network is reflected in the objective function of the model. Little problem is presented by the three assumptions of the model .(See Section 4.1). Any flow model relies 65 66 upon the assumption, that production and consumption occur at a set of points in space. Natural gas production and consumption data are only available for large areas. As will be discussed in Chapters 5 and 6, this assumption may be "met" by employing relatively small areas repres ented by centroids. The third algorithmic assumption is that transport costs are a linear function of flow. In fact, the cost of gas transmission is extremely sensitive to load factor, i.e., for a given size pipe, the cost of gas transmission at a 5P per cent load factor is almost double the cost at a 100 per cent load factor. As will be. explained in Section 7*3» this non-linearity is met using a modified version of the OKA developed specific ally for this problem (MOKA). (The OKA computer program by Dr. Howard L. Gauthier has been modified by the addition of a subroutine that incorporates this non- linearity into the OKA model.) Thus, all three assumptions may be handled with little problem. The natural gas pipeline network fits well within the OKA's conceptual framework and offers a number of advantages. 1) It is a relatively simple and efficient proce dure. While "realism" should never be sacrificed for simplicity, the latter is certainly desirable in any modeling format. 2) The optimal flow pattern may be compared with the actual flow pattern to indicate the extent of sub optimality in various portions of the actual system. 3) Pipelines are directed arcs, a situation easily handled by the OKA. In addition, direction con straints may be removed and changes in pipeline direction suggested. 4) An optimal flow pattern is outputed. Currently, the FPC must approve all interstate natural gas sales. Approval of sales (and pipeline construction) is made on the basis of ''present or future public convenience or necessity" as described by the Natural Gas Act (March, 1974). A major criterion employed is whether or not sufficient supply will exist at A and demand at B for a given period of time (usually twenty years). The ques tion being addressed here is the advisability of A serving B in the first place (Figure 14). Given that C is currently serving D, it is quite possible that a transport cost savings could be realized if, instead, C were to serve B and A serve D. If pipelines are not currently in-place from C to B and/or A to D, the advis ability of the plan could be determined by subtracting the cost of new facilities from the transport cost savings. If the result is positive, the optimal flow » pattern is recommended. I Demand Nodes Actuol Flow — * Optimal How Proposed Flow . Figure 14.— Conceptualization of a Regional Approach to Determine "Present or Future Public Convenience or Necessity" for Flow Contract and Pipeline ^ Construction Approval by the FFC. : 69 5) If alternative routes have been proposed for a new pipeline (as is the case for the Alaskan pipeline), each may be tested to indicate which would incur lowest transport costs. This testing takes place by introducing, in turn, each alternative to the system. In Figure 15i two links have been proposed to connect a new source of supply (a*) into the current system. First, the modified OKA procedure is run with link (a’,c^) added, then with this link removed and (a',b^) added. The transport costs may be compared to determine the least-cost addi tion and the savings compared with differences between the two routes in environmental, social and political costs. 6) In the case where demand is greater than supply, all capacity constraints may be removed on the arcs in the set (A,a^) (the dummy supply arcs) or increased proportionately, so that all demand may be met from existing sources, allowing the pipeline system to limit the flow. This makes possible the identification of bottlenecks in the system that would result if production levels were to increase. In addition, the final flows on the (A,a^) arcs would indicate the optimal production levels at each supply node. DUMMY DEMAND NODE EXISTING PIPELINE ♦ — • — PROPOSED PIPELINE v, t .. ,. Fisure 15»—“The Qut-of-Kilter Algorithm as a Vehicle for ^alustm^ the Systemwide Implications for Various Proposed Pipeline Routes, o 71 In sum, the relatively flexible framework of MOKA, the modified version of the OKA, offers a number of advantages for the development of a natural gas pipeline network regional planning model. These include its simplicity and efficiency, its ability to account for directed arcs, its identification of an "optimal" flow pattern, its ability to act as a link-addition algorithm, its ability to determine optimum production levels, and its ability to account for the nonlinear cost-flow relationship. The above capabilities are illustrated in Chapter 8; the model has additional capabilities which are discussed in Chapter 9* t CHAPTER 5 THE DEMAND SUBMODEL. 5.1 The Definition of Demand Regions The OKA and related optimization approaches for examining natural gas flow assume that consumption occurs at a set of points in space. The gas utility industry services about 4-5 million customers, necessitating the definition of aggregate demand points. Since the goal of this dissertation is to provide a basis for the development of a regional approach to planning the natural gas delivery system, the definition of demand areas consistent with this purpose is important. Past research has unsatisfactorily defined demand regions for spatial analysis. Many studies either have assumed away the spatial nature of the industry, or as in MacAvoy's work (19?l)i this factor is recognized, but poorly exploited. MacAvoy employs two demand points: Los Angeles (to represent western consumption); and Cleveland (to represent eastern and midwestern 72 73 consumption). Not only is one point used to represent vast regions, but entire sections of the country are ignored. Although Lawrence (1973) improves upon the spatial specificity of previous models by employing the nine U.S. census divisions as demand regions, problems still ensue. For example, one point represents the entire Rocky Mountain region (Idaho, Montana, W y o m i n g N e v a d a , Utah, Colorado, Arizona, and New Mexico), an elongated land area of over 850,000 square miles. No useful recommenda tion can be offered concerning pipeline capacity into such a large region. Lawrence's model indicates that efficiency would be served by providing additional pipe line capacity from the Permian Basin to the Rocky Moun tain region. However, the planner is provided no guid ance as to exact origin and destination. Although this problem is somewhat alleviated in smaller eastern census divisions, it is here that the most natural gas is consumed and the greatest detail desired. Lawrence does not identify representative nodes for each area. Waverman (1973) employs nineteen North American demand regionst ten contiguous U.S. regions as defined by the Gas Requirements Committee (Gas Requirements Committee, 1975) and nine Canadian regions, including Quebec, British Columbia, Alberta, Saskatchewan, Manitoba, and four regions in Ontario, Each of these regions (except for those in Ontario which are defined on the . basis of the structure of the pipeline network) suffer from the same drawbacks as those used by Lawrence. Waverman considers three factors in selecting nodes to represent his demand regions: the weighted centroid of consumption and the average and maximum distance gas must travel within each region. In New England, for example, he selects a point jus't south of Boston, since there is little consumption north of this city. In Ontario, the consumption points are the end points of the existing pipelines. MacAvoy and Pindyck (1975) work at two different geographic scales. The first divides the nation into five apparently arbitrary "aggregate consuming'regions" which do not appear to be coextensive with the demand regions of any agency. The second scale includes most of the Lower 48 states as separate consumption points. Although this second scale represents an improvement over that of previous approaches, the regions are still too large for the purposes of this dissertation. MacAvoy and Pindyck are not explicit concerning their selection of a node to represent each region, but their.usage of the "average mileage between producing and consuming regions" implies the use of some average consumption point. Brooks (1975) employs the two-tiered system of MacAvoy and Pindyck but specifically notes (p. 235) that it is unrealistic to assume that gas is consumed at one central location within each state, particularly for California and Texas. He suggests that breaking states into smaller demand regions would result in a more efficient model, but recognizes the problems of obtaining * t , or estimating data for smaller units. Oisleeb and Sheskin (1977) employ the population centroids of fifty-six states and provinces as demand points. Given their purposes, such demand points are reasonable, although not optimal. Population centroids are employed as average consumption points given the assumption of a direct relationship between population and natural' gas consumption. Although a progression may be noted from an aspatial approach to one in which fifty-six demand areas are rep resented by average consumption points, all of these approaches are basically inappropriate for the develop ment of a model consistent with a regional approach based upon a least-cost criterion. 76 Multi-state or one-state regions represent "artifi cial" demand units for two reasons. First, states often contain two or more distinct demand areas in that various sections are served by different transmission companies. For example,.South Dakota should be composed of two dis tinct demand areas (Figure 16)* 1) western South Dakota, served by the Montana- Dakota Utilities Company, which obtains most of its gas from Montana and Wyoming} and 2) eastern South Dakota* served by the Northern Natural Gas Company, which obtains most of its gas from the south central part of the U.S. The population centroid of South Dakota (the point of average consumption) is in Buffalo County, 35 miles from the closest city served by natural gas in the east and approximately 2?0 miles from the closest city in the west. Clearly, this point is not representative of the location of natural gas consumption in South Dakota. Second, states form arbitrary demand areas because some transmission companies serve communities in more than one state with the same main line. For example, Northern Natural Gas Company serves eastern South Dakota, part of Iowa, and Minnesota from the same trunkline (Figure 16). In considering the ability of this pipeline to service its demand area, it is clear that future Multi-state or one-state regions represent "artifi cial" demand units for two reasons. First, states often contain two or more distinct demand areas in that various sections are served by different transmission companies. For example, South Dakota should be composed of two dis tinct demand areas (Figure 16)i 1) western South Dakota, served by the Montana- Dakota Utilities Company, which obtains most of its gas from Montana and Wyoming; and 2) eastern South Dakota* served by the Northern Natural Gas Company, which obtains most of its gas from the south central part of the U.S. The population centroid of South Dakota (the point of average consumption) is in Buffalo County, 35 miles from the closest city served by natural gas in the east and approximately 270 miles from the closest city in the west. Clearly, this point is not representative of the location of natural gas consumption in South Dakota. Second, states form arbitrary demand areas because some transmission companies serve communities in more than one state with the same main line. For example, Northern Natural Gas Company serves eastern South Dakota, part of Iowa, and Minnesota from the same trunkline (Figure 16). In considering the ability of this pipeline to service its demand area, it is clear that future ■ 7? demand in the extreme western parts of Iowa and Minnesota will influence this capability, while the level of demand in western South Dakota will have no affect. Such problems are not limited to South Dakota. Per usal of a pipeline map reveals that only Delaware does not contain at least two demand areas. Only about twelve states are serviced by pipelines not having short "spur" lines into neighboring states, as is illustrated in eastern South Dakota. The above argues for the development of a set of demand areas that are small and compact enough to be reasonably represented by a single node and are based upon the market areas served by the various transmission companies. Therefore, some geographic unit smaller than states is sought with which to form demand areas. A three-step procedure is employed to define the set of demand nodes: 1) the establishment of generalized pipeline company market areasj 2) the precise definition of each demand area using counties as "building blocks"j and 3) the definition of demand nodes to represent each demand region. Step 1. Initially, general boundaries forming "cohesive" pipeline market areas are defined. While many of these regions are served by only one company, some compact areas are serviced by two or more. Some attempt is made NORTH DAKOTA MONTANA - SOOTH DAKOTA WYOMING MINNESOTA RAPID CITY POPULATION CENTROID IOWA NEBRASKA • SERVED COMMUNITY. Figure 16— Principal Natural Gas Pipelines of-South Dakota 79 to keep the demand areas of "reasonable size" to facili tate the demand-estimating procedure described, in Section 5*2. For ease of interpretation, each region is contained in as few states as is possible. If a "spur" line of a main line serving demand area Y in state X also serves a "handful" of communities in a neighboring state Z, these cities are included in demand area Y in state X. However, if a spur line serves a significant number of communities in a neighboring state, a separate demand area is formed.- Additionally, an attempt is made to limit the spatial extent of the demand regions, part icularly in high demand areas, so that one point can adequately represent the entire region. The number of demand areas in each state is a func tion of the criteria above, the size of each state and its counties, and the structure of the pipeline network, Obviously, some subjective judgment is employed, but it is believed that the 177 demand regions represent cohe sive, logical units (Figure 17 and Appendix A). Step 2. The second step in defining demand regions is to identify those counties within the "general" boundaries that are currently served or are likely to be served with natural gas in the future. Counties are employed as they are generally small enough to enable the forma tion of compact demand areas wi*thout the inclusion of nr 9 9 101 9 0 97 126 124 9 6 79 ttt> 100 m 173 1 2 0 9 9 7 6 171 7 7 140 W 172 177 79 139 ?D< 4 0 4 5 5 0 nt J * * £ 1 « 9 ITS 102 47 41 170 9 0 4 3 103 .9* 2 2 I 2 3 4 4 Q1 123 *64 20 sa \ 60 191 106 3 5 .3 4 to T I2 135 3 6 m 155 66 3 0 10 m . 154 38 152 66 6 7 156 160 UiUmerved Area 4 00 Ml lES Figure 17.— Demand Regions Based Unon the Structure of the Piueline Network (See Appendix A for a full description of the demand regions.) 81 large unserved areas. Additionally, a reasonable number of demographic and economic variables (needed for the model developed in Section 5*2) are available for counties. Four rules are adopted to more accurately define each demand, area. An implicit assumption in these rules is that the population surrounding a served commun ity influences the level of demand in that community by adding to the labor pool and the retail market. 1) Each demand area includes counties that contain served communities as identified on the pipeline maps of. the FPC or the Oil and Gas Journal. Although not all served communities appear on these maps, the use of rules two and three below and some judgment should ensure that most served counties are within some demand area. 2) - If any county in a Standard Metropolitan Statis tical Area is served, all counties within the SMSA are included within the demand area. 3) All counties within five miles of a served community are included. The five mile limit is extended for large cities. 4) Independent cities are included within the closest county. Step 3. The final step in the definition of demand regions for use in a linear programming model is their representation by a single node-. Two criteria are 82 established* The demand node should be located on the pipeline network itself and be as close to the population centroid of the demand region as possible. In some instances, additional considerations arise (See Section 7 .3 ). Since each demand node only represents a small section of the country, their siting is a less critical problem than in past research. 5.2 The Determination of Future Demand and Consumption in Each Demand Region Section 5*1 has described the procedure employed to derive 177 natural gas demand areas using counties as basic building blocks that are based upon the pipeline network structure. Although this provides a logical set of demand units, a rather serious drawback is introduced* Demand data at levels lower than the state are not avail able. Estimated county data by end use for Ohio for 1970 have been obtained from the Ohio Emergency Energy Commission (special study by Mathematics), which employs econometric and survey techniques. If such data are available for other states, estimates are probably based upon varying sets of assumptions. Brooks (1975) has also noted the lack of such data. Although the initial intention had been to develop an econometric model of demand by county, two problems arose* 1) Estimation of a regression equation implies the knowledge of the values of the dependent variable for some year. Although these data are available for Ohio, extrapolation to other states is improper. 84 2) The types of explanatory variables needed in such a model are not available at the county level. Thus, some procedure is required such that state- level data may be apportioned to the 177 demand areas. * Two decisions are necessary* the selection of state- level demand estimates and the identification of a method to apportion these estimates to the 177 demand regions. Selecting State-Level Demand Data. Two types of demand data are available* econometric estimates of future demand and survey estimates of current consumption and future consumption and demand. Econometric Models. MacAvoy (1962 ) estimates a demand equation for residential and commercial consumption in fifty-two U.S. Cities for 1959 using marginal price of gas, price of fuel oil, average temperature, population, and median income. Although reasonable results are obtained, this model is rejected as inappropriate since an equation at the city level is not necessarily applica ble to states. In addition, the equation' is dated and was estimated during a period of excess supply. Use of MacAvoy1s equation (and most of those below) implies the ability to forecast accurately the explana tory variables, the temporal stability of the coeffi cients, and the applicability of the coefficients 85 outside the range of the explanatory variables used to estimate them. These factors represent some draw back to the use of econometric models. Wein (1963) develops a forty-four state model for residential-commercial consumption in 1961. .The explan atory variables are price of gas and oil, average * temperature, and the number of customers in the resi dential-commercial sector. The latter variable is of questionable value. Balestra (196?) develops a short-run model for the residential-commercial consumption of each of thirty-six states for 1950-1962. The independent variables are price of gas, level of per capita income, capacity of the pipelines into the state (actually a supply constraint since capacity estimates were unavailable) and a factor concerning the stock of gas appliances. His dynamic model assumes that gas consumption is a function of price of gas, population, population increase, per capita income, change in per capita income, and gas consumption in the previous year. Balestra's formula tions have the advantage of being spatial, but not all states are estimated by his equations as some were not yet served in 195°-1962, and his empirical results are not satisfactory. \ Lawrence (1973) uses a Balestra-type formulation but estimates residential and commercial use in separate models. He also estimates a model for industrial demand based upon the price of gas, total fuel consumption by industry, and a climatic factor. As in the Balestra model, the results are not encouraging. Brooks (1975)« also following Balestra, estimates equations for industrial and non-industrial demand in five regions. New demand is dependent upon the wholesale price of.gas, the price of alternative fuels, and an economic growth variable, g. For the non-industrial equation, g is either state population or income; for the industrial model, capital investment or value-added in manufacturing. The results are not overly encouraging' a six-variable model of North Central residential-commer- 2 2 cial consumption yields an R of .307* The highest R (.7^5) is a six-variable model for North Central indus trial demand. All equations contain a large number of dummy variables. MacAvoy and Pindyck (1975)» employing the same independent variables and regions as Brooks, achieve vastly different results, illustrating a weakness of the econometric approach. Future demand is affected by a large number of fac tors which are not easily quantifiablei 1) the price of 8? gas and alternative fuels; 2) population; 3) income; Jf) life styles; 5) general level of economic activity; 6) geographic location;- ?) supply constraints;and a host % of other factors. The econometric models fail to account m ►< ...... for all of these factors in a satisfactory manner. This author, then, agrees with the FPG that; the number of problems inherent in existing econometric models tend to make them to varying degrees unsuitable for use in policy simulation (FPC, 1975* P* 187). The Gas Demand Task Group of the National Petroleum Council (NPC) Committee on U.S. Energy Outlook reviewed the work of a number of econometricians for their re port to the NPC. They concluded that none would be suitable for their quantitative prediction of trends in gas demand (FPC, 1975* 188). Thus,.although work . on econometric models should continue, sources of survey data were examined for use in this project. Survey Estimates. The Gas Requirements Committee's (GRC) Future Gas Consumption in the United States series has been selected for state-level estimates as it contains the most complete data set and includes projections of both future demand and consumption. In addition, it is used by the FPC, the natural gas industry itself, and has been employed by Waverman (1973) and Osleeb and Sheskin (1975* 1977)* The GRC is sponsored by the Gas Industry Committee representing the American Gas Association (AGA), the American Petroleum Institute (API), and the Interstate 88 Natural Gas Association of America (INGAA). The FPC calls the report "the most detailed and comprehensive gas requirements forecast available" (FPC, 1975i 184-). The chairman of the Gas Industry Committee,, in a letter to survey participants states* No other reports of this kind are able to draw upon the combined expertise of the gas distribution, transmission, and production industries. Because of this combined strength reflected in the Committee membership and the report itself, the reports have had a high credibility with a wide variety of audiences. Certainly, during these times when energy data are often chal lenged for being self-serving, it is even more important to have a report that can withstand these criticisms (GRC, 1975, 85 ). The GRC uses a survey approach, requesting every company or organization which is a final supplier of gas to forecast their individual requirements based upon a set of assumptions. Of the 1,4-47 survey questionaires mailed in May, 1975 for preparation of Volume 6 of their reports, 1 ,0 7 8 responses were received, representing some 93 P®r cent of total 1974 consumption. Estimates are made by regional Work Committees for non-reporting companies on the basis of reports filed with state utility commissions and/or data provided by the pipeline compan ies serving non-respondents. Forecasts of future demand 89 and consumption for non-respondents are prepared on the basis of appropriate trends and other data for each area. Additional evidence of the reliability of the GRC data is provided by a comparison of actual 1975 consump tion with the estimated figures of GRC Volume 5 (made in early 1973) and GRC Volume 6 (made in mid-1975)• State • estimates from Volume 5 average a 2$ per cent deviation from the actual figures, ranging as high as a 65 per cent 1 error for Arkansas. Obviously, survey participants vastly underestimated the effect of the supply shortage. Volume 6 estimates are far superior, since they were compiled during the year being estimated and the contin uance of the natural gas shortage was evident at that time. In only eight cases does the error pass 10 per cent, and only for Arkansas is there a serious discrep ancy . The percentage error for Volume 5 is high, not sur prising since 1973 was a year of great change in the industry. For the first time, consumption of gas decreas ed (Figure 18). Estimates should become more reliable as the direction that consumption is expected to take has become evident.