USING GEOPHYSICAL WELL LOG ANALYSIS AND GEOSTATISTICS TO MAP

GROUNDWATER TDS DISTRIBUTIONS IN THE FRUITVALE AND ROSEDALE

RANCH OIL FIELDS, KERN COUNTY, CALIFORNIA

A Thesis

Presented to the faculty of the Department of Geology

California State University, Sacramento

Submitted in partial satisfaction of the requirements for the degree of

MASTER OF SCIENCE

in

Geology

by

Michael J. Stephens

SUMMER 2017

USING GEOPHYSICAL WELL LOG ANALYSIS AND GEOSTATISTICS TO MAP

GROUNDWATER TDS DISTRIBUTIONS IN THE FRUITVALE AND ROSEDALE

RANCH OIL FIELDS, KERN COUNTY, CALIFORNIA

A Thesis

by

Michael J. Stephens

Approved by:

______, Committee Chair Dr. David Shimabukuro

______, Second Reader Dr. Steven Skinner

______, Third Reader Dr. Jan Gillespie

______Date

ii

Student: Michael J. Stephens

I certify that this student has met the requirements for format contained in the University format manual, and that this thesis is suitable for shelving in the Library and credit is to be awarded for the thesis.

______, Graduate Coordinator ______Dr. Kevin Cornwell Date

Department of Geology

iii

Abstract

of

USING GEOPHYSICAL WELL LOG ANALYSIS AND GEOSTATISTICS TO MAP

GROUNDWATER TDS DISTRIBUTIONS IN THE FRUITVALE AND ROSEDALE

RANCH OIL FIELDS, KERN COUNTY, CALIFORNIA

by

Michael J. Stephens

With the recent drought in California, a greater demand has been placed on groundwater resources. Publicly-available data indicate that produced water from oil and gas extraction in California is commonly being injected into the subsurface for disposal at relatively shallow depths in some oil fields. This may conflict with the U.S.

Environmental Protection Agency (EPA) Safe Drinking Water Act and California Senate

Bill 4. These measures protect groundwater containing < 10,000 ppm total dissolved solids (TDS), also defined as underground sources of drinking water (USDW).

Groundwater TDS maps are needed to identify and protect the USDW because there is no current survey of the USDW boundary. Direct measurements of groundwater TDS are not common, which necessitates using alternative methods to quantify TDS. This study uses the resistivity-porosity (RP) method to calculate TDS from resistivity, porosity, and iv temperature measurements recorded in borehole geophysical data. We use existing measured geochemical data to guide proper parameterization of the petrophysical equations by examining comparisons with the ground truth data.

The RP method is only accurate within clean, wet sand intervals. Hydrocarbons and shale, if present, distort the TDS calculations, rendering inaccurate results. Due to the large number of wells needing to be analyzed, an algorithm was coded in Python to process digitized geophysical well data to identify clean sand intervals where TDS calculations are more accurate.

The RP-derived TDS data were fed into a 3D geostatistical kriging model to create an interpolated volume model of TDS. The model is validated by comparing the predicted TDS values to the measured TDS data. The average error is 11%, with a correlation of R2 = 0.97. The model was used to visualize a cross section throughout the

Fruitvale and Rosedale Ranch oil fields in the San Joaquin Basin of California.

Groundwater TDS in the area varies significantly. The 10,000 ppm TDS boundary is at

~3,500 ft in Rosedale Ranch and deepens to the southeast in Fruitvale to ~4,500 ft.

According to the data, several factors including depth, stratigraphy, faults, and fresh water recharge control the TDS distribution. Within the Rosedale Ranch area, Miocene normal faults and a low-permeable clay layer isolates aquifers from fresh water recharge from the Kern River. Stratigraphic control seems to dominate the TDS structure in the area between the fields. The groundwater in the Fruitvale area is flushed by recharge from the Kern River. v

This study provides a realistic and effective approach to quantify formation water

TDS with available data as well as a better understanding of the controls on groundwater

TDS, which can assist future mapping efforts and lead to better information for water resources managers.

______, Committee Chair Dr. David Shimabukuro

______Date

vi

ACKNOWLEDGEMENTS As these things are never the result of a single person’s work, I’d like to recognize those that have supported me throughout the development of this thesis. First and foremost, my deepest appreciation to Dr. Dave Shimabukuro for providing guidance throughout my graduate career. The time and energy he spent working on this project with me is immeasurable. To Dr. Steve Skinner who taught me programming. His course and guidance enabled me to take on this project. Thank you to Dr. Jan Gillespie for her advice and guidance throughout this project - her knowledge of California geology was essential in making my thesis a success. Finally, many thanks to Will Chang for serving as an informal advisor for much of this project and for sharing his knowledge of geostatistics which aided in the completion of my thesis.

Thank you to the California State Water Resources Control Board and the U.S.

Geological Survey for providing funding for this project. They have been valuable sources of scientific knowledge and collaboration, and I am grateful for the opportunity to work with these organizations. As this research was aided by copious data, I am grateful to the Water Resources Group at CSUS that spent countless hours collecting and quality checking data used in this study.

Thank you to my parents, Bob and Linda, who have always supported me and encouraged me to continue my education. They have personally demonstrated the value of education. Lastly, thank you to my wife, Sarah, who inspires me to follow my passions regardless of the challenges that may arise. vii

TABLE OF CONTENTS Page Acknowledgements ...... vii

List of Figures ...... xi

INTRODUCTION ...... 1

BACKGROUND ...... 7

Regional Geology ...... 7

Local Geology ...... 9

Production History ...... 14

Hydrology ...... 17

METHODS…...... 18

Available TDS Data ...... 18

Petrophysical Equations ...... 21

Porosity Model ...... 25

Temperature Model ...... 28

TDS Calculations ...... 30

Geostatistics ...... 35

Exploratory Data Analysis and Transformation ...... 37

The Variogram ...... 39

Kriging System ...... 41

Stratigraphic Data ...... 43

Fault Data ...... 43 viii

RESULTS & DISCUSSION...... 45

Groundwater TDS Distribution...... 45

Model Validation ...... 52

Geostatistical Model Validation ...... 52

RP-Calculations Validation ...... 55

Potential Controls on TDS Structure ...... 63

CONCLUSIONS...... 71

Appendix A. Resistivity-porosity derived TDS values ...... 72

Appendix B. Example code for TDS calculations ...... 82

References ...... 87

ix

LIST OF FIGURES Figures Page

1. Wastewater injection depth in California ...... 2

2. Map of the San Joaquin Valley ...... 4

3. Map of the study area ...... 5

4. Stratigraphic columns for the San Joaquin Basin ...... 8

5. Map of major components of the San Joaquin Basin ...... 10

6. Stratigraphic column of Rosedale Ranch ...... 11

7. Stratigraphic column of Fruitvale ...... 12

8. Fruitvale injection and production data ...... 15

9. Rosedale Ranch injection and production data ...... 16

10. Measured geochemical data ...... 20

11. Digitizing borehole geophysical data...... 21

12. TDS conversion chart ...... 24

13. Porosity models ...... 26

14. Temperature models...... 29

15. TDS calculation ...... 31

16. Flow chart of Python algorithm ...... 35

17. RP-derived TDS spatial distribution ...... 36

18. RP-derived TDS histograms ...... 38

19. Experimental variogram...... 40 x

20. Map of all the wells and faults in the study area ...... 44

21. Cross section of groundwater TDS ...... 46

22. Cross section of groundwater TDS prediction certainty ...... 48

23. Contoured surface of the depth to 10,000 ppm TDS ...... 50

24. Contoured surface of the depth to 3,000 ppm TDS ...... 51

25. Epsilon residuals of the original data ...... 54

26. Epsilon residuals of the transformed data ...... 55

27. TDS comparison with Humble parameters ...... 57

28. TDS comparison with Archie parameters ...... 59

29. TDS comparison with custom parameters ...... 61

30. Formation permeability ...... 62

31. Cross section with formations ...... 64

32. Groundwater elevation contours ...... 66

33. Measured TDS vs depth ...... 67

34. Regional geologic cross section ...... 69

xi

1

INTRODUCTION

In California, groundwater resources are in high demand. The recent drought throughout the State has shifted water supply from surface water to underground sources.

In an effort to protect finite water resources, California Senate Bill 4 (SB4, 2013) has revised the monitoring and protection practices of underground sources of drinking water

(USDW). SB4 and the federal Safe Drinking Water Act (1974) defines a USDW as

An aquifer or portion of an aquifer that supplies any public water system or that contains a sufficient quantity of ground water to supply a public water system, and currently supplies drinking water for human consumption, or that contains fewer than 10,000 mg/l total dissolved solids and is not an exempted aquifer.” (40 CFR § 146.3).

This definition includes aquifers (and portions of aquifers) that do not currently supply water to a public water supply but are capable of producing that water.

Locating USDW is an initial challenge for proper monitoring and protection. To map USDW and design monitoring programs, the California State Water Resources

Control Board (SWRCB) has contracted the U.S. Geological Survey (USGS) to carry out the scientific studies needed for the implementation of SB4. California State University,

Sacramento (CSUS) is working with the USGS to assist with data acquisition, management, and analysis.

A primary focus is to determine if oil and gas wastewater operations may be contaminating USDW. Water associated with oil and gas production is commonly

2 referred to as produced water and often has high salt content [Clark and Veil, 2009]. Oil production efficiency from older reservoirs in the San Joaquin Valley has declined over the last several decades, resulting in large produced water to oil ratios [Clark and Veil,

2009]. Produced water is often injected back into the reservoir for improved and/or enhanced oil recovery operations or into a different aquifer for disposal. In California, the disposal injection depths can be shallow, often under 2,000 ft (Figure 1). Due to the drought in California and an increasing dependence on groundwater resources, it is important to ensure produced water injection is not contaminating usable water.

Figure 1. Wastewater injection depth in California

3

Preliminary data indicates shallow wastewater injection in California. Data shown here are the number of wells and their depths to the uppermost perforation. This corresponds to the depth of wastewater injection assuming any fluid injected into these wells will move into the rock formation at the upper most perforated interval. Data are from 1977- 2016 and the depths are grouped into 250 foot bins [Shimabukuro et al., 2015].

Previous work in the San Joaquin Valley has shown groundwater total dissolved solids (TDS) generally increases from east to west [Bertoldi et al., 1991]. This is because the dominant source of recharge for the area is runoff from the Sierra Nevada Range to the east bringing freshwater into the hydrologic system. Conversely, the western margin of the southern San Joaquin Valley is in a rain shadow from the Coast Ranges rendering minor freshwater input [Faunt et al., 2009]. The known general trends of groundwater

TDS within the San Joaquin are helpful, however, more detailed, oil field-scale maps are needed to provide adequate information for wastewater injection operations.

The objective of this project is to map TDS content of groundwater within the

Fruitvale and Rosedale Ranch oil field area located in Kern County, California, and attempt to determine the controls on TDS structure in the subsurface (Figure 2 and 3).

