Hydrocarbon production forecast for Louisiana—Producing field module

Mathematical and Computer Modelling 55 (2012) 564–589

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Hydrocarbon production forecast for Louisiana—Producing field module Mark J. Kaiser ∗ Center for Energy Studies, Louisiana State University, Energy Coast & Environment Building, Nicholson Extension Drive, Baton Rouge, LA 70803, United States

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Article history: Received 19 August 2010 Received in revised form 22 August 2011 Accepted 22 August 2011 Keywords: Forecast modeling Producing assets Reserves estimation

abstract Oil and gas from conventional producing fields in Louisiana are forecast using an algorithmic classification based on traditional decline curves and heuristic techniques. Fields are classified according to geographic area, product type, age, and production class. Production arising from the inventory of conventional oil and gas assets circa 2009 is estimated to be 343 MMbbl oil, 18 Tcf gas, and 510 MMbbl gas liquids. At $80/bbl oil and $4/Mcf gas, the present value of gross revenues is estimated to be $60.8 billion. The model framework and limitations of the analysis are described along with a discussion of the model results and sensitivity analysis. © 2011 Elsevier Ltd. All rights reserved.

1. Introduction Drilling for oil took place in Louisiana as early as 1866, but it was not until the success at Spindletop in 1901 that drillers returned to Louisiana and discovered oil at Jennings. After the spectacular oil gusher at Spindletop and hearing that the discovery was drilled in an area where gas had been observed seeping out of the ground, five businessmen created ‘‘The S.A. Spencer Company’’ and leased an area surrounding several gas seeps near Jennings [1]. At 1700 ft and with only 4 ft to go on his last piece of drill pipe, Scott Heywood drilled into the top of a sand which resulted in a blowout (Fig. 1). Within a few years, a number of wells were drilled near the crest of the salt dome underlying the field (Figs. 2 and 3) and production increased rapidly (Fig. 4). After these reservoirs were drained, deeper sands were found on the flank of the dome and production increased again in the late 1930s. The Jennings field accounted for about two-thirds of the total oil and gas production in the state through 1920 and is still producing.1 In 1937, wells were drilled at Ferry Lake from a wood deck erected on a platform supported by cypress trunks [2]. By the mid-1940s, operations were being conducted offshore in the Gulf of Mexico, and by 1955, production in state waters commenced after a legal dispute with the federal government on boundary delineation – the so-called tideland’s controversy – was resolved and Louisiana’s offshore waters were defined to extend three imperial miles from the coastline [3]. Today, oil and gas production in Louisiana plays an important role in domestic US production. In 2009, Louisiana ranked 5th in oil production and 4th in gas production in the United States, and according to the Energy Information Administration, Louisiana has proved reserves of 388 MMbbl oil, 11.6 Tcf gas, and 300 MMbbl gas liquids — about 2% of the US proved oil reserves, 5% of its proved gas reserves, and 3% of its natural gas liquid reserves [4–6]. The purpose of this paper is to forecast oil and gas production and estimate proved reserves from conventional fields in Louisiana. We begin with an overview of state production and reserves categories. The assets of oil and gas companies consist mostly of hydrocarbons in the ground (reserves) and are subdivided into proved, probable and possible categories according to the degree of uncertainty associated with recovery of the volumes. Petroleum resources are classified by development status and technology, and producing fields are categorized by geographic area, product type, age and production class. A wide variety of production profiles occur in practice and require an algorithmic approach for classification. A flowchart

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Tel.: +1 225 578 4554; fax: +1 225 578 4541. E-mail address: [email protected].

1 In 2009, the Jennings field produced 80 thousand barrels of oil and 35 thousand cubic feet of gas. 0895-7177/$ – see front matter © 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.mcm.2011.08.033

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Fig. 1. Jennings Oil Company number 2 well. A 4 inch stream of oil gushes in the background. W. Scott Haywood is pictured at the far right; Elmer Dobbins, one of the drillers at Spindletop, is at the center. Source: Louisiana Geological Survey.