* One may argue that the forecasts examined above are not long-range and be skeptical of survey data of this nature because it may be self-serving to the industry TRILLIONS OF CUBIC FEET (1000 BTU) - 0 4 0 2 10 50 - 0 3 60 iue 8—US Gs osmto n Rqieet, 1956-1995 Requirements, and Consumption Gas U.S. 18.— Figure - 1966 - ctval A ore GsRqieet omte, 19 Committee, Requirements Gas Source* 1970 1975 EstimatedConsumption 19B0 Estimated Consumption Volume 6 Volume — s Volume 5 Volume Requirements Volume 5 Volume 1985 75* 1990 !• 1995 91 and different companies will employ varying interpretations of assumptions in making predictions. Nevertheless, survey • data appear to represent a superior alternative to the econometric models reviewed. Note, however, that although survey data take advantage of knowledge of existing and probable contracts, surveys still rely upon interviewee's intuition with respect to some of the variables used in the econometric models, and thus, suffer from some, of the same problems. Two different volumes of the GRC report are available. Volume 5 estimates both future requirements (demand) through 1995 and consumption through 1985t Volume 6 estimates con sumption through 1985* The demand data are based on the following assumptions1 1) there will be an adequate supply of gas for all requirements for all periods covered by the . » survey; 2) the 1970 price relationship of gas to competing fuels will remain essentially the same in the future, but • individual companies should consider known changes in these relationships in their market areas; 3 ) there will be no . major war, depression, or other catastrophe during the forecast period; and 4) technological development will be of an evolutionary nature. The first assumption is unrealistic in view of the nat ural gas shortage but is necessary to estimate demand. In contrast, for Volume 6, respondents were asked to estimate consumption rather than demand. Consumption is defined as; 92 that proportion of future gas require ments which individual companies plan on meeting over a specified period of time based on their best judgment as to future local and regional market conditions and reflecting their realis tic expectation of gas supply from supplemental sources, imported gas, and natural gas produced and purchased under present or future contracts (GRC, 1975* 9^)* Selecting Variables to Apportion State-Level Demand to the 177 Demand Regions. The model developed to apportion * state-level demand takes the following form* °i = J* [pij + vu (cj> ] vi (7> where, = the estimated consumption in demand region i 4*V\ P . . = the percentage of the j state's 1975 P°P- J ulation residing in counties assigned to demand region i C 1?1 = the state's consumption of gas for non- J industrial uses C"? - the j^ 1 state's consumption of gas for indus- J trial uses V-i = the percentage of the j state's 1972 •* value-added in manufacturing in counties assigned to demand area i N = the number of states spanned by demand area i (The equation for deriving gas demand in each region i is the same as the above except that the variable C is given a demand interpretation.) Equation 7 states that non-industrial use is appor tioned to the demand areas on the basis of population, 93 and industrial use,, on the basis of value-added in manu facturing (VAM). Industrial uses are separated from other uses since industry demands great volumes both for space heating and as a raw material. Lawrence (1973) suggests that residential and commercial use be separated, but, for reasons explained below, they are treated togeth er. Note that the choice of apportioning variables (Pij and in Equation 7) (justified below) is limited to data available at the county level. For example, apportioning natural gas usage on the basis of total energy usage by county is an obvious approach, but these data are not available. Non-industrial consumption includes gas used in the ' residential and commercial sectors and for electricity production. The underlying hypothesis employed by equa tion 7 is that there exists a positive relationship between population and each of these natural gas end uses. A number of econometric models reviewed above show such a relationship. In addition, a correlation analysis between 1973 non-industrial consumption by state and population yields a significant correlation (R = •7^i C C s *01). It is recognized that a significant relationship at one geographic scale does not necessar ily imply a relationship at another. Nevertheless, the rather high correlation obtained at the state level is 94 encouraging. An examination of the exact nature of the non-industrial usage categories lends further credence to employment of P. . in equation 7* J* J Residential use is chiefly by private homes, small multiple dwellings, and larger units with individually- metered apartments. Obviously, the greater the popula tion., the more such use. Commercial use includes trade establishments, service enterprises, business offices, hotels, warehouses and similar establishments, i.e. , central functions. This catagory also includes centrally- metered apartment dwellings, public institutions, and some small industrial users. Since the relationship between population in both central city and surrounding, area and the number and size of central functions is well-established theoretically (Christaller, 1933) and empirically (Berry and Garrison, 1958) and because some "non-commercial" uses are classified as commercial, a variable such as the number of workers in retail trade is not employed for commercial use in Equation 7 . Gas used by electrical utilities for power genera tion presents somewhat of a problem since the electricity produced is employed by all sectors of the economy. Use of population, then, may introduce a small margin of error. 95 Industrial use includes gas consumed by manufactur ing plants and process companies. Three industry-related variables at the county-level are availablet total employees in manufacturing; total number of production workers} and value-added in manufacturing (YAM). At the state-level, little difference between the variables may be discerned; correlations between them are not signi ficantly different from one. VAM is employed since it shows the highest correlation of the three with industrial use (R - .30, Ct= .05) and a number of researchers, including Brooks (1975) and MacAvoy and Pindyck (1975)* have- shown a relationship between VAM and industrial use. A problem is created by the non-disclosure of VAM 4 for a number of counties. The following formulation is employed to derive estimates for these counties* v*= b ■ J!l va> 7 li n* J (s) where, t V, = the estimated VAM in county k, where k has a non-disclosed value Vj - the total value-added in state j V* «' the VAM in county A of state j, where A has a disclosed value- n = the number of counties with VAM disclosed m = the number of counties with VAM not disclosed Nk « the number of establishments in county k. 96 This procedure involves apportioning the non-dis closed VAM to the counties on the basis'of the number of establishments' in each county. Although this procedure is not satisfactory, most non-disclosed counties are in rural areas and tend to be equally distributed among the various demand regions in each state. The results of the model may be evaluated for Ohio by comparing the percentages for and derived for equation 7 with the actual percentages calculated from data .estimated by the Ohio Energy Emergency Commission (Table 3). Overall, the results compare very favorably. The derived percentages average only a 2.2^ per cent error for non-industrial use and a 1.36 per cent error for industrial use. As would be expected, greater errors occur in regions of fewer counties. For the county group assigned to region j in Kentucky, some rather serious discrepancies appear (.28 vs. .91 for industrial use). These areas have such small comsumption, however, so as not to affect the overall validity of the model. In r regions of many counties, errors at the county level (i.e., residuals that would appear in a regression between county population and non-industrial use) tend to cancel each other. Although it can not- be assumed that the model will be accurate for other states on the basis * TABLE 3 TEST OP DEMAND SUBMODEL EMPLOYING OHIO COUNTY CONSUMPTION DATA Non-Industrial Use Industrial Use Ohio Region Model % Actual % Model 55 Actual % 1 24.81 25.09 24.57 24.28 2 6.50 3-06 4.64 2.41 3 28.48 31.50 30.41 27.71 4 18.39 - 17.44 I8.58 18.44 5 13.86 15.67 15.08 19.5^ Counties Assigned to Region h in Pa. •50 .49 .43 •35 Counties Assigned to Region j in Mich. •6.06 6.04 6.01 6.37 Counties Assigned to Region k in Ken. 1.39 .70 .28 .91 Total 100.00 100.00 100.00 100.00 Source: Author and Ohio Energy Emergency Committee 9 8 of these results, some empirical justification has been provided. In applying the results of equation 7 to future demand and consumption, it must be assumed that nd major population or industry shifts will occur at the intra state level. Although population is expected to grow at regionally varying rates and there has been a trend toward migration to middle-size cities, it is doubtful that the location of the major population and industrial centers within each state will shift significantly. It is conceivable that the addition of a small number of large industrial users could alter the percentage of industrial consumption in the various areas, and such a possibility is accepted as a drawback to this methodology. Working against locational shifts in natural gas usage are regulations in some areas prohibiting new users. 5*3 Additional Demand Areas Although some U.S. companies deliver small volumes of natural gas to Canada and Mexico, no projections of these deliveries could be found. Thus, present demand is considered to remain constant into the future. This is ’ i not unrealistic since many export contracts are for a given volume per year for some term. These export points are shown on Figure 12. Although the pipeline network of Alaska is not studied here, both Alaska and Japan (which receives LNG from the south slope of Alaska) are considered as demand regions whose demand is subtracted from south slope production estimates. Estimates of Alaskan demand are available from the GRC (1975)* Exports to Japan are assumed to continue at current levels. CHAPTER 6 THE SUPPLY SUBMODEL 4 6.1 The Identification of Supply Regions The out-of-kilter algorithm and related approaches for examining natural gas flow assume that production • occurs at a set of points in space. The existence of over 127,000 producing natural gas wells necessitates the definition of aggregate supply points. Since the goal of this dissertation is to provide a Basis for the develop ment of a regional approach to planning the natural gas delivery system, the definition of supply areas' consis tent with this purpose is important.. Past work has unsatisfactorily defined demand regions for spatial analysis. Lawrence (1973) notes that many researchers either have ignored the spatial nature of the industry or, as MacAvoy (1971) has done, concentrated supply at one location (Louisiana)'. Lawrence (1973) improves upon this approach by employing fourteen supply regions. Problems still arise. Texas is considered as 100 101 one supply region, although it clearly contains at least three separate supply regions linked by varying companies to different demand regions (Figure 12). One result is that, in Lawrence's model, El Paso Natural Gas Company has access to gas reserves in all parts of Texas (which in reality is not the case). Since Texas has the greatest volume of gas reserves in the nation, this problem is particularly acute. A second type of problem is introduced by Lawrence's use of multi-state supply regions. In the Rocky Mountain region, for example, the field in northern Montana is approximately 825 miles from the one in southern Colorado. Inaccuracy is introduced when both fields are represented by the same node (Figure 12). Waverman (1973 ) employs nineteen supply nodes (five in Canada).* Some detail is provided in areas of great production; New Mexico and Louisiana contain two regions each; Texas contains four. No region contains more than one.state or province, although the problem of spatially disparate fields still occurs in California, Wyoming, and Alberta. In addition, thirteen states with significant supplies (New York, Pennsylvania, Ohio, Arkansas, Utah, Colorado, Montana, Michigan, and others) are omitted. MacAvoy and Pindyck (1975) divide the U.S. into four regions for estimating gas production: Permian Basin; 102 Gulf Coast and Midcontinent} other continental} and Louisiana south offshore. While this breakdown may be satisfactory for their purposes, it suffers from the types of problems mentioned above. Osleeb and Sheskin (1975» 1977) employ the thirteen National Petroleum Council (NPC) and four Canadian National Energy Board (NEB) regions (Figure 19)■ Although these regions are convenient due to data availability and are used by government and industry for planning purposes, representing these vast regions with one node leads to errors in predicted flows. For example, A problem arose because the eastern region has small supplies in several states (Ohio, Pennsylvania, West Virginia, and New York). The centroid was located near Wheeling, West Virginia. Thus, instead of satisfying a small portion of the demand in each state, all of the Eastern supply went to satisfy Ohio demand (Osleeb and Sheskin, 1977, 83). Brooks (1975) employs about thirty-five nodes repre- ■ senting supply regions in the U.S. and Canada. Sufficient detail is provided in areas of great reserves and very few supply areas include more than one state. Although a progression from an aspatial approach to one in which thirty-five supply regions are employed may be noted, the above regions are not satisfactory for this research. Supply regions should not be composed of 103 FIGURE 19 • U.S. National Petroleum Council and Canadian National Energy Board Supply Regions Key to Region Names 1. Alaska 9* Conventional Canadian « 2. Pacific Coast 10. Mackenzie Delta 3. West Rocky Mountains 11. Arctic Islands k. East Rocky Mountains 12. East Coast (Sable Island) 5. Permian Basin 2A. Pacific Offshore 6. Western Gulf Basin 8A1. Georges Bank 7. Midcontinent 8A2. Baltimore Canyon 8. Eastern 8 A3 . Georgia Embankment 4 Figure 19 U.S. National Petroleum Council and Canadian .National Energy Board Supply Regions 105 arbitrary spatial units, but should be small and compact enough to be represented by a single node and be based on the "gathering areas" of the various pipeline companies. Thus, some small geographic unit is sought with which to form supply areas. Counties are chosen as "building blocks"to form sixty U.S. supply regions in the Lower 48.states. All gas-producing counties, as identi fied by the Independent Petroleum Association of America (1975) are assigned to one of the sixty supply regions. Data limitations with respect to the model developed in Section 6.2 below prevent full compliance with the criterion of basing the supply regions on. pipeline company gathering areas. No serious problem is introduced if a company owns reserves in more than one supply area. ' When more than one company owns reserves in a supply area, the model assumes that each company has access to reserves within the area. The regions are small enough and the pipeline network sufficiently interconnected within most supply areas so as to allow intercompany purchases and ease the impact of this assumption (Figures 12 and 20). Most of the regions employed are FPC gas areas, parts of FPC gas areas, and states. A final step in defining supply regions for a linear programming model is the representation of the region by a single node. Two criteria are established to identify « M tlE S Figure 20. — Supply Regions Employed in this Dissertation 106 j 10? such a point: the supply node should be located on the pipeline network and as close to the center of production as possible. The second criterion is impossible to meet precisely since this would require data on the output of individual natural gas wells and such data are not available in any usable form (The FPC has these data, but on 90>000 separate pages.). Consequently, the physi cal centroid of the natural gas fields within each supply region is employed. In many instances, some compromise is reached between the above criteria. Since each supply node represents a relatively small region, no critical problem is presented. 6.2 The Determination of Future Production in Each Supply Region Although the procedure described in Section 6.1 provides natural gas supply areas small enough to elim inate many of the problems encountered by other research ers, a drawback is introduced. Projections of supply data of any type are not available for any of these, regions. The original intention had been to develop an econ ometric model of supply by county, but a number of problems obviated this pathi 1) Regression models imply the knowledge of the dependent variable for some year. No data on natural gas supply by county are available. Osleeb (1976) notes that such data are collected by the FPC, but are unavailable in a usable form; and 2) The types of explanatory variables needed are not available by county. Thus some procedure is needed such that data at available levels of aggregation may be apportioned to the sixty supply regions. Two tasks are involved: the 108 109 selection of future production estimates and the develop ment of a procedure to apportion these estimates (gener ally only available at an aggregate level) to the sixty supply regions. Selection of Future Production.Estimates. Future produc tion is a function of reserves. Figure 21 presents a number of alternative reserves estimates. Note that the i estimate of Theobold et al. differs from that of Mobil by 429 per cent. The existence of such a wide range of estimates leads to the conclusion that the preferred investigatory procedure for this dissertation is to employ various estimates of future production represent ing a range of assumptions concerning the variables employed in such forecasts. Three types of projections of natural gas supply are available * econometric, mathe matical, and geological. Each is described below. Econometric Projections of Natural Gas Supply. Wein (1963) predicts the number of exploratory wells as a. function of the total number of wells, price of crude, interest rate, and exploratory well success ratio. He t concludes that the final effect of raising wellhead price is to lower exploration and supply, a result that has been widely criticized. (Lawrence, 1973, 81). MacAvoy (1971) develops a four equation model of future supply in fifteen drilling regions in which the OIL COMPANIES SHELL* Hubbtrt 1967 MOBIL (1974) 374 VS. GEOLOGICAL SURVEY Hendricks 1.3CC 1J20 Theobold, et al. 1972 £93-2.000 Office of I Resources, Hubbert 540 1974 NATIONAL RESEARCH COUNCIL 1975 530 ' 1 I 1 _L • L J '{excludes AloskoJ 250 500 750 1.000 1,250 1.500 1.730 2,000 Trillions of Cubic Feet Figure. 21.— Alternative Estimates of U.S. Undiscovered Natural Gas Resources Source* National Academy of Sciences, 1975, 89* i n number of wells is a function of price of gasj new reserves are a function of number of wellsj deliveries from new contracts are a function of new reserves, price of crude and interest rate? and price of gas is related to new reserves, distance from market, population change, and change in per capita income. This work demonstrates the importance of price in the exploration (and conse quently the production) decision. Khazzoom (1971) and Erickson and Spann (1971) develop models of a similar nature. Lawrence (1973) develops a four equation model for twenty-three states for 1958-1969 in which exploratory effort is a function of wellhead price, price of crude oil, total wells drilled historically, and total past discoveries of gas and oil. Discoveries are a function of exploratory effort and price of gas and crude. Extensions and revisions to reserves are a function of discoveries and other variables, new reserves, a func tion of wellhead price. The latter two regressions in clude lagged values of the dependent variable as independent variables. Lawrence admits that his results are poor and states that "the results of the spatial model will probably reflect the weakness of the response of new reserves to price" (p. 126). 