Petroleum Production and Exploration

To my family

List of Papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Jakobsson, K., Söderbergh, B., Höök, M., Aleklett, K. (2009) How reasonable are oil production scenarios from public agen- cies? Energy Policy, 37(11):4809-4818 II Jakobsson, K., Bentley, R., Söderbergh, B., Aleklett, K. (2011) The end of cheap oil. Bottom-up economic and geologic modeling of aggregate oil production curves. Energy Policy, in press III Jakobsson, K., Söderbergh, B., Snowden, S., Aleklett, K. (2011) Bottom-up modeling of oil production. Review and sensitivity analysis. Manuscript. IV Jakobsson, K., Söderbergh, B., Snowden, S., Li, C.-Z., Aleklett, K. (2011) Oil exploration and perceptions of scarcity. The fallacy of early success. Energy Economics, in press V Söderbergh, B., Jakobsson, K., Aleklett, K. (2009) European energy security. The future of Norwegian natural gas production. Energy Policy, 37(12):5037-5055 VI Söderbergh, B., Jakobsson, K., Aleklett, K. (2010) European energy security. An analysis of future Russian natural gas production and exports. Energy Policy, 38(12):7827-7843 VII Höök, M., Söderbergh, B., Jakobsson, K., Aleklett, K. (2009) The evolution of giant oil field production behavior. Natural Resources Research, 18(1):39-56

Reprints were made with permission from the respective publishers.

The author’s contribution to the papers: Papers I-IV: principal authorship and major contribution to modeling Papers V and VI: contribution to modeling Paper VII: minor contribution to modeling

Complementary paper not included in the thesis:

Aleklett, K., Höök, M., Jakobsson, K., Lardelli, M., Snowden, S., Söder- bergh, B. (2010) The peak of the oil age: Analyzing the world oil production reference scenario in World Energy Outlook 2008. Energy Policy, 38(3):1398-1414

Contents

1 Introduction ...... 11 1.1 Cheap energy and the industrial society ...... 11 1.2 The end of cheap oil? ...... 13 1.3 Reconciling natural science and economics – a bottom-up approach 15 1.4 Aims and disposition ...... 16 2 Resources and reserves ...... 18 2.1 Conventional petroleum accumulations ...... 18 2.2 Reserve estimation and classification ...... 19 2.3 Reserve growth ...... 22 2.4 Global URR estimates ...... 24 2.5 Reserve interpretation caveats...... 25 3 Production ...... 28 3.1 Reservoir dynamics ...... 28 3.2 Production optimization ...... 34 3.3 Economic theory of non-renewable resource production ...... 37 4 Exploration and discoveries ...... 41 4.1 The purposes of exploration ...... 41 4.2 Size-frequency distribution of fields ...... 42 4.3 Discovery process models ...... 43 4.4 Creaming curves ...... 48 4.5 The success rate ...... 49 4.6 Estimating undiscovered amounts: USGS World Petroleum Assessment ...... 51 5 Production forecasting models ...... 54 5.1 Top-down models ...... 54 5.1.1 The Hubbert curve ...... 54 5.1.2 The Maximum Depletion Rate Model ...... 56 5.1.3 Econometric models ...... 58 5.2 Bottom-up models ...... 60 6 Results ...... 63 6.1 Paper I ...... 63

6.2 Paper II ...... 64 6.3 Paper III ...... 65 6.4 Paper IV ...... 66 6.5 Papers V and VI ...... 66 6.6 Paper VII ...... 67 7 Concluding discussion ...... 68 7.1 The purpose of modeling – applicability of the bottom-up approach 68 7.2 Causes for concern ...... 71 8 Svensk sammanfattning ...... 73 9 Acknowledgments ...... 77 10 References ...... 78

Abbreviations

1P Proven reserves 2P Proven + probable reserves 3P Proven + probable + possible reserves b Barrel (= 159 liters) bcm Billion (109) cubic meters DCF Discounted cash-flow EIA Energy Information Administration (U.S. Department of Energy) EU European Union EUR Estimated ultimate recovery (equivalent to URR) Gb Giga (109) barrels GIIP Gas initially in place GOR Gas-to-oil ratio IEA International Energy Agency LNG Liquefied natural gas Mb Mega (106) barrels Mboe Million barrels of oil equivalents NGL Natural gas liquids NPD Norwegian Petroleum Directorate NPV Net present value OECD Organisation for Economic Co-operation and Develop- ment OIIP Oil initially in place OPEC Organization of the Petroleum Exporting Countries PIIP Petroleum initially in place RF Recovery factor R/P Reserve-to-production ratio URR Ultimate recoverable resource (equivalent to EUR) USGS U.S. Geological Survey

1 Introduction

[S]ince a large portion of the earth’s surface still remains entirely unculti- vated; it is commonly thought, and is very natural at first to suppose, that for the present all limitation of production or population from this source is at an indefinite distance, and that ages must elapse before any practical necessity arises for taking the limiting principle into serious consideration. I apprehend this to be not only an error, but the most serious one, to be found in the whole field of political economy. (John Stuart Mill, Principles of Political Economy, Book I, Ch. XII, Pt. 2-3)

The theme of this thesis is the physical depletion of petroleum (crude oil and natural gas). Given that petroleum is finite and non-renewable, what are the near-term implications of its depletion? To put it drastically, should we be concerned about an ‘end of cheap oil’ in the near future? Concern would obviously depend on a suspicion that it will be a considerable challenge to adjust the economy to a future of more expensive oil. By any measure, there is still more recoverable petroleum left than has been used up to this point, so concern would also depend on the counterintuitive notion that petroleum can become less available although remaining reserves are seemingly abun- dant and new discoveries are continuously being made.

1.1 Cheap energy and the industrial society No material human need can be satisfied without the use of physical work, and physical work requires access to ordered energy. In pre-industrial societies, the necessary work was mainly generated in the muscles of human la- borers and draft animals. The primary energy source was the incoming sun- light, chemically stored in edible plants and animals. The British industrial revolution and the development of steam engines during the 18th and 19th centuries initiated a dramatic shift in the use of energy. Allen (2009) argues that Britain’s unique combination of expensive labor and cheap energy from fossil coal was a necessary (although not sufficient) condition for the profitable development of steam engines and the subsequent mechanization of industrial production. As steam engines became more fuel efficient, they became profitable to use virtually everywhere. That coal had a special role in

11 the new industrial economy was recognized already by the economist Jevons (1866):

Coal in truth stands not beside but entirely above all other commodities. It is the material energy of the country—the universal aid—the factor in every- thing we do. With coal almost any feat is possible or easy; without it we are thrown back into the laborious poverty of early times.

The development of internal combustion engines and gas turbines created new uses also for oil and natural gas. The relatively low cost of energy compared to other factors of production made it possible and economically rational to transform the society. Technologies used in agriculture, industry and transportation are now designed to save presently scarce resources – human labor, space and time – by instead using large amounts of cheap energy.

Figure 1. The composition of the world primary energy supply in 2009 (percentages are based on heating value). Source: International Energy Agency, Energy Balances Database.

The share of fossil fuels in the world’s primary energy supply is around 80% (Figure 1). Oil and natural gas stand for more than half of the primary energy supply. In transportation, the reliance on oil is almost 100%. It is no coin- cidence that the world has become fossil-dependent. Fossil fuels, and particularly oil, have a number of attractive features (adapted from Hall et al., 2009):

12 High energy density (in relation to weight and volume) Transportable and storable Safe and relatively clean at the point of use High energy return on the energy invested in production Available for use at any time, almost anywhere, at almost any rate At present, there are no alternative energy sources that are competitive in all of these respects.

1.2 The end of cheap oil? There is a lively debate regarding the future availability and affordability of oil. This debate has two quite distinct camps. Those who are ‘concerned’ see a peak in oil production – and as a likely consequence the end of cheap oil – now or within a relatively near future (e.g. Aleklett and Campbell, 2003; Bentley, 2002; Campbell and Laherrère, 1998; Deffeyes, 2001). On the other hand, the ‘unconcerned’ see no availability problems in the foreseeable future (e.g. Maugeri, 2004; Odell, 2004; Odell, 2010; Radetzki, 2010). In the case of natural gas, concern revolves around regional supply issues rather than an immediate global production decline. Natural gas is still characte- rized by regional markets due to bottlenecks in the intercontinental distribution, although the growing trade in liquefied natural gas (LNG) is gradually making the gas market more globally integrated (Neumann, 2009; Siliverstovs et al., 2005). Concern about impending oil scarcity has been expressed at several times during the last century, most recently in the wake of the ‘oil crises’ of the 1970s, but the concerns have so far turned out to be premature (Lynch, 2002). This circumstance is not in itself a valid reason to categorically dis- miss the issue as irrelevant, but it is fair to ask what is different this time. A number of circumstances undoubtedly are different from the situation in the 1970s. Firstly, the oil price has risen dramatically since 2004 (Figure 2). In contrast to previous oil price shocks, which were, at least in part, associated with geopolitical events and threats of supply disruptions, the recent price surge appears to be mainly due to a combination of strong demand growth (particularly from China and India) and a stagnating global production (Hamilton, 2009; Kesicki, 2010).

Figure 2. Global oil production (crude and lease condensate) and the Brent spot price. Source: U.S. Energy Information Administration, Petroleum Navigator.

Figure 3. Columns: Norwegian North Sea oil discoveries (oil initially in place including unrecoverable oil, of currently producing fields, backdated to the year of discovery). Areas: production field by field. Line: the price of Brent crude. Discov- ery data: Norwegian Petroleum Directorate, Resource Account 31 December 2009. Production data: Norwegian Petroleum Directorate, Fact Pages. Price data: U.S. Energy Information Administration, Petroleum Navigator.

Secondly, there is now more empirical experience of how discoveries and production develop in oil producing regions over time. The Norwegian

14 North Sea, the most mature of the oil producing regions on the Norwegian Continental Shelf, is one example of a region where several large discoveries were made early. The majority of those large fields now have declining production, and the additional production from new fields is too small to fully compensate for the decline (Figure 3). Thirdly, since the 1970s there is a significant drop in both the number and average sizes of ‘giant’ oil and gas discoveries (containing more than 500 Mboe of initial reserves). The world’s giant fields, most of which were discovered several decades ago, contain the bulk of remaining reserves (Horn, 2007; Robelius, 2007). The above mentioned circumstances do not provide conclusive evidence that the end of cheap oil is imminent, but they indicate that the issue must be approached without preconceived notions. The present situation is in several ways different from previous episodes of concern.

1.3 Reconciling natural science and economics – a bottom-up approach The debate around the future availability of oil and gas is important. It has, however, hitherto been less fruitful and constructive than it could be, for several reasons. Firstly, the debate has tended to revolve around the merits and drawbacks of one particular simple forecasting model proposed by the petroleum geologist Hubbert (1956; 1982). This model is described in some detail in section 5.1.1. Although discussion of the Hubbert model is certainly justified in its own right, debating one particular model will not provide an adequate an- swer to the most relevant question – whether there is reason to be concerned or not. It is of course possible to be skeptical about the Hubbert model and its predictions, and still find other reasons to be concerned. Secondly, the debate has to an excessive degree been focused on production forecasts and the exact timing of the peak. From an economic point of view, the future price is more relevant than the peak in production. The peak is a symptom of a change in the relation between supply and demand, but it is not synonymous with the end of cheap oil. The price might rise although production is still increasing. It is even conceivable that diminishing demand would cause a peak and decline in production without any price increase. The ‘concerned’ have not been able to convincingly formulate the threat of depletion in economic terms. Thirdly, the debate is often described as a controversy between natural scientists (particularly geologists) and economists (Mills, 2008). Indeed, there is a tendency that ‘concerned’ analysts are geologists or other natural scientists (Aleklett and Campbell, 2003; Campbell and Laherrère, 1998;

15 Deffeyes, 2001; Hubbert, 1956), while the ‘unconcerned’ are economists (Adelman and Lynch, 1997; Gordon, 2009; Lynch, 2003; Odell, 2010; Radetzki, 2010; Simon, 1996; Watkins, 2006). The attitude of each side to- wards the other often appears intransigent, sometimes even contemptuous. It would, however, be a mistake to interpret the controversy as a clash of scientific disciplines. The views and assumptions of ‘concerned’ and ‘unconcerned’ are often only vaguely related to geology or economics. For example, although Hubbert was a geologist, his model is a simple mathematical function with no explicit foundation in geological or physical principles. Likewise, one prominent ‘unconcerned’ analyst, the economist Simon (1996), reaches the conclusion that oil (and other natural resources) will become less scarce indefinitely by referring to historical price trends. What he calls the “economist’s approach” is thus nothing more than naïve trend extrapolation. We argue that the current lack of a common understanding between ‘concerned’ and ‘unconcerned’ is both harmful and unnecessary. Reconciling geological and economical views is not only feasible – it is also a scientific project that should have a high priority. One likely reason for the present lack of a common understanding of depletion is the prevailing ‘top-down’ perspective that focuses on aggregate numbers and models, having little or no connection to the decisions occurring at the micro-level. In contrast, in the production from an individual petroleum reservoir and in the exploration for new reservoirs, physics, geology and economics are intertwined. Physical and geological factors enter as parameters and constraints in the producer’s economic optimization problem. Few economists would probably deny that the physics of reservoirs is relevant for production decisions, and few natural scientists would question that petroleum production occurs in the first place because of economic motives. Forming a common understanding of depletion would likely have to start at the micro-level. ‘Bottom-up’ modeling therefore holds promise as an analytical approach.