illustrating the computational steps is described followed by a general description of the producing field module. A summary of the model results is provided and conclusions complete the paper. In Appendix A, the manner in which the product stream input is selected is described; in Appendix B, summary templates illustrating each production class algorithm is presented. 2. Louisiana production statistics Oil production in Louisiana rose rapidly after World War II and has been in steady decline since peaking in 1970 (Fig. 5). Crude oil in the state is reported with natural gas liquids and lease condensate. Today, oil production is 24% of its 1965 peak in North Louisiana, 12% of its 1970 peak in South Louisiana, and 9% of its 1970 peak in state waters. Average annual decline rates in North, South, and offshore Louisiana is 3.3%, 5.4%, and 6.3%, respectively. Gas production has followed a similar trend but in recent years has begun to reverse its decline (Fig. 6). Gas production is expressed as marketable gas, non-associated and casing head, adjusted to exclude reinjected gas, extraction loss, and non hydrocarbon gases. Gas production peaked alongside oil but its decline has been less dramatic, and in recent years, production has increased rapidly in North Louisiana. South Louisiana and offshore gas production are 13% of their 1970 peaks and declining at annual rates of 5.2%, while production in North Louisiana is increasing at a significant pace due to shale gas development in the Haynesville play. Most oil is produced in South Louisiana and offshore has never exceeded more than ten percent state production (Fig. 7). In 2010, oil production in the South achieved 25 MMbbl, compared to 6 MMbbl in the North and 3 MMbbl offshore. Gas production in the North has been on a steep upward trend and is now the main gas producing region in the state (Fig. 8). In 2010, regional gas production levels were 1678 Bcf (North), 411 Bcf (South), and 68 Bcf (offshore).

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Fig. 2. Contour map of Jennings field. The small black symbols denote the location of oil wells. The lines show the depth to the top of the salt dome. The earliest wells were from sands lying above the salt; later wells produced from sands on the flank of the salt dome. The inset at the lower right shows a three-dimensional representation of the salt dome which served to trap oil pockets. Source: Louisiana Geological Survey.

Fig. 3. Jennings field development circa 1902. This is a time before oil regulations were firmly in place as seen by the large number of derricks. Each operator leased a small tract of land and drilled to capture the oil underneath their lease before it was extracted by their neighbor. The rule of capture does not allow any legal recourse if oil is drained from below a track by a neighboring track. Source: Louisiana Geological Survey.

Over 80% of Louisiana’s oil production is derived from fields discovered prior to 1977, while for gas, approximately 60% of state production has been brought online within the past five years. These statistics frame our production forecast and are broadly reflective of expected future trends. In Figs. 9 and 10, oil and gas production by decades of discovery is depicted; note that the time horizon begins in 1977 because this is the first year of electronic reporting for field production.2

2 Field production from 1940–1976 is available in hard copy but were not processed because of time and resource constraints.

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Fig. 4. Jennings field oil production. Early production was from shallow sands lying above the crest of the salt dome. Production increased again in the 1930s when deeper oil sands were found on the flank of the salt dome. Source: Louisiana Geological Survey.

Fig. 5. Louisiana oil production by region (1945–2010).

Fig. 6. Louisiana natural gas production by region (1945–2010).

3. Reserves categories The SPE/WPC/AAPG/SPEE3 Petroleum Resources Management System (PRMS) is an industry standard system for classifying and reporting oil and gas reserves and resources [7]. On December 29, 2008, the Securities and Exchange Commission (SEC), the regulatory agency that oversees the stock market in the US and the manner companies evaluate and report their assets and cash flows, published revised rules for disclosure of oil and gas reserves that closely align with guidelines in PRMS [8]. 3 Society of Petroleum Engineers, World Petroleum Congress, Society of Petroleum Evaluation Engineers, American Association of Petroleum Geologist.

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Fig. 7. Regional oil production (1960–2010).

Fig. 8. Regional gas production (1985–2010).

Fig. 9. Oil production by decades of discovery (1977–2008).

Proved reserves are defined as the estimated remaining quantities of oil and gas anticipated to be economically producible, as of a given date, by application of development projects to known accumulations (reservoirs) under existing economic and operating conditions. In addition, there must exist, or there must be a reasonable expectation that there will exist, the legal right to produce or a revenue interest in the production, installed means of delivering oil and gas to market,

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Fig. 10. Gas production by decades of discovery (1977–2008).