This study uses geophysical well log analysis combined with geochemical measurements to determine groundwater TDS. In the San Joaquin Valley, measurements of groundwater

TDS alone are sometimes too sparse to develop the detailed maps that are essential to groundwater resources management. Analysis of borehole geophysical data from oil and gas wells can provide improved vertical and spatial coverage to supplement the observed

TDS values. The geophysical well logs are found in raster form on the California

4

Department of Conservation’s Division of Oil, Gas, and Geothermal Resources’

(DOGGR) website, and are digitized to expedite computations.

Figure 2. Map of the San Joaquin Valley The San Joaquin Valley located in the southern portion of the Central Valley of California. The study area, the Fruitvale and Rosedale Ranch oil fields, is in the southern region of the San Joaquin Valley.

5

Figure 3. Map of the study area The Fruitvale Calloway area is the northwest portion of the Fruitvale field while the rest of the field is referred to as the main area. TDS was calculated at the wells represented by black markers. The red markers indicate locations of wells where measured TDS values are available from geochemical analyses. The A-A’ line is the location of cross section. The Kern River flows through the southeast section of the Fruitvale field and is a major source of recharge to the shallow aquifer system. Well location and field boundary data are from the California Division of Oil, Gas, and Geothermal Resources (DOGGR) [http://www.conservation.ca.gov/dog/maps/Pages/GISMapping2.aspx, accessed 2015- 2017].

6

Inferring groundwater TDS from geophysical data can be accomplished in different ways. Archie [1942] provided the foundational work to derive the resistivity of groundwater from the resistivity read from geophysical well logs using the well- correlated relationship between conductivity and TDS. Many studies have documented successful application of geophysical well log analysis for groundwater TDS determination [Lyle, 1988; Lindner-Lunsford, 1995; Schnoebelen, 1995; Jorgensen, 1996;

Hamlin and de la Rocha, 2015, Gillespie et al., 2017]. A method review study by Lyle

[1988] reports successful TDS determination using both the resistivity-porosity (RP) method, and the spontaneous potential (SP) method. This study utilizes the preferred RP method which relates deep-reading resistivity logs to groundwater TDS [Schnoebelen,

1995; Kong, 2015, Gillespie et al., 2017]. Although measured TDS values within oil fields are not plentiful, the available data are used to evaluate the accuracy of the analysis.

The study area, the Fruitvale and Rosedale Ranch oil fields (Figure 3), started producing oil as early as the late 1920s. Oil extraction operations in near proximity to the urban area of Bakersfield, CA has rendered the study area as high priority by the USGS

[Jordan and Gillespie, 2016]. Prioritization, along with preliminary observations from measured geochemical samples showing a significant contrast in groundwater TDS between the two fields, has made this area attractive to map groundwater quality and explore what factors control groundwater TDS distributions (i.e. faults, stratigraphy, recharge, etc.)

7

BACKGROUND

Regional Geology

The San Joaquin Valley comprises the southern part of the Great Central Valley of California, which began its existence as a forearc basin in the Late Mesozoic

[Dickinson, 1974, 1976]. The initiation of the San Andreas transform during the Miocene signaled the end of subduction along the California coast [Atwater, 1970]. Although the sedimentary record in the San Joaquin Basin (SJB) is incomplete, especially in the northern section, (Figure 4) basin sedimentation history is formed by depositional sequences of transgressive-regressive units from sea-level changes, and basin-wide and localized tectonics [Bartow, 1991].

The SJB is a northwest-trending asymmetrical structural trough filled with

Tertiary and Quaternary marine and nonmarine sediments [Croft, 1972]. The southern portion of the SJB contains Eocene to Pleistocene-age interbedded sands and shales.

Marine deposition dominated the earlier deposits and culminated in deep water shale, chert, and turbidite deposits of the late Miocene Monterey Formation which forms one of the major hydrocarbon source rocks in the basin (Figure 4). The hydrocarbons sourced from these deposits have migrated into many formations within the southern SJB

[Scheirer and Magoon, 2007]. Following deposition of the Monterey Formation, latest

Miocene and Pliocene sediments are formed primarily of shallow marine deposits and record the final withdrawal of the sea from the San Joaquin Valley [Reid, 1995]. The

Pleistocene Tulare Formation which was deposited in fluvial and lacustrine

8 environments, along with the overlying alluvium, form the major fresh water aquifer system in the southern portion of the SJB.

Figure 4. Stratigraphic columns for the San Joaquin Basin

9

The marine deposits of the Miocene are the origin of much of the hydrocarbons in the region. The fluvial and lacustrine deposits of the Tulare are in the south [Scheirer and Magoon, 2007].

Local Geology

In the subsurface, the northeast-trending Bakersfield Arch is a major structural feature in the study area (Figure 5) [Bartow, 1991; Reid, 1995]. Many oil fields within the

SJB are located along the arch, including Fruitvale and Rosedale Ranch. Oil and gas accumulation in the Fruitvale and Rosedale Ranch fields is attributed to a combination of faulting and variable reservoir permeability [Betts, 1955; Hluza, 1965]. The Fruitvale and

Rosedale Ranch area is composed of an Eocene to recent, southwesterly dipping, sedimentary package approximately 10,000 ft thick that overlies Upper Jurassic basement rocks (Figure 6 and 7). The study area contains two oil fields: the Fruitvale and Rosedale

Ranch. The Fruitvale field consists of two producing areas: the Fruitvale main area and the Calloway area which occupies the northwestern-most area of the field. The Rosedale

Ranch field is located northwest of the Fruitvale field. Each of the fields/areas have separate oil-bearing zones and Rosedale Ranch is likely structurally separated from

Fruitvale [Betts, 1955].

10

Figure 5. Map of major components of the San Joaquin Basin Oil fields are shown with the line pattern. Note the many fields along the Bakersfield arch, including the Fruitvale and Rosedale Ranch fields [Reid, 1995].

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Figure 6. Stratigraphic column of Rosedale Ranch The typical spontaneous potential (SP) and resistivity curves are included on the far right. Note the Macoma Claystone within the Etchegoin and its distinctive electrical log response. The basal sands within the Etchegoin are the major oil producing rocks at Rosedale Ranch [modified from Betts, 1955].

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Figure 7. Stratigraphic column of Fruitvale The nonmarine Chanac Formation is divided into five different members, all of which produce oil. The Fairhaven Sand zone in the basal part of the overlying Etchegoin Formation also produces oil in the field. The Kern River Formation is the major aquifer in the area [modified from Hluza, 1965].

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The Miocene to Holocene units in the study area include the shallow marine Santa

Margarita Formation (~5,000 ft depth), the nonmarine Chanac Formation (~4,000 ft), the shallow marine Etchegoin Formation (~3,000 ft), and the fluvial Kern River Formation

(~2,600 ft to surface) [Betts, 1955; Hluza, 1965; Scheirer and Magoon, 2007] The Upper

Miocene Santa Margarita Sandstone is ~1,100 ft thick and is composed of micaceous sandstone with pebbles that coarsens upward. The Santa Margarita Formation was a minor oil producer and now is mainly used as a water disposal zone. The Mio-Pliocene

Chanac Formation conformably overlies the Santa Margarita Formation and is comprised of fine-to-coarse sands with interbedded siltstones and claystones. The section is 900 to

1,300 ft thick and is a major oil producing zone. Uncomformably resting on the Chanac is the marine Etchegoin Formation of Pliocene age. It is also made up of fine-to-coarse grained sands and shales and produces oil from the basal Lerdo (or Fairhaven) sands. The

Etchegoin also contains the Macoma Claystone in its lower portion which serves as a hydraulic barrier in the area. The Macoma Claystone thickens to the west and is better documented within the Fruitvale Calloway area and Rosedale Ranch part of the study area. Finally, the Plio-Pleistocene Kern River Formation overlies the Etchegoin and extends to the surface with recent alluvium on top. The fluvial Kern River Formation thickness ranges from 2,400 to 2,900 ft and is composed of sandstone and conglomerate with interbedded siltstone and mudstone. It was deposited by braided river channels while the finer-grained interbeds likely represent ephemeral lakes or floodplain deposits

[Bartow and Pittman, 1983].

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Production History

The first oil well in Fruitvale was completed in February 1928 into the Chanac

Formation [Hluza, 1965]. By 1936, 81 wells were producing, and by 1965 almost 400 wells had been drilled. Exploratory wells were drilled in the Fruitvale Calloway area during the 1930s and 1940s, but successful production did not occur until 1957. Seven zones produced within Fruitvale, most of them within the Chanac. Other zones are in the basal Etchegoin (Fairhaven Sand) and minor production from the Santa Margarita

Formation. Currently, there are over 1,000 wells within the Fruitvale oil field, and according to post 1977 data, peak oil and gas production was during the early 1980s at

~90,000 barrels (bbl) per month (Figure 8) [DOGGR, 2017].

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Figure 8. Fruitvale injection and production data Data on the upper graph show water/steam injection and water production volumes for the Fruitvale field. Below, oil and gas production are shown. Data from both graphs show similar trends that generally peak in the early 1980s. All data are from digital records (1977-present) [DOGGR, 2017].

Eight dry wells were drilled in Rosedale Ranch from 1928 to 1943 that encircle the present producing zone. In 1945, new wells in the Upper Miocene sands in the lowermost Chanac Formation started producing 100 bbl per day [Betts, 1955]. By March of 1955, 46 wells had been drilled at Rosedale Ranch. Currently, there are 160 wells.

Post-1977 data show oil production had two peak times, first in the early 1990s at nearly

30,000 bbl per month and another with gas production centered around 2010 (Figure 9).

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Figure 9. Rosedale Ranch injection and production data The data on the upper plot show water/steam injected and water production volumes for the Rosedale Ranch field. Data on the lower graph show oil and gas production. Data trends are similar for the water injected and produced. The oil and gas production trends are similar with an exception of higher oil production throughout the late 1980s and 1990s. Data are from 1977-present [DOGGR, 2017].

In Fruitvale, produced water volume peaked in 1983 at around 1.2 million bbl per month (Figure 8) [DOGGR, 2017]. Water injection rates follow the same trend but reach higher volumes at 1.8 million bbl per month, however, the data include water used for the enhanced oil recovery methods of cyclic steaming and waterflooding. Water production and injection data for Rosedale Ranch are more static, but slightly increase after 2007 to

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650,000 bbl per month (Figure 9). The water production trends are similar to the water injection trends in both fields.

Hydrology

The Kern County area has a hot Mediterranean climate with an average annual temperature of 67 °F, and receives about 6 inches of precipitation per year as rainfall typically from November through February. Evaporation rates are approximately 65 inches per year [California Department of Water Resources, 2017].

The aquifer system within Kern County is generally unconfined to semi-confined and approximately 2,900 ft at its thickest in the east, and thins toward the west [Shelton et al., 2008]. The aquifers exist within the Tulare Formation, Kern River Formation, and the overlying alluvium. Recharge in the study area is largely from the Kern River. Other recharge is from artificial groundwater banking systems that are widespread throughout the region [Shelton et al., 2008]. Additional recharge comes from agriculture and municipal irrigation.

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METHODS

This study uses the well-established RP method to calculate groundwater TDS from borehole geophysical data, and interpolates the data using a geostatistical model.