1.4 Aims and disposition The appended papers treat a number of issues relating to the depletion of oil and natural gas. All except Paper I have a micro-level perspective where individual fields are the units of analysis. Scenarios are constructed using bottom-up approaches. The specific aims of the papers are as follows: Paper I: Critically examine top-down scenarios of global oil production generated by the EIA. Paper II: Construct scenarios of regional oil production with a bottom-up model incorporating both geologic and economic factors. Paper III: Review existing bottom-up models and perform sensitivity analysis.

16 Paper IV: Simulate exploration, success rate and expectations with a bottom-up model to investigate the role of exploration in false perceptions of decreasing scarcity. Papers V and VI: Construct bottom-up scenarios of future natural gas production in Norway and Russia, and evaluate implications for future exports to the EU. Paper VII: Empirically investigate the production profiles of giant oil fields. The remainder of the thesis has the following disposition. Chapters 2-5 provide a theoretical background to the appended papers. Chapter 2 treats the issues related to the reporting of petroleum reserves and resources. Chapter 3 describes reservoir dynamics and how it relates to the producer’s choice of production profile. Chapter 4 treats models of exploration, discoveries and estimation of yet undiscovered resources. Chapter 5 discusses top-down and bottom-up production forecasting approaches. Chapter 6 summarizes the results of appended papers. Chapter 7 contains a concluding discussion on production modeling and the reasons for concern about future oil availability. A thesis summary in Swedish can be found in chapter 8.

17 2 Resources and reserves

2.1 Conventional petroleum accumulations Petroleum consists of hydrocarbons formed from fossil organic matter, primarily plankton, which has been buried in sediments and formed a source rock. The high temperature at large depths has induced the formation of liquids and gases. Due to its low density, the petroleum has then migrated to- wards the surface. In the cases where there has been a trap (an impermeable layer), the petroleum has not reached the surface but instead settled in the voids of a porous reservoir rock, thus forming an accumulation (Bjørlykke, 2010). This thesis will focus on conventional petroleum, which is geologically defined as occurring in discrete accumulations bounded by a down-dip water contact and being significantly affected by the buoyancy of petroleum in water (USGS, 2000). In addition to conventional petroleum, the earth contains large amounts of unconventional petroleum in continuous-type deposits. Examples are shale gas, gas hydrates, oil shale and tar sands. The spatial distribution of continuous-type deposits is different from conventional accumulations, and they require other recovery techniques. A few important concepts will be used throughout the thesis with the following definitions, which are adapted from the U.S. Geological Survey (2000) and Klett (2004): Reservoir: An isolated oil or gas accumulation with a single natural pressure system. Field: A production unit consisting of one or several reservoirs related to a single geological feature. Play: A set of known or postulated oil and gas accumulations shar- ing similar geologic, geographic, and temporal properties, such as source rock, migration pathway, timing, trapping mechanism, and hydrocarbon type. Since oil and gas have a common origin, they often occur together in the same field. Whether a certain field is considered an oil or gas field depends on the gas-to-oil ratio (GOR). The USGS defines an oil field as having a GOR of less than 20,000 cubic feet ( 570 m3) of gas per barrel of oil.

18 2.2 Reserve estimation and classification The terms ‘reserve’ and ‘resource’ have particular meanings in petroleum assessments, and the distinction between them is fundamental. Reserves are the subset of remaining petroleum in the earth’s crust that is both known and judged to be recoverable under the current economic circumstances. The amount of reserves is, in other words, determined by a combination of geological, technological and economic factors. The term ‘resources’ or ‘resource base’, on the other hand, might either refer to all existing petroleum (including reserves), or only to the fraction that is not currently reserves. Since only petroleum that is both known and economic will be produced, current remaining reserves are the only source of current production. Re- maining reserves might be seen as an in-ground inventory that is being depleted through production but at the same time ‘replenished’ through the inclusion of previously unknown or unrecoverable resources (Adelman, 1990). The ultimately recoverable resource (URR) is the estimate of the initially recoverable amount, and is therefore the sum of remaining reserves and historical cumulative production. The term estimated ultimate recovery (EUR) is sometimes used synonymously. The determination of URR for a reservoir begins with an estimation of the amount of petroleum initially in place (PIIP). When referring specifically to oil or gas reservoirs, the abbreviations OIIP and GIIP are used. PIIP can in principle be estimated volumetrically (Jahn et al., 1998):

ShAPIIP (1) where PIIP = petroleum initially in place [m3] A = areal extent of the reservoir [m2] h = reservoir thickness [m] = reservoir rock porosity [%] S = saturation of petroleum in reservoir fluid [%]

More detailed estimations of PIIP are necessary if there are large variations in some parameter, e.g. porosity, within the reservoir. Only a certain percentage of the PIIP is technically and economically recoverable. The URR can therefore be expressed as:

RFPIIPURR (2) where RF is the recovery factor [%]. The RF, which depends on how effi- ciently the petroleum is displaced during production, can be estimated by comparison to analogous reservoirs with similar geophysical properties, by reservoir simulation, or by analysis of production performance (SPE, 2007).

19 RF is affected by both the natural properties of the reservoir and the production strategy applied. In practice, the URR is only a point estimate of the initial reserves, since both PIIP and RF are subject to considerable uncertainty, particularly when no production has yet occurred. There are two approaches to accounting for this uncertainty. The deterministic approach consists of calculating a number of estimates, typically low/best/high estimates, of URR from judgmentally derived values of the geophysical parameters. The characterizations of the estimates are qualitative and often rather vague: the low estimate is attainable with ‘reasonable certainty’, while the best estimate is ‘more likely than not’ to be attained. In the probabilistic approach, probability distributions are instead assigned to the parameters and the resulting probability distribution for the amount of reserves is obtained with Monte Carlo simulation. Low/best/high reserve estimates will in this case refer to fractiles of the probability distribution (see Figure 4). For example, ‘P90’ is a low estimate that will be exceeded with 90% probability. When reserve figures from several reservoirs are aggregated only the mean values (should be distinguished from P50, which is the median) yield an unbiased estimate. It is not generally true that the sum of e.g. P90 estimates for individual reservoirs equals the correct P90 estimate for the same reservoirs taken as an aggregate.

Figure 4. Example of probabilistic reserve estimation. P90 indicates that the estimate is expected to be exceeded with 90% probability, etc.

There is no universally adopted reserve classification system, but the international oil industry tends to use the terminology developed jointly by Society of Petroleum Engineers, American Association of Petroleum Geologists, World Petroleum Council, and Society of Petroleum Evaluation Engineers

20 (SPE, 2007). This classification system (Figure 5) categorizes reserves as being either ‘proven’, ‘probable’ or ‘possible’, and the low/best/ high estimates are labeled ‘1P’ (proven), ‘2P’ (proven+probable) and ‘3P’ (proven+probable+possible). These estimates might be arrived at either with deterministic scenarios or probabilistic computations. In the latter case, the three estimates should correspond to P90, P50 and P10 respectively. Several countries, for example Norway and Russia, require reporting of reserves according to other definitions which are not immediately transferrable to the SPE terminology.

Cumulative production

Reserves

Commercial Commercial 1P 2P 3P Proven Probable Possible

Contingent resources Discovered PIIP

Unrecoverable Sub-commercial

Prospective resources Total petroleum initially in place (PIIP) (PIIP) in place initially Total petroleum

Unrecoverable Undiscovered PIIP

Figure 5. Example of a petroleum resource classification system. Adapted from SPE (2007).

21 2.3 Reserve growth Additions to reserves can either occur through the discovery of new fields or through ‘reserve growth’, meaning that URR estimates (not necessarily remaining reserve estimates) of already discovered fields are increasing. In recent years, reserve growth has stood for the major part of global reserve additions (Klett et al., 2007). What is uncertain is the relative importance of contributing factors and consequently the amount of reserve growth to expect in the future. Reserve growth might occur for a number of reasons (Thompson et al., 2009): Geology: improved knowledge about reservoir size and properties leads to revisions of PIIP and RF. Technology: improved recoverability and lower costs increase the attainable RF. Definitions: reporting units are merged; deliberately conservative initial estimates (e.g. 1P) are revised upwards. Models intended to forecast future reserve growth typically do not attempt to quantify the contribution of each factor, but rather treat the estimated URR as a simple function of time since discovery (Arrington, 1960; Attanasi and Root, 1994; Klett, 2005; Root and Mast, 1993; Schmoker and Crovelli, 1998; Verma, 2005). More specifically, based on historical reserve figures the models empirically estimate growth multipliers G(a,t) for fields presently of age a, t years into the future:

taddE ),( taG ),( d addE ),( d (3) where E(d,e) is the URR for all fields discovered in year d, estimated in year e. For example, according to the USGS’s (2000) model, the URR of a newly discovered field is expected to grow six-fold in 30 years’ time (G(0,30) = 6), and the bulk of this growth is expected to occur during the first ten years after discovery (see Figure 6).

Figure 6. Reserve growth function as assumed by USGS (2000). The 30-year growth multiplier indicates by what factor URR will grow from the present estimate in 30 years time, depending on the present age of the field. For example, the URR of a field discovered 15 years ago is expected to grow by approximately 50% during the next 30 years, relative to the present URR estimate.

A major subject of debate is how much of the reserve growth that can be attributed to ‘genuine’ improvements in knowledge and technology as op- posed to definitional factors such as the reporting of 1P instead of 2P estimates. The 1P estimate (including cumulative production) is of course very likely to grow over time as a field is depleted (to be more precise, it should grow in 90% of the cases if the probabilistic model is correct), while the 2P figure should give a more accurate picture on average. The fact that the USGS reserve growth model was calibrated on reserve data from the U.S. is cause for some concern, since it has been argued that the substantial growth in U.S. reserves is largely an artifact of an unusually conservative reserve definition and therefore not representative of the world as a whole (Laherrère, 1999). Before the rules were made less restrictive in 2010, the U.S. Securities and Exchange Commission required that U.S. oil companies only reported ‘proven reserves’ according to a definition roughly similar to 1P, in order to minimize the risk that companies would overstate their physical assets (SEC, 2009). Klett and Schmoker (2003) found in a study of 186 non-U.S. giant oil fields that the USGS model still had a good fit in the period 1981-1996 despite the fact that remaining reserves were the proprietary 2P figures compiled by the industry consultancy firm Petroconsultants/IHS. However, although the aggregate URR increased by a significant 26% in 15 years, the data does not give much support to the assumption of several-fold

23 increase in the first ten years since 159 of the 186 fields, standing for 88% of the reserve growth, were discovered before 1972 and thus older than ten years at the beginning of the period. Several studies of reserve growth in the North Sea (Klett and Gautier, 2005; Sem and Ellerman, 1999; Watkins, 2002) indicate that growth in the first ten years is far less dramatic than the USGS model assumes. Watkins (2002) reports that 80 fields in the UK sector of the North Sea with an average production life of 9.3 years grew by 23%, while the figure was 46% for the Norwegian sector (29 fields, 9.7 years of production on average). The less dramatic growth could be the result of a less conservative reserve definition, later publication of the initial estimate or improved technical ability to make good early assessments. Re- gardless of the causes, it points to the conclusion that reserve growth of several hundred percent is not a universal phenomenon. However, this does not negate the fact that reserve growth is an important phenomenon.