112 MacAvoy and Pindyck (1975) model production as a function of reserves and wellhead price for four'regions. Brooks (1975)» following MacAvoy and Pindyck, estimates production as a function of wellhead price and lagged reserves. Equations are estimated for seven production districts and convincing levels of explanation are achieved (all R2 2.84), although not all coefficients are significant. Two models predict the production from an area given predictions of reserves. The American Gas Association's TERA (Total Energy Resource Analysis) model employs the FPC's National Deliverability Schedule and Debannes' (1971)model of energy supply and demand limits production by a reserves life index (RL1). Use of econometric equations for estimating supply implies: 1) the ability to accurately forecast the indep endent variables; 2) the temporal stability of the coefficients; and 3) the applicability of the coeffi cients outside the range of the independent variables used to estimate them. Econometric techniques are not employed because of these problems and the less than satisfactory results of past research. The FPC agrees, as The commission interprets the (econometric) model not as a formula to obtain precise quantification of future supply responses 113 to price— an impossible objective by any method in our view— but as an instruc tive experimental effort, complementing other exhibits and testimony upon . which we rely for our specific findings and conclusions (FPC, 1975i 238 ). Mathematical and Geological Projections of Natural Gas Supply. The mathematical projection method relies upon discovery and performance data and does not consider geology. M. King Hubbert and Henry R. Linden (Institute .of Gas Technology) are the major proponents of this tech nique. The geological (volumetric) method compares factors controlling gas occurrence in areas of current production with factors present in prospective regions and applies historical success ratios. The Potential Gas Committee (PGC) and the U.S. Geological Survey provide the most widely quoted geological estimates. Controversy exists as to the worth of each technique. Schwernfurth, in an evaluation of potential gas supply estimates, states that: The only satisfactory way to estimate quantities of potential mineral resources . is by a thorough geological study, based on the latest available data, of the occurrence of known mineral deposits and the geology of the regions that appear to have conditions similar to those where the known deposits occur . . they should be revised on a more or less regular basis, as new data become available. The only study of poten tial undiscovered resources known 114 to this writer that most nearly fits the above criteria is the work of the Potential Gas Committee (FPC, 1975i 240). Support for Hubbert's mathematical method is also evident* The integral technique of prediction developed by Hubbert is the most rational which has been developed for the estimation of the duration of petroleum resources (FPC, 1975• 242). Great differences may be discerned between estimates made by varying procedures (Figure 21). The argument over reserves measurement has entered the popular press (Miller, 1975), with the allegation that industry under estimates reserves so as to force wellhead price increas es. Whether this be true or not, "it is. evident that estimates of potential gas supplies are only 'indicators' of gas that may be found and produced. They should be used cautiously by policymakers" (FPC, 1975» 243). FPC Production Estimates. The production estimates * employed in this dissertation are those of the Supply- Technical Advisory Committee of the FPC, which have the following advantages t * 1) The estimates are made with the cooperation of the United States Geological Survey, the U.S. Naval Petroleum and Oil Shale Reserves Office, the Office of Management and Budget, the Census Bureau, fifty-nine companies who furnished confidential information, and regulatory and conservation agencies in major producing 4 115 states, as well as independent experts.. The importance of input from independent experts is stressed by the FPC: In a given geological province, exploratory response to changed economic incentives will largely depend on the economic attractiveness of the remaining prospects. Experts who are currently active in exploration should have the best available knowledge in this regard. Therefore, the Task Force sought the best judgment of exploration experts in each of many separate geological provinces as a basis for regional gas supply estimates (FPC, 1975» 39)- These estimates, then, take advantage of information unavailable to others. 2) Separate estimates are available for ten inland regions, Alaska, and three offshore regions which corres pond to the NPC regions (Figure 19)• In addition, various estimates of Canadian exports to the U.S. are provided. 3) The uncertain nature of any gas supply estimate is recognized fully by the FPC. Four different supply estimates are provided (Cases I-IV), based upon varying assumptions concerning wellhead price, extent of offshore exploration, year of completion of an Alaskan gas trans port system, pipeline import levels, feasibility of production from low permeability reserves and the avail ability of SNG and LNG. In general, supply optimism increases from Case I to Case IV. Case I assumes that 116 * there will he little or no change from current trends. Case II is the "conservative-realistic" situation. Case III is the "optimistic-realistic" situation. Case IV represents the maximum future supply that can reasonably be expected to be available from each source (FPC, 1975* 261- 3 ). U) The Interagency Task Force on Natural Gas of Project Independence also employs these regions, making it possible to supplement the four FPC cases with the "business as usual" and "accelerated development" pro jections of Project Independence. 5) These data have been published relatively recently (1975) and include projections of production, reserve additions, year-end reserves, and reserves-to- production ratios for each of the four FPC cases at five year intervals from 1975 to 1990- In addition, projec tions of supplemental supplies are available. 6) They are widely employed by industry and govern ment and have been used by Osleeb and Sheskin (1975* 1977). Estimating Future Production for the Sixty Supply Regions The problem is to develop a procedure whereby future production estimates for. each NFC region may be appor tioned to the sixty supply areas. The following 117 procedure has been employed to use "proved recoverable reserves" as the apportioning variable^ 1) Estimates of proved recoverable reserves for thirty-eight of the sixty regions are available from the American Gas Association (AGA, 1975i 5-6). Current pro duction data are available, but it is believed that future production is related more closely to reserves than to current production. Areas presently exhibiting significant production may, in the future, have little or no production due to resource depletion. The use of the AGA figures may be criticized, but since it is the relative magnitudes from area to area and not the actual quantities that are employed, no severe drawback is introduced. Estimates which are either more or less optimistic probably do not differ significantly with respect to relative magnitudes. 2) The AGA proved recoverable reserves are appor tioned to the twenty-two gas supply areas for which the AGA does not provide estimates using dedicated reserves (reserves for which producing companies have signed contracts with pipeline companies guaranteeing delivery). Such reserves may not be sold to another company, and consequently, temporal stability may be expected as most contracts are for twenty years. Data on dedicated 118 reserves for the interstate market are available from the FPC for the thirty-five FPC gas areas and for each state (Figure 22) (FPC, 1976). Dedicated reserves in, for example, northern and southern Ohio (two of the twenty-two supply regions for which the AGA provides no estimates of proved recoverable reserves) are derived fromi Dedicated Reserves in Gas Area 10 -Dedicated Reserves in New York -Dedicated Reserves in Pennsylvania =Dedicated Reserves m northern Ohio (9) then, Dedicated Reserves in Ohio -Dedicated Reserves in northern Ohio ^Dedicated Reserves in southern Ohio (10) A similar procedure is employed for deriving dedica ted reserves estimates for subregions of Kentucky, Montana, Wyoming, Colorado, Arkansas, Oklahoma, southern Louisiana, Utah, and Texas Railroad Commission District One. Since FPC figures are only for interstate commerce, these figures are converted to percentages and applied to apportion interstate and intrastate proved reserves to the twenty-two non-AGA gas regions. Some inaccuracies may be expected if disproportionate shares of intrastate gas reserves are found in various regions of a state. (Million Mcl ot 14.73 F*io @ 60*F) IUa-4Ht4 HMl •0f*» am * i«T* aTMalaCniam SaSm*. ■*•»*»i»l »n AAAA^ACMIAN M S m . U A i > WH M*U*5J*»»»C.twC:JSAVM - *tA»AMA a**ai *;*»*« amo tLLfeoa ah a F f3 r 3 * L DOwA«« AC * T n f 0 * COinSlAMA TE143 CAitMOAC C O w OUT. « lC w *H f»H A3*AWS*1 T fiA lB a a ftO A O C O ** OUT. J T1 * ajL*0*C> CLAm 9iST 4 OT»**A CR4Ap*Qm A * G * T - t* N i h m UI SQ^T*C**10U i ! iam a - £>•♦*»** *C^TwfS«tCUdl*»A OMsiw* ?(■*) A4!L«0A0C0«m OUT, 7 TEi a » iAflAOAGCOMM PUT. A T f» *l. O ^ v w t T £i a S *4**040 CDm OUT 1 W * Ttl*S»AU*OAOCC«« CUT ?-i T{ i a % Aa '^ p o o COm o u t 7-C TriAitmPQiOCOM CUT I T iiiihui^ociM * car p a TEaAI AAttSQAS COM* CUT t . K m * scjti ; *;■?:** n > • »catco TEvaIP a^ bCa OCGm OUT. >B &a «A**C^A »a *«a*Qi C O lrtC * JO tfT K *IlT A AC A A**C**A AAAOAAAO A-%IT~■ A M jlt PiCtD * *** juAH BA)|M U^UC«!L>* »vr» M1M CttOAo^r-T,iibJ»iPAiiM ■Ch Ta h a ■OmT a a a Sa a OTA CTa E * a a c a I i W m a . U C tftO SOUlHfMM LC W 1UIA AWCA Chsr . 179 M 3 31TSTurn VO Figure 22.— Dedicated Gas Reserves and Production by FPC Gas Areas, All Interstate Pipeline Companies Sources FPC, 1975» P* 3^ 120 This procedure results in estimates of proved recov erable reserves for all sixty supply regions; thirty- eight estimates are taken from published data, twenty-two are derived by using dedicated reserves to apportion published proved reserves estimates to them. 3) The estimates of proved recoverable reserves are now used to apportion the estimated future production figures of the FPC. Each of the sixty supply areas is assigned to one of the NPC regions. This creates some problem since NPC boundaries bisect a few of these sixty areas. When this occurs, the supply region is assigned to the NPC region from which the majority of its produc tion derives. It is not believed that any great bias has been introduced. 4) The proportion of each NPC region's total proved reserves in each of the sixty subareas is calcu lated, and applied to the estimates of future production for each NPC region, to derive estimates of future pro duction in each of the sixty areas. 6.3 Supplementary Sources of Supply . The derivation of future production estimates for a number of supply sources is not amenable to the procedure developed in Section 6.2s the Atlantic offshore, Alaska, Mexico, Canada, and LNG and SNG sites. Atlantic Offshore. The Atlantic offshore region, from southern Florida to the Maine-Canada border, represents a large, relatively unexplored potential gas area. Three prospective subareas are: the Georges Bank, off New England; the Baltimore Canyon, off the Middle Atlantic; and the Georgia Embankment, off Georgia and South Caro lina (Figure 19.) * The FPC states thats '* projections for this area are highly speculative. They are presented only as an indication of future gas supplies that may result from the development of this area. At this time, there is no certainty as to whether the U.S. portion of the Atlantic offshore contains gas and oil, or if producible hydrocarbons will ever be found and developed . . . potential for finding and developing hydrocarbons is considered excellent (FPC, 1975» 286). Since the Atlantic offshore region contains three spatially disparate fields, some method is desired to disaggregate the FPC estimate, which is provided for the 1 2 1 entire Atlantic offshore. The Transmission Technical Advisory Committee of the FPC provides predictions of production from each of the Atlantic fields. Since their * Low, Medium, and High cases differ from the data reported by the FPC (1975) for Cases I-IVj the percentage of production in each of the three regions is computed and used to apportion FPC Cases I-IV. (The High case is applied to Cases III and IV.) Alaska. There exist two spatially disparate supply regions within Alaska— the north slope (Prudhoe Bay) and the south slope. Since the FPC provides only one esti mate of production for the entire state, and the Trans mission Technical Advisory Committee makes separate estimates, a procedure is employed analogous to that used for the Atlantic offshore. Mexico. U.S.-Mexican trade was of a local nature until 1957 » when the first interstate company was granted an* import certificate. From 1958 to 19^9 imports from Mexico averaged about 50 Bcf per year. Since then, imports have declined. Due to Mexico's relatively small reserves level, it has been reluctant to export. Thus, the FPC makes no estimate of future Mexican exports to the U.S. This research sets future Mexican exports at their contracted level (FPC, 1972, 1^0). Such exports • 123 enter from two ports of entry in southern Texas (See Figure 12). Canada. The modeling of the Canadian pipeline network has not been undertaken due to data limitations. Thus, each port of entry from Canada is considered a supply region. A number of factors make the prediction of future imports from Canada highly speculative. 1) Imports from Canada depend upon, the nature of the relationship between the two countries. 2) Canada's National Energy Board (NEB) must deter mine that proved reserves are at least thirty times greater than projected Canadian requirements, before additional export authorization. 3) Eighty-two percent of Canada's "ultimate- potential" supply is in the remote, high-cost frontier areas— the Arctic Islands, the Mackenzie Delta, and the Atlantic offshore (See Figure 19)- None of Canada's proved reserves lie in the two northern regions. The development of these northern regions depends upon expen diture for exploration and development, the cost of large-diameter pipelines, and the availability of capital to finance exploration, development and pipeline construc tion. In addition, some technical construction problems remain for gathering pipelines in the Arctic Islands. 124 The FPC has made four estimates of Canadian export to the U.S. (Table 4). TABLE 4 FPC PROJECTIONS OF CANADIAN EXPORTS TO THE U.S. (Tcf) Case 1^80 1985 I 1.0 0.9 II 1.3 1.4 III 1.9 2.2 IV 2.0 2.9 Source: FPC, 1975* 318* Case I assumes no new authorization will be made to export gas to the U.S. Case II ("conservative-realistic") assumes some additional exports will be authorized from the tradition al gas supply areas (Alberta, British Columbia), a pipe line will be in place from the Mackenzie Delta by 1984, and approximately .5 Tcf of frontier gas will reach Canadian markets by 1985* Case III ("optimistic-realistic") assumes that the Mackenzie pipe will be in place by 1979 (this is highly unlikely since such a link will take three years to complete and no pipe has been authorized as of May, 1977), with an increase in capacity by 1985 f that a line will be 1 2 5 in place from the Arctic Islands by 198*tj that the Canadian offshore area will be linked with New England by 1980i and that one Tcf of gas from the frontier will reach Canadian markets by 1985* Case IV, the most optimistic case, assumes all the northern pipelines will be in place by 1979* Since this is totally unrealistic, Case III is used in place of Case IV where appropriate. Natural gas enters the U.S. from Canada at eight locations (Figure 12). Approximately 70 P©*1 cent of imported gas is delivered to the west coast area, about 25 per cent to the Great Lakes area, 5 per cent to Montana and trivial amounts to New York and Vermont (Figure 23). The FPC projects that: Although the regional pattern of future Canadian imports will probably follow the established distribution pattern, with the possible exception of imports from the Arctic Islands and the Atlantic offshore region, the proportion of future imports coming into different regions could change considerably from the current distribution. This will depend on the completion schedule of the various proposed pipeline projects and the prevailing regional demand for Canadian gas (FPC, 1975. 319). 125 in place from the Arctic Islands by 198^j that the Canadian offshore area will be linked with New England by 1980t and that one Tcf of gas from the frontier will reach Canadian markets by 1985 . Case IV, the most optimistic case, assumes all the northern pipelines will be in place by 1979* Since this is totally unrealistic, Case III is used in place of Case IV where appropriate. Natural gas enters the U.S. from Canada at eight locations (Figure 12). Approximately 70 per cent of imported gas is delivered to the west coast area, about 25 per cent to the Great Lakes area, 5 per cent to Montana and trivial amounts to New York and Vermont (Figure 23). 1 The FPC projects that* Although the regional pattern of future Canadian imports will probably follow the established distribution pattern, with the possible exception of imports from the Arctic Islands and the Atlantic offshore region, the proportion of future imports coming into different regions could change considerably from the current distribution. This will depend on the completion schedule of the various proposed pipeline projects and the prevailing regional demand for Canadian gas (FPC, 1975. 319). 1 2 6 B C F II TOTAL 10 9 8 • 7 6 5 IDAHO 3 MINN. WASH. 2 MONT. 0 N.Y. (Vi CD r» .O' Figure 23,— Exports of Canadian Gas to the U.S. Sourcet Osleeb and Sheskin (1975) P* 1 2 ? Given this statement, and the assumption of each case, the following procedure is employed: For Case I: supply is apportioned to the eight border crossings on the basis of the maximum authorized annual imports (FPC, 1972). For Case II: for 19.80, the Case I procedure is employed* for 1985» the Case I procedure is employed for the first 1.3 Tcf. The extra .1 Tcf is to come from the Mackenzie Delta. No assumption is made as to its entry point* rather, various plausible locations are attempted to find a least-cost entry point (from the U.S. viewpoint). For Cases III and IV: all gas which represents add itional supply over and above that authorized from traditional areas (which is handled as in Case I), is handled as in Case II, 1985 . One additional problem enters in that plausible locations for gas from the north are not plausible for Atlantic' offshore gas. This is handled as follows. The normative model developed by Osleeb and Sheskin (1977), in which no Canadian deficits occur, has shown that Arctic Islands gas should supply the eastern Canadian markets and not the U.S. Thus, production from this region is ignored here. This model also indicates that all Atlantic offshore production should supply the U.S. 1 2 8 Given these results, the additional supply is split only between the Mackenzie Delta and' the offshore Atlantic. This split is made .by employing various estimates of production made by the NEB. •LNG Sites. Two LNG facilities under construction (Cove Point, Maryland and Savannah, Georgia) and one already in operation (Everett, Massachusetts) are employed as supply points. Projected locations also may be included. SNG Sites. Currently operating SNG facilities are also included (FPC, 1972). For both LNG and SNG facilities pipelines are assumed connecting the facility with the demand region in which it is located. CHAPTER 7 THE PIPELINE NETWORK SUBMODEL 7.1 The Abstraction of the Natural Gaa Pipeline Network as a Graph The magnitude of the natural gas pipeline network has heen discussed in Chapters 1 and 3* While it is theoretically possible to model the entire network, a significant degree of abstraction is necessary and desir able if the problem is to be computationally tractable and the results interpretable. Thus, no attempt is made to model the thousands of miles of intra-suppiy area gathering lines and intra-demand region distribution lines. Rather, this dissertation concentrates upon the major interstate and intrastate transmission lines, dealing, for the most part, with the wholesale market, except for some direct sales by wholesalers to some large * industrial users. The only past researcher who has modeled the natural gas pipeline network is Brooks (1975)* As discussed in 129 130 Chapter 2 » omission of a pipeline network model in past . research has led to conclusions with uncertain validity. Although the procedure employed below for developing graphs of nodes and links is similar to that of Brooks (1975)t this model has more demand and supply regions. Thus, it is not necessary to assume, as did Brooks, that intercompany exchanges all occur at one central point in each state, but rather at one central point within each of the demand regions (Figure 17). Since the demand regions in this model are smaller than states and are based upon pipeline network structure, this assumption is considerably more realistic. The systems of over 260 pipeline companies are mapped on the FPC pipeline map, representing all of the major, and most of the minor interstate and intrastate companies. The networks of some eighty-five companies are modeled explicitly in this study (See Appendix B.)* The vast majority of excluded companies are small intrastate lines, each serving only one of the 177 demand regionsj many companies serve only one or two urban areas. All compan ies operating lines crossing demand or supply region boundaries and all major companies (Class A and B— opera ting revenues over $1,000,000) are included. Graph theory (Taaffe and Gauthier, 1973) provides a convenient framework within which to couch the natural gas 131 delivery system. Essentially, a map is abstracted as a graph containing a set of nodes and a set of links which maintain the basic topological integrity of the network. Figure Zk illustrates this procedure for Company A. Gas is received from supply areas one and two, delivered to demand area one of State X and to demand areas two and three of State Y. In addition, Company A delivers gas to Canada, and to Company C from an intercompany connection in demand region two. "A" also receives gas from Company B in demand region one. About eighty-five such diagrams have been produced resulting in a network of approximately 1,000 nodes and 1,000 links. Accuracy is assured by employing both the FPC and Oil and Gas Journal pipeline maps. In addition, usage is made of the FPC's Natural Gas Transported in Interstate Pipelines (1976), which indicates the supply and demand regions each company received gas from, and delivered gas to, and where intercompany exchanges took place in 197**. The result of this procedure is an explicit model of the major interstate and intrastate pipeline companies. Minor intrastate companies in producing states are not modeled explicitly, but* because of data considera tions, are modeled as single links connecting supply and 132 CANADA 7 10 CANADA • STATE RORDER m STATE V STATE IOROIR STATE X A B 2 □ Supply Mod11 o Dtmond Nodii A Intmompany Nodu Figure 2k, Network of Hypothetical Pipeline Company A 133 demand regions (Section 7.