and all permits and financing required to implement the project. Since proved reserves are unobservable4 and represent quantities to be produced, there is uncertainty associated with their estimation. Estimates must be made with ‘‘reasonable certainty’’ and are defined conservatively in the sense that the reserves estimates are met. Engineering and geological data are needed to make the estimates, and generally speaking, the knowledge offered by greater amounts of engineering and geological data will improve the quality of the reserves estimate. The relative uncertainty of reserves is qualitatively characterized by reference to deterministic categories – proved, 1P (‘‘much more likely than not’’); probable, 2P (‘‘as likely as not’’); and possible, 3P (‘‘possible, but not likely’’) – or in probabilistic terms. If probabilistic methods are used, proved reserves require that there should be at least a 90% probability that the quantities actually recovered will equal or exceed the estimate. Similarly, for probable and possible reserves, the exceedance probabilities are 50% for probable and 10% for possible reserves [11,12]. For a review of the modernization of SEC reporting requirements and useful discussion on reserves overbooking, see [13–15]. 4. Field categorization 4.1. Evaluation unit There are many evaluation units used in production and reserves estimation — wells, reservoirs, properties, fields, and projects. The preferred unit for performance analysis is individual wells, but often, production history is only available for a multi-well lease, a production unit, or an entire field. The field level is the highest level for which reserves are estimated. A field is a geologic entity defined as the surface area directly above one or more producing reservoirs all related to the same geologic structural feature and/or stratigraphic condition. The Louisiana Office of Conservation reviews producing leases and production information submitted by operators, logs, geophysical records, and other data to establish5 the existence of a new field or the extension of an existing field [17,18]. Fields are classified according to development status (producing, undiscovered), technology status (conventional, unconventional), geographic area (North, South, offshore), product type (oil, gas), age, and production class (young, peak, normal, chaotic). See Fig. 11. 4.2. Development status Oil and gas resources are divided into three categories according to development status and project maturity: producing fields, discovered undeveloped fields and undiscovered fields.

4 Reserves have been called a corporation’s Black Hole because ‘‘they exert a huge influence on everything else in its orbit, yet emits very little light’’ [9]. Reserves volumes and values for publicly traded US companies are not directly reported on a company’s balance sheet but are attached to the financial statements and disclosed annually on Form 10-K. A firm’s financial health depends in large part on its oil and gas reserves and financial measures are directly impacted by the estimated values [10]. Market capitalization is correlated with reserves. 5 Louisiana field naming rules are not published but are similar to guidelines used by the Field Naming Committee of the Bureau of Ocean Energy Management, Regulation, and Enforcement (BOEMRE) [16]. Generally, the structure or stratigraphic condition with pay having the largest areal extent determines the field expanse, and reservoirs that overlap vertically are usually combined into a single field. According to BOEMRE procedures, structural lows are used to separate fields with structural trapping mechanisms, and faults are rarely used to separate fields no matter how many or how large the vertical separation between reservoirs.

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Fig. 11. Fields are classified according to geographic area, product type, age, and production class.

Producing fields Producing fields are fields that produce any amount of oil or gas in the year of analysis. Producing fields are ‘‘hard’’ assets because they have been developed through capital investment; their physical existence is established, and reserves are known to a reasonable degree of certainty. In Louisiana, fields are typically composed of multiple leases, units, and wells owned by several parties. For young fields, reserves estimates are generally more uncertain than mature properties. Undiscovered fields Undiscovered fields are those fields that are expected to be discovered and produced in the future, but which currently have not been discovered. The existence of undiscovered fields is speculative and depends upon geologic prospectivity, capital investment, technology development, and various other factors. Typically, a regional assessment is performed to assess resource potential, and with a discovery model potential future production is assessed, e.g., [19,20]. Discovery models range from the simple to complex and attempt, based on statistical outcomes and geologic conditions, to reflect the uncertainty of future production pathways. Discovered undeveloped fields Discovered undeveloped fields lie between producing fields and undiscovered fields. Most are discoveries that have been announced or known to exist but are not currently producing. Undeveloped reserves are those reserves of any category that are expected to be recovered from new wells on undrilled average, or from existing wells where a major expenditure is required for recompletion. Discovered undeveloped fields require investment to produce and are categorized separately from proved developed producing reserves. A common example of undeveloped fields are those reserves which underlie undrilled portions of a property adjacent to current producers and are, based on engineering and geological evaluation, reasonably likely to produce hydrocarbons. The inventory of discovered undeveloped fields is not publicly reported. 4.3. Technology status A conventional field is a discrete accumulation or set of accumulations that are bounded by a downdip water contact from which hydrocarbons in liquid or gaseous forms are extracted. Unconventional reservoir systems are often synonymous with ‘‘continuous’’ accumulations and include tight gas sands, shale gas, shale oil, and coalbed methane reservoirs. Unconventional fields are more expensive to develop than conventional fields and are more difficult to characterize, require novel or new technologies, and initially have a smaller market penetration than conventional production. Once market penetration exceeds a certain threshold or cost decline and are ‘‘comparable’’ to other technologies, the demarcation between ‘‘unconventional’’ and ‘‘conventional’’ becomes less clear.6 4.4. Geographic area Louisiana fields are located according to its center coordinates and are classified by region as North, South, and offshore. The cost of exploration, development and production activities vary depending on the terrain. Differences between onshore, coastal, and offshore environments translate into differences in development economics and the time production becomes noncommercial [21].