2.4 Global URR estimates Over the decades, many estimates of the global URR have been published. It is often difficult to make meaningful comparisons, since authors have defined the assessed resource differently. Sorrell and Speirs (2009) have compiled about 100 URR estimates for oil published between 1942 and 2008. Probably the most authoritative and widely cited estimates for conventional oil and gas are those of the USGS World Petroleum Assessment 2000. The probabilistic numbers are not URR estimates in a strict sense, since the assessment was constrained to resources that had the potential to be added to reserves within a 30-year perspective (1996-2025), a time-frame intended to reflect the choice not to consider possible impacts of technological paradigm shifts. The assessment included both reserve growth in known fields (estimated with the type of model described in section 2.3) and undiscovered resources (estimated according to a procedure described further in section 4.6). Table 1 summarizes the mean estimates for oil and NGLs, Table 2 for natural gas.

24 Table 1. Mean estimates of global URR for petroleum liquids (Gb). Adapted from Sorrell and Speirs (2009). U.S. total World (except World (except World total liquids U.S.) oil U.S.) NGLs liquids As of 1 Jan 1996: Cumulative production 171 539 7 717 Remaining 2P reserves 32 859 68 959 Reserve growth 76 612 42 730 Undiscovered 83 649 207 939 Estimated URR 362 2659 324 3345 Cumulative production 432 1996-2010 Estimated depletion level 34% (total cumulative production / URR) Sources: Estimates as of 1 Jan 1996 from USGS (2000), production 1996-2010 from IEA Oil Information Statistics Database.

Table 2. Mean estimates of global URR for natural gas (billion m3). U.S. World (except World total U.S.) As of 1 Jan 1996: Cumulative production 24183 25429 49611 Remaining 2P reserves 4870 130852 135723 Reserve growth 10052 93587 103640 Undiscovered 14923 132211 147134 Estimated URR 54028 382079 436107 Cumulative production 1996-2010 40854 Estimated depletion level (total 21% cumulative production / URR) Sources: Estimates as of 1 Jan 1996 from USGS (2000), production 1996-2010 from IEA Natural Gas Information Statistics Database.

2.5 Reserve interpretation caveats As the above discussion may indicate, interpreting reserve figures is far from straightforward. It is necessary to know which classification system is used since the term ‘proven reserves’ occurs in several systems with different definitions. It is also necessary to know whether the figure in question is a low, best or high estimate. An additional complication is that much of the

25 publicly available reserve data is of questionable quality. The annual sum- maries of global reserve figures published by Oil & Gas Journal and BP Statistical Review of World Energy are compiled from other sources and are not audited for consistent quality. The official ‘proven’ reserves of several OPEC countries have been questioned on the grounds that they have been dramatically revised upwards in a seemingly arbitrary way, have remained at exactly the same level for several years, and are in some cases larger than the 2P reserves reported in industry databases (Bentley et al., 2007). Apparent arbitrary reporting of OPEC reserves is not in itself a proof that the figures are overstated, but the lack of reliability and transparency is problematic since the great majority of the world’s official reserves are in OPEC countries (Figure 7).

Figure 7. World ‘proven’ reserves. Source: BP Statistical Review of World Energy, various issues.

However, the most important caveat in interpreting reserve figures is the fundamental distinction between reserves – a stock measure, and production – a flow. Petroleum availability is not only about the existence, or non- existence, of large reserves. The practice to report so-called reserve-to- production ratios (remaining reserves divided by current annual production) is insidious, since it encourages the interpretation that reserves are a homogeneous aggregate which can be depleted at any arbitrary rate until it sud- denly ‘runs out’. At any point in time, the bulk of remaining reserves are in fields that already produce at a constant or declining rate, determined by geology and economics (see chapter 3). The ability of current reserves to support increased production is therefore limited. For the same reason, a

26 historically increasing reserve trend should not be interpreted as evidence that production will increase in the future.

27 3 Production

We will adopt the established industry terminology and refer to petroleum extraction as ‘production’. This term is somewhat controversial since it has been interpreted by some as a euphemism used to gloss over the fact that a non-renewable resource is being depleted. However, when ‘production’ is formally defined as any activity that adds value (Shackle, 1970), then the term is technically correct. The value added during petroleum production is reflected in the significantly higher price paid for a barrel of oil in a tank compared to the same barrel in-ground.

3.1 Reservoir dynamics The following section is based on Bjørlykke (2010), Ahmed (2006), Slider (1976) and Jahn et al. (1998). Under natural conditions, the reservoir is a system in approximate equilibrium. The reservoir fluids (oil, gas and water) are stratified in horizontal layers according to their respective densities (Figure 8).

Figure 8. Schematic view of the initial fluid configuration in a reservoir that contains both oil, free gas and a water aquifer. Adapted from Bjørlykke (2010).

The oil saturation (the percentage of oil in the rock pores) is not 100% in the oil column, since there is usually a certain saturation of connate water. The gas-oil and oil-water contacts are not distinct as they would be in a tank, since capillary forces in the rock pores yield a transition zone where the satu-

28 ration changes gradually with depth. One definition of the oil-water contact is the level below which the oil saturation is zero. Similarly, the gas-oil contact may be defined as the level below which no free gas occurs. There is, however, often gas dissolved in the oil under the natural reservoir pressure. Conventional petroleum is produced through wellbores drilled into the reservoir. If the natural reservoir pressure is high enough, fluids initially flow spontaneously to the surface. As fluid is removed from the reservoir, pressure will decline in the vicinity of the wells and a pressure gradient across the reservoir is created. The remaining fluids will then flow toward the lower pressure. Darcy’s law is an empirically derived equation for the linear non- turbulent horizontal flow rate of a fluid through a porous medium:

pp )( Aq 21 L (4) where q = fluid flow rate [m3/s] A = cross-sectional flow area [m2] = absolute reservoir rock permeability [m2] = fluid viscosity [Ns/m2] 3 (p1 – p2)/L = pressure gradient over distance L [N/m ]

Darcy’s law only strictly applies to incompressible fluids (meaning that the fluid density does not change with pressure). In reality, all fluids are at least slightly compressible, but equation (4) works as an approximation for oil and water flow. Since gas is highly compressible, a certain flow rate (measured by volume) at different pressures does not represent the same amount of gas molecules. The linear flow equation for gas therefore becomes:

2 2 1 ppA 2 )( qg TzL (5) where 3 qg = gas flow at standard pressure and temperature [m /s] T = reservoir temperature [K] z = compressibility factor [ratio]

For an ideal gas holds that z = 1. Darcy’s law is also only directly applicable in the case of a single fluid phase (e.g. pure oil or pure water). When oil and water flow together, the flow rate for each phase is instead determined by its effective permeability, which is the product of the absolute permeability (a property of the reservoir rock) and a relative permeability for the phase:

29 o ro

w rw (6) The relative permeabilities ro and rw depend on the oil/water saturations in a non-linear manner (Figure 9). This implies that the fraction of oil in the produced liquid is not equal to the oil saturation in the producing part of the reservoir. During production from a reservoir with a water drive, the water will gradually displace the oil. The water saturation will increase up to the critical point where the relative permeability of oil is zero and only water is produced. The remaining residual oil is unrecoverable. The way in which water displaces oil is influenced by the relative mobility of the two liquids, expressed as the mobility ratio:

mobility ratio wrw oro (7) where w and o are the viscosities of water and oil respectively. When the mobility ratio is greater than one, water will tend to move preferentially through the reservoir and may circumvent the remaining oil. This is clearly undesirable from a production perspective since the water cut (the fraction of water in the produced fluid) increases and circumvented oil might be permanently trapped. In a similar way, free gas from an overlying gas cap might circumvent the oil from above. It is possible to avoid unfavorable displacement, even when the mobility ratio is greater than one, by producing at a slow rate since the gravity force will then dominate over the viscous forces influenced by the mobility ratio. The gravity force will keep the fluids stratified according to density. The fact that the amount of recoverable oil depends on the production rate has given rise to the concept of a maximum efficient rate (MER) of production, above which the amount of permanently trapped oil is significant (McKie and McDonald, 1962).

Figure 9. Relative permeabilities of oil and water as functions of the water saturation. Adapted from Bjørlykke (2010).

As fluids move toward the wellbores, the remaining fluids expand to fill the void. This expansion provides a number of natural drive mechanisms: Depletion drive: Oil expands as pressure declines. Since the compressibility of oil is low, this expansion is moderate and pressure drops significantly even after a small amount of production. Dissolved gas drive: When pressure has declined to the so-called ‘bubble point’, gas dissolved in the oil becomes liberated and expands. Gas cap drive: Free gas expands above the oil column. Since gas is compressible, pressure declines only slowly with cumulative production. Water drive: Water from an aquifer expands into the oil column. A relatively large aquifer is required, since water has a low compressibility. Pressure might be maintained, but the fraction of water in the produced fluid eventually increases. Primary recovery means that production occurs only through the natural drive mechanisms (several mechanisms may be active simultaneously). The only parameter the producer controls is the flow area (determined by the number of wells). However, as is indicated by Darcy’s law, there are several other parameters that can be manipulated in order to increase flows. Secondary recovery usually refers to manipulation of the pressure gradient. The reservoir pressure can be artificially maintained through injection of water or gas through designated injection wells. The bottom-hole well pressure can be lowered through pumping or, in the case of gas production, though installation of compressors.

31 Tertiary (enhanced) recovery involves altering the chemical properties of the oil and/or the displacing fluids. For example, the viscosity of heavy oil might be reduced with steam injection, or the viscosity of displacing water might be increased with polymer injection in order to lower its mobility and achieve a more favourable displacement pattern. One important implication of reservoir dynamics is that production results in gradually declining productivity. The direct cause is either declining pressure which leads to a lower flow rate, or increasing fractions of unwanted fluids (primarily water, but also gas if there is no nearby market for it). The declining productivity of a given number of wells (i.e. a given flow area) can be illustrated with simple reservoir simulation. Physical models of reservoirs can be more or less detailed depending on the purpose. The simplest variant is a ‘zero-dimensional’ or ‘tank’ model, in which it is assumed that all parameters (pressure, permeability, etc.) are homogeneous throughout the reservoir (see e.g. Beale, 1983; McFarland et al., 1984). We here present two simple but representative examples. In the first example, gas is produced with gas expansion as the only drive mechanism. This is quite typical of production from gas reservoirs. If the gas is approximately ideal (z = 1), the flow area A, permeability , temperature T, viscosity and length L are constant, then the flow (measured at standard pressure and temperature) is obtained from equation (5):

22 g 1 ppKq wr )( A (8) K 1 LT where pr = reservoir pressure pw = bottom-hole well pressure (constant)

The pressure decline in the reservoir is given by the ideal gas law (note that qg is proportional to the number of gas molecules):

dp r qK dt 2 g (9) RT K 2 V where V = reservoir volume (constant) R = gas constant

A numerical result is shown in Figure 10.

32 The second example is oil production with a strong water drive (which may occur naturally or through water injection). The reservoir pressure is assumed to be constant. The fractional flows of oil (qo) and water (qw) are given by:

ro o Kq 3 o

rw w Kq 3 (10) w ppA )( K wr 3 L The relative permeabilities are functions of the water saturation Sw (which is normalized to lie on the interval where both oil and water have positive permeabilities, see Figure 9):

S )1( 2 ro w (11) 2 rw 6.0 Sw All the liquid produced is replaced by an inflow of an equal amount of water. Therefore the water saturation increases at the rate of oil production relative to the initial amount of recoverable oil Ro(0):

dS q w o (12) dt Ro )0( A numerical result is shown in Figure 10.

Figure 10. Declining productivity for a given number of wells (i.e. a given flow area) in the cases of gas depletion drive and water drive. Note that during water drive, the total liquid production is not constant despite constant pressure, since the sum of the relative permeabilities of oil and water is not unity. Parameters for the gas depletion drive case: K1 = 0.1, K2 = 0.1, pw = 0, pr(0) = 10. Parameters for the water drive case: K3 = 10, o = 1, w = 1, Sw(0) = 0, Ro(0) = 100.

3.2 Production optimization In the development and production phases of a petroleum project, many design and operational choices must be made. These include the proper recovery techniques, number of production and injection wells, location of wells, timing of drilling, installed capacity of processing, storage and distribution facilities, production and injection rates, and timing of decommissioning (Jahn et al., 1998). These choices are all made with the aim of maximizing the net present value (NPV) of the project as a whole. The actual optimization problem faced by a producer is of course very complex. This is reflected in the voluminous literature on design and operations optimization under various technical and reservoir conditions (see e.g. Aboudi et al., 1989;

34 Amit, 1986; Barnes et al., 2007; Barnes et al., 2002; Elgsæter et al., 2010; Frair and Devine, 1975; Goel and Grossmann, 2004; Gunnerud and Foss, 2010; Haugen, 1996; Haugland et al., 1988; Iyer et al., 1998; Jonsbråten, 1998; Lee and Aronofsky, 1958; Ulstein et al., 2007; van den Heever et al., 2000). Although the producer’s optimization problem is complex when all technical details are considered, it can be explained quite simply in general terms. The NPV is the sum of annual net cash-flows over the lifetime of the project, adjusted by the producer’s discount rate:

T CFt NPV t t 1 r)1( (13) where T = expected decommissioning time CF = annual net cash-flow r = discount rate.