We use computer programming techniques to apply the RP method and the geostatistics.

This section explains the available measured TDS data that are used to validate the calculations, the petrophysical equations that were applied to calculate TDS, and the methodology of the geostatistical kriging model. Lastly, stratigraphic and fault data were used to help characterize potential controls on groundwater TDS distributions.

Available TDS data

Measured geochemical analyses from oil and gas fields within California have been complied [Gillespie et al., 2017]. The data include the following: well API

(identification number), well operator, well type (i.e. waste disposal, oil and gas, etc.), latitude, longitude, the upper most depth at which the well was perforated (top perforation), field name, geologic formation sampled, and the corresponding TDS value and the source of that value. The Fruitvale and Rosedale Ranch fields have two sources of TDS data: DOGGR, and the Underground Injection Control (UIC) program, which is operated by the U.S. Environmental Protection Agency (EPA). The geochemical data are often reported to these agencies by the oil company operating the well. This study uses the geochemical data from the Fruitvale and Rosedale Ranch fields. Changes in groundwater resistivity may occur near a well from oil production, well stimulation, and/or wastewater injection which results in subsequent resistivity measurements that do

19 not reflect the time of water sampling. Therefore, this study limits the separation time of the spud date (proxy for when the geophysical measurements were collected) and the geochemical sample date to 10 years to avoid non-representative resistivity measurements. Additionally, several wells have two different TDS values at the same location. To reconcile this, the sample closest in time to spud date was used. After these restrictions, there are 10 samples from Fruitvale and 36 samples from Rosedale Ranch.

The geochemical samples have limited coverage of the oil field, particularly in

Fruitvale (Figure 3). The variability of the depths at which the samples were taken and the TDS values are also limited (Figure 10). Therefore, the vertical and spatial gaps are filled with RP-derived TDS values from other wells. The additional wells selected to supplement the analysis were chosen by their location, the depth coverage, quality of the preserved well log, and type of well logs present.

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Figure 10. Measured geochemical data Distribution of the measured geochemical samples taken from the Fruitvale (left column) and the Rosedale Ranch (right column) fields. Depths at which samples are taken, ~3,000 ft to ~5, 000 ft, do not span the full depth range of interest. TDS values have low variability because the samples are always originate from similar depths, therefore, additional TDS values are needed to supplement the geochemical analyses.

The geophysical well logs are found on the DOGGR website

[https://secure.conservation.ca.gov/WellSearch, accessed 2015-2017] as raster images which are digitized using Neuralog software. The software allows the user to create a depth grid with the necessary scale and trace the curves. The digital output is the industry standard log ascii (las) file that contains the data from the well log curves and header information (Figure 11). Some wells were omitted from the analysis due to poor quality or not having all the desired curves. Preferably, well logs contain deep-reading resistivity,

21 shallow-reading resistivity, porosity, and SP curves.

Figure 11. Digitizing borehole geophysical data The Neuralog software can import a raster image of a well log. The curves are then traced and exported in a digital format. The output format is the industry standard log ascii (las) file that contains the well log data and header information.

Petrophysical Equations

The RP method has been successful and well documented since the 1980s [Lyle,

1988; Boeken, 1995; Lindner‐Lunsford, 1995; Schnoebelen, 1995; Jorgensen, 1996;

Hamlin and de le Rocha, 2015; Gillespie et al., 2017]. The RP method is based on a relationship G.E. Archie discovered when measuring the resistivity of water-saturated rock core. He found the resistivity of the water-saturated core was equal to a coefficient, called the formation factor, times the resistivity of the water:

22

푅0 = 퐹 × 푅푤 (1) where,

푅표 = resistivity of 100% water-saturated rock, 퐹 = formation factor,

푅푤 = resistivity of the water.

Further work by Archie showed that the formation factor is related to the porosity of the rock by

푎 퐹 = (2) 휙 푚 where, a = tortuosity factor, 휙 = porosity, m = cementation factor.

One uncertainty when using these equations for TDS calculations is determining values for the variables a and m within the formation factor in Equation 2. The variables a and m cannot be easily measured without fresh core material and lab analysis, therefore, values are typically used from other studies such as Winsauer et al., 1952; Carothers, 1968; and

Carothers and Porter, 1970. The Humble parameters for a and m established by

Winsauer et al., 1952, are a = 0.62 and m = 2.15. Other values often used are the Archie parameters a = 1.0 and m = 2.0 and the Tixier parameters a = 0.81 and m = 2.0 [Lyle,

1988; Asquith and Krygowski, 2004].

23

The reading from a resistivity curve on a well log, 푅푡, represents the total resistivity of the rock and the fluids present. Therefore, outside the oil producing zones where the only fluid present in the formation is water 푅푡 = 푅표. We can also rearrange

Equation 1 to

푅 (3) 푅 = 표. 푤 퐹

Knowledge of the formation factor enables us to determine 푅푤 using the resistivity recorded on a well log. 푅푤 can then be used to calculate TDS if the temperature of the zone is known or can be calculated.

Conductivity (inverse of resistivity) is well correlated to TDS because dissolved ions conduct electrical current. The relationship between resistivity, temperature, and

TDS is shown by the nomogram in Figure 12.

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Figure 12. TDS conversion chart Relationship between dissolved solids, resistivity, and temperature [Schlumberger, 2009].

TDS can be inferred from 푅푤 if the temperature of the fluid is known through the equation from Hughes, [2002] that describes the relationship shown in Figure 12:

푇퐷푆 = 10[(3.562−log10(푅푤75−0.0123))/0.955] (4) where,

푅푤75 = resistivity of water at 75°F.

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Porosity Model

The RP method requires knowledge of the porosity at the location of the calculation (Equation 2). However, many wells in the study area were drilled before porosity logs were in common use. Fortunately, some newer wells were drilled in

Fruitvale and Rosedale Ranch where neutron and density porosity logs are available.

These porosity logs were used to construct a porosity model for the study area to use in the RP-calculations (Figure 13).

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Figure 13. Porosity models Many wells in the study area do not have porosity logs, which are needed for the TDS calculations. The porosity logs that are available were used to create a model (best fit line) to use in the wells without porosity readings in lieu of estimating a constant porosity.

27

Density porosity logging tools measure the electron density of a formation by measuring the energy of Compton-scattered gamma rays returned from the formation

[Asquith and Krygowski, 2004; Ellis and Singer, 2007]. The scattered gamma rays that return are counted on a detector some distance from the emitting source on the logging tool. The number of electron collisions is a function of the amount of electrons, or the electron density. The electron density can be related to bulk density of the formation.

Higher densities within a given lithology represent lower porosity values. Density porosity logs are used with neutron porosity logs to estimate a porosity gradient for the area.

Neutron porosity tools measure the hydrogen concentration within the formation

[Asquith and Krygowski, 2004; Ellis and Singer, 2007]. Neutrons are emitted into the formation where they are slowed by hydrogen atoms. The mass of the hydrogen and the neutrons is nearly equal, leading to momentum loss by elastic scattering. Therefore, hydrogen atoms are responsible for the neutron energy loss. Pore space in the formation is often occupied by hydrogen. Consequently, detected energy loss can be related to porosity. Usually, neutron and density logs are used together for accurate porosity interpretations [Ellis and Singer, 2007].

Only porosity data from the sand intervals is used. Sands were identified where the neutron and density curves were within 2% of each other. Then, the neutron and density porosity data from each of the wells were combined using the root mean square formula from Asquith and Krygowski [2004]

28

휙2 + 휙2 휙 = √ 푁 퐷 . 푁−퐷 2 (5)

Porosity data from the wells were modeled with linear best fit regressions. Slopes and y- intercepts from those best fit lines were averaged to construct a porosity model for the study area (Figure 13). The model was used to create a porosity estimate at every depth for each well where TDS is calculated with the RP Equations 2, 3, and 4.

Temperature Model

푅푤 from Equation 3 must be calibrated to 푅푤75 to solve for TDS (Equation 4).

Therefore, the temperature of the formation water must be known. Similar to porosity logs, temperature logs are not abundant within the study area. However, temperature at the bottom of the borehole is often recorded on the well log header along with the bottom depth. Bottom-hole temperatures and corresponding depths were collected and plotted to create a temperature model (Figure 14). The equation of the best fit line was used to calculate a temperature at every depth for each of the wells in the model. The 푅푤 was converted to 푅푤75 using the modeled temperature gradient in the equation

푇 + 6.77 (6) 푅 = 푅 × 푤75 푤 75 + 6.77 where,

T = temperature in Fahrenheit.

29

Figure 14. Temperature models Temperature models are needed for the study area because the available well logs do not contain temperature curves. Temperatures and the corresponding depths found on well log headers in the study area were plotted to form a temperature gradient. The best fit line was used to calculate a groundwater temperature gradient. Data are from DOGGR.

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TDS Calculations

Because many wells needed to be processed, a code to calculate TDS using the

RP method has been developed with the programming language Python (Figure 15). The code performs the TDS calculations at one-foot depth intervals using the deep-reading resistivity (DRES) from the well log, the porosity model, and the temperature model. The

TDS calculations are only accurate in the clean (low shale-volume), wet sands.

Therefore, the code attempts to filter the calculated TDS curve (green curve in Figure 15) and only select from the sand intervals (blue markers in Figure 15). It selects low shale- volume areas by using the SP, the short resistivity (SRES), and the DRES curves to locate the cleanest sand intervals possible for more reliable TDS calculations [Archie,

1942].

31

Figure 15. TDS calculation This depicts a TDS calculation using the RP method. To the far left in black, the SP curve, along with the interpreted shale baseline (magenta) are used to detect the cleanest sand intervals possible where the petrophysical equations render more accurate results. The SP curve detects potential changes between permeable and non-permeable beds. Where the formation water is more saline than the drilling mud, opposite non-permeable beds (shales) the curve is relatively straight, defining the shale baseline. Conversely, the SP curve opposite permeable beds (sands) will deflect away from the shale baseline,

32 allowing to differentiate lithologies with reasonable accuracy [Ellis and Singer, 2007]. The deep resistivity curve (red) is used to calculate the TDS curve (green). The blue markers are the selected TDS values from low-shale volume intervals. The selected (blue) TDS values are chosen based on an algorithm developed for this study that detects intervals where the difference between the SP curve and the shale baseline is above a certain threshold and there is a significant difference between deep and short resistivity. The far-right column contains the selected values and represents the best estimation of the groundwater TDS profile.