^). Data considerations also prompted the further simplification of the network (Section 7.2).1 Space limitations prohibit the inclusion .of the graph of the pipeline network, copies are available from the author for the cost of reproduction (about $5)• 7.2 The Determination of Pipeline Capacities The determination of pipeline capacities developed into a more difficult problem than originally anticipated. i * Given the purposes of this research, accurate estimates of these capacities are crucial. Conversations with PPC staff members led to the conclusions that such data are not available at a disaggregate level due to disclosure prob lems and that, at best, only rough estimates can be made. Some researchers have ignored capacity. Balestra (1967 ) settles for a supply constraint in his short-run demand equation. Since it may be assumed that current pipeline capacity is sufficient to handle current demand, this is not a serious drawback in a short-run model. MacAvoy and Pindyck (1975)1 in constructing an input- output matrix to predict future flows, also ignore capac ity, but in a long-run model. Waverman (1973 ) commits an analysis error in assuming no existing pipeline network and allowing positive flows of any magnitude. He concludes that Canadian insistence that Albertan gas serve eastern Canadian markets costs them several hundred million dollars between the loss of 13^ 135 sales to the U.S. and the cost of constructing the Trans- * Canada pipeline. His optimum solution shows Texas-Louis- iana-Kansas serving the eastern Canadian market and Albertan gas serving much of the U.S. west now served from Texas. Implicit in his conclusion that such a scheme would have resulted in savings, is that sufficient capaci ty exists to handle increased flow in the Alberta to U.S. and Texas to Ontario pipelines. If sufficient capacity does not exist, his conclusions need be altered seriously, for the cost of increasing capacities in these routeways must be subtracted from projected savings. In fact,* an examination of load factors (Section 3.4) has shown the non-existence of such capacity. Osleeb and Sheskin (1977) also ignore capacity con straints, but the major thrust is the identification of deficit areas and not an examination of pipeline invest ment decisions. Nevertheless, this omission may have biased some of the results. Lawrence (1973) assumes capacities equal to 1969 flow levels, which he estimates from data in the Bureau of Mines' Minerals Yearbook, by starting with the most distant census district market area and working backwards towards Texas. This flow estimation procedure may be criticized in its own right, and, as Lawrence states: 136 "the capacity estimates are obviously biased downwards since they are based upon actual shipment figures" (p. 128). Brooks (1975) employs superior flow estimates on a more disaggregate level and adjusts the flow estimates to capacity estimates by applying an average load factor (89 per cent) for a sample of sixteen pipelines. Brooks states that: "this method tends to underestimate the capacity of underutilized pipelines and overestimate the capacities of those which have load factors greater than average" (p.‘14-2). Nevertheless, given the flow data now available from the PPC (1976a), this procedure represented an attractive possibility for capacity estimation. Examination of this procedure, however, showed it to be significantly inaccurate (Figure 25). The mean load factor for all pipelines' is a full 20 per cent below the figure for the sixteen pipeline sample employed by Brooks. Also, the large size of the standard deviation indicates that considerable error would be introduced if the mean load factor were to be employed. Three possible procedures are examined to develop • capacities for each pipeline: 1) employ the Weymouth Formulaj 2) disaggregate border capacities reported by . the FPC (19740 using pipeline diameters; and 3) dis aggregate FPC border capacities using flow volumes. 136 "the capacity estimates are obviously biased downwards since they are based upon actual shipment figures" (p. 12 8 ). Brooks (1975) employs superior flow estimates on a more disaggregate level and adjusts the flow estimates to capacity estimates by applying an average load factor (89 per cent) for a sample of sixteen pipelines. Brooks states that: "this method tends to underestimate the capacity of underutilized pipelines and overestimate the capacities of those which have load factors greater than average" (p. 142). Nevertheless, given the flow data now available from the FPC (1976a), this procedure represented an attractive possibility for capacity estimation. Examination of this procedure, however, showed it to be significantly inaccurate (Figure 25). The mean load factor for all pipelines is a full 20 per cent below the figure for the sixteen pipeline sample employed by Brooks. Also, the large size of the standard deviation indicates that considerable error would be introduced if the mean load factor were to be employed. Three possible procedures are examined to develop • capacities for each pipeline: 1) employ the Weymouth Formula; 2) disaggregate border capacities reported by . the FPC (1974) using pipeline diameters; and 3) dis aggregate FPC border capacities using flow volumes. LOAD FACTOR 71 ! Mean* 69-255 0- 20% f 3) Standard Deviation* 22-731 J Coefficient of Variation* 32.8225S I 21— 40 % ( . 1 3 ) I I 41-60% ( 41) * I I 61—80% ******♦*****♦***:***** ( 40) I I 81—100% **♦***♦***■*:**>***************:** ( 40) I I ...... I ...... I ...... I ...... I o 20 40 60 80 100 FREQUENCY iU Figure 25- Load Factors of U.S. Natural Gas Pipelines 138 Weymouth Formula. The preferred procedure is to employ one of a series of equations derived from a set of mechanical energy balance equations for the flow of compressible fluids in pipe. Two of the most popular are the Panhandle equation and the Weymouth Formula. The variable in these equations include internal and external diameter of the pipe, initial and terminal pressure and temperature and specific gravity of the gas. These variables are functions of pipe age, weld condition, material from which the pipe- - line is constructed, and the nature of the terrain travers ed. Such detailed data are not available on a nationwide basis. Disaggregating Border Capacities on the Basis of Pipeline Diameter. A second procedure attempted is to employ the Weymouth Formula making a number of assumptions about aver age conditions suggested by the FPC (1975) and Columbia Gas (1967 ) to disaggregate FPC border capacities. A "rough" capacity estimate for each pipeline at each border crossing is estimated and used to disaggregate the border capacities reported by the FPC (1975) on the basis of the relative per centage of border capacity in each pipeline. Unfortunately, this procedure often led to capacity figures well below the actual flow on the link as calculated from FPC data (1976 a ) . Disaggregating Border Capacities on the Basis of Flow Volumes. A third procedure, disaggregating the border capacities reported by the FPC on the basis of the 139 proportion of flow in each pipeline, is employed. In brief, if Company A has a flow of 2X across a given border and Company B, a flow of X, then two-thirds oif the border capacity is assigned to Company A, one-third to B. An implicit assumption is that both companies operate at the . same load factor. This procedure has two advantages: 1) It makes use of a published set of capacity estimates. If a border capacity is disaggregated improp erly, the total border capacity remains correct. 2) The link flow represents a lower bound, thus avoiding gross underestimation of capacities. The reasonableness of the disaggregated capacity estimates may be judged by whether or not reasonable load factors are indicated. A three step procedure is described below, in which: 1) company flow diagrams are developed? 2) capacities of links crossing state borders (BC links) are estimated? and 3) capacities of links not crossing state borders are estimated (NBC links). Development of Company Flow Diagrams. The first step in the development of capacity estimates is to derive an estimate of flow on each network link. The FPC (1976a) has developed a "flow matrix" for all 1?PC-regulated pipelines providing, for each pipeline company, the 140 volume of gas* received from each FPC gas area, Alaska, Canada, and Mexico; received from other pipeline companies; delivered to each state and foreign country; and delivered to other pipeline companies. Where necessary, major companies have been "partitioned" so that it becomes possible with the use of the FPC and Oil and Gas Journal pipeline maps, the FPC*s Gas Supplies of Interstate Pipe line Companies (1976b), and the Bureau of Mines' Minerals Yearbook, to derive estimates of flow on each network link. For example, flow on the Georgia-South Carolina link of the Transcontinental Gas Pipeline Corporation net-. work, which begins in Texas and ends in New York, is equal to the total flow in the system minus deliveries to Georgia and points west. h' number of problems arise in applying the FPC flow matrix to the network diagrams developed in Section ?.l. The first set of problems relate to obtaining supply and demand estimates for regions developed in Sections 5*2 and 6.2. The second relates to deriving flow estimates on each network link. First, the supply regions of this study are, in a few cases, disaggregated portions of FPC gas areas. The FPC flow matrix reports production by gas area. This problem is solved using data provided by the Gas Supplies i m of Interstate Pipeline Companies (197*0* which indicates the production level of each company in each state and FPC gas area, via a procedure analogous to that shown in Section 6.2 (Equations 9 and 10). Since the production figures in this source vary somewhat from those in the flow matrix, percentages are calculated and employed to apportion the flow matrix data for the FPC gas areas to the supply regions in this dissertation. Second, the demand regions for which the FPC flow matrix provides data are states, and not those developed for use in this research. Thus, some procedure is required to estimate the quantity of gas Company A delivers to regions one and two in State X (Figure 26). If Company A is the only company delivering gas to these two regions, an estimate of delivery to each is based upon the proportion of the two region population in each region. (Since flow data are not available by end use, it is impossible to employ Equation 7 in Section 5-2.) If either region one or two is served also by Company B, the procedure is somewhat more complicated. The total amount delivered by Company A to regions one and two is still disaggregated on the basis of population, but the quantity delivered by Company B to region two is sub tracted from the total delivery to region two, to yield an estimate of the gas delivered by Company A to region 4 lkz STATE X Co. A Region 3 Region 1 Figure 26. Disaggregating Deliveries of Each Pipeline Company to Demand Regions within a State 1^3 two. If Company B also serves more than one region in State X (say region three) (Figure 26), this procedure is not satisfactory. In most such instances, Company A delivers the major portion of State X's gas and delivery by Company B to each region is determined on a population ratio basis. The derivation of flow estimates on each link repre sents little problem in most cases. The vast majority of pipeline companies may be graphed as "tree" networks in which the number of links equals the number of nodes minus one. In such a network, there are no "circuits" and, consequently, there exists only one path from each node to any other node. Figure 27 illustrates the procedure used for tree networks. The flow from supply node one (SI) to demand node one (Dl) is 1200, the volume of gas received by Company X at SI. The flow from Dl to D2 is 950, equal to the 1200 units, minus the 5° units delivered to Company Y. The flow from D2 to D3 is 900, equal to the flow into D2 (95°) minus the 100 units demand at D2, plus the 50 units received by Company Z . In general, such flows are derived such that for each demand node jt (id 144 SOD 100 100 200 100 o 100 200 1200 □ Supply Nodci o Otmond Nodi! A tntinompony Nodlt Stott lordir Figure 2 7 . Flow Diagram for Company X for each 3upply node j: N M £ *ii ' A * si ( 1 2 ) and for each intercompany connections: X. . = C . (13) ij J where, X. . = the flow from node i to node j J. J X.i. “ the flow from node j to node k D j = the demand at node j J * S . = the supply at node 3 J N = the number of links entering node j M = the number of links out of node j C • - the volume of gas delivered to. or received J from another gas company Seven companies have graphs which contain one or more circuits. A problem arises in estimating flow on links { D 3 » W and {D^,D5) into D5 versus the direct flow from D3 to D5 (Figure 28). Two procedures are developed to estimate these flows. The preferred procedure depends upon the existence of a state border crossing one of the links in the circuit. The Bureau of Mines' Minerals Year book reports the quantity of gas crossing all state borders. Assume this source indicates that 500 units. cross state border R. Also, assume that Company Q has a link traversing this border with a flow of 100 units. Thus, *tOO units of Company X's gas must flow on link (D3.D5). Then, the flows on links (D3rD*f) and (D^,D5) are determined by Equation 11. If no border crossing exists, flow is allocated to the two routes on the basis of the relative capacities of the two pipelines entering D5 as calculated from the Weymouth Formula (assuming a set of average conditions). Disaggregating Border Capacities. Given eighty-five pipe line company flow diagrams, the second step is to derive capacities for those links crossing state borders (BC links). This process assumes that all links crossing a border operate at the same load factor. Only if load 4 factors are equal does the company with two-thirds of the flow have two-thirds of the capacity. A significant simplification is made to somewhat soften the.impact of this assumption and to more realistic ally model the actual network. If two different companies operate links over the same route, the flows over such links are aggregated and company distinctions ignored. In Figure 28, Company A and B run lines from S3 to Dl, but only one link is used in the model. The implied assumption is that gas can be transferred from the pipelines of A to B in S3 and/or Dl. This is, in fact, a very realistic assumption given the supply and demand region sizes. Al- r though there are about 120 intercompany nodes on the 1^7 Stall Boidir • t Qimand Nodu Co. A Co. I - Co. C Figure 28. The Simplification of the Pipeline Company Diagrams 148 « original set of pipeline company diagrams based on the FPC flow matrix, discussions with Mr. Bill Monroe of the FPC (who is in charge, of the flow matrix project), indicated that there are actually a considerably greater number of intercompany connections than can be gleaned from the flow matrix and the available pipeline maps. There are probably few regions served by more than one company where there is no connection between the companies because demand regions are developed on the basis, of network structure. This procedure results in a network containing 416 • links. One may now assume that intercompany shipments occur "internally" at the demand and supply nodes, and it is no longer necessary to model explicitly the inter company connections. Given one link defined between S3 and Dl, the flows of the two companies are added to derive a flow estimate for the"combined" link (S3,D1) (Figure 28). If (S3»D1) is the only link crossing state border X, then the capac ity of border X as reported by the FPC is simply assigned to this link. If, on the .other hand, Company C operates a link crossing state border X from, say, S4 to Dl, it is necessary to disaggregate the border capacity to yield an estimate of capacity on (S3,D1) versus (S4,D1) (Table 5)* 149 TABLE 5 DISAGGREGATING THE CAPACITY OF BORDER X TO OBTAIN CAPACITIES OF BORDER-CROSSING NETWORK LINKS BC Cur Adjusted % of Company Link Flow tailment Flow Flow Capacity C (S4,D1) 200 .25 250 56 280 A + B (S3.D1) 200 .00 200 44 220 Total 400 450 100 500 Assume border X has a capacity of 500* Suppose the flow on link (S3tDl) is 200 (100 from each company) and the flow on link (S4,D1) is 200, for a total flow of 400 cross ing border X. Curtailments occurred for a number of pipe line companies in 19?4 (FPC, 1977)* The assumption is made that the relative link capacities is related more closely to what the relative flows would have been had there been no firm contract curtailments. That is, it is probably that Company C has enough capacity on link (S4,D1) to handle a no-curtailment situation. Thus, the flow derived from the FPC flow matrix for link (S4,D1) is “inflated" to yield an adjusted flow* Fijk = Fijk + <=k Fijk s ad3us’ted flow company k over link (i, j) C^ = the 1974 curtailment of company'k Fijk = the fiow comPany k over iink (i,j) 150 The total adjusted flow is now 450. $6 per cent on link (S4,Dl)j 44 per cent on link (S3.D1). Thus, 56 per cent of the 500 unit capacity (280 units) is assigned to link (S4,D1)i 44 per cent (220 units) to link (S3,D1). This procedure results in capacity estimates for I85 of the 416 links. Note that the assumption of equal load factors on BC links has not heen eliminated, but must be applied considerably less often than had the link combination procedure not been followed. Two problems arise in using the above procedure. First, 1974 curtailments are available only by company. Curtailment data by company and by state would have been superior, but such data are not available for 19?4. Thus, it is. assumed that the curtailments of each company were f , equally spread among all served areas. If a company had an X per cent curtailment, then the flow on all links of the company are inflated by X per cent using Equation 14. This assumption seems reasonable as one would expect that some attempt is made to "spread around" curtailments between served areas. Only in the unlikely event that all curtailments occurred at a demand region close to the beginning of a line, would serious error be introduced. The reasonableness of the procedure is indicated further as the inflated flows (F^ ..,) cause most of the adjusted 1 JK 1 5 1 flow totals to approximate more closely the 1970 border crossing flows reported by the FPC (197*0 t a year before widespread curtailments, on firm contracts. A second problem arises due to the use of 197** flow data and 1970 capacity figures. For about seven important border crossings, the 197** flow exceeded the 1970 capacity. This could be due to: 1) additional capacity being added over the four year period} and/or 2) errors in the FPC capacity estimates. North Dakota, for example, receives almost all of its gas from Montana, and'North Dakota’s 1970 and 197** consumption was significantly greater than the Montana-North Dakota border capacity reported by the FPC. Capacities of Links that do not Cross State Borders. In order to derive capacity estimates for links that do not cross a state border (NBC links), the assumption is employ ed that the load factor on each NBC link of Company X is similar to the load factor maintained on the closest BC link of Company X. Figure 29 and Table 6 illustrate this procedure. TABLE 6 DERIVING CAPACITIES OF NON-■BORDER CROSSING LINKS Curtail Adjusted Closest Closest Load Cap- Company Flovir ment Flow Border Link Factor acitv A 200 .05 210 X (D1,D2) .90 233 B ?00 .10 330 Y (S2.D2) .80 413 Total 500 646 152 liomqpsou) %no lo tn • • «f • *Z 1 0 0 100(A) 0 |N'8 50,61 C^)i0,A1 Y 300181/ ^ ^ 7001^1 # ----- , , ©cfMis itr,r -m600 • «x LF-.9 CAP =444 100 | j Si'Pp'r Model 0 Dimond Hodti Co. A soo ------Co. I • ’• • Slot! Itrdif Figure 29. Flow Diagram for Two Companies Illustrating the Procedure for Estimating Capacities for Non-Border-Crossing Links i 153 The individual company flow diagrams indicate that Company A has 200 units flowing through NBC link (D2,D3)i Company B, 300* Initially, these flows are inflated by the curtailment factors to reflect more accurately pro vided capacities as described above (Equation 14). Next, the closest border (in miles) for each company is noted and the load factor for the closest BC link is calculated* ^jk ' Fijk/ CAP& <«> where, LF?^k = 'fche l°&d factor for BC link (i,j) for J company k = the adjusted flow of company k over link ■ 1JK (i> j) BC CAP* .k = the capacity of the border crossing link J (i*j) operated by company k The capacity of the NBC link is given by* CAPi f ■ 1 Fi3k / LF?°k ' where, CAP??0 = the capacity of NBC link (i,j) ^ J M = the number of companies operating lines over NBC link (i,j) All other variables are defined above. By substitution, (from Equations 14-16) CAP??0 = I"j (F. -v+C^F. .1_)NBC/( (F. .lr+C1_F. * J B0 ij ' 13k k 13k' /vv ljk k ijk' / 0 A P ^ k) (17) 15** where, All variables are as defined above. The reasonableness of this procedure is supported by the fact that the load factor at the next BC link "down the line" (in this case link (D*f,D5) for both companies) is, in most cases, within a small percentage of the. border load factor currently being employed (borders X and Y) to estimate the NBC link (D2,D3). Obviously, the further away an NBC link is from the nearest BC link, the less realistic this assumption. In the vast majority of cases, the NBC link has either its origin (i) or destination (j) in common with a BC link. 7>3 The Determination of Shipping Costs The out-of-kilter algorithm, and all normative tech niques whose objective function is to minimize transport cost, require the specification of shipping rates on the network links. Since the goal of this dissertation is to provide a basis for a regional plan for the pipeline net work based on a least-cost approach, the development of a set of accurate link shipping rates is especially important. The optimum situation would be to employ actual per mile transport costs along the network links, but such data are not available. Shipping costs are a function of mileage, capacity (itself a function of pipeline diameter and pressure), * i and load factor. As pipeline diameter increases, econo mies of scale in variable costs enter, since friction is reduced as a lower percentage of units of gas maintain contact with the pipe wall. Economies in fixed cost result since most fixed costs (right-of-way, labor, etc.) remain about the same, regardless of pipe size. The maintenance of a high load factor permits the realization of economies of scale. In addition, costs are a function 155 156 of both the level of competition between companies and terrain, which affects both operating and construction costs. Previous authors have used three methods for deriv ing shipping costs* Method 1 t compares delivered and wellhead prices Method 2: employs a constant per mile transport cost Method 3* apportions total company transmission cost to each link on the basis of the propor tion of flow-miles on each link Method 1 . MacAvoy and Pindyck (1975) develop a "pipeline markup equation" in which the differential between whole sale delivered price and average wellhead price is a function of pipeline capacity, average annual sales, interest rates, and the Herfindahl competition index. Lawrence (1973) estimates transport costs by sub tracting the average wellhead price' in the supply region from the industrial price in the demand region. Since industrial users are charged less than residential (by 650) and commercial users (by 390)(p• 132), industrial costs do not reflect the average cost of supplying each demand region. (One wonders why Lawrence did not develop a weighted average delivered price based upon the various . end uses in each demand area.) Note also that the devel opment of these cost differentials assumes each demand region receives natural gas from only one supply region. 