Positive cash-flow consists of the sales revenues, which are determined by production rates and the oil price. Since revenues are only generated as petroleum is produced and sold, if the producer were not limited by any other considerations, he would prefer to produce all the petroleum immediately in order to minimize the discounting of future revenues (this presupposes that the producer does not expect the price to increase faster than the discount rate). It is certainly technically possible to produce very rapidly in most circumstances. However, it requires a large capital investment. A smaller capital investment would suffice if the petroleum were instead produced at a lower rate. To weigh a rapid realization of revenues against a low capital investment is therefore the producer’s optimization problem in a nutshell. Consequently, maximizing NPV is not the same thing as maximizing production. Nor is it the same thing as maximizing ultimate recovery. It is conceivable that a new technology will be adopted despite actually decreasing recovery, if it enables a higher initial production rate. The production profiles observed in reality might be interpreted as the producer’s optimal re- sponse to the declining productivity of the reservoir, the market price and capital and operating costs. Fiscal costs (taxes, royalties, etc.) represent a significant negative cash-flow, but whether they tend to accelerate, postpone, or leave the production profile unaffected depends on the structure of the fiscal system. Figure 11 shows a schematic production profile for a petroleum project. After a discovery has been made, there is a period of appraisal activity to determine whether the discovery is profitable to produce. If a development decision is made, there is a certain lead-time before the initia- tion of production. The production itself can be divided into three phases: an initial build-up period, a plateau, and a decline. Decommissioning will occur

35 when the revenues no longer cover the operating costs. Figure 12 shows two examples of oil production profiles from the Norwegian North Sea.

Figure 11. Schematic production profile for a petroleum project. Adapted from Jahn et al. (1998)

Figure 12. Examples of oil field production profiles as shares of initial recoverable resources. Oseberg (producing 1986-present) has an estimated initial recoverable resource of 2372 Mb, Cod (producing 1977-1998) of 18 Mb. Source: Norwegian Petroleum Directorate, Fact Pages.

36 Historical data indicates that the production profile varies with the size of the field. Large fields tend to have a longer plateau and a slower decline than small fields (IEA, 2008).

3.3 Economic theory of non-renewable resource production There is not one homogeneous view among economists regarding the proper way to analyze non-renewable resources. There is, on the one hand, a ‘subjectivist’ tradition (Bradley, 2007) pioneered by Zimmermann (1933, 1951), which emphasizes the dynamic process of resource creation:

Resources are not, they become; they evolve out of the triune interaction of nature, man, and culture, in which nature sets outer limits, but man and culture are largely responsible for the portion of physical totality that is made available for human use. (Zimmermann, 1951)

The subjectivist view stresses that the definition of a resource depends on current needs and technical capabilities. For example, it has been argued, before the development of combustion engines oil was merely a useless black liquid, not a resource in any economic sense (Rothbard, 1974). A subjectivist view does not necessarily lead to the conclusion that resource scarcity is impossible; it merely doubts the meaningfulness of making long-term analysis of resource availability under the assumption that society will not change its definition and valuation of resources over time. On the other hand, the analytical tradition within mathematical economics often referred to as the ‘theory of exhaustible resources’ takes the economic value and non-renewable nature of the resource as given. However, also within the analytical tradition it is possible to distinguish two different approaches (Cairns, 1994). The more famous one focuses on how the equilibrium price (and by consequence the aggregate production rate) develops over time in a non-renewable resource market. The starting point is a paper by Hotelling (1931). The basic insight of the paper is that a resource in- ground is a capital asset to the owner, and by producing and selling one unit of the resource today the owner loses the opportunity to sell the same unit later. In addition to the direct marginal production cost, the owner must therefore also consider the ‘user cost’ of foregoing future incomes. Hotelling showed, in a simple example, that competitive market equilibrium required the net price (market price minus marginal production cost) to increase at the producers’ rate of discount, which is taken to equal the general interest rate r. This result, which has been called the ‘Hotelling r-percent rule’, is illustrated in Figure 13. It is important to note that increasing net price does not necessarily mean increasing market price, since the production cost might

37 decline over time due to technological development. It is then possible to have a U-shaped market price path (Slade, 1982). However, the Hotelling r- percent rule in its original form rests on a number of strong assumptions: The marginal production cost does not change with cumulative production Each producer knows the total size of the resource, including the resource owned by others Each producer foresees the demand at any price level at every mo- ment in time (or equivalently, there is a complete futures market until the time of exhaustion) Each producer foresees future technological development and its impact on cost The first assumption does not hold in the petroleum industry, because of declining productivity. However, Hotelling did adjust the rule for a scenario where cost increases with cumulative production. The other assumptions are problematic since they imply that producers have unreasonable amounts of information. For example, in reality the true resource size is only gradually revealed through exploration, and even if producers do consider the total resource size in their decisions, the available information might be biased (see the result of Paper IV). Subsequent extensions of Hotelling’s original model suggest that when these strong assumptions are relaxed, the r-percent rule has no clear-cut implications for price and production (for literature reviews, see e.g. Devarajan and Fisher, 1981; Krautkraemer, 1998). Perhaps unsurprisingly, several studies have concluded that the r-percent rule lacks support in empirical data from the petroleum industry. One specific example is that oil companies do not value reserves in-ground as highly as they should according to the rule (Adelman et al., 1991; Cairns and Davis, 1998, 2001; Livernois, 2009; Watkins, 1992). The second approach within the analytical tradition, with roots in two papers by Gray (1913, 1914), is not concerned with market equilibrium, but instead with the individual producer’s optimizing behavior. Gray postulated a producer with a U-shaped marginal cost function who makes production decisions based on the expected market price. His conclusion was that a rational producer would adjust production so that the difference between the market price and the marginal cost would increase at the rate of interest r (see Figure 13). Obviously the ‘Gray r-percent rule’ is conceptually very similar to the Hotelling rule (Brazee and Cloutier, 2006; Cairns, 1994; Crabbé, 1983). However, in Gray’s version of the rule the producer need not know the size of the total resource or the demand function, but only his own cost function and the size of his own resource. He might forecast the future market price according to a simple rule of thumb (in Gray’s example, the producer expects a constant price). Gray also speculated that the need for fixed capital would encourage the producer to choose an initial constant

38 plateau production level; an intuition that has later been confirmed analytically (Cairns, 1998, 2001; Campbell, 1980). The so-called ‘micro-micro’ perspective (Cairns, 1994) that has developed along the lines of Gray’s initial study makes more reasonable assumptions regarding the knowledge of producers than the market equilibrium perspective represented by Hotelling. Thereby it also to a large extent avoids the ‘subjectivist’ critique that society’s future valuation of resources may change, since it analyzes production based on what the producers expect of future market conditions rather than the actual outcomes. For these reasons we have adopted the ‘micro-micro’ instead of the market equilibrium perspective in our bottom-up economic modeling (Paper II).

Figure 13. Comparison of the analytical approaches of Hotelling (1931) and Gray (1914). In both cases the size of the resource is 100 units and the rate of interest r = 10%. Hotelling’s simplest model assumes that the market price equals the user cost rt (there is no production cost) and increases with the rate of interest: p0e . Producers face a downward-sloping demand function. Optimality requires that p0 is adjusted so that the resource is exhausted precisely when demand reaches zero. In Gray’s model, the price is constant and the producer has a U-shaped marginal cost function (the same function at every time step). Optimality requires that the difference between price and marginal cost increases at the interest rate. The producer therefore chooses a production schedule that exhausts the resource precisely when the marginal cost is minimal.

40 4 Exploration and discoveries

4.1 The purposes of exploration One direct incentive to explore, from the perspective of a private firm, is to increase reserves by discovering new reservoirs. However, reserves can also be increased through investment for enhanced recovery in existing fields or through direct purchase of reserves in-ground, so it is only motivated for a firm to explore if the expected NPV (adjusted for risk) per barrel of reserves in new discoveries is at least as large as for reserves added by alternative means (Adelman, 1970). Reserve additions through exploration and estimation of the amount of undiscovered resources are here treated in parallel, since the same models are often used for both purposes. Exploration can be described as a sequence of activities done in order to obtain information (Benkherouf and Bather, 1988; Bjørstad et al., 1989; Harris, 1990). Survey techniques (gravimetric, magnetometric and seismic) are used to identify sedimentary basins, potential reservoir rocks and traps (Jahn et al., 1998). If a promising prospect is identified, an exploration well (‘wildcat’) is drilled. Drilling is the most expensive exploratory activity, but also the only way to confirm the presence of petroleum. The number of wildcats drilled is often used as a proxy for the level of exploratory effort. It has been observed that exploratory effort responds positively to oil price increases (Mohn, 2008; Mohn and Osmundsen, 2008; Ringlund et al., 2008). The recent surge in exploratory drilling in the Norwegian North Sea (Figure 14) might be a result of the high oil price, but possibly also of recent policy measures (new acreage licensing since 2003 and tax rebates since 2005) intended to promote exploration (Valente, 2011). A byproduct of exploration is information, which might serve to increase the efficiency of future exploration (Cairns, 1990; Gilbert, 1981; Reynolds, 1999). Some economists have put emphasis on exploration’s role as a way to obtain better knowledge about the total size of the resource (Mason, 1985; Quyen, 1991; Swierzbinski and Mendelsohn, 1989). The reason for this emphasis is that the resource size is an important parameter in Hotelling’s (1931) market equilibrium model. However, the result of Paper IV puts into question the assumption that exploration would provide unbiased information about the resource size, if firms are simultaneously trying to maximize the yield per exploratory effort.

Figure 14. Exploratory activity in the Norwegian North Sea as measured by the number of wildcats drilled. Source: Norwegian Petroleum Directorate, Fact Pages.

4.2 Size-frequency distribution of fields The size-frequency distribution – the number of existing fields and their respective sizes in terms of petroleum content – is a fundamental factor that enters discovery and resource assessment models either directly or indirect- ly. A general observation is that the distribution both globally and within smaller regions is highly skewed: there are many small fields and few large ones. The distribution however has a ‘fat’ right tail: despite the small number of large fields, they are large enough to contain a major proportion of the URR. At the global level a few hundred ‘giants’ out of tens of thousands of known oil fields dominate both URR and production (IEA, 2008; Robelius, 2007). When the appropriate analytical form for the size-frequency distribution was first considered, the lognormal distribution seemed to fit available data from petroleum plays (Arps and Roberts, 1958; Kaufman, 1963). The lognormal is a skewed distribution with a mode representing the most common field size. It has later been argued that the apparent lognormal shape is an artifact of two types of biases in the data generation: Sampling bias: since small fields cover a smaller area, they are less likely to be discovered and therefore will be underrepresented. The sampling bias decreases gradually, but may cause a persistent ap- pearance of a lognormal distribution (Power, 1992). Economic truncation: explorers might not care to appraise and report a discovery if they suspect that it is too small to be commercial.

42 This truncation shifts with technological development and economic circumstances (Attanasi and Drew, 1985; Drew et al., 1988). It has been suggested that the true size-frequency relation is better described by a Pareto distribution, which does not have a mode (Houghton, 1988). As is shown in Figure 15, the lognormal and Pareto distributions may have very similar shapes for a wide range of field sizes, but the Pareto distribution pre- dicts a larger number of small fields. However, the right tail is of more practical importance for estimations of total URR. With the same input data, the Pareto distribution tends to predict more extreme sizes for the largest fields (Attanasi and Charpentier, 2002).

Figure 15. The true size-frequency distribution of fields is commonly assumed to be either lognormal or Pareto. The fitting to empirical field size data leads to a clearly visible difference at the left tail (small sizes), but also to a quantitatively more significant difference at the far right tail.