6 In 2010, for example, shale gas in the US is still considered as an unconventional resource even though it provides nearly 25% domestic production because of cost and technology issues, potential environmental constraints, and regulatory uncertainty. Coalbed methane contributes about 10% to total gas production in the US and is also considered as an unconventional resource because of its source and manner of production.

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4.5. Product type Fields are classified as oil or gas fields depending on the volume of produced gas (measured in cubic feet) per unit of produced oil (measured in barrels), or gas–oil ratio (GOR). Cumulative GOR (CGOR) is the aggregate gas–oil production ratio at the time of evaluation. A field with cumulative gas–oil ratio CGOR <10,000 cf/bbl is labeled an oil field and a field with CGOR >10,000 cf/bbl corresponds to a gas field.7 The relative amount of oil and gas production varies over time with the reservoir characteristics and production mechanisms. Depending upon the level of primary production, an ‘‘oil’’ or ‘‘gas’’ producer may still produce significant quantities of secondary product. 4.6. Age Fields are defined by their year of discovery. Land discoveries often coincide with first production, while coastal (wetland) and offshore development will be delayed by one or more years to secure permitting and to tie-in into existing transportation pipelines. For the vast majority of fields in Louisiana, discovery year coincides with year of first production. 4.7. Production class When aggregate well production history is displayed, historical trends depict a variety of complex behavior. Production may show a continual decline after peak production, but more often, the trends exhibit dramatic short-term spikes, long periods of activity, multiple peaks, and related characteristics that are not well-suited to traditional decline curve analysis.8 The petroleum engineer’s challenge is to create a coherent analysis based on information the wellbore data is able to convey [22,23]. Field production aggregates wells and reduces its resolution. We are forced to employ empirical and heuristic methods because of the limited amount and quality of information. As higher frequency higher resolution and more complete field data is available, forecast procedures become less subjective and more knowledge-based. It is often appealing to use mathematical curve-fitting procedures on the entire history of a field’s profile to forecast production and estimate reserves. Such an approach may be acceptable if well count is relatively stable, production conditions remain largely unchanged over the producing life, and intervention and other remedial work is remedial [24]. Often, however, these conditions do not hold and strict adherence to model fits will not yield acceptable results. A combination of heuristic and analytic techniques is used to generate a forecast and we adopt and modify a methodology previously developed for offshore fields in federal waters [25,26]. The purpose of a classification system is to create categories so that similar analytic techniques can be applied to similar field profiles. Four categories are defined based on age, timing of peak production, and the success of curve-fitting procedures:

• Young — Field with ten years or less production history. • Peak — Field older than ten years with less than five years after peak production. • Normal — Field older than ten years with at least five years production after peak and an initial best-fit decline curve R2 ≥ 0.90. • Chaotic — Field older than ten years with at least five years production after peak and an initial best-fit decline curve R2 < 0.90. 5. Field classification 5.1. Data source The Louisiana Department of Natural Resources Office of Conservation maintains a database of production data through the Strategic Online Natural Resources Information System (SONRIS) [27]. Seven lease unit well (LUW) administrative codes are used to describe production. State production data is reported on a monthly basis and each well of an LUW is assigned to one field. Field production aggregates wells according to the underlying reservoir and formation geology. In total, over 60,000 LUWs have been recorded and about 1700 fields have been identified in the state. In 2008, there were 11,586 active LUWs, 49,733 inactive LUWs, and 994 producing fields. 5.2. Process flowchart The first step of the analysis considers the age of the field, that is, the number of years since first production. Fields with a short production history pose difficulties because the field is unlikely to have achieved its peak production and the

7 The threshold used to delineate oil and gas producers can range from 3000 to 20,000. 8 All wells go off production for periodic maintenance and because of technical problems. Often, a well will return to production after a few months. In some cases, if downhole problems are serious or there is a damaged export pipeline, the well may be off production for a longer period of time. Production may also be curtailed due to low commodity prices.