The algorithm attempts to locate low-shale volume intervals through two methods: 1) using the SP curve, and 2) using the DRES and SRES curves. The first method consists of detecting SP deflections. The SP curve records potential changes between an electrode on the Earth’s surface and an electrode on the logging tool. To differentiate lithologies with reasonable accuracy, SP can be used to distinguish permeable and non-permeable beds [Ellis and Singer, 2007]. The SP response opposite non-permeable beds (shales) tends to be relatively constant which establishes the shale baseline [Asquith and Krygowski, 2004]. Permeable formations (sands) are present when the SP curve deflects significantly from the shale baseline. Where the drilling mud is less saline than the formation fluid, the SP curve deflects negatively, or to the left, next to permeable beds. It deflects positively, or to the right of the shale baseline, next to permeable beds if the drilling mud is more saline than the formation water. The latter scenario is referred to as SP reversal. Usually, shale baseline reversals occur at shallow depths where formation water is relatively low salinity. As an initial step to find the low- shale volume intervals, the algorithm creates a shale baseline by applying a moving window command that locates the SP maxima (minima for the reversals) and then

33 computes an average of the maxima (or minima) (usual condition shown by the magenta curve in Figure 15). The algorithm can handle SP reversals if the user identifies and enters the depth at which the reversal ceases. The algorithm now can find SP deflections from the shale baseline to detect sand beds.

To supplement this method, another technique using the resistivity curves is implemented. The second method finds intervals where the DRES and SRES curves are significantly different. The electrodes’ spacing on the DRES tool are farther apart than the SRES. This allows the DRES tool to measure resistivity farther away from the wellbore. The SRES readings are taken near the wellbore. The different measurement locations allow for identification of permeable and non-permeable formations. Where the drilling mud cannot penetrate the wellbore at non-permeable locations, the DRES and

SRES will both measure the formation resistivity and give similar responses. Where the drilling mud can penetrate the formation at permeable locations, the SRES will read the resistivity of the mud filtrate while the DRES will continue to read the formation resistivity. Thus, in permeable (sand) layers DRES and SRES will have differing measurements. The algorithm filters the SP-detected sand intervals by ensuring the DRES and SRES readings are significantly different. The algorithm does not weight the two methods, both conditions must be true to select the TDS value.

A drawback of the sand selecting algorithm is possibly missing some sand intervals. When the drilling mud resistivity and the formation resistivity are similar, the

SP deflection from the shale baseline may not be pronounced enough to be detected.

34

Also, sand intervals may be overlooked when using the DRES and SRES readings, because they too will be alike when the drilling mud and formations resistivity are similar. However, this condition does not occur frequently enough to misrepresent the data.

The most accurate values of RP-derived TDS are represented by the far-right column in Figure 15. After the TDS calculations and the sand bed identification, the code attaches the well latitude and longitude to the TDS values and corresponding depths for the final output data file. Although the code attempts the process automatically, due to variability in the well logs, the user must sometimes adjust parameters, such as depth or the SP deflection threshold, for the highest quality results. Moreover, the user must manually select and check TDS data near the producing zone using any available core analyses, mudlogs, or driller’s logs to ensure data is not used in the presence of oil or gas.

This process was completed for all the selected wells in the Fruitvale-Rosedale Ranch area rendering 364 TDS values with the corresponding xyz coordinates (Appendix A).

The code algorithm is also shown in a flow chart in Figure 16 (Appendix B).

35

Figure 16. Flow chart of Python algorithm Flow chart of Python algorithm used to calculate TDS from digitized well log data and select TDS values from low-shale volume sand beds.

Geostatistics

The RP-derived TDS data are spatially discrete (Figure 17), therefore, the data need to be interpolated for visualization and further analysis. This study uses ordinary kriging because it allows for optimal predictions of unknown values [Davis, 1986; Isaaks and Srivastava, 1989; Kitanidis, 1997; Oliver and Webster, 2014]. Ordinary kriging is a best linear unbiased predictor (BLUP). The predicted values by kriging are weighted linear combinations of the input data. For any given prediction, the weights of the data are selected so that the modeled error variance is minimum and average estimation error

36 is zero. Kriging the data allows for a 3D volume of groundwater TDS to be calculated.

From the 3D model, any cross section or map view style visualization can be constructed.

Figure 17. RP-derived TDS spatial distribution Three-dimensional projection of the RP-derived TDS distribution. The data are distributed throughout Rosedale Ranch (left) and Fruitvale (right). Most data points fall between ~500 ft. and ~5,000 ft.

37

Exploratory Data Analysis and Transformation

The RP-derived TDS data distribution is positively skewed (Figure 18a). TDS generally increases with depth, and due to the limited well depth coverage, higher TDS values (>20,000 ppm) are rarely collected, causing the data set to have approximately a lognormal distribution. Highly skewed distributions can cause biased outcomes in geostatistical analyses [McGrath et al., 2004]. Therefore, the RP-derived TDS data is log- transformed (Figure 18b). There are two reasons for the data transformation. First, the log-transformation provides a less skewed input for kriging. Second, and more importantly, the kriging residuals are more like unit normal variate (see Geostatistical

Model Validation section for further discussion) [McGrath et al., 2004; Oliver and

Webster, 2014].

38

Figure 18. RP-derived TDS histograms The upper histogram of the original RP-derived TDS data reveals the distribution is positively skewed. Generally, TDS increases with depth and the well logs do not typically extend to depths with high (>20,000 ppm) TDS values. Consequently, the TDS data exhibit a lognormal distribution. The TDS data were log transformed (lower histogram) because strongly skewed distributions can cause biased outcomes in geostatistical analyses [McGrath et al., 2004].

39

The Variogram

The experimental variogram provides information about the spatial structure of the data set [Kitanidis, 1997]. The x-axis is the sample interval vector, or distance between two samples. The y-axis is the squared difference between the samples. Thus, the experimental variogram shows data correlation as a function of sample separation distance. The experimental variogram assumes isotropy, and the data are the result of a random process [Matheron, 1963]. The variogram is a mathematical function defined by

1 2 (7) 훾(ℎ) = 퐸 [(푧(퐱) − 푧(퐱′)) ]. 2

Where h or (‖퐱 − 퐱′‖) is the separation distance, and 푧(퐱) and 푧(퐱′) are a coordinate pair of the data set. The process of computing the probability-weighted average over the assemblage is the expectation, denoted E.

The experimental variogram for this study uses the linear variogram model

[Kitanidis, 1997] (Figure 19). The linear model is recommended when the data set is not clearly stationary. A trend between the fields is suspected from examining the measured geochemical data. At similar depths, the measured TDS values in Rosedale Ranch are higher than values in Fruitvale (Figure 10). Also, the linear variogram model only requires two parameters to be estimated, the slope and nugget (behavior near the origin).

The kriging was performed using the Python software package PyKrige

(https://github.com/bsmurphy/PyKrige, Benjamin S. Murphy). The program calibrated the variogram slope to fit the data with 6 lags. The program minimizes the root mean

40 square error of the data and the fit line to determine the slope. The nugget, which accounts for variability within the shortest sampling distance, was manually selected.

Assuming the average error in the TDS calculations is between 15% and 30% [Kong,

2015], and conservatively choosing the upper middle range of 25% corresponds to a variance of 0.0625. This choice for the nugget parameter is also supported by the kriging residual distribution statistics (see Geostatistical Model Validation section). The final parameters for the slope and nugget are 15.37 and 0.0625, respectively.

Figure 19. Experimental variogram Experimental variogram of the RP TDS data from Rosedale Ranch and Fruitvale. The x- axis is the sample interval vector, or distance between two samples. The y-axis is the squared difference between the samples. Therefore, the experimental variogram reveals the spatial structure of the data. A linear variogram model was chosen because there is a

41 trend in the data. The slope is 15.37 and the nugget 0.0625. The nugget accounts for variability within the shortest sampling distance [Kitanidis, 1997]. Adjustments were made for anisotropy within the kriging system. Anisotropy occurs when the data not only depend on the separation distance but also the orientation

[Kitanidis, 1997; Olea, 2012]. For example, TDS may be more likely to be similar along horizontal trends rather than vertical trends due to stratigraphy. To account for this, the coordinate system can be stretched and/or rotated to essentially force the model to be isotropic [Kitanidis, 1997; Olea, 2012]. This type of anisotropy is referred to as geoanisotropy. For this study, we stretched the z-axis by a factor of 10, which was determined by examining the experimental variogram. By using this coordinate transformation, the model becomes isotropic and therefore the variogram is valid.

Kriging System

The kriging system uses a linear function from the input data and weights calculated from a system of linear equations to predict values at new locations. With n measurements at locations 퐱1, 퐱2, … 퐱푛, for a new location 퐱0, the ordinary kriging predicts the unknown value 푧̂ through

푛 (8) 푧̂(퐱0) = ∑ 휆푖 푧(퐱푖) 푖=1 where,

푧(퐱푖) = the input values,

휆푖 = weights at each input value.

42

The weights are determined by solving a set of linear equations with conditions that make them unbiased and have minimum variance. The latter is accomplished by selecting the weights that minimize the prediction error variance, while unbiasedness is achieved by requiring all the weights (scalars) to add up to one using the equations

푛 ∑ 휆푖 훾(‖퐱푖 − 퐱푗‖) + 푣 = 훾(‖퐱푖 − 퐱0‖) 푓표푟 푎푙푙 푗, 푖=1 (9)

푛 ∑ 휆푖 = 1 푖=1 (10) where,

푣 = a Lagrange multiplier (used to minimize the error variance),

퐱0 = location of predicted value.

It is common to use matrix form for the kriging system

퐀퐱 = 퐛. (11)

Solving for x by inverting A provides the weighted solutions for 휆1, 휆2, … 휆푛. And the kriging prediction error can be found using

2 T 휎 (퐱0) = 퐛 퐱 (12) where,

43

휎2 = kriging prediction error variance.

It follows that the kriging error standard deviation (휎) is the square root of the error variance. This system is used to interpolate the RP-derived TDS data to visualize groundwater TDS throughout the Fruitvale and Rosedale Ranch oil fields.

Stratigraphic Data

Formation picks from geophysical well logs for the Fruitvale field are available for selected units [Gillespie, unpublished data]. The data include well number, location

(latitude and longitude), measured depth, and the associated formation name. For this study, the discrete data for the formations have been interpolated into surfaces in the geological interpretation software Petra which produces a xyz grid format output. Data are available for the Macoma Claystone, Fairhaven Sand, Kernco, and the Santa

Margarita Sandstone (see Figure 7). These data are superimposed onto the groundwater

TDS cross section to investigate stratigraphic controls on TDS structure. Similar data from the Rosedale Ranch field were compiled from the DOGGR website and superimposed onto the cross section.

Fault Data

DOGGR Oil Field Summary of Operations documentation provides a contoured map of a formation near the oil horizon with fault locations. [Betts, 1955; Hluza, 1961,

1965]. The top of the Fairhaven Sand is contoured in the Fruitvale main area, the top of the “42-0” Sand (middle Chanac) in the Fruitvale Calloway area, and the top of the Lerdo

44 zone (underlies the Macoma Claystone) in Rosedale Ranch. The maps provide Public

Land Survey (PLS) sections for orientation. Using ArcGIS and the PLS coordinates the faults were digitized for analysis (Figure 20). These data are used to examine any fault control on TDS distributions in the subsurface.

Figure 20. Map of all the wells and faults in the study area Map showing all the wells within the study area along with the faults from Hluza, [1961, 1965], and Betts, [1955]. As suggested by Hluza, [1965] and the well locations in the eastern portion of Fruitvale, oil is apparently fault trapped. Fault location data were derived from contour maps with depths of ~3,000 ft in Fruitvale main area, ~3,800 ft in Fruitvale Calloway area, and ~3,800 ft in Rosedale Ranch. Well location data are from DOGGR.