4.3 Discovery process models The purpose of discovery process models is to forecast the future yield to exploratory effort by using the historical exploration and discovery record. Most existing discovery process models are variations on two basic approaches, commonly referred to as Arps-Roberts and Barouch-Kaufman after their originators. Arps and Roberts (1958) divided fields into discrete size classes, and assumed that the rate of discovery of new fields belonging to each class would be proportional to the average area of fields within the class and the remaining number of undiscovered fields:

43 wkdN ),( kNwkNCA ),(),( (14) dw k where k = field size class w = cumulative number of wildcats N(k,w) = number of discovered fields in class k after w wildcats N(k, ) = total number of existing fields in class k Ak = average area of fields in class k C = exploration efficiency parameter

The differential equation (14) has the solution:

wCAk ekNwkN )1)(,(),( (15) which implies that the number of discovered fields approaches the number of existing fields asymptotically as exploration proceeds. For values on w, C and Ak it is possible to estimate N(k, ) from equation (15). The expected yield Y when cumulative exploratory effort increases from w1 to w2 is the number of discovered fields in each size class multiplied by the average size:

1CAw k 2 CAw k 21 k )(,(),( eekNRwwY ) (16) k where Rk = average initial reserve size in class k

If the total area of size B, and the area covered by fields is small relative to B, then an exploration efficiency of C = 1/B implies random exploration throughout the entire area. Higher exploration efficiency means that the ex- plorer is able to exclude a subset of B from exploration without foregoing any potential discoveries (see Figure 16). Arps and Roberts assumed that C was constant over time and also equal across size classes. A version of the Arps-Roberts model was applied to the 1995 U.S. National Oil and Gas As- sessment performed by USGS (Drew et al., 1995). One of the modifications was the addition of reserve growth to the sizes of known fields, since the model otherwise tended to underestimate future discoveries.

Figure 16. The Arps-Roberts discovery process model showing the number of discovered fields in size class k as a function of cumulative exploration w for different exploration efficiencies C. N(k, ) = 100, Ak = 1, B = 100.

The Barouch-Kaufman approach relies more explicitly on a probabilistic model of the discovery process (Barouch and Kaufman, 1976; Kaufman et al., 1975). The original model rests on two assumptions: 1. In the area under exploration, there are N fields whose sizes are mu- tually independent and identically distributed random variables with a common density distribution (e.g. lognormal). 2. Discovery is a process of random sampling without replacement where the probability of discovering a certain field is proportional to its size. These two assumptions enable the calculation of several relevant parameters. Provided that the form of the field size distribution, its shape parameters and the number of fields N are known, then the most likely discovery size sequence can be obtained analytically. A simulation result of the size sequence in the case of a lognormal field size distribution is shown in Figure 17. Quite intuitively, the size is largest initially and then declines, since the largest fields are likely to be discovered early. There is, of course, still a certain statistical probability that a large field is missed. The recent Avaldsnes discovery in the North Sea is one example of a giant field being discovered in an otherwise mature area. The original Barouch-Kaufman model did only consider the sequence of discoveries, not the discovery yield per exploratory effort. It is, however,

45 straightforward to include an empty area in the model and generate curves of cumulative discoveries as functions of cumulative exploration (Figure 18). In practice the true field size distribution is never known initially, so one central purpose of the Barouch-Kaufman model is to estimate the distribution shape parameters that maximize the likelihood of the historically observed discovery sequence. Once the parameters of the distribution have been estimated, the expected sizes of future discoveries can be calculated. Modifications of the Barouch-Kaufman model have mostly been made with the aim to relax the assumptions of a specific form for the field size distribution (Smith, 1980; Smith and Ward, 1981) or to replace the rather complex maximum likelihood computations with more efficient alternatives (Chungcharoen and Fuller, 1996; Chungcharoen and Fuller, 1999; Fuller and Wang, 1993; Lee and Wang, 1985; Sinding-Larsen and Xu, 2005; Stone, 1990)

Figure 17. Simulation result from a Barouch-Kaufman discovery process showing the sizes of discoveries by order of discovery. The population of N = 100 fields are generated from a lognormal distribution with mean 500 and variance 5*105. The numbers shown are averages of 100 runs.

Figure 18. Simulation result from a Barouch-Kaufman discovery process showing cumulative discoveries as a function of cumulative exploration. The population of N = 100 fields are generated from a lognormal distribution with mean 500 and variance 5*105. 90% of the explored area is empty, and the empty part does not decrease in size with exploration.

Table 3. Summary and comparison of the Arps-Roberts and Barouch-Kaufman discovery process models. Herbert (1982), Sorrell and Speirs (2009). Arps-Roberts Barouch-Kaufman Requires information about the area of the Does not require information about the area exploratory region of the exploratory region Computes results for changes in the exploratory effort Does not require data on exploratory effort Computes changes in the number of fields in Computes the expected size of new discove- discrete size categories ries in a particular order Requires a time series of the number of fields in each size category, but does not require the Requires a time series on the order and the order of discovery size of discoveries Not necessary to estimate the population Necessary to estimate the population number number of fields to be discovered of fields to be discovered Computationally difficult involving maxi- Computationally straightforward mum likelihood methods Not based on probabilistic propositions Derived from probabilistic propositions

Although the two discovery process models are somewhat different in their approach and data requirements (see Table 3 for a summary and comparison), they share the same major advantages:

47 They provide a ‘bottom-up’ derivation of a declining discovery yield per exploratory effort from assumptions of the field size-frequency distribution and the nature of the exploration process. They provide estimates of the sizes of future discoveries, which is relevant from an economic perspective since the commercial viability of a discovery is related to its size. The two models also have the same important limitations: They can only be applied in an area where there exists an historical discovery record. The more well-explored the area, the more reliable are the estimates. The area must be homogeneous in terms of accessibility for exploration. If part of the area is initially inaccessible but becomes accessible later due to administrative changes or improved technology, it is possible to have a new unanticipated discovery cycle. The exploration strategy must not change significantly over time (e.g. become more selective). The sizes of past discoveries must be accurate (ideally PIIP numbers should be used where available, instead of reserve numbers which tend to grow over time).

4.4 Creaming curves An alternative to discovery process modeling is to fit a mathematical function to the data on cumulative discoveries versus cumulative exploration and extrapolate the function to obtain an estimate of future discoveries (Sorrell and Speirs, 2010). Since the fitted function usually is concave, there is an implicit assumption of a skewed field size distribution. The declining yield per effort phenomenon that the curves visualize is called ‘creaming’ and the curves are therefore usually called ‘creaming curves’. The advantage of this curve-fitting approach compared to discovery process modeling is its simplicity and smaller data requirements. It does however only provide an estimate of aggregate future discoveries, not of individual field sizes. It also shares the other limitations with discovery process models, namely that it cannot be applied at all in regions where little or no exploration has been done, it presupposes a consistent exploration strategy, it cannot anticipate new discovery cycles, and it requires accurate field size data. Figure 19 illustrates the effects of reserve growth and new discovery cycles on a creaming curve. There is a clear tendency to systematically underestimate future discoveries and URR when the assumptions underlying the creaming curve are incorrect.

Figure 19. Two problems in the extrapolation of creaming curves are the occurrence of reserve growth in known fields and the possibility of new discovery cycles, both of which cause a systematic underestimation of future discoveries and URR.

4.5 The success rate The additions to reserves through exploration during period t can be decom- posed in the following way:

Dt SR tt Et (17) Et where R = total reserve additions (volume) S = average size of discoveries (volume) D = number of discoveries E = exploratory effort (number of wildcats) D/E = success rate

The average discovery size will tend to decrease in a homogeneous area due to the depletion effect illustrated by discovery process models (Figure 17). However, it is not necessarily the case that the success rate decreases with time (see e.g. Forbes and Zampelli, 2000; Managi et al., 2005). The exploration record of the Norwegian North Sea, for example, shows no sign of decreasing success rate (Figure 20). Technological development may enable a global improvement over time in explorers’ ability to select prospects effi- ciently. There is also likely to be an area-specific information effect which

49 increases with cumulative exploration, as it is gradually revealed where the most promising prospects are located.

Figure 20. Success rate in the Norwegian North Sea, defined as the proportion of wildcat drillings that result in a discovery. The discovery is not necessarily commercial. Source: Norwegian Petroleum Directorate, Fact Pages.

Figure 21. Stylized creaming curve showing increasing yield per exploratory effort during the initial phase due to technological development and/or information obtained during the course of exploration.

As a consequence of technological development and the information effect, the monotonically declining yield per effort which is assumed in discovery

50 process models does not necessarily hold at all times. The depletion effect will still dominate asymptotically since the resource is finite, but the combined effects of technology and information might result in an initial phase of increasing yield per effort (Figure 21).

4.6 Estimating undiscovered amounts: USGS World Petroleum Assessment Due to the inherent limitations of discovery process models and creaming curves, they cannot be the only tools utilized in a comprehensive resource assessment. The ‘Seventh Approximation’ methodology used in the USGS World Petroleum Assessment (USGS, 2000) provides an example of an approach which to a considerable degree depended on expert judgment of geologic circumstances, although statistical analysis of the exploration record was used as a supporting tool. The assessment unit was the whole or part of a total petroleum system (all petroleum generated by a certain pod of mature source rock), and defined as “a mappable volume of rock within a total petroleum system that encompasses accumulations (discovered and undiscovered) that share similar geologic traits and socio-economic factors such as comparable accessibility to exploration and development” (Ahlbrandt and Klett, 2005). The undiscovered amounts being estimated were defined as oil and gas with the potential to be added to reserves within a 30-year time- frame (the choice of time-frame should be interpreted as an indication of the assumed technological circumstances rather than as an actual forecast). The major steps of the assessment process are summarized in Figure 22. For each assessment unit, a geologist assigned a minimum field size (based on considerations of economic viability, between 1 and 20 Mb), estimated the probability that the geologic conditions were favorable and that the area would be accessible for exploration. The geologist also provided minimum (F100), median (F50) and maximum (F0) estimates for the number of undiscovered fields, their sizes, and coproduct ratios (for oil fields: gas-oil and NGL-gas ratios; for gas fields: liquids-gas ratio). These numbers were then used to define probability distributions for the parameters (Figure 23). A probability distribution for the amount of undiscovered resources was generated through Monte Carlo simulation in the following way: 1. A number n was sampled from the number-of-fields distribution. 2. n independent samples were drawn from the field size distribution and were summed to a total resource size S. 3. S was multiplied with random samples from the coproduct ratio distributions to determine the amount of gas and NGL in oil fields and the amount of liquids in gas fields.

51 4. The geologic and access risks were considered. For example, if the combined risk of no reserve additions was 10%, the amount of resource would be reduced to zero with 10% probability and unchanged with 90% probability. 5. Steps 1-4 were repeated 50,000 times.

Figure 22. USGS’s probabilistic methodology for the assessment of undiscovered conventional resources. Adapted from USGS (2000).

Figure 23. The probability distributions used in Monte Carlo simulations in the World Petroleum Assessment (USGS, 2000). Triangular distributions were used for the number of undiscovered fields, coproduct ratios, and reserve growth. A lognormal distribution was used for the sizes of undiscovered fields. The lognormal distribution was right-shifted to have its zero point at the minimum field size, and truncated in the right tail so that the assumed maximum field size equaled the F0.01 frac- tile.

53 5 Production forecasting models

This chapter summarizes a number of approaches to forecasting petroleum production in a region consisting of several fields. How to usefully categor- ize and label such models very much depends on the purpose and context. For example, Brandt (2009; 2010) provides a comprehensive survey where models are classified according to their emphasis of physical or economic factors, hypothetical or mechanistic orientation, scale, and level of complexity. In this particular context, we want to emphasize the contrast between models that forecast aggregate production through some form of extrapolation of aggregate variables (here called ‘top-down’ models), and those that model aggregate production as the sum of output from individual production units (‘bottom-up’ models).

5.1 Top-down models 5.1.1 The Hubbert curve The geophysicist M.K. Hubbert was not the first to suggest that oil production rate in a region would follow a bell-shaped curve, but the notion is associated with him after his 1956 prediction that oil production in continental U.S. would peak between 1965 and 1975 (Hubbert, 1956). Production did in fact peak in 1970. Hubbert did not initially specify any mathematical function for oil production, but later he used the derivative of the logistic function for the purpose (Hubbert, 1982):

ttb 0 )( 0ebN t URRq 2 ttb 0 )( 1 0eN (18) where qt = production rate at time t URR = ultimate recoverable resource N0 = (URR - Q0)/Q0 Q0 = cumulative production at time t0 b = shape parameter

54 The shape of the ‘Hubbert curve’ is determined by the two parameters URR and b (see Figure 24).

Figure 24. Examples of Hubbert curves (the derivative of a logistic function) with different parameter values.