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Fig. 12. Flowchart for field production classification.

limited number of data points cannot reliably support forecast models. What constitutes a ‘‘young’’ field is subjective, of course, because a priori knowledge of the field’s design peak and timing is not known. Ten years is selected as the cut-off in identifying young fields in recognition that most fields in Louisiana will have peaked during this time period. All fields with less than ten years production are classified within the young class category and are forecast using a history match procedure based on BOE9 production. The cumulative GOR at the time of evaluation is used to decompose the BOE output in terms of oil and gas (left-branch in Fig. 12). For fields with more than a ten-year production history, we follow the right-branch and perform trend analysis to determine which product stream to apply (see Appendix A for additional details). The BOE and primary stream analysis flowcharts are similar in form but are based on different product streams. We begin with the BOE flowchart; the discussion of the primary stream workflow is analogous. BOE stream analysis If there is less than five years production after peak, then an adequate number of observations are not available to use regression techniques. Fields that do not have at least five years production after peak are classified as peak fields and an exponential decline on the BOE stream is adopted. Production of the secondary stream is forecast assuming a constant cumulative GOR. If there is more than five years production after peak, we follow the left branch in Fig. 13. Regression analysis is performed and if R2 ≥ 0.90, the field is classified as a Normal producer; otherwise, if R2 < 0.90, the field is classified as a Chaotic producer. For Normal producers, the computed model is considered as a reasonable predictor of future production. For Chaotic producers, if there are an adequate number of observations after peak (10 or more), production after peak is truncated by dividing the data series in half, a new peak is identified, and if there are more than five observations after peak, a best-fit curve is applied. If R2 ≥ 0.90, the profile is classified as a Chaotic I producer; otherwise, if there are less than 10 observations after peak, less than five observations after truncation, or if R2 < 0.90, the profile is classified as a Chaotic II producer.

9 A barrel of oil equivalent (BOE) combines the oil and gas output on a heat content basis using the conversion 1 bbl = 6 Mcf.

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Fig. 13. BOE stream analysis flowchart.

Chaotic I and Normal producers apply the BOE stream in evaluation. For Chaotic II producers, a five-year average production is computed for initialization with an assumed exponential model and a 10% decline rate. After the BOE stream is forecast, the oil and gas streams are constructed assuming a constant cumulative GOR. Primary stream analysis Primary stream analysis is analogous to BOE stream analysis except that all the evaluations are performed with the primary stream and the secondary stream is forecast using cumulative GOR trend analysis. In the BOE stream analysis, BOE production is forecast and decomposed into oil and gas streams by assuming a constant cumulative GOR; in primary stream analysis, the primary stream is forecast and the secondary stream is obtained from the cumulative GOR trend curve. 5.3. Production class Young Production of a young field is assumed to follow the production from ‘‘similar’’ fields that have previously terminated. Similarity is defined with respect to location (North, South, offshore), product type (oil, gas), and the level of cumulative

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Fig. 14. Average oil production profile from terminated oil fields.

Fig. 15. Average gas production profile from terminated gas fields.

production at the time of evaluation.10 Average production profiles are computed for various subcategories and used as reference (comparison) profiles. In Figs. 14 and 15, the average profiles depicted are based on 690 terminated oil and gas fields. Subcategory profiles are based on a subset of this data. The production history of the average field within each categorization that matches closest the cumulative production of the field under consideration is used as the forecast curve. Subcategories are selected and average profiles computed for each subcategory. Young fields are compared (matched) to subcategory profiles and the average profile used as reference profile to forecast young field production. An example illustrating the technique is described in Appendix B. Peak Production from fields with ten or more years production history but less than five years after peak are classified within the peak production class. Peak fields have produced for a number of years and because they are presumed to have peaked, we apply an exponential decline model to generate future production: q(f , t ) = q0 e−dt , where q(f , t ) denotes the production rate of field f in year t , qo represents the peak production rate, and the decline rate d is assumed to be 10%. The use of a 10% decline is a common industry practice in the absence of additional information. Empirical data based on historical decline rates could be employed but was not necessary considering the other sources of model uncertainty.

10 Engineers and geologist rely upon the use of analogies to estimate reservoir parameters and performance expectations during the early development stages of a field when no production and geologic data are available. Areal proximity is one of the most important features when establishing proof of analogy: ‘‘If performance trends have not been established with respect to oil and gas production, future production rates and reserves may be established by analogy to reservoirs in the same geologic area having similar characteristics and established performance trends’’ [28].