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RESULTS & DISCUSSION

Groundwater TDS Distribution

A TDS volume in the Fruitvale and Rosedale Ranch area was predicted using the

RP-derived TDS values and kriging. The difference in measured TDS between the two fields (Figure 10) served as a guide on where to visualize the TDS structure. The TDS appears to be significantly different at similar depths between the fields along a northwest-southeast trend. Figure 21 shows the cross section of groundwater TDS along the transect from Figure 3. As shown in Figure 21, groundwater TDS generally increases with depth. TDS values begin to increase rapidly with depth in the Rosedale Ranch area at ~3,000 ft and at ~4,500 ft in the Calloway area. Near the Kern River in the Fruitvale field, TDS values continue to increase only gradually throughout the depth coverage

(5,000 ft).

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Figure 21. Cross section of groundwater TDS Cross section showing groundwater TDS along the transect from Figure 3. A significant groundwater TDS gradient exists between the two fields. In the northwest end of the study area groundwater TDS reaches 10,000 ppm at ~3,500 ft. Toward the southeast,

47 groundwater TDS reaches 10,000 ppm at ~4,500 ft. Note the contour interval is not constant throughout the figure. The vertical exaggeration is 4.8.

The most significant TDS trend is northwest to southeast. To the northwest in the

Rosedale Ranch area, TDS reaches 10,000 ppm TDS at ~3,500 ft. In the Fruitvale area to the southeast, 10,000 ppm TDS is reached significantly deeper around ~4,500 ft. There is also a sudden change in the rate that TDS increases with depth in the Rosedale Ranch area.

Due to the locations of the wells, the data coverage adjacent to the cross section is inconsistent. This affects the certainty of the kriging predictions. The prediction certainty can be thought of as a function of distance to the data points. This is shown in Figure 22 where the kriging standard deviation is displayed along the cross section to demonstrate prediction certainty. This is the standard deviation for log TDS, which is modeled as a normal variate. In Figure 22, cooler colors represent areas nearby data points where the predictions are more certain and warmer colors are areas of less certainty farther from the input data locations. Because data coverage is poor in the deeper areas in Fruitvale where oil is present, the standard deviations are higher.

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Figure 22. Cross section of groundwater TDS prediction certainty Kriging prediction certainty along the cross section. Cooler colors represent lower kriging prediction standard deviation near the data points. The higher kriging standard deviations along the deeper portion to the southeast is due to a lack of data because oil in the producing zones prevents calculating accurate TDS values.

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From a regulatory view point, the depth to the 10,000 ppm TDS defines the

USDW boundary and is the base of protected water, provided the aquifer is not exempt due to the presence of hydrocarbons. This surface is visualized using the TDS volume calculated in the oil fields (Figure 23). The surface is contoured in the study area providing a map of the depth of protected water. The depth to the 10,000 ppm TDS boundary is ~3,500 ft in the Rosedale Ranch area, and deepens toward the southeast. The depth to the previous standard for protected water (3,000 ppm TDS) is shown in Figure

24. The extension of protection to 10,000 ppm TDS results in a depth difference of protected water of ~500 – 600 ft in Rosedale Ranch and up to ~1,000 ft in the Fruitvale area.

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Figure 23. Contoured surface of the depth to 10,000 ppm TDS Contoured surface of the depth of protected water or underground sources of drinking water (USDW) (<10,000 ppm TDS). The USDW extend to ~3,500 ft in the northwest field, Rosedale Ranch, and deepens to the southeast into the Fruitvale field.

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Figure 24. Contoured surface of the depth to 3,000 ppm TDS The previous standard for protected water or underground sources of drinking water (USDW) was 3,000 ppm TDS. Provided the aquifer is not exempt due to the presence of hydrocarbons, the USDW extend to ~3,000 ft in the northwest, and deepens to the southeast. See Figure 23 for the depths to the current standard of 10,000 ppm TDS.

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Model Validation

The TDS prediction model is tested in two ways 1) by validating the geostatistical component, and 2) by validating the RP-calculations. The first is achieved through the analysis of diagnostic statistics of the variogram model. The second is accomplished by comparing the measured TDS values to the predicted TDS values.

Geostatistical Model Validation

Verification of a geostatistical model is often accomplished by analyzing the kriging residuals [Isaaks and Srivastava, 1989; Kitanidis, 1997]. Residuals are the differences between the input data and the predictions. Obtaining a set of residuals that is normally distributed is ideal. For example, in the case of a linear regression, if the regression line follows the data points adequately, all the residuals (difference between the line and the data points) will have a normal distribution. This helps to verify that the model (regression line) is a good predictor of the data. In the case of kriging, the residuals are calculated by entering data points one at a time and predicting the value at the next location to be input. To avoid the same prediction at the second input location, the first prediction is omitted. Thus, there will be n – 1 residuals. The differences between the predictions and the observed values are denoted 훿푘 and calculated by

훿푘 = 푧(퐱푘) − 푧̂(퐱k) 푓표푟 푘 = 2, … , 푛. (13)

The 훿푘 are normalized by the standard deviation to obtain the kriging epsilon residuals 휀 through

53

훿푘 (14) 휀푘 = 푓표푟 푘 = 2, … , 푛. 휎푘

The original RP-derived TDS dataset (Figure 18a) was kriged. The distribution of the kriging epsilon residuals is shown in Figure 25. The transformed dataset (Figure 18b) was also kriged and the epsilon residuals are shown in Figure 26. The distribution statistics are significantly different for each epsilon set (see distribution statistics in insets). The transformed dataset’s kriging epsilon residual distribution is considerably more normal. Most notably the kurtosis, which is a measure of how likely extreme values are, is much lower for the model built with log TDS indicating that extremely inaccurate predictions are less common. This is interpreted to be strong evidence supporting the data transformation. That the epsilon residuals are approximately normal and the mean of the residuals is near zero suggest the selected model is appropriate.

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Figure 25. Epsilon residuals of the original data Distribution of the kriging epsilon residuals of the original RP-derived TDS data. The residual distribution is positively skewed and has high kurtosis (see inset). This indicates that the model is not consistently a good predictor and should be rejected.

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Figure 26. Epsilon residuals of the transformed data Distribution of the log transformed kriging epsilon residuals. Compared to the distribution in Figure 25, this distribution is more normal indicated by the statistics in the inset. The distribution is not skewed and has a much lower kurtosis indicating the model is a better predictor. This is evidence to support a log transformation of the RP-derived dataset before kriging.

RP-Calculations Validation

The RP-calculations of TDS values using the porosity model, temperature model, and the deep-reading resistivity curve from the well logs were compared to the measured

TDS values. The measured TDS values were obtained from the water sampled from the perforated interval from selected oil and gas wells. The depth of the uppermost perforated interval is considered to be the depth at which the TDS value originated. Together with

56 the longitude and latitude of the well, xyz coordinates for each TDS value can be established. Direct comparisons of measured and calculated TDS values are not possible because the measured TDS values always come from the producing interval. To compare calculations and measurements all RP-derived TDS values (n = 364) were put into a 3D kriging model and the predicted TDS value was interpolated for the xyz coordinates of the measured TDS values. These values were plotted against one another to determine the accuracy of the RP-calculations (Figure 27). Figure 27 shows the comparison between the measured TDS and predicted TDS using the Humble parameters for a (0.62) and m

(2.15). The average error between these values is 31%. The model’s prediction of TDS values are overall underestimated. However, TDS is predicted rather accurately in the

Chanac Formation in the Fruitvale field, but not in the Chanac in Rosedale Ranch. This is interpreted to indicate the Humble parameters are not well suited to predict TDS for all the rocks at the study area.

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Figure 27. TDS comparison with Humble parameters Cross plot of the measured TDS values and the predicted TDS values. The data are colored according to the formation the measured data originated. Square markers indicate data from Fruitvale, and the circle markers represent Rosedale Ranch. This indicates the model overall underpredicts TDS. The overall error using this model is 31%. The red line is the best fit line of the TDS data, and the black line is the one-to-one line.

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The a and m parameters are suspected to cause the overall underprediction in the

Etchegoin Formation and parts of the Chanac Formation because these values represent the physical rock properties. Physical rock properties such as pore geometry and cementation can vary by formation and even within a formation. Underpredicted TDS indicates the formation factor 퐹 from Equation 3 should be larger, resulting in lower 푅푤 and higher TDS values. The standard Archie parameters for a (1.0) and m (2.0) will render a larger 퐹 in Equation 2. The RP-calculations were recalculated using the Archie parameters. The comparison of this method is shown in Figure 28. The average error lowers to 19% and the model now slightly overpredicts in the Chanac Formation in

Fruitvale and underpredicts in Rosedale Ranch. This suggests that different rocks require different a and m parameters, sometimes even within the same formation.

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Figure 28. TDS comparison with Archie parameters Cross plot of the measured and modeled TDS values. The TDS data are colored by formation. Square markers indicate data from Fruitvale, and the circle markers represent Rosedale Ranch. Using the Archie parameters, the model’s predictions are now slightly over and under predicting TDS depending on the formation and location. The average error using this method is 19%. The red line is the best fit line of the TDS data, and the black line is the one-to-one line.

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Can we calibrate a and m using comparisons to the measured TDS data? If we customize a and m based off the formation and location of the calculations, we can achieve a better fit to the measured data (Figure 29). With custom parameters, the average error lowers to 11%, and we no longer systematically over or under predict TDS.

Using this approach, the Etchegoin Formation still uses the Archie parameters in both fields. However, the other formations in Fruitvale use a = 0.70 and m = 2.0, and the others in Rosedale Ranch use a = 1.0 and m = 2.04.

The specific reason for needing different a and m parameters is unknown.

However, it is possible that the environment of deposition and/or sediment sources are enough to contrast the physical rock properties. This idea may be supported by the

Pliocene Etchegoin Formation recording a marine transgression onto unconformable

Pliocene-Miocene rocks after a 1-million-year hiatus [Bartow, 1991; Scheirer and

Magoon, 2007]. Moreover, the marine Etchegoin is underlain and overlain by nonmarine sediments. The marine origins of the Etchegoin may play a role in the a and m parameter requirements. Lithological descriptions also vary somewhat for the Etchegoin. For example, it is the only interval in the study area commonly described as micaceous [Betts,

1955; Hluza, 1965].

Furthermore, the fact that the model predicts better using the same Archie parameters in the Etchegoin in both fields is supported by core analyses shown in Figure

30. Permeability from rock sidewall core from Fruitvale and Rosedale Ranch indicate that in both fields the Etchegoin Formation permeability is similar. Consequently, we

61 expect those rocks to require similar parameters. Conversely, the permeability within the

Chanac and Santa Margarita Formations differs between the two fields, suggesting that the a and m parameters will vary between the two fields. This supports using different values of a and m within the Chanac and other formations in Fruitvale and Rosedale

Ranch.