The use of the logistic model entails strong assumptions about the production profile. There is only a single peak, and it occurs when 50% of the URR has been produced. Others have relaxed the assumption of a symmetrical curve by using a mathematical function allowing the peak to occur earlier or later than at the 50% depletion level (e.g. Moore, 1962), or introduced additional logistic functions in the model to account for several production cycles (Nashawi et al., 2010; Patzek and Croft, 2010; Zhang et al., 2010) The usefulness of the Hubbert curve and its variations has been put into question both because of its limited predictive success and its lack of explicit theoretical foundations. As for predictive success, there is a conspicuous lack of references in the literature to successful predictions other than Hub- bert’s well-known 1956 forecast for continental U.S. It could also be argued that the accuracy of this particular prediction was a fortuitous result of two errors that canceled out: the URR of continental U.S. is most likely considerably larger than Hubbert assumed, but on the other hand the peak occurred before 50% was produced. Although a significant number of oil producing regions display a general growth-decline pattern in rough accordance with the model, the production profiles are rarely smooth or symmetrical (Brandt, 2007). The inclusion of several production cycles does not solve the problem of prediction. Historical data can of course be better fitted to a model with more free parameters, but if new unexpected cycles of production have occurred in the past, they are likely to occur also in the future. A

55 multi-cycle model does not enable the forecasting of these future cycles (Anderson and Conder, 2011), and the whole approach might therefore become a case of statistical over-fitting. As for theoretical foundations, several authors have pointed out that the curve-fitting approach which the Hubbert curve represents is unsatisfactory. Although these models are sometimes referred to as ‘geophysical’ or ‘geological’, this is misleading since they are not derived from any geophysical laws determining the fluid flow in reservoirs (Cavallo, 2004). Economists in particular have criticized the lacking consideration of economic parameters such as oil price and costs, and the fact that the URR figure depends on economic and technological factors (Adelman and Lynch, 1997; Lynch, 2002, 2003; Watkins, 2006). Conclu- sively, both the theoretical and empirical support for the Hubbert curve and its variations is rather weak. The main argument for using this type of model is its mathematical convenience.

5.1.2 The Maximum Depletion Rate Model The central assumption of the Maximum Depletion Rate Model (MDRM), as it is labeled in Paper I, is that the production rate must be less than or equal to a certain fraction of the remaining resource base. In other worlds, there is assumed to exist a minimum resource-to-production ratio, (R/P)min, which constrains production. Before the (R/P)min has been reached, production is not constrained by the remaining resource, but by the demand. There is thus two distinct phases: the first ‘demand-constrained’ and the second ‘resource- constrained’. The MDRM has been applied at different aggregation levels. The Work- shop on Alternative Energy Strategies (WAES, 1977) provides an early example of the use of the MDRM to forecast global oil production as one aggregate. A more recent example is Wood et al. (2004). Other authors have forecasted global production through a disaggregated approach by applying the MDRM at the country level (Campbell and Laherrère, 1998; Hallock et al., 2004). Different studies have also used different definitions of the resource base. The most common approach is to use a fixed estimate of URR, but WAES (1977) used proved reserves as a non-fixed resource base, assuming that the reserves would grow by 10 alternatively 20 Gb/y until the year 2000 and subsequently approach a global URR of either 1600, 2000, or 3000 Gb. The impact of using either a fixed or non-fixed resource base, when other parameters are held constant, is illustrated in Figure 25. A fixed resource base postpones the peak, but it also results in a steeper decline. The decline rate is actually exponential in this case.

Figure 25. Examples of the MDRM with either fixed (URR) or non-fixed (reserves) resource bases. In the fixed case, R0 = 1000; in the non-fixed case, R0 = 500 and dR/dt = 20e-0.04t which makes cumulative reserve additions approach 1000 asymptotically. (R/P)min = 30, and the default production growth is 2% in both cases. The notion that production is constrained to a fraction of the remaining resource has some theoretical foundation at the micro-level (a consequence of the diminishing reservoir productivity discussed in section 3.1), and exponential decline in field production is often used as a rule of thumb (see e.g. Arps, 1944) . However, it is not obvious that a model well suited for individual fields is also appropriate at higher levels of aggregation. As Figure 26 shows, an aggregate of fields does not necessarily decline at a constant rate although each individual field has a constant rate of decline. There are two mechanisms acting in opposite directions: With an increasing proportion of fields entering the decline phase, aggregate decline will accelerate. Since rapidly declining fields soon make up a negligible share of total production, only the slowly declining fields remain, and aggregate decline will decelerate. The aggregate decline rate is thus determined by the decline rates of individual fields, their relative sizes, and the time that they enter the decline phase. There is no analytical way of determining whether aggregate decline rate in general would accelerate, decelerate, or stay constant.

Figure 26. The aggregate decline rate as a function of decline in individual fields.

Conclusively, the MDRM lacks a strong theoretical foundation at the aggregate level, and the main argument for its application is the simple and trans- parent structure.

5.1.3 Econometric models The econometric approach consists of hypothesizing structural relationships between variables (e.g. that the production rate is influenced by the oil price), and estimate the parameters of these relationships from empirical data. Early econometric models (e.g. Fisher, 1964) were simple linear equa- tions specifying a variable of interest (such as the rate of exploratory effort) as a function of the oil price, average discovery size, success rate, etc. These early models did not consider the impact of depletion on the discovery rate and cost of production. Nor did they explicitly represent the optimizing behavior of producers. Several subsequent ‘hybrid’ models have incorporated both features. Accounting for depletion has been done in practice by including cumulative discoveries and remaining reserves as explanatory variables in the discovery and cost functions. For example, the discovery yield per exploratory effort has been specified as either a declining or a Hubbert-type function of cumulative discoveries (Favero and Pesaran, 1994; Favero et al., 1992; Pesaran, 1990; Pickering, 2002; Walls, 1994). The difference between econometric models and the previously discussed curve-fitting models is thus one of degree rather than kind. The predictive performance of such hy-

58 brid models has, however, not been particularly good. One example is given in Figure 27.

Figure 27. Oil production on the Gulf of Mexico Outer Continental Shelf as forecasted by a ‘hybrid’ econometric model (Walls, 1994) for the period 1989-2000 compared to actual production data. Source: Energy Information Administration, Petroleum Navigator.

The critique against econometric models as forecasting tools has mainly come from within the economic profession. Lynch (2002) states that the usual set of explanatory variables (oil price, etc.) is not enough to make de- pendable forecasts:

There are so many other factors that influence oil production at both the disaggregate and the aggregate level that any econometric model of drilling, reserves additions, capacity additions and production is unlikely to be successful.

Other petroleum economists have doubted the relevance of econometric models simply because they are an extrapolation of history (Adelman et al., 1976):

[A]n orderly summation of the past (which is what an econometric model is) is of limited help in forecasting future relations between prices and out- puts.

59 5.2 Bottom-up models ‘Bottom-up’ models are here defined as models that generate aggregate production curves by summing the production from smaller units (a common example is field-by-field modeling, see Figure 28) and explicitly represent the flows from resources to reserves and from reserves to production. The scenarios in the IEA’s influential annual World Energy Outlook and the EIA’s Annual Energy Outlook are generated with bottom-up models. This modeling approach is thus of considerable practical importance. Figure 29 shows how bottom-up models are generally structured. Since a detailed review of the different model components can be found in Paper III, the de- scription here will be brief. The basic strategy of bottom-up modeling is to make production forecasts disaggregated in order to utilize detailed data. Production data is often available at least for large individual producing fields and for planned developments within the next few years. It is therefore possible to empirically estimate reasonable production profiles from historical data. It is, however, generally not possible to derive quantitative scenarios from basic reservoir parameters (however, a qualitative model that does derive production profiles from reservoir parameters and optimizing behavior is formulated in Paper II). The IEA (2008) estimates standard production profiles for oil fields in different URR size classes and locations (onshore/offshore). A similar approach is used in Papers V and VI in the estimation of four-phase production profiles (see Figure 11) for Norwegian and Russian gas fields.

Figure 28. Example of an aggregate production scenario generated by the summation of production from individual fields.

Figure 29. General flowchart for a bottom-up model. Adapted from Adelman et al. (1976) and IEA (2010).

Existing bottom-up models vary considerably in their level of detail. Explo- ration and discoveries are in some cases forecasted with sophisticated discovery models, in other cases with simpler creaming curves. The economic evaluation might include detailed cost functions or more schematic represen- tations. Some models do not include economic evaluation at all. It is not self-evident that increased modeling detail is an advantage. Smil (2000) is one analyst who has questioned the usefulness of making forecasting models more complex:

[A]s my models were growing progressively more complex, I was getting more troubled by them. Greater complexity that was required to make the forecasts more realistic also necessitated the introduction of longer chains of concatenated assumptions—and this necessity was defeating the very quest for greater realism. (Smil, 2000)

The practical problem is the insufficient data available to fully utilize the potential of a detailed model. This is particularly the case in long-term scenarios where highly uncertain factors such as future discoveries, technological development and investment rates are important. To the extent that these factors are at all considered in a model, their forecasted impact must be rather speculative. Under some conditions the uncertainty in particular factors is relatively smaller, a circumstance that to some degree serves to reduce the total uncertainty in the modeling of future gas production in Norway (Paper V) and Russia (Paper VI). One example is the possible impact of new technology on the recovery factor, which is smaller for gas fields than for oil fields since gas fields typically have a high recovery factor already with conventional technology (Jahn et al., 1998). Another example is the rate of

61 future discoveries, which in Russia is a less critical factor than the development rate of the large number of already discovered fields. It should still be recognized that bottom-up modeling does not eliminate uncertainty. It does, however, make it feasible to identify the impact of specific uncertain parameters and thereby perform meaningful sensitivity analyses.

62 6 Results

6.1 Paper I According to the long-term scenarios of the International Energy Agency (IEA) and the US Energy Information Administration (EIA), conventional oil production is expected to grow until at least 2030. Wood et al. (2000; 2004) have published results from a MDR production model which ostensi- bly support such a scenario. However, it is here shown that the model, although it is suitable for long-term scenarios in principle, has been misapplied due to a confusion of resource categories. With reference to the U.S. as an analogous case, the authors choose a global (R/P)min of 10, which implies that the decline rate will be 10%. The choice of decline rate has a dramatic impact on the timing of the peak. The resource base for the forecast is estimates of global EUR which is fixed, but when the authors point to the U.S. as an analogous case, they refer to the R/P based on proved reserves, a resource base which is non-fixed and has grown considerably in the past. A relevant analogy would be the U.S. (R/P)min computed from the same resource base that the EIA assumes in their forecast (324-360 Gb EUR), which would yield an (R/P)min of around 70 rather than 10. A correction of this methodological error reveals that the authors’ scenarios require rather extreme and implausible assumptions regarding future global decline rates. Assuming more plausible decline rates, while maintaining the other parameters unchanged, makes the production peak occur considerably earlier (Table 4).

Table 4. Global production peak years and levels as forecasted with an MDR model. The increase rate is 1% per year in all scenarios.

Estimated ultimate 2248 3003 3896 recovery (Gb) Minimum R/P 70 50 30 70 50 30 70 50 30 Peak year 2007 2007 2019 2010 2023 2037 2028 2040 2054 Peak production 26.7 26.7 30.1 27.6 31.1 36.0 32.7 37.1 42.7 (Gb/year) Peak production 73.3 73.3 91.2 86.3 97.4 109.8 103.6 117.3 130.8 (Mb/day)

63 6.2 Paper II We critically examine two interrelated and seemingly plausible arguments for an unconcerned view of oil availability: (1) there is a growing amount of remaining reserves; (2) there is a large amount of oil with a relatively low average production cost. These statements are unconvincing on both theoretical and empirical grounds. Oil availability is about flows rather than stocks, and average cost is not relevant in the determination of price and output. We subsequently implement a bottom-up model of regional oil production with micro-foundations in both natural science and economics. An oil producer optimizes net present value under the constraints of reservoir dynamics, technological capacity and economic circumstances. Optimal production profiles for different reservoir drives and economic scenarios are derived (see examples in Figure 30). The field model is then combined with a discovery model of random sampling from a lognormal field size distribution. Regional discovery and production scenarios are generated (Figure 31). Our approach is not based on the simple assumptions of top-down models such as the Hubbert curve – however it leads to the same qualitative result that production peaks when a substantial fraction of the resource remains in the ground (in the scenarios, only 24-30% of the initial recoverable resource is produced at the time of peak).

Figure 30. Examples of generated optimal reservoir production profiles for depletion drive and water drive.

Figure 31. Regional production profiles in different scenarios of exploration and economic circumstances.