157 Thus, Lawrence assumes, for the purpose of developing trans port costs, that the Middle Atlantic region receives all its gas from Louisiana,, when, quite clearly, it also receives gas from the Appalacian region at a different wellhead price and a greatly different transport cost. Thus, the average industrial price in the Middle Atlantic region reflects gas purchased from both the Appalacian and Louisiana regions (along with a number of other places) and it is, thus, inappropriate to use this average industrial price to determine shipping costs from either one of these regions. The MacAvoy-Pindyck and Lawrence approaches are in applicable here since neither method allows shipping costs to be applied to individual network links. The cost of service procedure developed by the FPC (197*0. which pro jects costs of service for ten Gas Requirements Committee regions, is rejected for similar reasons. Method 2 . Waverman (1973) proposes a "fixed-charge" equation: d- jff- -F* • = a d- -X* . + b ) d. -e. • (18) lj6ij lj “ uijei3Aij w A. ijeij ' ' where, d .* = the straight line distance from i to j J (modified to "go around" lakes) g. . = a terrain factor "which adjusts shipping costs J for the topographical and geophysical charac teristics of the land over which the flow must travel. The terrain factor was normalized at < 1.0 for average prairie conditions and rises', to 5-0 for the most difficult terrain" (p.32). P. . « the per mile transport function a - the marginal cost per mile X. . = the flow from field i to market j ^ J b - the fixed cost per mile 1 if Xij > 0 0 if X.. -0 [ 1 J Waverman recognises the fixed and variable cost structure of transport costs, but, because this yields a total cost function which is non-convex between zero and one units of flow, he ignores the fixed cost term. The justification given is that the level of aggregation of his model is so high that the size of most flows could be handled only by the largest pipes. . In addition, as long as the fixed-to-operating cost ratio does not vary widely over different (i,j) combinations, ignoring fixed costs will not yield an incorrect solution. Waverman provides no indication of the procedure used to determine the terrain 'factor, nor does he appear to actually use it in his analysis. Ignoring fixed costs and the terrain factor, the average cost function ist fu a + b/xij (19) where, a, b = empirically derived constants 159 f. . = the average cost per mile from i to j in cents per Mcf per day per 100 miles xi j = ^ ow I*1,0111 i to j in MMcf per day C.L. Dunn (1959) has estimated this equation as* f. . = 1.1 + 140/x. . (20) J - J J* J Equation 20 seems to indicate that Waverman accounts for the non-linear relationship between flow level and transport costs. In actual fact, he simply assumes a cost of 1.10 per Mcf per 100 miles. Waverman performs sensitivity analysis on transport cost by rerunning the model with costs set at .50 and 2.30* Neither change led to major differences in trade movement (p. 102). Only in the case where total supply is considerably greater than total demand, could any . significant change be expected, as demand regions would begin to obtain gas from further fields with lower well head prices as transport costs decrease, and closer fields at higher wellhead prices as transport costs * increase. (Waverman's objective function is the joint minimization of wellhead prices and transport cost.) Since Waverman's model has an excess supply' of only 276 out of 48,670 units (.57 per cent), it is not surprising that the "sensitivity analysis" produces no major changes. Osleeb and Sheskin (1977) employ a similar trans port rate of 20 per Mcf per 100 miles, a figure provided 160 by the FPC (1975) for a typical 30 inch, 1000 mile pipe line operating during 1973 at an average 800 psi and at a 95 per cent load factor. About 90 per cent of this cost is fixed,* only 10 per cent represents operating and maintenance costs. Thus, this transport costs includes variable cost and an amortized portion of the fixed costs assigned to each flow unit. Osleeb and Sheskin (1977) also perform a sensitivity analysis but, instead of an "across-the-board" change in transport costs (as Waverman uses), an attempt is made to account for the fixed charge and terrain problems with relationship to the Alaskan and northern Canada proposed gas pipelines. In their transportation problem solution, the only major flows occurring over routes not currently having pipelines are those from northern (Alaskan and Canadian) supplies. Thus, to reflect the lack of such pipelines and the high construction costs for these lines, the transport costs are doubled for these routes only. No major changes in the states or provinces served from these northern areas result. This type of sensitivity analysis could be performed to derive a range within which all transport costs may vary without changing the optimal solution. Method 3 .' Brooks (1975) apportions the total fixed and variable costs of each company-to the various links in 1 6 1 each company's network on the basis of the proportion of flow miles in each link. This technique has the advantage of allowing shipping costs to reflect actual company cost differences. The importance of this factor is illustrated by Table 7* These figures were "prepared on an informal basis by the Pipeline Allocation and Rate Design Branch (of the FPC). These figures are from specific pipeline rate proceedings" (Correspondence from Mr. Ellis Boyd, FPC, March 1, 1977)* This table represents the only data of its type available and shows that pipeline company costs vary significantly between companies with a coeffi cient of variation close to 20 per cent in 1975* This coefficient would probably be significantly greater if calculated from more complete data. Note that all nine companies in Table 7 are Class A companies (annual oper ating revenues over $2,500,000). These cost variations between companies should reflect differences in capacities, flows, and load factors, as well as such items as adver tising and research and development expenses. Brooks' technique, however, ignores the fact that cost itself is a function of flow and that, in a normative procedure, by deriving costs in this manner, we have assumed that current flows are optimal. We would thus be biasing the results to reflect the real world, rather than deriving a normative solution. 162 TABLE 7 SHIPPING RATES OF EIGHT NATURAL GAS TRANSMISSION COMPANIES ‘ (IGO Mcf-Miles) Company Cost of Transmission Tennessee Gas Pipeline Co. 3-180 Panhandle Eastern P/L Co. 2.?0 El Paso Natural Gas Co. 3.03 Transcontinental Gas p/L Co. 4.77 Texas Eastern Trans. Corp. 4.10 Northern Natural Gas Co. 3.27 Natural Gas P/L Co. of America 2.90 Texas Gas Trans. Corp. 3.26 Average 3.400 Standard Deviation .650 Coefficient of Variation 19.2 % Source: Correspondence from Mr. Ellis Boyd, FPC. Descrip- tive statistics by author. Development of the Modified OKA Procedure. The objective function of the OKA: N r (c. + 1..) x. . (21) 1=1 j=i 1 ij where, f M « the number of supply regions N = the number of demand regions C^= the wellhead price in supply region 163 t. . = the per unit transport cost from i to j 1 J x. • = the flow from i to j J ^ should be constrained by a concave cost function* *ij = f(Xij) (22) where, t. ., X . . are defined above X J 1 J This relationship is concave since as flow increases toward the capacity of a line (i.e., as load factor increases), cost decreases. The effect of this concavity is illustrated by Figure 30* The equation for this cost surface is * LN (COST) = 7.24825 -.94455 LN (LF) - .42991 I*N (CAP) (.01852) (.01266) R = .99406 F = 18?6 ' (23) OR COST a 1405.64 (LF) ~ ' ^ 5 $ (CAP) " * ^ 991 (24) where, COST = cents per Mcf per 100 miles LF = load factor ' CAP « capacity in MMcf per day (Valves in parantheses are standard errors.) At a capacity of 800 MMcf per day, for example, a drop in load factor from 100 per cent to 75 per cent yields a 31 per cent increase in costs. At a load factor of 75 per cent, the per unit cost decreases by approxi mately 45 per cent if a line of capacity of 800 MMcf per * Source: Leeston, A.M., J.A» Crichton, and J.C. and Crichton, J.A» A.M., Leeston, Source: zoo CENTS PER MCF PER IOO M IL E S 0 0 3 too 0 3 0 6 0 9 50 70 20 0 4 BO rsueBs: 9 psio .9 M Bose: Pressure IO Pipeline Capacity, and Load Factor Load and Capacity, Pipeline Relationship Between Shipping Cost, Shipping Between Relationship aos (1963) Jacobs MLIN O UI FE PER FEET CUBIC OF (MILLIONS AIU DY OUE THROUGHPUT VOLUME DAY MAXIMUM ZOO 0 0 6 0 0 4 iue 30 Figure DAY} 7 5 V. LF V. 5 7 0 0 8 1000 165 day is used in place of a line of 200 MMcf per day. The implication of this analysis is that transport costs vary significantly as a function of load factor and capacity. Thus, the decision has been made to incorporate the constraint represented by Equation 22 in the form of Equation 2k. A number of problems arise. First, since no other information is available on the relationship between cost and flow, it is impossible to incorporate any type of terrain factor into the model. That is, no graph like Figure 30 exists for "rough" ver sus "smooth" terrain. Although Waverman (1973)* Brooks (1975)» and Osleeb and Sheskin (1977) have recognized the importance of this factor, none of these authors have been able to incorporate terrain in .any satisfactory manner. Second, Figure 30 is from a 195^ FPC hearing and is significantly dated. Correspondence with the FPC indicates that this work has not been updated. The reasonable assumption is tendered that the relationship shown in the graph remains the same and that the Y-axis only need be multiplied by some constant inflation factor (I) to obtain a closer estimate of current costs. The following procedure is employed to obtain the inflation factor, I. The average 1975 transmission cost, for the eight companies in Table 7 is 3.k$ per 100 Mcf- miles. Calculations performed in Section 7.2 indicate 166 that these companies operate at about a 95 per cent load factor on most lines. Most of the pipelines operated by these companies are large-diameter, high capacity lines. Substituting a load factor of 95 per cent and a capacity of 800 MMcf per day into Equation 24 yields a 1954 cost of .1.070 per 100 Mcf-miles. In 1975» this cost was evidently around 3.40 (See Table 7), that is, 3.17757 times greater. Thus, the entire cost axis is multiplied by I = 3-17757 to obtain an estimate of current shipping ‘ costs. The final form of the concave cost constraint, in which* 1 ) capacity is adjusted to yearly capacityt 2) cost is adjusted to cents per MMcf per milej and 3) the inflation factor (I) is incorporated, is* LN (COST) = 13-24339 - .94455 LN (LF) - .42991 LN(CAP) (.01852) (.01266) R = .99406 F = I876 (25) * or, COST = 564,327 (LF)"*9^ 55 (CAP)",/f2991 (26) where, All variables are as defined above (Equation 23). (Values in parentheses are standard errors.) Third, introduction of the concave cost function (Equation 26) transforms the problem into a nonlinear program. Unfortunately, the available nonlinear program ming algorithms are not well-suited to a problem this size. In addition, the use of such an algorithm would greatly reduce the simplicity and flexibility of the final model. Instead, a non-linear procedure using the OKA is employed: 1) Some initial load factor is assumed such that the cost of each link 56^32? (LF)?:94**55 (CAP)T:42" 1 M where, t.. = the transport cost from i to j A J LF. . - the load factor on link (i,j) J CAP. . = the capacity of link (i,j) 1J M. . - the miles from i to j 1 J All the constants are empirically derived. 2) The out-of-kilter algorithm is run and an optimal flow pattern derived. 3) Given each X . . (flow from i to j) a new load factor ^ li (equal to X. ./CAP. .) is calculated for each link where A J 1 J X^j 21 0 and a new set of transport costs (t^^) are derived from equation 2?. b) if t?. - t . .1 * MAXDIF for fewer than MAXNUM links, ij J-J| GO TO 5 . If t- J>MAXDIF for more than MAXNUM links 168 £ Set t . . a t . . for (i,j) where X. . *» 0 ij •ij tij = for (i,j) where - 0 and, if the number of iterations is less than MAXIT, GO TO 2. If the number of iterations is greater than MAXIT, GO TO 5. 5) Select the iteration of lowest cost as the "best" solution. NOTEi MAXDIF, MAXNUM, and MAXIT are user-supplied values. Figure 31 and Table 8 illustrate the effect of the iterative procedure and the logic of the influence of an initial choice of load factor upon the solution. Note that this example uses equation {2k) so that Figure 31 may be consulted. The logic would not differ if equation (27) were employed, as is the case for the analysis reported in Chapter 8 .- Two possible scenarios are dis cussed. Scenario 1. Assume an initial load factor of 90 per cent on both links. Thus, the cost per 100 Mcf-Miles on link X is 1.030, while on link Y, it is 1.200, reflecting the greater capacity of link X. Thus, in the first iteration, all flow (?00 Mcf from S) will flow from A to B on link X, The costs per mile are recalculated— link X now has a load factor of 70 per cent (700/1000). The LF on link Y remains at 90 per cent, and in the next iteration offers 16? CAP =700 n;=200 AB link Y Link X m. =2 30 AB CAP =1000 AB Figure 31* The Effect of MOKA on Flow Pattern TABLE 8 BEHAVIOR OF THE MOKA MODEL Scenario 1 Input Paramters First Iteration Second Iteration 100 " " 106 ' ~ . 100 Link CAP LF M* Cost/ M /Mcf Cost/Mcf Flow LF Cost/ M /Mcf Cost/Mcf Flow Cost/ M /Mcf X 1000 90 2 .3 0 1 .0 3 2.37 700 70 1 .3 0 2 .9 9 0 Y 700 90 2 .0 0 1.20 2.40 0 90 1.20 2.40 2 00 1.085 2 =(2.990)(700) = 20930* Z =(1.0850)(700)(2 Miles) = 15190 Scenario 2 Input Paramters First Iteration Second Iteration 100 100 100 Link CAP LF M Cost/ M /Mcf Cost/Mcf Flow LF Cost/ M /Mcf Cost/Mcf Flow Cost/ M /Mcf X 1000 90 2 .3 0 1 .0 3 2.37 750 75 1.22 2.80 50 15*77 Y 700 90 2.00 1.20 2 A 0 0 2° 1.20 ZAO £00 1.085 Z =(2.8O0)(75O) = 21000 Z =(15*770)(2.3 Miles)(50) +(1.0850)(2 Miles)(700) 33320 * Z is the total cost of a given shipping pattern and is equal to the sum of the flow on each link times the cost of each link. Note that the costs per Mcf used in calculating Z are "based upon the LFs at the end of the given iteration. a less expensive alternative. (See Figure 30— A link with a capacity of 1000 and operating at a 70 per cent LF is more expensive than a link of capacity 700 operating at a 90 per cent LF.) After the second iteration, then, Y has • a 100 per cent LF, link Y then is the least expensive path. Note that had the iterative procedure not been used the flow pattern developed by the OKA or any linear.pro gramming technique would have produced a more expensive solution (18200 versus 15^90• Table 8). Note that had an original LF of 50 per cent been selected, this switch from link X to link Y would not have occurred. Scenario 2. In some instances, the model may fail to find the superior route. Suppose that Xg^ = 75° Mcf (Figure 31). In the first iteration, all 750 Mcf will flow on link X as above, yielding a 7596 LF'for use in second iter ation, which again causes Y to be a. less expensive route. In the second iteration, then, the OKA will maximize the flow on the less expensive route, Y, such that the flow will be 700 Mcf and the flow on X, 50 Mcf. As shown on Table 8, this leads to a total cost of 309^0 versus 18300 if all 750 Mcf flow on X as in the first iteration. Note that had an initial choice of LF equal to any value less than 88 been made, that the cost on Y would have been «' greater than the cost on X and the iteration one flow pattern would maintain. Thus, the need is to find an 172 initial load factor value such that the occurrence of "flow shifts" as in scenario 1 is maximized, while the occurrence of shifts as in scenario 2 is minimized. Thus, the path taken here is to allow LF to vary, i.e., to iteratively select values and then choose the solution that results in the minimum value for the objective function. In actual practice, the effect of scenario 1 is sig nificantly greater than that of scenario 2. The model does behave so as to lower transport costs. In the "Alaska into Minnesota" run discussed in Chapter 8,for example, the model converges to a least-cost solution in eight itera tions, saving $92,921,268 over the initial solution, decreasing monotonically for the eight iterations needed. In some runs, some erratic behavior is found when the number of links on which flow is changing is small and the final solution is, not the least-cost (necessitating Step 5 in the model). In such cases, small cost increases are caused by flow patterns arising, as in Scenario 2. The basic advantage of the model is not lost, however. Al though an optimal least-cost pattern may not have■been found, the modified OKA model does find a lower-cost solution than would have been obtained from a simple linear program. Determination of Link Mileages.. Mileage is an important determinant of transport cost. Most past researchers have 173 employed straight-line distance from supply to demand region. Brooks (1975)» however, measures mileage along the pipelines on the FPC map. Comparison of city locations on this map with locations in an accurate atlas indicates that a considerable cartographic license was taken in preparing the FPC map. That is, pipelines are distorted in distance and“direction to enable the fitting of place names, etc. Thus, the Oil and Gas Journal pipeline map, which appears to be significantly more accurate, is employed. The demand and supply nodes developed in Sections 5*1 and 6.1 are modified for the distance measuring procedure when a demand region is served by two or more companies and when a link is a combination of two or more companies, as described in Section 7-2. Figure 32 illustrates the first of the above consider ations. Actually, two separate nodes are employed to represent demand area B, both of which lie on the pipeline network as close as possible* to the population centroid. • Thus, the distance from demand region A is measured from network node Al, which is the point on the pipeline closest . to the population centroid of demand region A, to node Bl, the point on this link closest to the centroid of demand regi on B . Figure 33 and Table 9 illustrate the procedure em ployed to measure the distance between demand regions A DEMAND REGION A DEMAND REGION I supply REGION C 0 rOPUlAIION CENTROID □ GAS FIELD CENTROID • NETWORK NODE PIPELINE OF COMPANY X Figure 32. The Measurement of Link Distance to a Region served by Pipeline Entering from Two Other Regions 175 DEMAND REGION A DEMAND REGION I 0 FOFULATION CENTROID Q GAS FIELD CENTROID • NETWORK NODE FI FELINE OF COMFANT X Figure 3 3 . The Measurement of Link Distance to a Region Served by Pipelines Entering from One Other Region 176 and B if two companies (X and Y) both operate over this route (these companies being represented by one link as specified in Section 7.2), and there exists a significant difference (within measurement tolerance) between the lengths of the pipelines operated by the two companies. Basically, a weighted average distance (D..) is computed* J TABLE 9 THE MEASUREMENT OF LINK DISTANCE TO A REGION SERVED BY PIPE LINES ENTERING FROM ONE REGION Company Link Distance (D. .) Capacity (C..) D. • C • • * 1 J k ^ J -13— i 3 X (Al.Bl) 50 100 5000 Y (A2.B2) 60 150 9000 o Total ro. 14000 D. . It (27) ij (Dijk CiJk> / 1 Cijk where, D^jk = the distance along link (i,j) of company k Gijk ” caPacity company k's link (i,j) N = the number of companies traversing link (i,j) Thus, for the link in Figure 33, the average distance is 56 miles (14 ,000/250). Another problem arises with respect to the link distance to apply between demand and supply regions which are mostly or wholly coterminous. The best solution seems to be to apply a zero distance, leading to an underestima tion of costs for gas delivered to such areas, but avoiding an unrealistic flow pattern. Imagine supply and demand regions existing as'in Figure 3^* Company X receives supply from supply region C and delivers to demand region B. Zero distance is assigned to link (D,B) since to measure the distance over to the center of the gas fields of D and back to B would be highly unrealistic. In actual fact, Company X is probably receiving and delivering * supplies over short distances at many points along its pipeline. All of the distances along the current pipeline routes are found using a "map measure". The curvature of the earth is not taken into account using this method.. Since links tend to be no more than a "state" long, this seems to pose little problem, as the error introduced over short distances is small and should be equally spread among the links. Since it is the relative distances that affect allocation! these errors should have little influ ence. Consideration was given to calculating distances using latitude and longitude, but the problems inherent in deriving the latitude and longitude of all network nodes and pipeline bends and the associated error would . probably obviate any small gain in accuracy from the ability to account for earth curvature. DEMAND REGION A DEMAND REGION B SUPPLY REGION C 0 POPULATION CENTROID □ GAS FIELD. CENTROID • NETWORK NODE — I I - PIPELINE OF COMPANY X SUPPLY REGION BORDER “ DEMAND REGION BORDER Figure The Measurement of Link Distance when Supply and Demand Regions are Coterminous 7 .k The Intrastate Pipeline Network Since intrastate pipeline companies are not subject to FPC regulation, the data available for these companies are • minimal, even though'they deliver approximately one-third of U.S. consumption. Although the purpose of this research is not to examine the intrastate system, the capacity of this system can not be ignored. Basically, the procedure used to model intrastate pipelines employs an historical apportionment factor between the interstate and intrastate markets. 