Figure 29. TDS comparison with custom parameters

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Cross plot of the measured and modeled TDS values. The TDS data are colored by formation. Square markers indicate data from Fruitvale, and the circle markers represent Rosedale Ranch. Using the Archie parameters in the Etchegoin Formation and calibrated parameters elsewhere, the model’s predictions and the measured data are strongly correlated. The average error using this method is 11% with R2 = 0.97. The red line is the best fit line of the TDS data, and the black line is the one-to-one line.

Figure 30. Formation permeability

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Sidewall core analyses of permeability in Fruitvale and Rosedale Ranch. The average permeability of the Etchegoin Formation in Rosedale Ranch is 662 mD and in Fruitvale it is 671 mD. This supports using the same parameters for a and m in both fields. However, the permeability in the other formations are not similar between fields, this supports using different a and m parameters in each field in the other formations.

Potential Controls on TDS Structure

Understanding what determines the TDS distributions can assist in future groundwater TDS mapping. The distribution of groundwater TDS (Figure 21) may be controlled by several factors. Depth, faulting, groundwater recharge, and stratigraphy are likely the dominant controls. Generally, TDS increases with depth because the water at depth has more time to interact with the rock and is less likely to be flushed by recharge.

Faulting can provide preferential pathways for fluid migration or inhibit fluid flow via fault gouge or by displacement causing non-permeable beds to lie next to permeable beds. Bedding planes and relative permeability are stratigraphic factors that can influence groundwater flow paths allowing for similarly sourced waters to stay isolated from one another. Faulting and stratigraphy are actually just influencing groundwater recharge which can freshen the more saline connate water. Fresh water recharge likely becomes a more significant factor when the recharge source is proximal.

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Figure 31. Cross section with formations Cross section from Figure 3 showing groundwater TDS values with formation data superimposed. The arrow connects the base of the Macoma Claystone over a data gap. It appears that TDS may be fault controlled in the northwest, stratigraphically controlled in

65 the center of the section, and freshened by the Kern River toward the southeast. The white box in the lower right indicates the location of the Kern River at the surface.

Available formation data and the Kern River location was superimposed onto the groundwater TDS cross section to investigate the controlling factors of TDS (Figure 31).

The Kern River lies in the southeast portion of the transect. The river is a significant contributor of groundwater recharge in the area. It is possible that shallow and deep hydraulic connections exist beneath the river, allowing fresh water input to replace the more saline connate water as suggested by the TDS trends below the river. We contoured groundwater elevation data [California Department of Water Resources, 2017] to reveal the recharge source in the study area. The data are from the 2000 water year, which has the best spatial coverage. Groundwater flow is orthogonal to groundwater contours

[Fetter, 1996]. Groundwater surface elevations shown in Figure 32 are higher near the river and indicate flow originates around the Kern River. Thus, the Kern River does supply the area with fresh water input from the Sierra uplands to the east. The TDS contoured surfaces shown in Figures 23 and 24 also support this hypothesis. However, the surface trends are not orthogonal to the river, possibly due to preferential groundwater flow complexities along fault lines (Figure 20). Further work is needed to determine if any such deep-shallow hydraulic connections exist.

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Figure 32. Groundwater elevation contours Groundwater elevation data from wells (black markers) in the study area contoured to show the water surface elevations to reveal groundwater flow directions. The data are elevation above sea level in feet. Apparently, shallow groundwater flow originates from the Kern River, indicating it provides fresh water recharge to the area. This supports the hypothesis that the river freshens deep groundwater beneath the river provided there exists a deep-shallow hydraulic connection. Data from the California Department of Water Resources.

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In the Fruitvale Calloway area (center of the cross section) the TDS trend appears to parallel the stratigraphy (Figure 31). This suggests the TDS structure in this area may be controlled by the stratigraphy. However, it is notable that a large range of TDS values exist laterally within the same formation (i.e. Chanac) (Figure 31 and 33).

Figure 33. Measured TDS vs depth Plot showing the measured TDS data and the corresponding depths colored by formation. Square markers indicate data from Fruitvale, and the circle markers represent Rosedale Ranch. This demonstrates that TDS values can vary greatly within a single formation.

The TDS distribution may be fault controlled toward the northwest area as shown in the cross section. A major normal fault in the area is located near the highest TDS gradient between the Calloway and Rosedale Ranch area (Figure 32) [Bartow, 1984]. A

68 cross section from the work of Bartow [1984] shows a normal fault exists within the

Fruitvale-Rosedale Ranch area. However, the fault is not shown to penetrate shallow enough to affect the formations shown on the cross section in Figure 31. It is possible that the major fault extends farther than previously documented. Additionally, Betts [1955] reports that Rosedale Ranch oil accumulations are structurally separated from Fruitvale reserves rendering Rosedale Ranch its own field designation. The faults mapped in the

Rosedale Ranch field (Figure 20) are at similar depths as the abrupt TDS gradient. Small, vertical displacements and fault gouge likely render these faults fluid barriers [Betts,

1955]. The hydraulic isolation provided by the major and minor faults in the area along with the low-permeable Macoma Claystone may have prevented fresh water recharge into the Rosedale Ranch area leaving groundwater with higher TDS at more shallow depths than waters in Fruitvale. This suggests that groundwater TDS is in part controlled by Miocene faults within the study area.

69

Figure 34. Regional geologic cross section

70

Cross section showing the major normal fault of Miocene age in the study area. The cross section passes directly through the Rosedale Ranch and Fruitvale fields. The fault is highlighted by an arrow in the western part of the cross section and penetrates the Fruitvale Shale. The overlying Santa Margarita Sandstone (pink), Chanac (red), and Etchegoin (light blue) are not shown to be faulted. However, it may be possible smaller faults stemming from the major fault could be acting as a fluid barrier not allowing fresh water recharge into the northwestern area of the oil fields (Rosedale Ranch). Cross section and map modified from Bartow, [1984].

71

CONCLUSIONS

This study used the resistivity-porosity method to map groundwater TDS distributions in the Fruitvale and Rosedale Ranch oil fields located near Bakersfield,

California. A subsurface temperature model along with a porosity model was used in concert with digitized geophysical borehole data from oil and gas wells to calculate groundwater TDS. The inferred TDS data were used in a three-dimensional geostatistical kriging model to interpolate the TDS values. The model was tested using diagnostic statistics and by comparing predicted and observed TDS values from geochemical analyses. Predicted TDS and measured TDS comparisons shown in Figures 27, 28, and

29 indicate different rocks require specific parameters in the petrophysical equations to render the most accurate predictions of TDS.

After validation, the model was used to visualize a cross section of groundwater

TDS (Figure 21) to understand the TDS structure within the study area. A prediction certainty was also quantified to assist with interpretation and future data acquisition efforts (Figure 22). Depth of USDW maps were also constructed to show the overall trends of the 3,000 ppm TDS (previous standard) and 10,000 ppm TDS (current standard) boundaries (Figures 23 and 24). Several potential controls on TDS distributions were considered, including depth, freshwater recharge, stratigraphy, and faulting. It appears these factors play a role in establishing the groundwater TDS distribution, although more work is needed to identify the mechanisms of the proposed factors. A better understanding of these controls on TDS can assist future TDS mapping efforts.

72

Appendix A

Resistivity-porosity derived TDS values API Depth (ft) TDS (ppm) Latitude Longitude 02906727 1055 470.82 35.411429 -119.080169 02906727 1134 754.22 35.411429 -119.080169 02906727 1269 610.72 35.411429 -119.080169 02906727 2935 1200.64 35.411429 -119.080169 02906727 3442 2251.88 35.411429 -119.080169 02906727 3950 6048.76 35.411429 -119.080169 02906741 1023 679.23 35.357343 -119.063893 02906741 1332 524.90 35.357343 -119.063893 02906741 1793 955.10 35.357343 -119.063893 02906741 1957 776.21 35.357343 -119.063893 02906741 2113 887.59 35.357343 -119.063893 02906741 2229 838.29 35.357343 -119.063893 02906741 2412 892.58 35.357343 -119.063893 02906741 2600 854.48 35.357343 -119.063893 02906741 2831 1369.21 35.357343 -119.063893 02906741 3073 1939.56 35.357343 -119.063893 02906741 3979 4562.50 35.357343 -119.063893 02906741 4204 8153.67 35.357343 -119.063893 02906778 976 525.15 35.396215 -119.085649 02906778 1625 650.24 35.396215 -119.085649 02906778 2340 941.03 35.396215 -119.085649 02906778 3031 969.66 35.396215 -119.085649 02906778 3638 3199.30 35.396215 -119.085649 02906778 3799 4117.84 35.396215 -119.085649 02908225 1109 973.83 35.406634 -119.038061 02908225 2005 690.50 35.406634 -119.038061 02908225 2189 735.17 35.406634 -119.038061 02908225 2341 1140.59 35.406634 -119.038061 02908225 2601 993.22 35.406634 -119.038061 02908225 2653 1028.83 35.406634 -119.038061 02908225 2800 2084.12 35.406634 -119.038061 02908234 759 999.27 35.417419 -119.055286 02908234 1129 823.42 35.417419 -119.055286

73

02908234 1441 1056.75 35.417419 -119.055286 02908234 1568 691.73 35.417419 -119.055286 02908234 1672 789.14 35.417419 -119.055286 02908234 1709 646.62 35.417419 -119.055286 02908234 2584 793.94 35.417419 -119.055286 02908234 2673 623.25 35.417419 -119.055286 02908357 637 559.54 35.415172 -119.108753 02908357 819 629.63 35.415172 -119.108753 02908357 1353 614.68 35.415172 -119.108753 02908357 1467 525.28 35.415172 -119.108753 02908357 1576 609.09 35.415172 -119.108753 02908357 2515 677.03 35.415172 -119.108753 02908357 3161 1166.66 35.415172 -119.108753 02908357 3837 4739.22 35.415172 -119.108753 02908386 524 610.15 35.395339 -119.050619 02908386 1691 641.31 35.395339 -119.050619 02908386 2033 1115.32 35.395339 -119.050619 02908386 2605 778.76 35.395339 -119.050619 02908386 2919 1152.61 35.395339 -119.050619 02908386 2968 2034.63 35.395339 -119.050619 02908404 558 455.49 35.393377 -119.055216 02908404 618 543.02 35.393377 -119.055216 02908404 1180 709.86 35.393377 -119.055216 02908404 1564 542.93 35.393377 -119.055216 02908404 1898 956.15 35.393377 -119.055216 02908404 2021 765.94 35.393377 -119.055216 02908404 2608 696.22 35.393377 -119.055216 02908404 2820 735.12 35.393377 -119.055216 02908404 3111 1308.80 35.393377 -119.055216 02908472 689 515.92 35.41332 -119.110861 02908472 1002 883.59 35.41332 -119.110861 02908472 1057 288.34 35.41332 -119.110861 02908472 1594 432.06 35.41332 -119.110861 02908472 2025 635.18 35.41332 -119.110861 02908472 2847 1015.51 35.41332 -119.110861 02908472 3468 4278.03 35.41332 -119.110861 02908472 4220 4784.38 35.41332 -119.110861 02908473 996 516.37 35.413495 -119.108526