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Normal Normal fields are modeled by selecting the best model fit from the exponential, harmonic, and hyperbolic decline curves [29]. The hyperbolic decline is given as q(f , t ) = q0 (1 + Di bt )−1/b , where Di and b are unknown parameters determined from historical data and regression analysis. The two-parameter hyperbolic decline often results in the best curve fits. The exponential and harmonic curves are special cases of hyperbolic decline. Chaotic Fields that exhibit multiple peaks during their life cycle or other unusual behavior, such as long periods of inactivity, will not yield to traditional decline curve analysis. The Jennings field described in the Introduction is a typical example, where after several years in decline, new discoveries were made which resulted in a significant spike in production. Prior to 1930, such a trend would not be expected. Similar patterns occur throughout field profiles and are impossible to predict except on a statistical basis. There are several ways to analyze multi-peak profiles, all of which are subjective and (we believe) result in roughly equivalent levels of reliability. Heuristic techniques are used to generate forecast curves for chaotic producers. In Appendix B, the two chaotic model classes are illustrated. 5.4. Production statistics A total of 1684 fields have been discovered and produced in Louisiana. Over time, producing fields deplete and stop production as new fields are discovered and start production. In 1977, there were 1183 producing fields in the state: 474 oil fields and 709 gas fields. In 2008, a total of 994 fields were producing: 398 oil fields and 596 gas fields (Table 1). The majority of field discoveries were made before 1977 and most active fields as well as the majority of production are from pre-1977 discoveries.11 Louisiana’s producing fields circa 2009 are classified by production class, product type, and year of discovery (pre-1977 and post-1977) in Table 2. For field discoveries before 1977, the entire production history is not available electronically; thus, all model fits begin in 1977. Producing fields discovered before 1977 are either normal or chaotic; obviously, they do not fall into the young and peak categories because of their age. For fields discovered before 1977, the chaotic class applies more than half of the time, primarily because mature fields are the largest and most prolific producers in the state and often undergo multiple investment and development cycles which account for their longevity and production volatility. For fields discovered after 1977, normal and young producers are the most common model class. We do not observe any significant differences between oil and gas production. Since old fields tend to be chaotic, it is reasonable to surmise that a portion of fields discovered after 1977 will eventually turn chaotic. 6. Producing field module 6.1. Methodology Oil and gas production is forecast using a five-step procedure:

• • • • •

Classify each producing field according to its production class. Forecast future production assuming stable reservoir and investment conditions. Forecast future revenue based on a given hydrocarbon price deck. Terminate production when gross revenue falls below the field’s economic limit. Compute annual production, total cumulative production (remaining reserves), and discounted future gross revenue.

6.2. Production and revenue forecast Let qo (f , t ) and qg (f , t ) denote the amount of oil and gas produced by field f in year t and initialize time to the year 2009 (t = 1). After each field is identified according to production class, the forecast model is applied to yield the future profiles: qo (f ) = (qo (f , 1), qo (f , 2), . . .), qg (f ) = (qg (f , 1), qg (f , 2), . . .). Oil and gas revenue is computed by multiplying the production forecast by the expected market price in the year received (Fig. 16a): r o (f , t ) = qo (f , t )P o (f , t ), r g (f , t ) = qg (f , t )P g (f , t ), 11 From the 1684 producing fields, 1159 were discovered before 1977 and 525 were discovered after 1977. From the 994 active fields in 2008, 835 fields are pre-1977 discoveries.

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Table 1 Number of producing fields in Louisiana by year. Year

1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

Oila

Gasa

Total

North

South

Offshore

Unknownb

North

South

Offshore

Unknownb

216 219 228 233 242 244 243 247 241 237 232 227 218 214 212 209 204 199 191 187 189 187 186 184 183 180 180 176 172 171 170 170

222 229 232 237 239 240 239 235 242 240 241 240 241 237 234 233 231 228 226 224 225 221 216 210 209 209 207 204 203 202 199 199

24 24 24 26 26 26 26 26 26 26 25 25 25 26 26 26 26 25 26 26 25 24 25 25 25 24 23 23 22 22 22 22

12 12 12 14 14 8 9 8 8 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 8 9 8 7 7 6 6 7

198 199 205 217 222 227 222 219 215 211 210 212 209 204 203 200 197 193 189 187 186 185 181 174 174 166 165 166 167 161 159 160