1) Given total production for each supply region (American Gas Association, 197*0 and for the interstate market (FPC, 197*0» it is possible to compute the production level for the intrastate market. The historical apportion ment factor (H) is defined as the percentage of production in each supply region that is sold in the intrastate market. In a number of cases the total production figures from the American Gas Association are not in as disaggregate a form as is needed for the supply.regions of this study.. In.such cases, the percentage of interstate production in each region is used to apportion intrastate production. 180 2) Each supply region is connected by an intrastate link to the closest demand region at a zero cost. With few exceptions, this is a demand region with which the sup ply region is coterminous. If a supply, region is cotermin ous with a number of demand regions (as in Kansas), the intrastate links are connected to each demand region and intrastate gas is apportioned on the basis of population. 3) Each intrastate link is given a lower capacity equal to the volume of intrastate production determined by the historical apportionment factor and an upper capacity set equal to the lower capacity. This assumes that H will remain constant and that the intrastate system will have sufficient capacity to handle its percentage of gas. The use of the lower bound assures that the intrastate system is used to "do its share" such that interstate lines may be used to deliver to interstate markets. 4) The transport costs on the intrastate links may be set at zero since the demand and supply regions are coter minous, The cost on this intrastate link, however, may also be set equal to the interstate minus intrastate wellhead price, so that this differential may be accounted for in the model. 7*5 Summary The purpose of Chapters 5-7 has been to describe the major data inputs— the location and volume of demand and supply and the shipping costs and capacities of the network links— to the modified OKA. For each input, the drawbacks of the methodologies employed by past researchers and the reasons for the non-employment of optimal methodologies have been discussed. Although improvements may be noted over past research in the quality of data input, such as the spatial specificity of supply and demand regions, the deter mination of pipeline capacities, and in the explicit model ing of the pipeline network, and in the ability of the procedure employed to deal with the non-linear cost-flow relationship via MOKA, a better approximation of reality is all that has been achieved. Chapter 8 presents some select ed results from the model. CHAPTER 8 * RESULTS OF THE MODEL The purpose of this chapter is to illustrate the utility of the MOKA model for planning the natural gas delivery system. Unfortunately, the size of the net work (over 1200 arcs and close to 300 nodes) precludes full display and interpretation within the framework of this dissertation. The utility of this model may he illustrated more simply hy the presentation of results for a small hypothetical network (Section 8.1). Section 8.2 presents selected results from a number of runs of the actual model using data developed by the demand, supply, and pipeline network submodels of Chapters 5-7* 182 8.1 Presentation of Results for a Hypothetical Network * The problem addressed here is to develop a planning model for the natural gas pipeline network of "Hypothetico", a small island. The following types of data are neededt 1 ) the location, volume, and wellhead price of supply; 2 ) the location and volume of demand; and 3 ) the structure of the pipeline network, including the capacity and mileage of each link. (Figure 35*) Hypothetico contains one National Petroleum Council region for which the FPC has estimated a future (1985) production of 300. 000 MMcf. Three supply regions (S1,S2, S3): have been defined as per Section 6.1. The 300,000 MMcf have been apportioned to these three regions on the basis of the percentage of proved recoverable reserves in each region; Region # of Reserves 1985 Production (MMcf) 51 33.3 100,000 52 2 5 .0 75.000 53 41.7 125.000 Total 100.00 300,000 Hypothetico also contains one state in which natural gas is demanded. On the basis of the structure of the I83 REVERSE DIRECTION CURRENT DIRECTION Figure 35* Hypothetical Network for MOKA Note: Link labels are: cost, lower capacity, upper capacity, flow, company name 185 pipeline network, counties have been grouped into three demand regions (Dl, D2, D3)• The GRC projects 200,000 MMcf of non-industrial consumption and 150,000 MMcf. of industrial consumption in 1985* 0° the basis of population and value added in manufacturing (VAM), the following estimates of 1985 consumption are derived: Region % of Population $> of VAM 1985 Consumption (MMcf) Dl 50.0 16.6 125,000 D2 2 5 .0 6 6 .7 150,000 D3 25.0 16.7 75.000 Total 100.0 100.0 350,000 The demand and supply constraints are accounted for in the MOKA model via the use of the upper bounds on the sets of "dummy” supply |(S,S1), (S,S2), (S,S3)j and demand |(Dl,D), (D2,D), (D3,D)j links (Figure 35)- Note that the costs on the dummy supply links are set equal to the average wellhead price in each supply region, but that the costs on the dummy demand links are set to zero (rather than to some distribution cost). In this manner, the model minimizes wholesale delivered price. Three companies (A, B, and C) operate in Hypothetico. Each company operates along the following paths: Company Path A S2, SI, Dl B S2, D3, D2, Dl C S2, S3, D3, D2 186 The pipeline network is abstracted as a graph and. each pipe line or group of pipelines (with common origin* and destin ation) shown as a single link in Figure 35* The state border that crosses BC links (S1,D1), (S2,D3), and (S3,D3) is reported to have a total capacity of 370,000 MMcf by the FPC. The flow diagrams of Company A, B, and C indicate that the 1974 flow on each link is as follows* Link Flow (MMcf) % of Flow 51, Dl 139*725 40.5 52, D3 55*890 16.2 53, D3 149,040 43.2 Since link (SI, Dl) has 40.5 per cent of the flow, it is assigned 40.5 per cent of the capacity (150,000 MMcf). BC links (S2, D3) and (S3,.D3) are assigned capacities in a similar manner. There are four NBC links* (S2, Dl), (D2, Dl), (D2, D3), and (S3, S2). NBC link (S2, SI), operated by Company A, is given a capacity of 5»0°0 MMcf, equal to the 1974 flow of 4658 MMcf inflated by the 93*15 per cent load factor of Company A on the closest BC link (SI, Dl). Capacities of the other BC links are obtained in a similar manner. The mileages of each link are measured from the pipe line map of the Oil and Gas Journal. In the case of link (D2, D3)* on which both Company B and C operate, the six 187 mile distance is a weighted average of B's line, which is five miles long and ships 37t500 MMcf and C ’s line, which is seven miles long and ships 37*500 MMcf. Since it is possible to reverse pipeline direction, arcs are provided both for the direction of current operation and the reverse direction, wherever such reversal may be reasonable (in running the actual network, no such prejudgment is made). The demand, supply, and pipeline network submodels have provided all the necessary parameters for MOKA. Table 9 shows the results from an initial MOKA run. For this simple network, only one iteration is necessary. Note that the link costs in Table 10 have been determined by equation 26 (p.165). The following information is provided by these results. 1) The optimal (least-cost) flow pattern. For exam ple, 105,000 MMcf reach Dl— 100,000 from SI, and 5,000 from S2 via link (S2, SI). The implication of this is that if Company A operates the route (S2, SI, Dl.) and Company B, the route (S2, D3i D2, Dl), Company A should receive approval for sale to Dl, and not Company B, which . should sell to D3 and D2. One hundred fifty thousand MMcf are delivered to D3i 60,000 on (S2, D3) and 90,000 on (S3, D3)• Seventy-five thousand of these 150,000 MMcf are consumed at D3 and another 75,0°.° are shipped on to D2. Table 10 MOKA Output HYPOTHETICAL NETWORK UPPER LOWER LOAD ARCS COST CAPACITY CAPACITY FLOW FACTOR Si Dl 60? 150000 0 105000 69 S2 03 321 60000 0 60CC0 100 S3 D3 7 26 160000 0 00000 56 SI S2 830 5000 0 0 0 sa SI 374 5 COO 0 5000 100 £2 S3 463 50000 0 0 0 S3 S2 463 5C000 0 0 0 01 02 1031 100000 0 0 0 D2 01 1031 100000 0 0 0 02 03 777 75000 0 0 (t 03 02 350 75000 0 7500C 100 01 J 0 125000 c 1O50CC’ 83 ' 02 0 0 15CCG0 0 75000 50 D3 0 0 75000 0 75000 100 S SI 130 100000 0 100000 100 S S2 128 75000 0 65000 86 S S3 135 125000 0 90000 71 Total Cost = 210,0?5 ,683 Total Flow = 255,000 . Table 11 Use of the Lower Bound to Assure Area HYPOTHETICAL NETWORK UPPER LC1WFR LOAD ARCS COST CAPACITY CAPACITY FLOW FACTOR SI 01 61.7 150CG0 0 105000 69 S2 03 3 ; i 60C00 0 60000 100 S3 03 726 160000 0 90000 56 SI S2 830 5CC0 0 0 0 S2 SI 374 5CC0 0 5000 100 S2 S3 463 50000 0 0 0 S3 S? 463 50000 0 0 0 01 02 7870 ICOOGU 0 5000 4 02 01 1031 100000 0 0 0 02 03 777 75000 0 0 0 03 02 350 75000 0 75000. 100 01 U Ci 125000 0 100000 79 02 0 0 150CCC 8C000 noooo 53 03 0 0 7 5 000 G 75000 100 S SI n o 100OOO 0 I00000 100 S S2 1?8 75000 0 65000 86 s S3 135 125000 0 90000 71 Total Cost a 249,429,011 Total Flow * 255,000 189 2) The existence of "bottlenecks". For example, link * (D3, D2) is a bottleneck since, while the two links deliv ering gas to D3 j(S2, D3) and (S3, D3)j have a combined capacity of 220,000 units, and D3 can only consume 75»000 of these, only 75,000 of the remaining 145,000 may flow to D2. 3) The existence of deficits. Deficits may be at tributed to either insufficient supply (in this example demand exceeds supply by 50,000 MMcf) or to bottlenecks in the pipeline network. Examination of the load factors on the dummy links in Table 10 indicate a 17 per cent deficit at Dl and a 5° per cent deficit at D2. In this case, the location of deficit regions is determined by the location of bottlenecks. If these bottlenecks were to be removed through additions to pipeline capacities, then D2 would suffer the full impact of the 50»000 MMcf system deficit because it is most distant from the supply areas. 4) The existence of production that will be unable to reach market. Note that due to the bottlenecks, S3 can produce at only 71 per cent of capacity. 5) The need for pipeline reversal. Note that cur rently gas flows from (D2, D3)» while in the optimal pattern this link should be reversed. The present direc tion may be due to a currently inefficient flow pattern 190 and/or a spatially different production pattern than will exist in year X. 6 ) The wholesale delivered price in each demand region and for the whole system. Seventy-five thousand units are delivered to D3 at a total cost of 861 units, composed of the wellhead price of 135 units at S3 and the cost of 726 units along the (S3* D3) corridor. The total minimum wholesale delivered price is $210,075*683 for the 255i000 MMcf flowing in the system. Additional information may be obtained by varying the input parameters. 1) The optimal flow pattern under some "forced" allocation scheme (Table 11). Suppose that the optimal flow pattern of Table 9, that leaves D2 with a 50 per cent • deficit, curtails essential users. If a regulatory agency were to insist that D2 receive at least 80,000 units, such that essential users are not curtailed, a lower bound of 80,000 may be placed on link (D2, D). Note that this leads to a greater deficit in Dl and that the total cost increases by 3 9 *353,328 (from 210,075,683 to 2^9 ,^2 9 ,011). Such a forced allocation scheme may also be achieved by a simple extension of the model. (See Chapter 9*) 2) The optimum production levels in each supply region (Table 12). Each dummy supply link is provided with an infinite production possibility. In this example, 191 Table 12. Determining Optimum Production Levels in Each Supply Area of Hypothetical Network HYPOTHETICAL NETWORK UPPER LOWER LOAD ARCS COST CAPACITY CAPACITYFLOW FACTOR SI Dl 433 1500CG 0 150000 100 S2 D3 321 60000 0 60000 100 S3 D3 726 In0000 0 90000 56 SI S2 R30 5000 . 0 0 0 S2 SI 830 5000 0 0 0 12 S3 463 50000 • 0 0 0 S3 S2 463 50000 0 0 0 01 DZ 1721 100000 0 25000 25 02 Dl 1031 100000 0 0 0 02 D3 777 75000 0 0 0 03 D? 3 SO 75000 0 75000 100 01 D 0 125000 0 125000 100 , 02 D 0 150000 0 .100000 • 66 ’ 03 D 0 75C0C 0 75000 100 S SI 130 995999 0 150000 15 S S2 128 999999 0 60000 6 s S3 135 999999 0 90000 9 1 192 SI should raise production for year X to 150,000 (from the current projected production of 100,000), while S2 and S3 (given that the bottlenecks are not removed), should de crease' production. Thus, from the standpoint of minimizing wholesale delivered price, without expanding the pipeline network, exploration in SI.should be encouraged. This assumes the ability to adjust production levels. Thus, this type of analysis is particularly useful in cases where the supply nodes are LNG and SNG sites at which production level is varied relatively easily. 3) The "best" route (from a least-cost standpoint) of a finite set of proposed routes may be selected. Suppose that Company A has proposed a twelve mile link from S2 to D2, while Company B proposed a line of fourteen miles from S3 to D2, both of a 75,000 unit capacity (the projected deficit of the current network). MOKA is run twice— first with link (S2, D2) added to the current network (Table 13), then with link (S3, D2) (Table 14). Both proposals would bring all 300,000 units of production to market, but link (S2, D2) accomplishes this at a lower cost by 37.310,900 units. Note that the flow level on the proposed links indicates the necessary capacity in order to handle the optimal flow level of 1 9 8 5 . Note that the addition of either link would signifi cantly alter the flow pattern (Table 10). With (S2, D2) 193 Table 13 Use of MOKA as a Link-Addition Algorithm Company A Proposal HYPOTHETICAL NETWORK UPPER LOWER LtlAO ARCS COST CAPACITY CAPACITY FLOW FACTOR $2 02 701 750GC 0 75000 100 SI 01 636 150COO 0 100000 66 S2 05 735 60000 0 0 0 S3 03 532 16GUC0 0 125000 78 5.1 S2 820 5C0C 0 0 0 * S2 SI 63 0 5003 0 0 0 52 S3 463 50G00 0 0 0 S3 S? A 63 50000 0 0 0 01 02 1051 100000 0 0 0 02 01 1051 100COO c 0 0 02 02 777 75 COO 0 0 0 03 02 514 75000 0 50000 66 . 01 0 0 125000 0 100000- 79 02 0 0 150000 fiOOOO 125000 03 0 5 0 0 75000 0 75000 100 S SI 130 lOOUiCt 0 100000 100 s S2 123 75000 0 75000 100 s S3 135 125000 0 125000 100 Total Cost = 258,364,864' Total Plow = 3°0* 000 Table 14 Use of MOKA as a Link-Addition Algorithm Company B Proposal HYPOTHETIC AL NETWORK UPPER LOWER LOAD ARCS COST CAPACITY CAPACITY FLOW FACTOR S3 D2 i3:*5 75000 0 45000 59 SI 01 ■ «> 07 150GGC C 105000 69 S2 03 321 600C0 0 60G00 100 S3 0)726 160000 0 90000 56 SI S2 830 5000 0 0 0 S2 SI 374 •3000 0 5000 100 S2 S3 954 50000 0 10000 19 S3 S2 463 5G0GJ 0 0 0 01 02 1031 100000 0 0 0 02 01 1031 LOCCGo 0 0 0 02 03 777 75000 0 0 0 03 02 350 75000 0 75000 100 . 01 D 0 125000 0 105000 83 02 0 G ISCCOO bOOOO 120000 79 D3 n 0 75000 0 75000 100 S SI 130 I 0000(1 0 100000 100 S s;* 128 75C00 0 75 000 100 S S3 135 125C00 0 125000 ICO Total Cost = 247,943,856 Total Plow = 300 ,000 With S2, D2 Added 194 added, all three supply nodes produce at full capacity (Figure 36). No flow occurs over (S2, D3), rather D2 receives supply over the new (S2, D2) link and on the • (D3, D2 ) link. (S3, D3) now carries 125,000 MMcf into D3, instead of the 90,000 MMcf carried prior to the addition of link (S2, D2). In addition, 5000 MMcf no longer travel the (S2, SI, Dl) path. The flow pattern also changes if link (S3, D2) is added, resembling that of Table 9 except that 10,000 MMcf are sent from S2 to S3 and then on to D2 via the new link, as are 35»000 35iOOO MMcf from S3 (Figure 37)* The location of deficits also changes with the addition of each link. The original network shows a 17 per cent deficit at Dl and a 50 per cent deficit at D2. D3 suffers no deficit. The addition of either link causes no change at D3* Either link significantly reduces the deficit at D2{ a slightly greater deficit occurs at Dl when (S2, D2) is added, while the opposite prevails at D2. 10 . 0 . 150000 , 100.000 2 . 0 , 5,000,0 9 , 0 , 100,000 . 0 . 75000,75.000 12 . 0 , 75.000 , 75.000 150.000,125,000 3, 0, 50,000,0 10 , 0 , 160.000 , 125.000 REVERSF DIRECTION CURRENT DIRECTION Figure 36* Hypothetical Network with Proposed Company A L i n k vO VJ1 Note* Link labels are: cost, lower capacity, upper capacity, flow 10 , 0 , 150000 , 10S.000 2 , 0 , 5,000 , 5,000 It Of 100,000 Q2 >0 . 0 . 150000 ,120.000 128 0 . 7 S 0 0 0 , 7&I 3 , 0 . 50,000,10,000 ( 0 , 75,000 75,0006 160000 . 90.000 REVERSF DIRECTION •CURRENT DIRECTION VO Os Figure 37* .Hypothetical Network with Proposed Company B Link Note: Link labels are: cost, lower capacity, upper capacity, flow 1 8.2 Selected Results of the Actual Model The purpose of the following discussion is to illus trate the utility of the demand, supply, and pipeline net work submodels (using data developed in Chapters 5-7) and MOKA for the development of a regional approach to planning the natural gas pipeline network. No definitive answers are provided* rather, indications are given as to what is likely to be the "best" course of action given a restric tive set of assumptions and a less than optimal data set. If the assumptions are deemed unrealistic, however, MOKA can be rerun easily given varying sets of assumptions, or, if superior data become available, the computerized supply, demand, and pipeline network submodels may easily incorpor ate these data. Selection of a Route for the Alaskan Gas Transportation System. Now that the oil from Alaska's North Slope is flowing down the Alyeska pipeline for the Lower 48 markets, the question of a market for the natural gas has arisen. Some of the latest estimates,of proved reserves are put * at twenty-six tcf* total reserves may be twice this figure. Bringing the North Slope gas to market, then, is a high 197 198 priority project* especially since the abnormal cold of the Winter of 1977 demonstrated that gas supplies are limited and often located at a considerable distance from market. The routing decision, under a 1978 act that bypasses the Natural Gas. Act, is to be made by the,President and Congress. In addition, Canada must approve any pipeline through its national territory. The importance of this decision is emphasized by the fact that construction of a transport system is expected to be the most expensive construction project ever; estimates run as high as $13 billion. As may be seen from Figure 3 8 , a number of different proposals are being considered. The choice between these proposals will be made based upon a large number of factors, including environmental, social, political, and economic concerns. The factors upon which a recommendation is made in the analysis below are* 1) which proposal results in the lowest total cost to wholesalers for gas delivered by all pipelines to the Lower 48 states; and, 2) which proposal results in the greatest volume of gas being delivered by-all pipelines to Lower 48 markets; that is, which proposal results in the fewest deficits. I 199 K [ V , ' A V; ... - 7+i I Figure 38* Alaskan Gas Pipelin.e Alternatives 200 To simplify the analysis, only four possibilities for delivery of Alaskan gas are considered* California Proposals PROPOSAL ONE* Shipment via pipeline to Valdez, Alaska, and then via LNG carrier to southern California PROPOSAL TWO* Shipment via pipeline into northern California Midwest Proposals PROPOSAL THREE* Shipment into Montana, through the Dakotas and into the midwest PROPOSAL FOUR* Shipment into Minnesota and into the midwest Thus, the decision among varying route proposals through Alaska, Yukon Territory and Northwest Territory % are not considered. Rather, the problem addressed is one of asking where to "inject” large volumes of additional supply into a currently-operating, complex distribution system. The model is run as a link-addition algorithm as described in Section 8.1. That is, MOKA is run first with proposal one added to the system, then with proposal two replacing proposal one, etc. Selected results are shown in Tables 15 and 16 and Figures 39-^1* The following data and assumptions are employed* 1) The supply submodel is used to apportion the 1985i Case II production estimates of the FPC (1975) to the sixty supply areas. Supplemental supplies are included as indicated in Section 6 .3 . 201 2) Gas Requirements Committee demand data from Volume Five (1973) are apportioned to the 177 demand regions and all additional demand areas (Section 5*3) are included. 3) Since demand exceeds supply, the demand in each of the 177 demand regions is deflated by an equal percent age to equate supply and demand. The assumption is that equal numbers of consumers in different areas of the country will have switched to some alternative fuel, and thus these deflated values will more closely resemble future consumption levels. k) The pipeline network submodel is employed to yield capacities and mileages on the network links. The actual network employed has over 1 ,2 0 0 arcs, including dummy supply and demand links, network links oriented toward the 197 ^ direction of flow, network links reversed from this direction, links from the supplementary supply nodes, and links to the additional demand nodes. 5) Wellhead prices for the sixty non-supplementary supply regions are those reported by the American Gas Association (1975)* The wellhead price of Alaskan gas is set at $1.09/Mcf, of Canadian gas at the border at $2.00/Mcf, and of Alaskan gas delivered by LNG tanker at $3.30/Mcf (based upon conversations with Dr. Osleeb of the 202 PEA). Gas from the offshore Atlantic is given a wellhead price of $l.