6.3 Paper III Oil production scenarios generated by so-called bottom-up models have a concrete policy impact through the highly influential energy outlooks published annually by the International Energy Agency (IEA) and the Energy Information Administration (EIA) of the U.S. Department of Energy. It is therefore desirable to make a systematic review of bottom-up models and their sensitivity to assumed parameter values. We systematically describe how oil production is determined in nine different published bottom-up models, and assess the output sensitivity of a typical bottom-up model to changes in parameter values. The conclusions are that for a time horizon of 25-50 years (a period over which they are often applied today), bottom-up models are unlikely to reduce the quantitative uncertainty of forecasts compared to simpler top-down models. The advantages of these models are more likely to be realized in policy evaluations, qualitative investigations of the determinants of production rates, and possibly in short-term forecasts. It is in such applications that further development of bottom-up models is likely to be the most fruitful.

65 6.4 Paper IV It has been suggested that oil exploration may lead to false perceptions of decreasing scarcity. We perform a simulation of the exploration process using Bayesian updating. The approach enables us to isolate the information effect on the success rate and also to quantify the subjective expectation of the total resource size. The area under exploration consists of a number of regions which may differ in their oil content. Exploration is performed with the goal to maximize the expected success rate. The resulting information about the distribution of oil and the total resource size is assumed public knowledge. A number of scenarios with variations in the dimensions of the area under exploration, the oil distribution and initial beliefs are considered. The results indicate that the information effect on the success rate is significant but brief – it might have a considerable impact on price but is an unlikely mechanism behind a long-term declining price trend. However, the information effect on expectations is gradual and persistent. Since exploration is performed in regions where the expected success rate is the highest, the historical success rate will not be representative of the area as a whole. An ex- plorer will tend to overestimate the total resource size, thereby suggesting an alternative mechanism for false perceptions of decreasing scarcity, a mechanism that could be called the ‘fallacy of early success’.

6.5 Papers V and VI The European Union (EU) is expected to meet its future growing demand for natural gas by increased imports. In 2006, Norway had a 21% share of EU gas imports. The Norwegian government has communicated that Norwegian gas production will increase by 25–40% from today’s level of about 99 billion cubic meters (bcm)/year. The bottom-up scenarios in Paper V indicate that only a 20–25% growth of Norwegian gas production is possible from currently existing recoverable reserves and contingent resources. A high and a low production forecast for Norwegian gas production is presented. Nor- wegian gas production exported by pipeline peaks between 2015 and 2016, with minimum peak production in 2015 at 118 bcm/year and maximum peak production at 127 bcm/year in 2016. By 2030 the pipeline export levels are 94–78 bcm. Total Norwegian gas production peaks between 2015 and 2020, with peak production at 124–135bcm/year. By 2030 the production is 96– 115 bcm/year. The results show that there is a limited potential for increased gas exports from Norway to the EU and that Norwegian gas production is declining by 2030 in all scenarios. Annual Norwegian pipeline gas exports to the EU, by 2030, may even be 20 bcm lower than today’s level. Russia is likely to play a crucial role in meeting the anticipated growing gas demand of the EU. Paper VI presents a field-by-field study of 83 giant

66 gas fields showing that the major producing Russian gas fields are in decline, and by 2013 much larger supplies from the Yamal Peninsula and the Shtok- man field will be needed in order to avoid a decline in production. Gas from fields in Eastern Siberia and the Far East will mainly be directed to the Asian and Pacific Rim markets, thereby limiting its relevance to the European and CIS markets. As a result, the maximum export increase to the European and CIS markets amounts only to about 45% for the period 2015–2030. The dis- course surrounding the EU’s dependence on Russian gas should thus not only be concerned with geopolitics, but also with the issue of resource limitations.

6.6 Paper VII The giant oil fields (having a URR larger than 500 Mb or a peak daily production rate of more than 100,000 barrels) are only a small fraction of the total number of fields, but they are very important for the global oil supply. Over 50% of the world’s oil production came from giants in 2005 and more than half of the world’s URR is found in giants. Based on this, it is reasonable to assume that the future development of the giant oil fields will have a significant impact on the world oil supply. This study has used production data from 331 giant oil fields in order to determine lead-times, depletion rates at peak, depletion levels (% of URR) at peak, decline rates and time from production start to decline. Fields are categorized as onshore/offshore and OPEC/non-OPEC. The peak production generally occurs before half of the URR has been produced. A strong correlation between depletion-at-peak and average decline rate is also found, indicating that a high depletion rate leads to a rapid decline. Offshore fields have longer lead-times, faster decline rates and shorter production times than onshore fields. OPEC fields have lower decline rates and earlier decline than non-OPEC fields. There is a tendency that fields developed in later decades enter decline later and decline more rapidly. Our result also implies that depletion analysis can be used to rule out unrealistic production expectations from a known reserve, or to connect an estimated production level to a needed reserve base.

67 7 Concluding discussion

7.1 The purpose of modeling – applicability of the bottom-up approach [T]he sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work – that is, correctly to describe phenomena from a reasonably large area. (von Neumann, 1955)

When does a model ‘correctly describe phenomena’? Both within natural and social science, it is commonly taken to mean that that the model (or theory) produces accurate predictions. According to the instrumentalist line of thought, perhaps most famously (and controversially) expressed by Friedman, testable predictions are actually the only relevant evaluation criteria:

[T]he relevant question to ask about the ‘assumptions’ of a theory is not whether they are descriptively ‘realistic’, for they never are, but whether they are sufficiently good approximations for the purpose in hand. And this question can be answered only by seeing whether the theory works, which means whether it yields sufficiently accurate predictions. (Friedman, 1953)

However, if we are to determine whether a model yields sufficiently accurate predictions, we must first know more precisely what we mean by ‘prediction’. There are at least three different interpretations (of which the third can be subdivided into a probabilistic and a deterministic version), defined by the type of question that is being answered by the prediction (Troitzsch, 2009): 1. Which kinds of behavior can be expected [from a system like this] under arbitrarily given parameter combinations and initial conditions? 2. Which kind of behavior will a given target system (whose parameters and previous states may or may not have been precisely measured) display in the near future? 3.

68 a. Which are the expected value and the confidence interval around the expected value of the state the target system will reach in the near future, again given parameters and previous states which may or may not have been precisely measured? b. Which exact value will the state of the target system have at a certain point of time in the near future, again given parameters and previous states which have been precisely measured?

For example, the statement that earthquakes are most likely to occur along the boundaries of tectonic plates would be a prediction of type 1, while the time, place and magnitude of the next earthquake is a prediction of type 3b. Within science in general, the ability to make exact predictions of type 3b is the exception rather than the rule. It requires that all but a few factors have a negligible impact on the outcome, and also that all the important factors are measurable. This is rarely the case outside the field of astronomy. For example, the theory of plate tectonics does predict the conditions under which earthquakes are likely, but there is presently no way to exactly predict the time and place of an earthquake. The reason is not primarily lacking knowledge of the causal mechanisms, but rather the inability to observe all the relevant variables (Troitzsch, 2009). As for the forecasting of petroleum production, it has been driven to a large extent by a wish to make predictions of type 3b. Accurate quantitative predictions have been seen as an important feature of a good model, and inaccuracies have therefore been considered failures. Measured by this yardstick, it is hard to describe the modeling effort as a whole as anything but a failure. No model has been presented that consistently delivers reliable predictions of future production rates. The fact that some models occasional- ly have yielded roughly accurate predictions is not much cause for optimism. Occasional correct predictions can be obtained merely by chance. Likewise, given the large number of production forecasts that exist today, it would be surprising if not at least one will turn out to be roughly correct. But having one hundred forecasts out of which any could be the correct one is no more helpful than having none. As in the case of earthquakes, the inability to make predictions is, at least in part, an issue of incomplete information and is therefore not likely to be solved by finding the ‘right’ model. Making models more detailed is generally not a guarantee for better quantitative accuracy. There are, however, situations where highly uncertain and speculative factors (such as future discoveries and technological change) are less important. Under these circumstances, the higher detail of bottom-up models might be an advantage. These models also enable interpretable sensitivity analyses. Some forecasts have been formulated in probabilistic terms (predictions of type 3a). This is also the case for the resource assessments of USGS. The final probability distribution is obtained by combining distributions for several input parameters in Monte Carlo simulations. In most cases, the distribu-

69 tions of the input parameters only reflect the forecaster’s subjective assessment of the reasonable uncertainty range (one example is the use of a triangular distribution for the number of undiscovered fields within a play). As a consequence, the final confidence interval must also be interpreted as only a subjective assessment, essentially saying that the forecaster would personally be surprised if the actual outcome fell outside of the interval. This is not objectionable, as long as the result is clearly presented as subjective. How- ever, if this is not the case, the reader might be given the false impression that the uncertainty is well-defined and quantifiable. The inability to make exact quantitative predictions does not make modeling meaningless. The formulation of models serves several purposes (Epstein, 2008; Rubinstein, 1998), including: Making qualitative ‘predictions’ of types 1 or 2. Giving normative recommendations (policy guidance). Guiding data collection. Discovering new research questions. Illuminating core uncertainties. Challenging the robustness of prevailing theory. Exposing prevailing wisdom as incompatible with available data. Sharpen intuition about complicated situations. Educating the general public. For all of these purposes, a model must be convincing in the eyes of the user. Convincingness is admittedly a somewhat vague concept, but probably the most relevant to use. We presume that a user is convinced by a model if s/he understands its dynamics and sees its primitive assumptions as reasonable approximations of reality (or at least justified in the modeling context). Oth- er modelers have made a similar presumption. Kaufman (1975) actually argued for the use of detailed bottom-up discovery process models instead of simple creaming curves on the grounds that the more detailed models would be more convincing:

The user will generally have more confidence in forecasts generated by a model that passes tests of the validity of primitive assumptions from which it is structured, independently of tests of the predictive quality of its output.

To emphasize the importance of convincingness is in one sense in conflict with Friedman’s (1953) view that the realism of assumptions is irrelevant. Friedman is certainly correct in that realism should not be the overarching goal of modeling. A model is indeed pointless if it is not simpler and more manageable than the reality it represents. However, realism and a high level of detail are not ends in themselves, but means to make a model convincing. The controversy surrounding petroleum forecasting models, and particularly that surrounding the Hubbert curve, illustrates quite clearly that scientists (not least economists) actually see realistic model assumptions as very im-

70 portant. Ironically, by Friedman’s criteria the Hubbert curve would be a rather good economic model. It has no obvious superior in terms of predictive performance, and it certainly has among the simplest assumptions imagina- ble. Most economists still reject it, since they take it as self-evident that a relevant model must in some way connect the production rate to the profit- seeking behavior of producers. The controversy also illustrates that convincingness is subjective and that the notion of what is convincing depends on the researcher’s background. The challenge, from a modeling perspective, is to make a model that is simultaneously convincing to scientists from different backgrounds. We argue that the bottom-up approach described in Paper II has the potential to be convincing to scientists from different disciplines. It includes the optimizing behavior that economists expect as well as the reservoir dynamics and field size distribution that natural scientists recognize. The bottom-up approach is extendable and structurally robust to changed assumptions. In Paper II, there are several heuristic assumptions that could be relaxed in further model development. Doing this would naturally change the output to some extent, but it would not cause the model to break down. Other modeling approaches appear less extendable and robust by comparison. For example, Holland (2008) presents four different economic models that can generate roughly bell-shaped aggregate production curves, but all of these models rely on Hotelling’s assumption that the producers know the total size of the resource. This assumption is not even approximately true, but relaxing it would necessitate radical changes in the model structure. Likewise, it is difficult to usefully extend the Hubbert and MDR models, since the major argument for using them is their simplicity. Any extension would make them more complex. Econometric models are a bit different, since the more detailed versions strive to combine economic and geologic assumptions. If these models were also further disaggregated, they would in practice become bottom-up models. Conclusively, of all the existing modeling approaches, bottom-up modeling appears to hold the most promise for the purpose of forming a common understanding of petroleum depletion between scientists from different disciplines.

7.2 Causes for concern We have, through bottom-up modeling of exploration and production, provided some positive theoretical evidence of the possibility that petroleum scarcity occurs long before the recoverable resource is close to exhaustion. This result is a consequence of both geologic and economic factors, and can be seen as a corroboration of the qualitative assumptions of top-down models. There is no particular reason to believe that a 50% depletion level would have any significance, as is assumed in Hubbert’s original model. Scarcity may occur considerably sooner. Just as important as positive evidence are

71 the negative results which indicate that several statements and forecasts being invoked in support of an ‘unconcerned’ view are at best uncertain (long- term scenarios generated by bottom-up models), and at worst relying on questionable assumptions (analyzing reserves rather than production flows, using irrelevant reserve definitions, using average cost instead of marginal cost). The future of petroleum availability is determined by many factors, of which several are uncertain. This circumstance should be acknowledged by both sides of the current debate. However, uncertainty regarding an issue of such importance to welfare and security is in itself a cause for concern.