452 458 467 472 475 482 484 484 478 470 465 460 456 451 445 443 440 429 424 415 416 411 403 402 395 388 389 384 372 367 358 359

58 60 60 62 62 65 68 69 75 76 75 73 74 73 72 66 67 70 69 72 71 71 75 75 74 73 77 76 69 68 67 68

1 3 3 3 5 5 5 4 4 3 3 3 3 3 3 3 3 4 4 4 5 4 4 5 7 8 8 7 7 8 7 9

1183 1204 1231 1264 1285 1297 1296 1292 1289 1268 1256 1245 1231 1213 1200 1185 1173 1153 1134 1120 1122 1108 1095 1081 1075 1057 1057 1043 1019 1005 988 994

Oil fields are defined by CGOR < 10,000; gas fields are defined by CGOR > 10,000. A total of 52 fields do not have their location or discovery year identified. For fields that produce after 1976 we use the first producing year after 1976 as their discovery year. a

b

Table 2 Producing field classification by year of discovery (2009). Production Class

Before 1977

After 1977

Oil

Gas

All

Oil

Gas

All

Chaotic I Chaotic II Young Peak Normal

51 113 – – 159

66 267 – – 179

117 380 – – 338

6 18 18 4 54

11 19 64 13 52

17 37 82 17 106

Total

323

512

835

100

159

259

where P o (f , t ) and P g (f , t ) represent the oil and gas price received in year t for field f . We assume that commodity prices are constant throughout the life cycle of production. Hydrocarbon quality (gravity, sulfur content, heat content) and transportation expense to deliver production to market is not considered. Total revenue in year t is computed as the sum of the oil and gas stream revenues (Fig. 16b): r (f , t ) = qo (f , t )P o + qg (f , t )P g . The revenue forecast vector for field f starts in 2009 and is denoted as r (f ) = (r (f , 1), r (f , 2), . . .). 6.3. Abandonment time When the marginal cost of production of an asset exceeds its marginal revenue, the asset is considered uneconomic and operations will cease. The time at which a field is no longer commercial is determined by comparing the revenue in year t, r (f , t ), to an estimate of its economic limit, τa (f ), and selecting the earliest time when revenue falls below the cost of operation (Fig. 16c): Ta (f ) = min{t | r (f , t ) = τa (f )}.

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Fig. 16a. Oil and gas revenue is computed on an annual basis by multiplying the production forecast by the expected oil and gas price assumed constant per field and future time.

Fig. 16b. Total revenue in year t is computed as the sum of the oil and gas stream revenues.

The economic limit τa (f ) is empirically-derived based on historical data and is correlated with field characteristics such as product type and location [21]. Ta (f ) denotes the time for a given production forecast and price deck a field will no longer be commercial. At t = Ta (f ), a rational profit-maximizing operator will stop producing, terminating the cash flow vector: r (f ) = (r (f , 1), r (f , 2), . . . , r (f , Ta (f ))). 6.4. Cumulative production and discounted revenue Cumulative production, Q i (f ), is computed from the annual production profiles, qi (f , t ), beginning in 2009, t = 1, through the time of abandonment, t = Ta (f ): Q i = Q i (f ) =

Ta (f )

−

qi (f , t ).

t =1

See Fig. 16d. Cumulative production represents the estimated quantity of proved reserves. The discounted revenue, V (f ), is computed from the annual revenue streams, r (f , t ), beginning from the time of evaluation through abandonment and discounted by D: V = V (f ) =

Ta (f )

− r (f , t ) . (1 + D)t t =1

Discounted gross revenue is a proxy of the value of the reserves.

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Fig. 16c. Remaining production and abandonment time. The time when a field is no longer commercial is determined by comparing the revenue, r (f , t ), in year t to an estimate of its economic limit, τa (f ), and selecting the earliest time when revenue falls below the economic limit.

Fig. 16d. Cumulative production, Qi (f ), is computed from the annual production profiles through the time of abandonment at Ta . The discounted revenue, V (f ), is computed from the annual revenue stream, r (f , t ), through abandonment and discounted by an industry discount rate, D.