*f2/Mcf, the current federal price ceiling. Production costs for LNG and SNG sites are as given by the FPC (1972)• 6 ) Initial results indicated that the current pipe line network from offshore California to demand region 16 (D016) (southern California) will not be sufficient to handle offshore California production in 1985* Since it is desired to guage the impact of. the Alaskan gas transport system, and one of the alternatives is to bring LNG into D016, the pipeline capacity from offshore California has been increased to handle the projected production, as it is likely that the short-distance routes from offshore will be built. No other changes in the Lower ^8 .pipeline net work are assumed. The total cost and gas delivered to market by all pipelines under each proposal are shown in Table 15 • Exam ination of Table 15 reveals that the midwest routes are superior to the routes into California, since both result in delivery-of considerably more gas to market by all pipelines than either California proposal. Both midwest proposals deliver gas to an area that would otherwise suffer large deficits. The logic behind the California proposals is to supply California with Alaskan gas, reduce the flow from the Permian Basin (west Texas) to California, 203 TABLE 15 1985 FPC CASE II MOKA RESULTS FOR ALASKAN GAS TRANSPORT PROPOSALS Delivered Cost of Gas Delivered by Gas/Year to all all Pipelines/ Proposals Wholesalers ($) Year (MMcf) 1. LNG to California 9,567 ,423,311 19,118,997 2. California (pipe) 9,567,423,311 19,118,997 3. Montana 11,332,408,063 20,129,514 4. Minnesota 11,156,724,966 20,129,248 and, thus, allow Permian Basin gas to satisfy demand in the eastern part of the country. This model shows that insuf ficient pipeline capacity exists in the routes from the Permain Basin to the east to permit this flow pattern shift. Thus, in neither California case can any Alaskan gas flow to the Lower 48. Both California proposals result in large deficits to New England, New York, and parts of Michigan, Wisconsin and the southeast (Figure 39) which do not appear if either of the midwest proposals are institut- , ed (Figures 40 and 41). These deficits occur in regions far from great supply (New England) and in regions served by small-capacity (high-cost) links (eastern Tennessee and the eastern Carolinas).* *It is recognized that a pattern in which a 100 per cent deficit appears in some regions with no deficit in neigh boring regions is somewhat unrealistic. This results from ignoring the importance of distributing gas by end use. If the gas were distributed by end use, the model would indi cate shortages in low priority sectors in all of New England and the Middle Atlantic, rather than the pattern shown in Figure 39* See Chapter 9 for an extension in this direction. [IOC OotMMO KGIOR 0 « « t« MlttlT U JWHT ItCIDK — nomio looit 9 10m otncii kcion MILES Figure 39. LNG and Pipeline to California Proposals for the Alaskan Gas Transportation System M7, !si dOO MILES Figure 40. Montana Proposal for the Alaskan Gas Transportation System ro o vn Q dumnd it e m O rtttUT BlflttT □ surrtT iieion — riorosto toou MILES Figure 41. Minnesota Proposal for the Alaskan Gas Transportation System 20? Thus, if California is to be the destination of Alaskan gas, additional pipeline capacity is needed from the Permian Basin to the eastern half of the country. Two routes are proposed from the Permian Basin to the: 1) Texas Panhandle, at the origin of pipeline corri dor three (p. 56), which leads from Texas, Oklahoma, and Kansas to the area between the eastern Dakotas and Michi gan (Figure 12); and, 2) Gulf Coast, at the origin of corridor one, which serves Florida and the eastern seaboard, and on to corridor two, from northern Louisiana to Ohio, Pennsylvania, New York, and New England (Figure 12). The results are shown in Table 16 and Figures 42 and 43, assuming the gas is delivered as LNG to Los Angeles. TABLE 16 RESULTS FOR PROPOSED ROUTES TO LINK THE PERMIAN BASIN TO THE EASTERN U.S. Delivered Cost of Total Gas Deliver- LNG Delivered Gas/Year to all ed by all Pipe- to California Route Wholesalers ($) lines (MMcf) (MMcf) 1 10,859.165,089 1 9 ,622,818 276,112 2 1 0 ,8 ^8 ,900,870 19,609,717 . 263,011 1 + 2 1 2 ,2 4 5,984,462 20,010,231 663,871 In all cases, a significant reduction of gas flowing from the Permian Basin to California results. Construction of either route 1 or 2 results in large deficits (Figures [lOOj m. DEMM IECI0R 400 momkeo leart MILES Figure 42. Route 1 Proposal to Deliver Permian Basin Supplies to the East [iao [47 SDttlT KCION 4 0 0 M I1E S Figure 4-3 • Route 2 Proposal to Deliver Permian Basin Supplies to the 2 09 East 210 42 and 43). Route 1 provides significant relief for Michigan, Wisconsin, Nebraska, Connecticut, and southern • New York (compare Figures 39 and 42). Route 2 provides relief to some of New England, but leaves Michigan and South Dakota with deficits. Both proposals relieve the deficits in Tennessee and the Carolinas. An important conclusion is that even with the construction of either of these links, insufficient capacity exists in corridors one to three to handle additional flow. Also, the spatial pattern of deficits indicates a lack of pipeline capacity between corridors one, two, and three. For example, when route two is chosen, there is insufficient capacity from corridor two into corridor three (through Illinois and Indiana), and into Michigan, which, consequently, suffers a deficit. If both routes 1 and 2 are added to the network (Table 16), the pattern of deficits is comparable to the midwest proposals (except for a 26 per cent deficit in Milwaukee), although the total system cost is $1,089 billion more than the Minnesota proposal. Thus, even with the addition of both routes connecting the Permian Basin to the east, the midwest proposals are superior. Of the midwest proposals, the pipeline into Minnesota appears to be superior, with a savings of $176 million, although slightly less gas is delivered to market (The « 211 Montana route manages to eliminate a 2 per cent deficit in eastern South Dakota left by the Minnesota proposal.)* Other Selected Results. Selected results from the Montana proposal are shown in Table 17 and Figure 44 and are explained below. Section I (Table 17 ) shows the necessary capacity of each link in the Montana proposal. Thus, a capacity of 1»053»023 MMcf/year is needed from demand region 97 (D097) to D125 (Figure 40). Note that: 1) Alaskan gas is marketed only as far east as Gary, Indiana (D045) and the link from Ohio to Pennsylvania (D131»D139) is used for Lower 48 gas; and 2) the high cost on (D045.D046) is due to its "loading" at a very low load factor at eui earlier iteration. Section II shows a small sample of arcs in the Lower 48 pipeline network. The pipeline from D008 to D009 has a per unit cost of 2.8970 pet* 100 Mcf-miles, a capacity of 1,027,675 MMcf/year and a flow of 908,2591 which yields an 88 per cent load factor. Section III shows a sample of reverse network links. Thus, gas currently flowing from D019 to D022 would.reverse direction under the MOKA scheme. Section IV shows dummy supply links. The costs are • the wellhead prices and the upper capacities, the Case II 212 TABLE 17 SELECTED PORTIONS OF MOKA OUTPUT FROM ALASKA INTO MONTANA PROPOSAL Section I: Links of Proposed Pipeline From Alaska to Ohio via Montana UPPER LOWER LOAD ARCS COST c a p a c i t y CAPACITY FLOW FACTOR S0640097 43676 1039009 0 1039C09 100 DC-97 »12* 5103 105302a 0 1053023 100 Dll'51* 147 2527 1065699 0 1066699 100 0147,'106 i 3536 1045600 0 1045500 100 DC63UOSO 1350 1076650 0 1076550 100 00501*051 1640 1246187 0 1246137 100 00510040 5414 641176 0 841178 100 D0400G45 1921 24 79 34 0 247934 100 00450046 224146 337560 0 0 0 DC4t>D123 1164 535149 0 0 0 D1230131 796 3 535149 0 0 0 0131D139 1795 937323 0 93732B 100 Section II : Pipeline Network Links CU01D151 1403 1330425 .0 698235 52 00020034 42780 223971 0 7102 ■ s ' 00030001 1666 5o601G 0 0 0 00030004 6155 135F.7P 0 0 0 DC 040002 6201 264329 0 44636 16 OC04DO36 1863 1119*57 0 1119857 100 DO05 0004 1004 1429660 0 1255149 87 00050006 2856 309240 0 110487 35 00060031 7737 63992 0 45387 70 D006D016 li)tt893 191*75 0 0 0 [•0070030 4477 367190 0 301671 82 00060005 2397 1027^75 0 908259 98 Section lilt Reverse Pipeline Network Links D014D013 4193 51059 0 37193 7? 00150013 6041 711481 0 0 0 DO 150014 6980 154642 0 0 Q 00060014 3930 740 320 0 0 0 00921)015 4091 965053 0 0 0 S049UG16 5705 lo2 120 0 0 0 SG4-10G 1ft 496? 42641* 0 0 0 0022t)UlQ 802 9 104902 0 02 4 IB 75 DL230019 19772 3444 0 3444 100 CH120019 !106966 184? 0 Q 0 SQ460G20 1751C 19711? 0 0 0 r 213 TABLE 17— continued Section IVt Dummy Supply Links UPPER LOWER LOAD ARCS COST CAPACITY CAPACITY* FLOW FACTOR S S038 19610 567105 0 5.67105 100 S S039 I /M O 10058 0 1BG3R 100 S S040 17620 5071 0 5070 100 S S 041 17620 57991 0 57991 ■ 100 S SC-42 22160 73433 0 72330 98 S S04J 22160 35191 0 22356 63 s . S044 l9o:;o 254647 0 247972 97 s S04*> 19060 130931 0 138931 100 s S046 18020 61091 0 61091 ion s S047 ro 140 4713 0 4713 100 Section V* Intrastate Pipeline Network Links SCG10120 0 4485 4485 4485 100 S0020139 0 45658 45658 45658 100 S0020140 0 12372 12872 12872 ICO $003 D129 0 15359 15359 15359 100 S0040I31 0 42500 42500 42500 100 S005D169 • 0 D39n 8398 8398 ICO S005D170 0 4335 4335 4335 100 Section VI: Atlantic Offshore Links SO 610069 140 0 0 0 0 S061D073 16757 16605 0 16605 100 S062DU6 159 0 0 0 0 SC-620110 6357 138051 0 138051 100 $0620109 91 0 0 0 0 $0620025 18374 9094 0 9099 100 $0620070 lt>3 0 0 0 0 S062D164 18? 0 0 0 0 $062D 121 266 C 0 0 0 S0630029 13619 42174 0 42174 100 Su630032 102 0 0 0 0 SO 63DC33 75 0 0 0 0 $0630 In** 21354 8131 0 8131 100 $063D 145 68 0 0 0 0 $0630121 1096? 10690 0 10890 100 Section VII: LNG and SNG Sites S S073 114000 73000 0 73000 100 S0730G77 0 73000 0 73000 100 S $074 150000 7500 0 7500 100 S074L116u 7500 0 7500 100 S S075 77C00 45625 0 31551 69 S075P109 L 45625 0 31551 69 S S076 130000 6000 0 6000 100 £076DO73 0 6000 0 6000 100 S SC77 10500C 36500 0 36500 100 $0770070 0 36500 0 36500 100 Section VIII* Dummy Demand Links 00 ?5 T 0 39008 0 39008 100 0026 T 0 202796 0 70914 34 0027 T 0 149275 0 80345 53 0023 T 0 95959 0 95959 100 DC 29 T 0 88 527 0 88527 100 D030 T 0 24616 0 24616 100 0031 T 0 45387 0 45387 100 DC 32 T 0 48763 0 48763 100 D033 T 0 46562 0 46562 100 0034 T 0 194522 0 194522 100 0035 T 0 24715 0 24715 100 214 production estimates. Note that supply area 43 (S043) can only produce at 6$ per cent of capacity due to bottlenecks. Section V shows intrastate pipeline links, all of which are forced to deliver the historically-determined volume. Section’VI and Figure 44 indicate the optimum routes for the Atlantic offshore links. For supply region 62, for example, Dll6, DUO, D109, D025, D0?0, D164, and D121 are chosen as feasible market areas; the model indicates that a pipeline of capacity 9i099 should be built to D025 and of 42,174 to D029. Section VII shows LNG and SNG sites. Note that D109 can consume only 69 per cent of the projected production (45,626) of the SNG plant in northern New Jersey. Section VIII and Figure 40 show deficits in the demand regions. Since supply and demand have been equated, all of these deficits are due to bottlenecks. It is suspected that the deficits in the two Texas regions are due to underestimation of intrastate capacity. It is possible, ■ in each case, to isolate individual links that act as bottlenecks. For example, only 34 per cent of the demand in Miami, Florida is met, leaving a 66 per cent deficit. The bottleneck is in the link of the Florida Gas Trans mission Company from D029 to D028 (Figure !?)• 215 MILES Figure 44. Pipelines From the Atlantic Offshore Referral to Table 1 shows that shortages in southern Florida, for example, will have the greatest effect on the electrical utility industry (51 per cent of Florida's con sumption) an'* lesser effects on other industry (28 per cent) and commerce (10 per cent). Although little gas is used directly for residential purposes (8 per cent), much of. th£ electricity produced from gas is for domestic uses. Since only 20 per cent of Florida's energy consumption is derived from gas, it is probable that the impacts from such deficits will not be-serious. Summary. This chapter has illustrated the utility of the modeling system developed in this dissertation for examina tion of the natural gas pipeline network. Although the conclusions with respect to the Alaskan gas pipeline are tentative since they are dependent upon the particular set of assumptions employed, the power of the model has been' illustrated. In addition, it should be emphasized that this section has been meant only to illustrate the utility of the model. Thus, the analysis above is but one of many possibilities. Chapter 9 discusses the advantages and limitations of the model, as well as some simple exten sions which would increase its utility. f CHAPTER 9 ADVANTAGES, LIMITATIONS, AND EXTENSIONS OP THE MODEL This dissertation has developed and illustrated the utility of a planning model of the U.S. natural gas pipe line network that facilitates a regional approach based upon a least-cost criterion. The development of a highly disaggregated spatial data set from available aggregate data has been shown to have advantages in producing a model which can be used to address policy-related questions. The model of the U.S. natural gas pipeline * * network, including the demand, supply, and pipeline net work submodels and MOKA, the nonlinear version of the out-of-kilter algorithm, represents an improvement over past research in three ways. 1) The level of geographic detail employed. The use of 187 demand regions (based upon network structure) and seventy-seven supply regions, rather than a small number of large regions, has permitted an accurate replication of the pipeline network. This permits 217 218 modeling of the network within a normative framework, without serious violation of the assumption that produc tion and consumption occur at a set of points in space. This geographic detail also allows far the identification of reasonably specific origins and destinations for pro posed pipelines and a more specific identification of deficit regions. 2) The inclusion of capacity constraints on the network links. The availability of accurate flow data and aggregate capacity data has made possible the devel opment of capacities on the network links. Only Brooks' (1975 ) model has tried to capacitate the links, and his procedure has been shown to be significantly flawed. Accurate capacities are essential to the judgment of system capability, the derivation of a realistic flow pattern, and the calculation of shipping costs. 3) The ability to account for the nonlinear rela tionship between cost and flow. The development of MOKA permits the inclusion of the effects of the nonlinear relationship between cost and flow. No other model has been able to account for this relationship, which has been shown to have a significant affect on shipping cost and, consequently, flow pattern. In addition, the proce dure for the measurement of mileage along network links contributes to significantly mo.re accurate link costs. 219 Although these factors contribute to making this .model of the natural gas pipeline network one of the more accurate available, the shortcomings are fully recognized. It is believed that the data set developed is the best that can be derived from available data. However, it must be stated that the non-existence of essential data (and the existence of conflicting data published by different sources) has seriously hampered this effort, and, in many cases, has resulted in the employment of estimated data that may, in some instances, bear less resemblance to reality than might be desired. A great number of assumptions have been employed in messaging the available data into usable form. This must be kept in mind when interpreting the results. The model has been set up, however, such that superior data that become available may be easily incorporated. A number of limitations are due to factors not currently accounted for in the model. Most of these may be handled via an extension of the existing modeling structure. 1) The natural gas transmission industry includes facilities for transporting gas through time— over 360 underground storage pools are found in twenty-six states and ninety liquefied natural gas storage operations 220 exist. The ability to store gas is important as it allows load factors to be increased by permitting gas to be shipped during off-peak (summer) months and stored for use during the peak (winter) period. This can be incor porated .into MOKA as shown in Figure ^5* First, the demand node D is divided into winter and summer nodes. Then, demand for the year is apportioned to summer and winter months* the upper capacity of link (D_,T) is set equal to the summer demand; of link (DW ,T), to the winter demand. The upper capacities of links (D,D) and (D,Dm ) s w are sot equal to one-half the yearly capacity. The link (D ,D ) is given the following specifications: s w 1. . - the minimum storage volume to maintain pressure J- J u. • = the available storage capacity J- J . t. . = the cost of storing gas 1 J In this manner, the optimal winter and summer shipping volumes and optimal storage levels may be obtained. Loca tions for increased storage may be suggested by removing * capacity constraints upon storage levels. Extensions to a quarterly demand situation are also possible. 2) Although only currently operating SNG and LNG sites have been included in the model, extensions could allow for consideration of proposed sites. Given the choice between locating a coal gasification facility at 221 SUMMER DEMAND NODE ORIGINAL 63 DUMMY DEMAND NODE NODE WINTER DEMAND NODE Figure 45. Introduction of Storage Capacity to the MOKA Framework 222 X or Y, the model can address this problem in a manner analogous to that used for selecting among proposed routes. SNG facilities, for example, may be included as t follows. Suppose SI in Figure 35 is a proposed SNG site. The following parameters may be employed for (S,Sl)i 1.• = the threshold size of an SNG plant ■J" J uij = max^-inuin output from the plant t. • = the cost per unit for coal gasification A J Note that if SI, S2, and S3 are all coal gasification' sites, the procedure developed (p. 186) to determine optimum production levels is particularly useful. 3) While the MOKA model does account for the non linear cost-flow relationship and yields a lower-cost solution than would be obtained from a simple linear programming format, no optimal solution can be guaranteed. * The development of a "true" nonlinear program for the natural gas pipeline network, although greatly reducing efficiency and flexibility, probably would yield a superior solution. *0 In the current version of the.model, total demand in each demand region is employed, rather than demand for each consuming sector. This limitation can be remedied by the following extension (Figure ^6 ). / J se c to r a l d e m a n d no des HIGH PRIORITY DUMMY DEMAND NODE ORIGINAL DEMAND NODE I Q ] {DS MEOIUM PRIORITY LOW PRIORITY Figure 46. Introduction of Sectoral Allocation to the MOKA Framework 223 zzk Each demand node is replaced by a separate node for each • * consuming sector. A priority allocation scheme can then be modeled by. A) establishing priorities for the various end uses, such as residential first, commercial second, and industrial third; B) setting the upper capacities of the (D1,DS^) fh links equal to the demand in the i sector; and C) setting the costs on th6 (D1,DS^) link of the highest priority sector at zero, of the second highest priority sector at M (some large number), of the third, at 2M, etc. In this manner, the excess demand in the higher priority sectors is minimized. The present model could be simply modified to allow a priority allocation schedule since Equation 7 (p.92) is capable of appor tioning demand to each sector within each demand region. It is merely for simplicity that this capability has not been installed at this stage. The effect of such an inclusion would be, for example, that the Route 1 proposal (Figure ^2) would be shown to lead to curtailments of low-priority users . throughout New England and New York, rather than 100 per cent deficits in some regions and full demand being met in other regions. 225 5) The model has examined only natural gas. Obvious ly, the availability of substitutable commodities such as oil or coal should be taken into account in planning the: U.S. energy system. Although the Project Independence model (PIES) of the U.S. government does include all energy forms, the natural gas model within the PIES model employs ten large demand regions, the National Petroleum Council supply regions, and has uncosted, uncapacitated links. Thus, some merging of the model in this disserta tion with the PIES model should prove useful. 6) The current model optimizes the system for a given year. This does not guarantee a multi-period optimization, which could be accomplished by successive linkages of the dummy supply and demand nodes (Figure 35)* Unfortunately, such an undertaking for even a ten year period would increase the number of system links from over 1200 to over 12,000. 7) The current model does not adequately handle the intrastate pipeline network, due to a lack of data on wellhead prices and flows of intrastate gas. The FPC has just recently released a new version of their "flow matrix" which includes intrastate flow volumes. This should make possible a more accurate representation of the intrastate network. 226 To some extent, most of these "limitations” may be viewed as "advantages" since they may easily be included in the model. Thus, this dissertation not only presents a model, which in its curren.t form, provides a framework for addressing a number of critical policy-related questions about the pipeline network, but which may also be simply extended to examine additional problems. A major contribution of this dissertation is the procedures employed to develop a highly disaggregated spatial data set from available aggregate data. These procedures include the development of demand regions based upon the structure of the transportation network, the apportion ment of demand and supply from spatially aggregate to spatially disaggregate regions, and the specification of a detailed pipeline network model including capacitated links. A secondary contribution is the development of the modified out-of-kilter algorithm which accounts for the nonlinear relationship between cost and flow. The power of this model when applied to the spatially dis aggregated data set has been illustrated through an examination of a number of proposed routes for the Alaskan Gas Transportation System and selected results for 1985 assuming the Alaskan pipeline enters via Montana. The nature of these results serves to illustrate 22? why the approach taken in this dissertation represents a significant advance over previous models. APPENDIX A Region State Counties (or Description) . 1 AL Lauderdale, Colbert, Franklin, Lawrence, Morgan, Limestone, Madison 2 AL Jackson, De Kalb, Marshall, Cullman, Etowah, Cherokee, Calhoun, Cleburne 3 AL Marion, Lamar, Fayette, Pickins AL Walker, Jefferson, St. Clair, Shelby, Tuscaloosa, Greene, Bibb, Chilton, Loosa, Tallapoosa, Randolph, Clay, Talladega 5 AL Sumter, Hale, Perry, Dallas, Wilcox, Marengo 6 AL All counties S and E of Chambers, Lee, Macon, Elmore, Autauga, Lowndes, Butler, Covington GA Chattahoochee, Troup Coweta 7 AL Washington, Clarke, Monroe, Conecuh, Escambia, Mobile, Baldwin FL Escambia, Santa Rosa 8 AZ Navajo, Apache 9 AZ Mohave, Coconino, Yavapai 10 AZ Gila, Graham, Greenlee, Cochise, Santa Cruz, Pima 11 AZ Yuma, Maricopa, Pinal 12 AR Benton, Carroll, Boone, Marion, Madison, Washington, Crawford, Sebastian, Scott, Logan, Franklin, Johnson, Pipe, Yell, Conway, Clebprne . OK Sequoyah, LeFlure 228 229 Region State Counties (or Description) 13 AR Pulaski, Saline, Garland, Montgomery, Hot Springs, Clark, Pike,. Howard, Dallas, Clevelandj Calhoun, Ovachita, Nevada, Hempstead, Union, Columbia, Lafayette, Miller, Little River TX Bowie AR Ashley, Chicot, Bradley, Drew, Desha, Lincoln, Arkansas, Grant, Jefferson, Lonoke 15 AR All counties E of Clay, Lawrence, Indepen dence, White, Prairie, Monroe, Phillips TN Upton, Shelby, Desoto 16 CA All counties S of San Luis, pbispo, Kern, San Bern'adino 17 CA All counties S of Mendocino, Glen, Butte, Yuba, Nevada except El Dorado, Alpine, Calaveras, Toulumne, Mariposa, Mono Inyo, Region 16 18 CA Siskiyou, Shasta, Trinity, Humbolot, Tehama 19 CO Fremont, Pueblo, Huerfano, Las Animas, Bala, Prowers, Bent, Otero, Crowley 20 CO Grand*, Eagle, Summit, Lake, Park, Chaffee, Gunnison, Saguache, Alamosa, Conejos, Rio Grande, Archuleta, La Plata, Montezuma, Dolores, San Miguel, Montrose UT Grand, San Juan . 