74

02908473 2267 816.37 35.413495 -119.108526 02908473 2741 595.22 35.413495 -119.108526 02908473 3075 729.51 35.413495 -119.108526 02908473 3108 731.76 35.413495 -119.108526 02908473 3146 1550.08 35.413495 -119.108526 02908473 3855 4578.21 35.413495 -119.108526 02908476 668 705.55 35.429298 -119.108762 02908476 815 471.81 35.429298 -119.108762 02908476 850 666.93 35.429298 -119.108762 02908476 1006 302.36 35.429298 -119.108762 02908476 1124 569.45 35.429298 -119.108762 02908476 1190 739.90 35.429298 -119.108762 02908476 1852 975.11 35.429298 -119.108762 02908476 2558 758.14 35.429298 -119.108762 02908476 2851 1136.23 35.429298 -119.108762 02908476 2914 820.70 35.429298 -119.108762 02908476 3204 2049.50 35.429298 -119.108762 02908476 3377 2343.15 35.429298 -119.108762 02908483 1207 578.30 35.406186 -119.106549 02908483 1787 1039.84 35.406186 -119.106549 02908483 2088 955.84 35.406186 -119.106549 02908483 2891 1102.28 35.406186 -119.106549 02908483 3010 988.00 35.406186 -119.106549 02908483 3408 2824.36 35.406186 -119.106549 02908483 3723 5582.25 35.406186 -119.106549 02908483 4358 13251.81 35.406186 -119.106549 02908495 1672 929.64 35.376226 -119.040899 02908495 1827 861.83 35.376226 -119.040899 02908495 2366 940.86 35.376226 -119.040899 02908495 3838 852.96 35.376226 -119.040899 02908495 4095 705.50 35.376226 -119.040899 02908495 4483 2566.39 35.376226 -119.040899 02908495 4712 2973.51 35.376226 -119.040899 02930945 1002 643.05 35.400878 -119.110975 02930945 2035 666.91 35.400878 -119.110975 02930945 2191 793.16 35.400878 -119.110975 02930945 3500 4262.19 35.400878 -119.110975 02930945 3944 8000.65 35.400878 -119.110975

75

02930945 4670 27956.77 35.400878 -119.110975 02930956 686 341.35 35.395323 -119.110989 02930956 919 399.84 35.395323 -119.110989 02930956 953 469.87 35.395323 -119.110989 02930956 2336 775.56 35.395323 -119.110989 02930956 2408 716.70 35.395323 -119.110989 02930956 3123 1306.93 35.395323 -119.110989 02930956 3289 2025.94 35.395323 -119.110989 02930956 3351 2574.99 35.395323 -119.110989 02930956 3513 3892.79 35.395323 -119.110989 02930956 4018 7480.57 35.395323 -119.110989 02930956 4264 21215.55 35.395323 -119.110989 02930956 4343 20468.90 35.395323 -119.110989 02930961 2091 831.28 35.421921 -119.060103 02930961 2288 539.95 35.421921 -119.060103 02930961 2407 1057.80 35.421921 -119.060103 02930961 2464 959.10 35.421921 -119.060103 02930961 2607 1257.82 35.421921 -119.060103 02930961 2878 1569.26 35.421921 -119.060103 02930961 3125 2353.08 35.421921 -119.060103 02940552 1020 410.35 35.42044 -119.111611 02940552 1935 931.27 35.42044 -119.111611 02940552 2235 624.84 35.42044 -119.111611 02940552 2488 727.17 35.42044 -119.111611 02940552 3063 1070.80 35.42044 -119.111611 02940552 3112 694.54 35.42044 -119.111611 02940552 3325 1198.73 35.42044 -119.111611 02940552 3978 3826.06 35.42044 -119.111611 02940552 4192 4684.27 35.42044 -119.111611 02940552 4254 6096.60 35.42044 -119.111611 02940552 4470 16802.71 35.42044 -119.111611 02940552 4578 22647.43 35.42044 -119.111611 02944174 1527 1409.15 35.376981 -119.099964 02944174 2397 1877.74 35.376981 -119.099964 02944174 3373 1307.26 35.376981 -119.099964 02944174 3411 2453.42 35.376981 -119.099964 02944174 3604 2652.43 35.376981 -119.099964 02944174 3776 7165.87 35.376981 -119.099964

76

02944174 4305 8605.07 35.376981 -119.099964 02949051 695 1942.80 35.415679 -119.055683 02949051 777 1569.51 35.415679 -119.055683 02949051 1154 1927.34 35.415679 -119.055683 02949051 1426 2102.31 35.415679 -119.055683 02949051 1737 1997.87 35.415679 -119.055683 02949051 2103 1825.81 35.415679 -119.055683 02949051 2221 1848.51 35.415679 -119.055683 02954448 1924 1965.15 35.418587 -119.061575 02954448 2112 1779.27 35.418587 -119.061575 02954448 2152 1736.66 35.418587 -119.061575 02954448 2196 2043.26 35.418587 -119.061575 02954448 2377 1562.51 35.418587 -119.061575 02954448 2450 1784.13 35.418587 -119.061575 02954448 2542 1114.93 35.418587 -119.061575 02954448 2684 1535.43 35.418587 -119.061575 02954448 2772 1354.78 35.418587 -119.061575 02954448 2871 1569.11 35.418587 -119.061575 02954448 3185 2483.10 35.418587 -119.061575 02954448 3363 2517.14 35.418587 -119.061575 02954448 3880 1195.01 35.418587 -119.061575 02954448 4090 2579.76 35.418587 -119.061575 02954448 4265 3824.28 35.418587 -119.061575 02954448 4455 9377.46 35.418587 -119.061575 02961054 964 492.21 35.380751 -119.057022 02961054 996 469.35 35.380751 -119.057022 02961054 1130 405.25 35.380751 -119.057022 02961054 1403 969.53 35.380751 -119.057022 02961054 1615 1085.89 35.380751 -119.057022 02961054 1911 938.99 35.380751 -119.057022 02961054 1989 854.57 35.380751 -119.057022 02961054 2346 1823.84 35.380751 -119.057022 02961054 2534 1577.29 35.380751 -119.057022 02961054 2670 2174.81 35.380751 -119.057022 02961054 2740 1947.89 35.380751 -119.057022 02961054 2854 1796.04 35.380751 -119.057022 02961054 3152 1043.14 35.380751 -119.057022 02961054 3231 652.32 35.380751 -119.057022

77

02961054 3728 2646.96 35.380751 -119.057022 02961054 3856 4128.36 35.380751 -119.057022 02961368 1320 761.11 35.423577 -119.091672 02961368 1474 771.58 35.423577 -119.091672 02961368 2203 1483.93 35.423577 -119.091672 02961368 2642 2285.64 35.423577 -119.091672 02961368 3478 2483.25 35.423577 -119.091672 02961368 3820 3396.94 35.423577 -119.091672 02961368 3861 3289.68 35.423577 -119.091672 02961368 4060 4490.77 35.423577 -119.091672 02961368 4620 16000.86 35.423577 -119.091672 02961368 4781 17181.68 35.423577 -119.091672 02961368 4849 15004.52 35.423577 -119.091672 02965217 2146 1363.96 35.367999 -119.077206 02965217 2756 1196.98 35.367999 -119.077206 02965217 2982 1941.97 35.367999 -119.077206 02965217 3019 1420.06 35.367999 -119.077206 02965217 3466 1931.86 35.367999 -119.077206 02965217 3677 1942.85 35.367999 -119.077206 02965217 3747 4532.71 35.367999 -119.077206 02965217 3794 6053.47 35.367999 -119.077206 02965217 3821 7491.30 35.367999 -119.077206 02965217 3986 6534.18 35.367999 -119.077206 02965217 4053 9413.75 35.367999 -119.077206 02965217 4120 10113.11 35.367999 -119.077206 02965550 1367 923.38 35.384478 -119.060236 02965550 1522 980.71 35.384478 -119.060236 02965550 1572 1015.81 35.384478 -119.060236 02965550 1691 1211.66 35.384478 -119.060236 02965550 2715 1179.89 35.384478 -119.060236 02965550 2874 848.28 35.384478 -119.060236 02965550 3082 1421.88 35.384478 -119.060236 02967952 828 1193.30 35.386659 -119.072518 02967952 966 1252.11 35.386659 -119.072518 02967952 1877 1386.75 35.386659 -119.072518 02967952 2207 1428.55 35.386659 -119.072518 02967952 2608 2021.60 35.386659 -119.072518 02967952 3103 1734.02 35.386659 -119.072518

78

02967952 3688 3050.28 35.386659 -119.072518 02974054 1213 706.98 35.392284 -119.095723 02974054 1214 728.18 35.392284 -119.095723 02974054 2192 924.07 35.392284 -119.095723 02974054 2891 634.55 35.392284 -119.095723 02974054 3827 3659.18 35.392284 -119.095723 02974054 4375 11783.83 35.392284 -119.095723 02988999 963 870.33 35.378493 -119.073935 02988999 1061 913.54 35.378493 -119.073935 02988999 1214 956.88 35.378493 -119.073935 02988999 1333 1081.81 35.378493 -119.073935 02988999 1875 1380.01 35.378493 -119.073935 02988999 2680 1018.21 35.378493 -119.073935 02988999 3382 3853.83 35.378493 -119.073935 02988999 3574 2089.89 35.378493 -119.073935 02988999 3975 3773.50 35.378493 -119.073935 02988999 4146 3958.45 35.378493 -119.073935 02988999 4394 7673.55 35.378493 -119.073935 02988999 4566 10911.12 35.378493 -119.073935 02988999 4640 12315.14 35.378493 -119.073935 02900704 1035 756.73 35.407958 -119.149922 02900704 1093 632.55 35.407958 -119.149922 02900704 1232 583.67 35.407958 -119.149922 02900704 1347 658.81 35.407958 -119.149922 02900704 1473 549.83 35.407958 -119.149922 02900704 1695 694.85 35.407958 -119.149922 02900704 1914 715.74 35.407958 -119.149922 02900704 1958 619.00 35.407958 -119.149922 02900704 2145 762.62 35.407958 -119.149922 02900704 3310 7991.77 35.407958 -119.149922 02900704 3343 8755.59 35.407958 -119.149922 02916785 998 1040.87 35.431366 -119.126375 02916785 1164 787.34 35.431366 -119.126375 02916785 1364 1313.79 35.431366 -119.126375 02916785 1529 1188.37 35.431366 -119.126375 02916785 2043 1268.41 35.431366 -119.126375 02916785 2763 998.61 35.431366 -119.126375 02916785 2984 1120.95 35.431366 -119.126375