72 8 Svensk sammanfattning

Temat för denna avhandling är tömningen av petroleum (en samlingsbeteck- ning för olja och naturgas). Kommer det faktum att resurserna är ändliga att leda till ett slut för den billiga oljan inom en nära framtid? De ekonomiska konsekvenserna skulle i så fall kunna bli avsevärda. Olja och naturgas står idag för över hälften av den globala tillförseln av primärenergi. Det finns för närvarande inte några alternativa energikällor som kan konkurrera med petroleum i alla relevanta avseenden. Det pågår en intensiv debatt kring hur oljeproduktionen kommer att ut- vecklas i den närmaste framtiden. Somliga ser en snar topp och efterföljande nedgång i den globala produktionen, troligtvis sammanfallande med slutet för den billiga oljan. Andra ser ingen anledning att tro på sådana scenarier. Ifråga om naturgas, där marknaderna ännu delvis är regionala på grund av flaskhalsar i den interkontinentala distributionen, gäller inte farhågorna i första hand en global topproduktion utan snarare regionala försörjningspro- blem. Debatten beskrivs ibland som en kontrovers där det finns en djup klyfta mellan ”bekymrade” geologer/naturvetare och ”obekymrade” ekonomer. Detta är en skadlig klyfta som kan och bör överbryggas. Det finns ingen inneboende motsättning mellan geologi och ekonomi som discipliner. En trolig orsak till svårigheterna att nå en gemensam förståelse för resurstöm- ning är snarare det ”top-down”-perspektiv med fokus på aggregerade data och modeller som hittills har dominerat diskussionen. På mikronivån där- emot, i produktionen från en enskild petroleumreservoar och i prospekte- ringen efter nya reservoarer, ingår geologiska och fysikaliska faktorer natur- ligt som parametrar i producentens ekonomiska optimeringsproblem. Ett ”bottom-up”-perspektiv framstår därför som en lovande väg för att skapa en gemensam förståelse för tömningsproblematiken. Av världens totala återstående petroleumresurs är det endast en viss del som vid varje given tidpunkt betraktas som ”reserv”, det vill säga är känd och ekonomiskt utvinningsbar med existerande teknik. Det finns inget uni- versellt vedertaget system för att klassificera reserver, vilket gör tolkningar och jämförelser av reservdata vanskliga. Reserver utökas dels genom fynd av nya reservoarer, dels genom positiva revideringar av reserver i redan kända reservoarer, så kallad ”reservtillväxt”. Denna tillväxt kan antingen bero på bättre kunskap om geologiska förutsättningar, bättre teknologi eller revide- ring av medvetet konservativa reservuppskattningar. Det är viktigt att inte likställa stora reserver med stor potential för produktionsökning. Den spridda

73 användningen av reserv-produktionskvot som statistiskt mått bidrar till missuppfattningen att det skulle vara möjligt att producera petroleum i god- tycklig takt tills det plötsligt ”tar slut”. Större delen av återstående reserver finns i fält som redan producerar med konstant eller sjunkande takt. Petrole- umreservoarer karaktäriseras av gradvis avtagande produktivitet, vilket yttrar sig antingen i minskande reservoartryck eller ökande proportion av oönskade fluider (vatten eller gas). Det finns ingen väldefinierad teknisk gräns för produktionstakten, men producentens strävan att maximera återstående re- servers nettonuvärde resulterar i en produktionsprofil som i typfallet har en ledtidsfas, uppbyggnadsfas, platåfas och nedgångsfas. Storleksfördelningen för fält är mycket skev – det finns få stora fält, men de står för en stor del av reserverna. Den skeva storleksfördelningen leder till att fyndtakten i en region tenderar att avta med kumulativ prospektering. Det kan dock även finnas en informationseffekt som leder till mer effektiv framtida prospektering. Modeller för prognostisering av petroleumproduktion klassas här som antingen ”top-down” eller ”bottom-up”. Viktiga top-down-modeller, som an- vänder aggregerade data, är den omdiskuterade Hubbertmodellen, MDR- modellen samt ekonometriska modeller. Bottom-up modeller bygger upp produktionsscenarier från mindre produktionsenheter, såsom enskilda fält. Avhandlingens delarbeten behandlar olika aspekter av petroleumtömning, med bottom-up-perspektivet som genomgående tema. Delarbete I, det enda som har ett top-down-perspektiv, är en kritisk granskning av hur Energy Information Administration har tillämpat en MDR-modell för att skapa scenarier för global oljeproduktion. Den minima- la globala R/P-kvoten har antagits vara så låg som 10 på grund av en felaktig jämförelse med historiska data från USA. Dessa data bygger på ”bevisade reserver”, medan resursen i scenarierna är EUR (vilket är en uppskattning av den mängd som totalt kommer att utvinnas). Alternativa scenarier med mer realistiska och metodmässigt konsistenta R/P-värden ger betydligt långsam- mare nedgångstakt och därmed tidigare topproduktion. I delarbete II genereras produktionsprofiler för reservoarer genom en ekonomisk optimering som inkluderar en enkel reservoarmodell med två alternativa drivmekanismer. Dessa produktionsprofiler kombineras till regionala scenarier med hjälp av en fyndmodell (slumpvis dragning från en lognormal fältstorleksfördelning). Simuleringen ger samma kvalitativa resultat som Hubbertmodellen – att den regionala produktionen avtar när en stor del av den utvinningsbara resursen återstår (i dessa scenarier när endast 24-30% har producerats). Delarbetet innehåller också en kritisk diskussion kring två vanliga argument för en ”obekymrad” attityd till tömningsproblematiken: (1) de återstående reserverna är stora och ökande; (2) en stor andel av den åter- stående oljan har låg genomsnittlig produktionskostnad. Storleken på reserverna ger inte en fullständig bild av det möjliga produktionsflödet, och ge- nomsnittskostnaden är inte relevant för prisbildningen eftersom den skiljer sig från marginalkostnaden.

74 Delarbete III innehåller en studie av nio publicerade bottom-up-modeller, samt en känslighetsanalys av en modell med en typisk struktur. Slutsatsen är att den kvantitativa osäkerheten är avsevärd inom den tidshorisont på 25-50 år som är vanlig i publicerade scenarier. Bottom-up-modeller är därför mer relevanta för kvantitativa scenarier med kort tidshorisont (där tillgången till data är bättre) eller för kvalitativa scenarier. Delarbete IV simulerar prospektering där sannolikheten att finna olja va- rierar mellan regioner. Bayesiansk uppdatering används som beslutsmetod och för att kvantifiera förväntningar om sannolikheten att göra fynd. Ande- len framgångsrika prospekteringar förbättras initialt av en kraftig men kort- varig informationseffekt. Förväntningarna tenderar däremot att få en mer långvarig positiv snedvridning. Detta är en tänkbar mekanism för ett falskt intryck av avtagande resursknapphet, vilket tidigare har föreslagits bero på andelen framgångsrika prospekteringar. Delarbetena V och VI innehåller kvantitativa bottom-up-scenarier för framtida naturgasproduktion i Norge och Ryssland, de två viktigaste expor- törerna av gas till Europeiska Unionen. Scenarierna för Norge inkluderar både kända fält, så kallade betingade resurser samt uppskattningar av framtida fynd. Resultaten indikerar att en topproduktion kan förväntas mellan 2015 och 2020 på en nivå av 124-135 bcm/år. Exportkapaciteten till EU kan år 2030 vara lägre än dagens nivå. Scenarierna för Ryssland bygger på 83 fält som är kända. Den kritiska faktorn för exportkapaciteten till EU är hur snabbt nya fält på Yamalhalvön samt Shtokmanfältet kan komma i produk- tion och kompensera för nedgången i dagens producerande fält i Västra Sibi- rien. Den maximala exportökningen till EU är ca 45% under perioden 2015- 2030. Delarbete VII är en empirisk studie av 331 gigantfält (fält med mer än 500 Mb olja i URR eller en daglig topproduktion större än 100 000 fat). Led- tider, tömningstakt vid topproduktion, tömninggrad (% av URR) vid topproduktion, nedgångstakt samt tid från produktionsstart till nedgång är parametrar som har uppskattats. Fält offshore har längre ledtider och snabbare ned- gångstakt än fält onshore. OPEC-fält har lägre nedgångstakt och tidigare nedgång än icke-OPEC. Fält som utvecklats under senare decennier tenderar att ha senare nedgång och snabbare nedgångstakt än äldre fält. Modellering av petroleumproduktion syftar ofta till att göra kvantitativa prognoser. Med detta kriterium har modelleringen hittills inte varit fram- gångsrik. Det är inte heller troligt att träffsäkerheten i prognoserna kommer att öka med mer detaljerade bottom-up-modeller, eftersom en stor del av problemet är brist på relevanta empiriska data. Bottom-up-modeller kan vara motiverade för kvantitativa prognoser med korta tidshorisonter eller i situa- tioner där osäkra parametrar, såsom fyndtakt och reservtillväxt, har mindre betydelse. Dessa modeller underlättar också tolkningsbara känslighetsanaly- ser. Kvantitativa prognoser är dock inte det enda legitima skälet att göra modeller. När en modell används för kvalitativa prognoser, policyvärdering

75 eller pedagogiska syften är det viktigt att den är övertygande, det vill säga att användaren förstår modellens struktur och anser dess antaganden vara rimli- ga. I detta avseende har top-down-modeller inte varit framgångsrika, medan bottom-up-modeller däremot har potential att bli accepterade av forskare från olika discipliner. Vi har, med hjälp av bottom-up-modellering av prospektering och pro- duktion, funnit teoretiskt stöd för hypotesen att tillgången på petroleum kan avta långt innan den utvinningsbara resursen är tömd. Resultatet är en följd av både geologiska och ekonomiska faktorer. Vi har också visat att flera argument för en ”obekymrad” attityd är i bästa fall osäkra (de som bygger på långtidsscenarier från bottom-up-modeller) och i värsta fall bygger på tvivel- aktiga antaganden (sammanblandning av reservkategorier, likställande av reserver med produktionskapacitet, hänvisning till genomsnittskostnad istäl- let för marginalkostnad). Framtiden för petroleum påverkas av många faktorer, av vilka åtskilliga är osäkra. Detta bör medges av båda sidor i den pågå- ende debatten. Dock är denna osäkerhet kring en så viktig faktor för välfärd och säkerhet i sig ett skäl att ta frågan om resurstömning på stort allvar.

76 9 Acknowledgments

The work presented in this thesis was carried out at the Department of Phys- ics and Astronomy at Uppsala University. External financial support was generously provided by the Swedish Energy Agency. I would like to thank all the people who have enabled and facilitated the writing of this thesis, in particular: Kjell Aleklett, my main supervisor, for his enthusiastic support and for giving me the opportunity to work with a fascinating subject; my co- supervisor Simon Snowden who was far-sighted enough to suggest the potential of a bottom-up simulation approach; and my co-supervisor Chuan-Zhong Li who introduced me to resource economics. Rob Hart, the examiner of my licentiate thesis; Roger Bentley, an expe- rienced co-author with a lot of thoughtful input; Bengt Karlsson, who has provided Matlab programming tips; Pang Xionqi and Feng Liangyong who arranged seminars at the China University of Petroleum as well as an unfor- gettable visit to the Daqing oil field in Manchuria. Bengt Söderbergh, Mikael Höök and Noriaki Oba – my PhD colleagues, co-authors and friends; Fredrik Robelius, who invited us to a fascinating study visit at the Tishreen oil field in Eastern Syria; Sven Kullander, Kersti Johansson, Karin Liljequist, Aram Mäkivierikko, Emma Nygren, Ulrika Lundén, Simon Larsson, Hanna Vikström, Anna-Lotta Söderberg, Christoffer Strandberg, Mårten Berglund, and all past members of the Global Energy Systems research group. Sophie, Pär-Anders, Erik, Patrik, Henrik, Cecilia, Annica, Inger, and all co-workers at the department; colleagues and friends in the faculty PhD student council and the PhD student committee of Uppsala Student Union. The members of “Ib-Karinz” – the world’s best physics department rock band – Karin, Eva, Tord, Ane, Ib, Christofer, Fredrik, Henrik and Christer. Anne-Mari, Bertil and Josefin, who always support and encourage me in every way.

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