21 CO Mesa, Garfield, Rio Blanco, Moffat, Routt UT Vintah 22 CO Colorado Springs, Denver-Boulder, Greeley, and Fort Collins SMSA's WY Laramie 23 CO All counties E of Logan, Morgan, Washing ton, Lincoln, Kiowa NE Kimball, Cheyenne, Devel, Chase, Dundy 24 CT All except one-half of Litchfield RI Washington 230 Region State Counties (or Description) 25 DE New Castle, Kent, Sussex NJ Salem MD Cecil, Talbot, Dorchester, Wilomico 26 FL Dade, Broward, Palm Beach £? FL Tampa SMSA, Polk, Highlands Hardee, Manatee, Sarasota 28 FL Orlando SMSA, St. Lucie, Indian River, Brevard, Volusia, Lake, Sumter 29 FL Taylor, Madison, Suwanefe, Columbia, Jack sonville SMSA, Putnam, Marion, Citrus, Levy Alachua, Bradford 30 FL Okaloosa, Walton, Holmes, Jackson, Washing ton, Gulf, Bay, Leon, Wakulla AL Geneva 31 GA All counties S and W of Stewart, Webster, Sumter, Macon, Crisp, Turner, Ben Hill, Coffee, Berrien, Lowndes FL Gasden, Hamilton 32 GA Putnam, Hancock, Baldwin, Jones, Bibb, Peach, Houston, Twiggs, Wilkonson, Wash ington, Pulaski, Bleckley, Dodge, Laurens, Emanuel, Telfair, Wheeler, Toombs, Jeff Davis, Tattnall, Appling, Bacom, Ware, Pierce, Wayne, Long, Liberty, Glynn, Lamden 33 GA All counties E of Columbia, McDuffie, Warren, Jefferson, Burke, Jenkens,' Bulluch, Bryan SC Aiken 3^. GA Atlanta SMSA, Walton, Rockdale, Henry, Fayette, Douglas, Carroll, Haralson, Polk, Paulding, Cherokee, Bartow, Floyd, Gordon; Whitfield, Walker, Dade, Catoosa TN Chattanooga SMSA 35 GA Stephens, Banks, Hall,* Porsyth, Jackson, Barrow, Oconee, Morgan, Greene, Oglethorpe, Clarke, Madison, Elbert, Hart Counties (or Description) Newton, Jasper, Bitts, Spalding* Lamar, Monroe, Upson, Talbot, Meriwether, Harris Jefferson, Madison, Bonneville, Bingham, Caribou, Bannock, Bear Lake Blaine, Gooding, Jerome, Minidoka, Power, Cassia, Twinn Falls Owyhee, Elmore, Ada, Canyon, Gem, Payette, Washington All counties N of Kanakakee, Kendall, La Salle, Putnam, Bureau, Henry, Mercer (except Carroll, includes one-half of La Salle) Clinton, Dubuque, Scott All counties within Henderson, Warren, Knox, Stark, Marshall, Peoria SMSA, Logan, Dewitt, Springfield SMSA, Morgan, Brown, Pike (except Adams) Randolph, Monroe, St. Clair, Madison, Bond, Montgomery, Macoupin, Jersey, Calhoun, Greene, Scott Franklin (E half), St. Charles, St. Louis, Jefferson LaSalle (S. half), Grundy, Livingston, Ford, Iroquois,' McLean, Champaign, Ver million, Piatt, Macon, Christian, Moultrie Shelby, Effingham, Jasper, Cumberland, Coles, Edgar, Douglas All counties S of Jackson, Perry, Washing ton, Clinton, Fayette, Marion, Wayne, White « All counties N and W of Lagrange, Elkhart, Kosciusko, Wabash, Miami, Cass, Caroll, White, Benton (except Newton, Jasper) Fort Wayne SMSA, Noble, Whitley, Hunting ton 232 Region S ta te Counties (or Description) *17 IN Warren, Fountain, Tippelande, Montgonery, Clinton, Boone, Hendricks, Marion, Hamilton, Tipton, Howard, Grant, Madison, Hancock, Rush, Henry, Delaware, Blackford, Jay, Randolph, Wayne *+8 IN Terra Haute SMSA, Putnam, Owen, Morgan, Johnson, Shelby, Fayette, Decatur, Barthol omew, Monroe, Greene, Jackson, Lawrence, Martin, Daviess, Knox, Jefferson, Ohio, Washington, Orange, Gibson k9 IA Lyon (E half), Osceola, Dickinson, Emmet, Kossuth (W half), Palo Alto, Clay, O'Brien, Plymouth (E half), Cherokee, Buena Vista, Pocahantes, Sac, Ida, Woodbury, Monona NE Dakota 50 IA Warren (N half), Iowa (W half) (E half), Benton (E half), Poweshiek,'Jasper, Polk-, Dallas, Carroll, Greene, Boone, Storyi Marshall, Tama, Benton (Whalf), Hamilton, Webster, Calhoun, Wright, Humboldt, Kossuth (E half), Hancock, Cerro Gordo, Floyd, Chickasaw, Mitchell, Worth, Winnebago 51 IA Howard, Winneshiek, Allamakee Clayton, Fayette, Bremer, Butler, Franklin, Hardin, Blackhawk, Buchanan, Delaware, Linn, Jones, Jackson, Ceder, Johnson, Iowa (E half), Muscatine, Washington, Keokuk, Mahaska, Louisa, Wapello, Jefferson, Henry, Des Moines, Lee, Davis 52 IA Crawford, Harrison, Shelby, Audubon, Guthrie, Adair, Cass, Pottawattamie, Mont gomery, Union, Page, Fremont NE Douglas, Sarpy 53 IA Madison, Warren, Marion, Lucas, Clarke 5*f KS All counties N and W of Greeley, Kearny, Finney, Lane, Gove (W half), Sheridan, Decatur 55 KS All counties S and W of Hamilton, Grant, Haskall, Gray, Ford, Comanche 233 Region States Counties (or Description) « 56 KS W half of Smith, Osborne, Russelj Phillips, Norton, Graham, Rooks, Ellis, Treco, Gove (W half), Ness, Rush, Barton, Pawnee, Edwards 57 KS E half of Smith, Osborne, Russell, all counties N of Ellsworth, Saline, Dickinson, Geary,'Riley, Pottawatomie, Nemaha (W half) NE* Nockolls• 58 KS All counties within Barber, Pratt, Stafford, Rice, McPherson, Marion, Butler, Cowley 59 KS Morriss, Shawnee, Douglas, Johnson, Wyandotte, Leavenworth, Jefferson, Jackson, Atchison, Nemaha (E half), Brown,. Doniphan MO Cass, Jackson, Ray, Clay, Platte, Clinton, Caldwell, De Kalb, Andrew, Nodaway 60 NE All counties S and E of Miami, Franklin, Osage, Lyon, Greenwood, Elk, Chatauqua MO Vernon (W half) 61 KY Greenup, Boyd, Lawrence, Morgan, Johnson, Martin, Floyd, Pike, Knott, Perry OH Lawrence WV Wayne, Cabell. 62 KY Lexington SMSA, Boyle, Mercer, Harrison, Nicholas, Bracken, Mason, Lewis 63 KY Madison, Rock Castle, Pulaski, Laurel, Clay, Whitley, Knox, Bell 64 KY Ballard, Carlisle, McCracken, Graves, Calloway, Marshall, Trigg, Crittenden, Caldwell, Hopkins, Christian, Todd, Logan, Simpson, Allen, Warren, Barren, Monroe, Hart, Metcalfe, Adair i- 65 KY Union, Webster, McLean, Muhlenberg, Ohio, Henderson, Davies, Grayson, Breckenridge, Hardin, Larue, Marion, Nelson, Meade, Louisville SMSA, Anderson, Shelby, Franklin, Henry, Trimble IN Evansville SMSA, Louisville SMSA 23^. • Region State Counties (or Description) 66 LA . All counties N of Sabine, Natchitoches, Winn, La Salle, Catahoula, Concordia 67 LA All counties E of West, Feliciana, Points- Coupee,•Iberville, Assumption, St. Mary 68 LA All counties not in regions 66 or 67 69 ME • Cumberland, York NH Strafford, Rockingham * 70 MD Washington and Baltimore SMSA, Frederick (E half) VA Washington SMSA 71 MD Garrett, Allegany, Washington, Frederick (W half) WV Mineral 72 MA Berkshire, Franklin, Hampshire, Hampden CT Litchfield (N half) 73 MA All counties not in Region ?2 (except Dukes and Nantucket) . RX Rhode Island, Kent, Washington, Newport 7^ MI Mackinaw Peninsula (all counties) WI Marinette 75 MI' All counties N of Benzie, Wexford, Missau kee, Roscommon, Ogemaw. Iosco (except Montmorency and Oscoda) 76 MI Manistee, Mason, Lake, Osceola, Clare, Oceana, Newaygo, Mecosta, Isabella, Mid land, Bay, Tuscola, Saginaw,, Gratiot, Montcalm, Muskegon, Ottawa, Kent, Ionia (N half) 77 MI Detroit and Flint SMSA's, Clinton, Eaton, Ingham, Calhoun (E half), Jackson, Wash tenaw, Monroe, Lenawee OH Toledo SMSA (except Ottawa) 78* s MI Ottawa (S half), Ionia (S half), Allegan, Barry, Calhoun (W half), Kalamazoo, Van Buren, Hillsdale, Branch, St. Jospeh, Cass Berrien 235 Region State Counties (or Description) 79 MN Kittson, Roseau, Lake of the Woods, Koochiching 80 MN Beltrami, Itasca, St. Louis, Lake WI Douglas 81 MN Marshall, Pennington, Polk, Clearwater, Norman, Clay, Becker, Wilkin, Otter Tail, Wadena, Douglas, Stevens, Pope, Stearns (N half), Benton,.Sherburne (N half), Morrison, Mille Lacs, Kenabec, Isanti, Chisago, Pine, Carlton ND Grand Forks, Cass, Richland 82 MN Swift, Kandiyohi, Meeker, McLeod, Sibley, Renville, Redwood, Lyon (N half), Yellow Medicine, Lac Qui Parle 83 MN Lyon (S half), Murray, Cottonwood, Brown, Waltonwan, Faribault, Martin, Jackson, Nobles 8 ^f MN Minneapolis-St. Paul SMSA (except Chicago), Goodhue (N half), Rice, Le Sueur, Blue Earth, Brown (E half), Nicollet, Sherburne, Sterns (S half) 85 MN Counties S and E of Goodhue(S half), Steeve, Waseca, Freeborn 86 • MS Tunica, Clahoma, Bolivar, Alcorn, Tishom- 'ingo, Prentiss, Lee (N half),Pontotoc, Lafayette, Panola, Yalobusha, Grenada, Montgomery, Carroll, LeFlore, Sunflower, Washington, Humphreys, Sharkey 87 MS ' Lee (S half), Calhoun, Chickasaw, Monroe, Clay, Webster, Lowndes, Oktibbeha, Choctaw, Noxubee, Winston, Attala, Holmes, Leake, Yazoo, Warren 88 MS All counties S and W of Claiborne, Hinds, Madison, Scott, Smith, Simpson, Jefferson Davis, Lawrence, Walthall 89 MS All counties S. and E of Marion, Covington, Jasper, Newton, Neshoba, Kemper 236 Region State Counties (or Description) 90 MO Macon (N half), Adair, Sullivan, Schuyler IA Monroe, Appanoose, Decatur 91 MO St. Clair, Vernon (E half), Ceder, Polk, Barton, Dade, Greene, Christian, Lawrence, Jasper, Newton, Barry 92 MO All counties E of Oregon, Carter, Wayne, Iron, St. Francois, St. Genevieve (except Perry) 93 MO Bates, Henry, Benton, Morgan, Monteau, Cole, Cooper, Pettis, Johnson, Lafayette, Saline, Howard, Ray, Carroll 9k MO Grundy, Livingston, Linn, Chariton, Macon (S half), Randolph, Shelby, Marion, Monroe, Ralls, Pike, Audrain, Boone, Callaway, Montgomery, Lincoln, Warren, St. Charles (W half), Franklin (W half), Gasconade 95 MT' Flathead, Glacier, Toole, Pondera, Teton, Cascade, Lewis and Clark (N half) 96 MT Fergus, Judith Basin, Wheatland, Golden Valley 97 MT Phillips (E half), Valley, Roosevelt. Rich land, McCone, Dawson, Wibaux (W half), Fallon, Carter, Powder River ND Slupe, Bowman 98 MT • AIL counties.JS and W of Missoula, Powell,. Lewis and Clark (S half), Broadwater, Gallatin i 99 MT Park, Sweet Grass, Stillwater, Yellowstone, Carbon 100 MT Big Horn, Rose Bud, Custer, Prairie 101 MT Liberty, Hill,.Blaine, Choteau, Phillips (N half) 102 NE Sioux, Dawes, Sheridan, Box Butte, Scotts Bluff, Morrill, Garden, Keith, Perkins 237 Region State Counties (or Description) 103 NE All counties within Red Willow, Frontier, Lincoln, Dawson, Buffalo, Howard, Merrick, Hamilton, York, Seward, Fillmore, Thayer (except Nuckolls (S half)) 104 NE All counties within Custer, Loup, Brown, Rock, Holt, Knox, Ceder, Pierce, Stanton, Cuming (W half), Platte (N half), Nance, Greeley, Sherman 105 NE All counties E of Dixon, Wayne, Cuming. (E half), Colfax, Platte (S half), Polk, Butler, Lancaster, Saline, Jefferson (except Dakota, Omaha SMSA, Richardson) 106 NV Clark 107 NV All counties except Clark, Esmeralda, Lincoln, White Pine 108 NH Belknap, Merrimack, Hillsborough 109 NJ Cumberland, Atlantic, Cape May 110 NJ Ocean, Monmouth, Mercer, Middlesex, Somer set, Sussex, Hunterdon, Morris, Union, Hudson, Essex, Passaic, Bergen 111 NM Sierra, Dona Ana, Luna, Grant, Hidalgo 112 NM Colfax, Mora, San Miguel 113 NM San Juan, Rio Arriba, Taos, Santa Fe, Bernalillo, Socorro, Valencia, McKinley, Sandoval, Los Alamos 114 NM Quay, Curry, Roosevelt, Lincoln, Chaves, Lea, Eddy, Otero TX El Paso 115 •NY St. Lawrence 116 NY Long Island, NYC, Rockland, Westchester U 7 NY Orange, Putnam, Ulster, Dutchess, Greene, Columbia, Albany-Schenectady-Tiroy SMSA, Fulton, Washington, Warren, Sullivan 238 Region State Counties (or Description) 118 NY Syracuse SMSA, Oneida, Herkimer, Jefferson, Lewis 119 NY Delaware, Otsego, Chenango, Cortland, Tompkins, Slhuyler, Yates, Steuben (E half), Chemung, Tioga, Broome PA Susquehanna 120 NY All counties W of Cayuga Seneca, Ontario, Steuben (W half) (except Chautauqua (S half)) 121 NC Northampton (S half), Halifax, Nash, Edgecombe, Wilson, Pitt, Beaufort, Johnston, Wayne, Greene, Lenoir, Craven, Jones, Harnett, Moore, Scotland, Hoke, Rubeson, Cumberland, Sampson, Bladen, Wilmington SMSA 122 NC Greensboro (except Davidson) and Raleigh SMSA's, Alamance, Chatham, Lee, Rockingham, Caswell, Person, Granville, Vance, Warren, Franklin, Davies 123 NC Davidson, Montgomery, Richmond, Anson, Stanly, Charlotte SMSA, Cabarrus, Rowan, Iredali, Alexander, Caldwell, Burke, Catawba, Lincoln, Cleveland, Rutherford, Polk, Henderson, Transylvania, Haywood, Buncombe, Madison 12^ ND Kidder, Stutsman, Barnes, Foster, Eddy, Benspn, Ramsey, Walsh, Cavalier, Pembina 125 ND Golden Valley, Wibaux (E half), Billings, Stark, Hettinger, Morton, Burleigh 126 ND Williams, McKenzie, Mercer, McLean, Ward, Mountrail, Burke 12? OH Auglaize (S half), Logan, Shelby, Darke, Madisonj Springfield, Dayton, and Cincin nati SMSA's, Clinton (W half) IN Dearborn KY Cincinnati SMSA 239 Region State Counties (of Description) 128 OH All counties W and N of Mercer, Auglaize (N half), Hardin, Lima, Putnam, Henry, Williams 129 OH Astabula (W half), Cleveland SMSA, Lorain, Ashland, Richland, Crawford, Wyandot, Hancock, Seneca, Sandusky, Ottawa, Erie, Huron 130 OH Akron SMSA, Trumbull, Mahoning, Columbiana, Stark,. Wayne, Holmes, Tuscarawas 131 OH All counties except those in regions 127- 130 and Brown, Adams and Vinton WV Wheeling SMSA, Wood, Mason 132 OK All counties W of Ellis, Woodward, Woods, Alfalfa 133 OK All counties S and W of Roger Mills, Dewey, Custer, Caddo, Canadian, Oklahoma, Cleve land, McLain, Garvin, Murray, Johnston, Marshall; except Harmon (S half), Jackson (S half), Kiowa (S half), and Tillman 134 OK Grant, Kay, Osage (W half), Garfield, Major, Blaine, Kingfisher 135 OK Tulsa SMSA (except Osage (W half)), Wash ington, Nowatha, Craig, Ottawa, Cherokee, Payne, Lincoln, Pottawatomie, Muskogee, Okmulgee, Okfuskee, Seminole, Garvin (E half), Pontotoc, Coal, Atoka, Hughes, Pittsburg, Latimer, Haskell, McIntosh 136 OR Josephine, Jackson, Douglas, Lane, Linn, Benton, Lincoln, Linn; all counties W of Marion, Clackamas, Multnomah WA Clark 137 OR Malheur, Baker, Umatilla WA Walla Walla 138 OR Wasco, Deschutes, Klamath 139 PA All counties S and W of Lawrence, Butler, Armstrong, Indiana, Cambria, Blair, Hunt ington, Franklin* 240 Region State Counties (or Description) 140 PA All counties W and N of Potter, Cameron, Centre, Clearfield, Jefferson, Clarion, Venango, Mercer OH Ashtabula (E half) NY Chataqua (S half) 141 PA Tioga, Bradford, Wyoming, Wayne, Pike, N. PA SMSA, Columbia, Northumberland, Union, Clinton, Wyoming 142 PA All counties S and E of Adams, Harrisburg SMSA, Schuylkill, Carbon, Northampton NJ Warren, Philadelphia SMSA 143 SC Greenville SMSA, Cherokee, Oconee, Anderson, Abbeville, Laurens, Newberry 144 SC • York, Chester, Richland (E half), Lancaster, Chesterfield, Marlboro, Kershaw, Sumter, Lee, Darlington, Marlboro, Dillon, Florence, Marion, Hurry, Georgetown 145 SC Lexington, Richland (S half), Charleston SMSA, Barnwell, Hampton, Baufort Pt. 146 SD Butte, Lawrence, Meade, Pennington 14? SD Brown, Spink, Clark, Codington, Hamlin, Beadle, Kingsbury, Brookings, Miner, Lake, Davison, Hanson, McCook, Minnehaha, Turner, Lincoln, Yankton, Clay, Union 148 TN Kingsport SMSA, Hamblen, Greene, Cocke, Jefferson, Sevier, Knoxville SMSA, Roane, Louden, Monroe, Rhea, McMinn VA Johnson City SMA 149 TN Lake, Obion, Weakley, Henry, Benton, Henderson, Madison, Fayette, Haywood, Lauderdale, Crocket, Dyer, Gibson 150 TN Nashville SMSA, Stewart, Houston, Humphreys, Hickman, Cannon, DeKalb, White, Cumberland, Morgan, Scott, Overton, Jackson, Smith, Trousdale, Macon 151 TN Maury, Marshall-, Bedford, Warren, Moore, Franklin, Lincoln, Giles Region State Counties (or Description) 152 TX . Presidio, Hudspeth, Culberson, Reeves, Pecos, Terrell, Crockett, Crane, Upton, Winkler, Ector, Midland, Glasscock, Sterling, Howard, Martin, Andrews, Gaines, Dawson, Garza, Lynn, Terry, Yoakum, Hockley, Lubbock, Crosby 153 TX All counties.N of Bailey, Lamb, Hale, Ployd, Motley, Cottle NM Union OK Harmon (S half), Jackson 15^ TX All counties within Hardeman, Foard, Knox, Haskell, Jones, Fisher, Scurry, Mitchell, Nolan, Taylor, Runnels, Tom Green, Schleich er, Sutton, Coucho, McCulloch, Brown, Comanche, Somervell (E half), Eastland, Stephens, Young, Jack, Clay OK Kiowa, Tillman 155 TX All counties within Montague, Wise, Parker, Pinto Hood, Johnson, Ellis (N half), Kaufman, Van Zanot, Wood, Hopkins (W half), Red River OK Bryan, Choctaw, McCurtain, Pushmataha 156 TX All counties within Cass, Morris, Titus, Franklin, Wood (E half), Smith, Henderson (E half), Cherokee, Houston, Walker, San Jaonito, Polk, Angelina, San Augustine, Sabine (except Bowie) 157 TX All counties within Newton, Jasper, Tyler, Hardin, Liberty, Montgomery, Grimes, Wash ington, Austin, Colorado, Wharton, Matagurda 158 TX All counties between San Saba, Llano, Burnett and Regions 15^-157 159 TX All counties within Travis, Lee, Fayette, Lavaca, De Witt, Karnes, Wilson, Dexar, Comol, Hays; Medina, Uvalde, Kinney, Val . Verde, Maverick, Zavala, Dimmit, La Salle 160 TX All counties S of Jackson, Victoria, Goliad, Bee, Atascosa, Frio, McMullen, Webb 242 Region State Counties (or Description) 161 VT . Emery, Carbon, Duchesne, Wasatch, Summit; Utah, Tooele, Salt Lake, Davis, Weber, Morgan, Box Elder, Cache 162 VT Grand Isle, Franklin, Chittenden 163 VA Pulaski, Craig, Bute Tourt, Lynchberg SMSA, Appomattox, Halifax, Pittsylvania, Henry Roanoke 164 VA All counties within Gloucester, James City, Charles City,., Richmond SMSA,, Petersburg SMSA, Brunswick NC Hertford, Northampton (N half) 165 VA Alleghany, Rockbridge,.Nelson, Buckingham, Fluvanna, Albemarle, Augusta, Louisa, Orange, Greene, Rockingham, Madison, Page, Shanendoah, Stafford, Fauquier, Warren, Clarke, Frederick WV Morgan-Hampshire, Hardy, Pendleton 166 WA Whatcom, Skagit, Island, Snohomish, King, Pierce, Lewis, Skamania, Cowlitz, Thurston, Grays Harbor, Mason, Kitsap. 16? WA Chelan, Douglas, Grant, Kittitas, Yakima, Klickitat, Benton, Franklin, Adams (W half) 168 WA Stevens, Lincoln, Adams, Whitman, Spokane ID Boundary, Bonner, Kootenbi, Shoshone, Latah, Lewiston 169 WV Wetzel, Monongalia, Preston, Grant, Tucker, Randolph, Upshur, Lewis, Dodridge, Ritchie, Pleasants, Tyler, Dodridge, Harrison, Barbour, Taylor, Marion 1?0 WV Gilmer, Calhoun, Roane, Jackson, Putnam, Lincoln, Logan, Boone, Kanawha, Clay, Braxton, Nicholas, Greenbrier, Fayette, Raleigh, Wyoming, Summers, Monroe, McDowell, Mercer VA Giles 171 WI Green Bay and Milwaukee SMSA, Manitowoc, Sheboygan, Manitowoc, Waupaca, Fond Du Lac, Green Lake, Waushara (E half), Dodge, Jefferson (E half), Walworth, Kenosha, Racine 243 Region State Counties (or Description) 172 WI All counties within La Crosse, Monroe, Juneau, Adams, Waushara (W half), Marquette, Columbia, Jefferson, Roch 173 WI Wood, Portage, Marathon (E half), Shawano, Menominee, Oconto, Langlade, Lincoln, Oneida, Forest, Florence 174 WI Bayfield, Ashland,- Price, Rusk, Barron, Polk, Dunn, Chippeng, Eau Claire, Taylor, Marathon (W half), Clark, Jackson, Trempealeau, Buffalo, Pierce, St. Cruix 175 WY . Lincoln, Uinta, Sweetwater, Carbon, Albany 176 WY Goshen, Platte, Converse, Naitrona, Johnson, Campbell, Crook, Sheridan 177 WY Fremont, Hot Springs, Washakie, Park, Big Horn 1 APPENDIX B PIPELINE COMPANIES INCLUDED IN THE PIPELINE NETWORK SUBMODEL The following companies are modeled explicitly in the pipeline network submodel. The states in which each company operates and the "class" of each company is also provided. (See Table at end of listing for explanation of class.) Company Name States Class Alabama-Tennessee Natural Gas Co. AL, MS, TN A Algonquin Gas Trans mission Co. CT, MA, NJ, NY, RI A Arkansas-Louisiana Gas Co. AR, KS, LA, OK, TX A Arkansas-Missouri Power Co. AR, MO A Black Marlin Pipeline Co. TX B Blue Dolphin Pipe Line •. C o . TX B Carnegie Natural Gas Co. SC I Cascade Natural Gas Corp. CO I Chandeleur Pipe Line Co. MS B Cities Service Gas Co. KS, MO, NE, OK, TX A Coastal State Gas Producing Co. TX I Colorado Interstate Gas Co. CO, KS, NM, WY A 2 k5 Company Name States Class Columbia Gas Trans WV, KY, MD, NJ, VA, mission Corp. NY, PA, OH A Columbia Gulf Trans mission Co. LA, MS, TX, TN, KY A Consolidated Gas Supply Corp. NY, PA, VA, WV, OH A Consumer Power Co. MI I East Ohio Gas Co. OH I East Tennessee Natural Gas Co. TN, VA A Eas.tern Shore Natural Gas Co. DE, MD, PA A El Paso Natural Gas Co. AZ, CO, NM, OK, TX A Equitable Gas Co. PA, WV, KY A Florida Gas Transmission Co. AL, FL, LA, MS, TX A. Gas Transport, Inc. OH, WV B Granite State Trans mission Corp. NH, ME A Great Lakes Transmission MI, MN, WI Co. (Import/export) A Inland Gas Co. KY, OH, WV A Inter-City Minnesota MN Pipeline, Ltd., Inc. (Import/export) A Kansas-Nebraska Natural Gas Co. CO, KS, NE, OK, WY A Lone Star Gas Co. OK, TX A Louisiana-Nevada Trans it Co. AR, LA B zke Company Name States Class McCulloch Interstate ■ Gas Corp. WY A Michigan Consolidated Gas Co. MI I Michigan Gas Storage Co. MI A Michigan-Wisconsin Pipe IL, IA, MI, IN, KS, MO, A Line Co. WI, KY, LA, MS, OH, OK, TN, TX (Imports) Mid Louisiana Gas Co. LA, MS, TX A Midwestern Gas Trans MN, ND, IL, IN, KY, A mission Co. WI, TN (Imports) r Mississippi River Trans mission Corp. IL, MO, AR, LA A Montana-Dakota Utilities MT, MN, ND, SD, WY A Montana Power Co. MT (Imports/exports) U Mountain Fuel Supply Co. UT, WY, CO A National Fuel Gas Supply and Distribution Corp. NY, PA A Natural Gas Pipeline Co. AR, IL, IA, KS, MO, A of America NE, OK, TX North Carolina Natural Gas Corpl NC I North Penn Gas Co. PA .A Northern Natural Gas Co. IL, IA, KS, MO, CO, MN, A NE, MT, NM, QK, SD, TX, WI, MI (Import/export) Northern Utilities Inc. WYA Northwest Pipeline Corp.. NM, CO, UT, WY, ID, OR, A WA (Import) Zk7 Company Name States Class Pacific Gas and Electric C o < CA I Pacific Gas Trans mission Co. ID, OR, WA (Import) A Pacific Lighting Service Co. CA I Panhandle Eastern Pipe IL, IN, KS, TX, MI, . A Line Co . WY, MO, OH, OK, CO (Export) Pennzoil Pipeline Co. TX I Raton Natural Gas Co. NM, CO C Sabine Pipe Line Co. TX, LA B St. Lawrence Gas Co. NY (Import) *U Sea Robin Pipeline Co. LA A South Texas Natural Gas Gathering Co. TX, LA A * Southern California Gas Co. CA I Southern Natural Gas Co. AL, GA, LA, MS, SC, TX A Southern Union Gas Co. AZ, CO, NM, TX I Southwest Gas Corp. CA, NV, AZ A Tennessee Gas Pipeline AL, AR, CT, KY, LA, MS, A Corp. NH, NJ, NY, OH, PA, RI, TN, TX, WV, MS (Import/export) Texas Eastern Trans AL, AR, IL, IN, KY, LA, A mission Corp. MO, NY, NJ, OH, PA, TN, TX, MD, MS (Imports) Texas Gas Transmission AR, IL, IN, KY, LA, MS, A Corp. OH, TN, TX 248 Company Name States Class Texas Gas Utilities Co. TX I Transcontinental Gas AL, GA, LA, MD, MS, NJ A Pipeline Corp. NY, NC, PA Transwestern Pipeline Co. AZ, KS, NM, OK, TX A 4 , Trunkline Gas Co. AR, IL, IN, KY, LA, MS, A TN, TX United Gas Pipeline Corp. AL, FL, LA, MS, TX A Valley Gas Transmission, LA, TX A Inc. 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