79

02916785 3108 1103.91 35.431366 -119.126375 02916785 3176 2364.12 35.431366 -119.126375 02916785 3309 3594.07 35.431366 -119.126375 02916785 3980 11585.42 35.431366 -119.126375 02916785 4769 19291.56 35.431366 -119.126375 02916810 1022 2007.87 35.428804 -119.142285 02916810 1477 1286.62 35.428804 -119.142285 02916810 1569 1292.21 35.428804 -119.142285 02916810 1727 1082.39 35.428804 -119.142285 02916810 2330 1908.06 35.428804 -119.142285 02916810 2440 1689.97 35.428804 -119.142285 02916810 2642 1355.22 35.428804 -119.142285 02916810 2797 1560.10 35.428804 -119.142285 02916810 2979 2318.42 35.428804 -119.142285 02916810 3358 5634.89 35.428804 -119.142285 02916810 3493 7560.90 35.428804 -119.142285 02916810 3619 7928.17 35.428804 -119.142285 02916840 910 721.09 35.435414 -119.133116 02916840 1046 577.04 35.435414 -119.133116 02916840 1142 815.37 35.435414 -119.133116 02916840 1647 747.82 35.435414 -119.133116 02916840 2723 1102.51 35.435414 -119.133116 02916840 2776 1160.85 35.435414 -119.133116 02916840 3004 1633.26 35.435414 -119.133116 02916840 3129 1867.13 35.435414 -119.133116 02916840 3310 4634.63 35.435414 -119.133116 02916840 3431 7422.49 35.435414 -119.133116 02916840 3508 8668.73 35.435414 -119.133116 02916840 3685 14758.77 35.435414 -119.133116 02916857 1438 705.39 35.428974 -119.145977 02916857 1489 1433.40 35.428974 -119.145977 02916857 2748 1377.01 35.428974 -119.145977 02916857 2881 1863.81 35.428974 -119.145977 02916857 2940 2211.94 35.428974 -119.145977 02916857 3432 7706.22 35.428974 -119.145977 02916857 3465 7826.98 35.428974 -119.145977 02916857 3509 10281.25 35.428974 -119.145977 02916857 3603 13504.33 35.428974 -119.145977

80

02916857 4903 26422.63 35.428974 -119.145977 02916866 1230 573.76 35.420314 -119.133076 02916866 1400 1157.54 35.420314 -119.133076 02916866 2862 965.04 35.420314 -119.133076 02916866 3228 2636.15 35.420314 -119.133076 02916866 3286 2315.86 35.420314 -119.133076 02916866 3399 4049.07 35.420314 -119.133076 02916866 3481 5401.21 35.420314 -119.133076 02916866 3660 10893.81 35.420314 -119.133076 02916866 4477 22618.31 35.420314 -119.133076 02916866 4803 35835.00 35.420314 -119.133076 02916870 850 1181.76 35.436933 -119.127407 02916870 1045 574.24 35.436933 -119.127407 02916870 1451 1063.78 35.436933 -119.127407 02916870 1491 1442.07 35.436933 -119.127407 02916870 2257 1135.02 35.436933 -119.127407 02916870 3056 1110.62 35.436933 -119.127407 02916870 3250 2558.71 35.436933 -119.127407 02916870 3360 3679.73 35.436933 -119.127407 02916870 3436 5457.13 35.436933 -119.127407 02916870 4270 13844.18 35.436933 -119.127407 02969816 1526 1091.65 35.428974 -119.145977 02969816 2174 921.48 35.428974 -119.145977 02969816 3305 4084.44 35.428974 -119.145977 02969816 3655 12712.75 35.428974 -119.145977 02969816 4510 37558.91 35.428974 -119.145977 02976080 803 1922.94 35.435947 -119.145829 02976080 1265 1247.00 35.435947 -119.145829 02976080 1306 1511.40 35.435947 -119.145829 02976080 1984 1126.26 35.435947 -119.145829 02976080 2340 1129.41 35.435947 -119.145829 02976080 3056 4367.53 35.435947 -119.145829 02976080 3087 4979.55 35.435947 -119.145829 02976080 3125 4686.79 35.435947 -119.145829 02976080 3155 4713.84 35.435947 -119.145829 02976080 3215 5384.69 35.435947 -119.145829 02977100 847 733.24 35.437341 -119.145462 02977100 1254 880.83 35.437341 -119.145462

81

02977100 1599 847.58 35.437341 -119.145462 02977100 1673 849.51 35.437341 -119.145462 02977100 2422 697.63 35.437341 -119.145462 02977100 2907 2289.28 35.437341 -119.145462 02977100 3299 5603.90 35.437341 -119.145462 02985483 1921 828.12 35.44549 -119.150052 02985483 2069 1521.78 35.44549 -119.150052 02985483 3062 3413.83 35.44549 -119.150052 02985483 3100 3773.20 35.44549 -119.150052 02985483 3228 6048.09 35.44549 -119.150052 02985483 3418 14723.67 35.44549 -119.150052 02986354 991 1086.55 35.449667 -119.109141 02986354 2717 812.38 35.449667 -119.109141 02986354 3045 1315.40 35.449667 -119.109141 02986354 3665 1977.93 35.449667 -119.109141 02986354 3940 4129.73 35.449667 -119.109141 02986354 4700 37936.02 35.449667 -119.109141 02987344 873 730.63 35.443388 -119.143235 02987344 1183 796.16 35.443388 -119.143235 02987344 1259 692.84 35.443388 -119.143235 02987344 1434 861.72 35.443388 -119.143235 02987344 2575 1744.50 35.443388 -119.143235 02987344 2714 1716.50 35.443388 -119.143235 02987344 2828 1591.60 35.443388 -119.143235 02987344 3070 3306.71 35.443388 -119.143235 02987344 3195 4360.01 35.443388 -119.143235 02987344 3365 6294.27 35.443388 -119.143235

82

Appendix B

Example code for TDS calculations. from matplotlib import pyplot as plt import pandas as pd import numpy as np

############ read in the well log data ############ filename = '02906741.txt' f = open(filename) lines = f.readlines() f.close()

# this skips the header by finding '~A' which denotes the start of the data counter = 0 for line in lines: l = line.strip().split() if l[0] == '~A': counter break else: counter = counter + 1

# splits up the header line to get column names and API number line = lines[counter].strip().split() names = line[1:] APInum = lines[20].strip().split()

# creates the dataframe df = pd.read_table(filename, skiprows=counter+1, names=names, sep = '\s +') df[df<-900.0] = None

########### rename columns to standardize name for the curves ######### ###

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# deep resistivity dres_old_names = ['DRES', 'A010', 'AM64"', 'AM64''', 'AO10FT', 'INDUCT' , 'LLD', 'DEEP','INDUC', 'ILD',"64''AM",'RESAM64'] dres_new_name = ['DRES'] * len(dres_old_names) df.rename(columns=dict(zip(dres_old_names, dres_new_name)), inplace=Tru e)

# short resistivity sres_old_names = ['AM16', 'AM16''', 'AM10IN', 'SN', '18''NORM', '18"NOR M', 'SHALLOW', 'LLS', 'AM16"', 'GUARD', '16"N',"16''AM",' RESAM16'] sres_new_name = ['SRES'] * len(sres_old_names) df.rename(columns=dict(zip(sres_old_names, sres_new_name)), inplace=Tru e)

## Calculating TDS values ##

################### Archie parameters #####################

# temperature gradient df['TEMP'] = 0.01035047 * df.DEPTH + 72.8927376

# porosity gradient df['POR'] = -0.0027314169948304992 * df.DEPTH + 37.266846368601492

# Calculates 'F' a = 1.0 m = 2.0 df['F'] = (a / (df.POR * 0.01) ** m)

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# formation resistivity R_o = df.DRES

# water resistivity df['R_w'] = (R_o / df.F)

# calculates resistivity @ 75 F for equation below df['R_w75'] = ((df.TEMP + 6.77) * (df.R_w)) / (75.0 + 6.77)

# calculates TDS df['TDS'] = 10.0 ** (((3.562 - np.log10(df.R_w75 - 0.0123)) / 0.955))

###################### Humble parameters ######################

# temperature gradient for Fruitvale df['TEMP'] = 0.01035047 * df.DEPTH + 72.8927376

# porosity gradient for Fruitvale df['POR'] = -0.0027314169948304992 * df.DEPTH + 37.266846368601492

# Calculates 'F' a = 0.62 m = 2.15 df['F'] = (a / (df.POR * 0.01) ** m)

# formation resistivity R_o = df.DRES

# water resistivity df['R_w'] = (R_o / df.F)

# calculates resistivity @ 75 F for equation below df['R_w75'] = ((df.TEMP + 6.77) * (df.R_w)) / (75.0 + 6.77)

# calculates TDS

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df['TDS_hum'] = 10.0 ** (((3.562 - np.log10(df.R_w75 - 0.0123)) / 0.955 ))

############### Determine low-shale volume intervals ##############

# creates shale baseline df['SPmax1'] = df.SP.rolling(window=30).max() df['SPmax2'] = df.SPmax1.rolling(window=30).max() df['SPmax3'] = df.SPmax2.rolling(window=30).max() df['SPmax4'] = df.SPmax3.rolling(window=30).max() df['Shale_baseline'] = df.SPmax4.rolling(window=40, center=True).mean()

# difference between SP and shale baseline df['SP_diff'] = (df.Shale_baseline - df.SP)

# this asks if df.SP_diff is over or under a certain number then assign s a lithology ###### adjust criteria as needed ####### for index, row in df.iterrows(): if row['DEPTH'] <= 3700 and row['SP_diff'] <= 0.13: row['SP_diff'] = '0' #shale if row['DEPTH'] < 3700 and row['SP_diff'] > 0.13: row['SP_diff'] = '1' #sand elif row['DEPTH'] > 3700 and row['SP_diff'] <= 0.3: row['SP_diff'] = '0' #shale elif row['DEPTH'] > 3700 and row['SP_diff'] > 0.3: row['SP_diff'] = '1' #sand

# difference between the short and deep resistivity curves df['res_diff'] = abs(df.SRES - df.DRES)

# makes column of consecutive counts of 1's or sand intervals df['consec'] = df['SP_diff'].groupby((df['SP_diff'] == 0).cumsum()).cum count()

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# calculates the stats of the consecutive counts to find bigger sand in tervals ###### adjust criteria as needed ####### df['consec_min'] = df.consec.rolling(window=10, center=True).min()

# put the big sand intervals into new dataframe ###### adjust criteria as needed ####### df2 = pd.DataFrame(df.loc[(df.consec_min >= 20) & (df.consec_min <= 20) & (df.DEPTH <= 3900) & (df.res_diff >= 3.9)] ) df3 = pd.DataFrame(df.loc[(df.consec_min >= 4) & (df.consec_min <= 4) & (df.DEPTH > 3900) & (df.res_diff >= 3)]) df4 = pd.concat([df2,df3]) df5 = pd.DataFrame(df4.loc[(df4.DEPTH >= 800) & (df4.DEPTH <= 4225)])

############ export data #############

#### set x and y ##### lat = [35.411429] * len(df5.DEPTH) lon = [-119.080169] * len(df5.DEPTH)

#### make the data file for export ######## d = {'API': APInum[2][:-1], 'lon': lon, 'lat': lat, 'DEPTH': df5.DEPTH, 'TDS': df5.TDS} krige = pd.DataFrame(d) krige.to_csv('{} scatter for krige.txt'.format(APInum[2][:-1]), sep=',' , index=False)

# manual adjustments to export data may be needed especially around oil interval #

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