6.5. Aggregation Model output for field f includes the forecast production profile, qi (f , t ); cumulative production, Q i (f ); discounted revenue, V (f ). The final step is to aggregate the production profiles and discounted revenue streams for all fields according to geographic area, product type, age and production class. Aggregation yields regional and total state oil and gas production and discounted revenue from the producing field inventory. 7. Model results 7.1. Production forecast Oil and gas production is forecast for fields discovered before 1977 and for fields discovered after 1977. Oil and gas liquid production is depicted in Fig. 17. Oil production from fields discovered before 1977 represents about 90% of the total state production. In 2009, old fields (pre-1977 discoveries) contributed about 50 MMbbl compared to 6 MMbbl for post1977 discoveries. Mature fields exhibit a slower decline than younger fields and their contribution to total production will increase over time. Gas production from fields discovered before and after 1977 is depicted in Fig. 18 according to associated and nonassociated production. Gas production associated with oil fields contributes a small slice across each profile. In 2009, gas production from pre-1977 fields represents about 85% (700 Bcf/830 Bcf) total production from existing assets. 7.2. Regional production In Figs. 19 and 20, oil and gas production by region is depicted. In 2009, oil production in the South contributes the majority of production (Fig. 19), but by 2020 production in the North is expected to dominate. Gas production in the North consists of more than half the production in the state from producing assets (Fig. 20). The relative contribution of oil and gas production by region is depicted in Figs. 21 and 22. In 2009, 20% of oil was produced in the North and is expected to exceed 60% by 2039 (Fig. 21). More than 50% of conventional gas production originates in North Louisiana and is expected to exceed 70% by 2039 (Fig. 22). Unconventional gas production is already a dominant play in the state, contributing about 60% of state output, and if total gas production is considered, these percentage contributions will be accelerated.

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Fig. 17. Projected oil and condensate production from fields discovered before and after 1977.

Fig. 18. Projected associated and non-associated conventional gas production from fields discovered before and after 1977.

Fig. 19. Conventional oil production forecast by region (2009–2039).

7.3. Proved reserves Proved reserves are depicted by region, product type, and price scenario in Table 3. Price plays a role in reserves estimates because at higher prices field revenues increase, which delays the time of abandonment allowing additional production. Increased price also leads to additional development across producing fields. We only model the increase in reserves due to the shift in the economic limit. Table 3 shows that oil, gas, and gas liquid reserves increase only modestly across the price scenarios — less than a two percent increase for liquid production and negligible for gas production. Oil fields are estimated to contribute 343 MMbbl oil and 861 Bcf associated gas reserves, while gas fields will contribute 510 MMbbl gas liquids and 17.1 Tcf dry gas. Most of the 343 MMbbl oil reserves are located in the South (210 MMbbl),

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Fig. 20. Conventional gas production forecast by region (2009–2039).

Fig. 21. Regional conventional oil production relative contribution (2009–2039).

Fig. 22. Regional conventional gas production relative contribution (2009–2039).

followed by 78 MMbbl in the North and 55 MMbbl offshore. The 510 MMbbl gas liquid reserves are regionally distributed as: North (311 MMbbl), South (177 MMbbl), and offshore (22 MMbbl). For conventional gas reserves, the North (12.4 Tcf) dominates the South (4.1 Tcf). According to the EIA reserves estimates, our estimates are lower in terms of oil reserves (343 vs. 388 MMbbl), greater for gas reserves (17.9 vs. 11.6 Tcf), and greater in gas liquid reserves (510 vs. 300 MMbbl). On a regional basis EIA’s 388 MMbbl crude oil reserves estimates are distributed as follows: South (277 MMbbl), North (60 MMbbl), offshore (51 MMbbl); for gas: North (7.9 Tcf), South (2.8 Tcf), offshore (898 Bcf), and for gas liquids: South (142 MMbbl), North (95 MMbbl), offshore (63 MMbbl).

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Table 3 Louisiana proved reserves estimates (MMbbl for oil, Bcf for gas). Price scenarioa

I

II

III

IV

V

North

South

Offshore

All

Oil

Gas

Oil

Gas

Oil

Gas

Oil

Gas

Oil fields Gas fields

78 311

84 12,360

208 174

635 4060

48 21

116 561

333 506

834 16,981

All

389

12,444

382

4695

69

676

840

17,815

Oil fields Gas fields

78 311

84 12,364

209 176

638 4097

52 21

129 577

339 509

852 17,038

All

389

12,448

385

4735

73

706

848

17,889

Oil fields Gas fields

78 311

85 12,366

210 177

640 4116

55 22

136 585

343 510

861 17,067

All

390

12,451

387

4755

76

721

853

17,927

Oil fields Gas fields

78 312

85 12,368

210 177

641 4127

56 22

140 590

345 511

866 17,085

All

390

12,452

388

4768

78

731

856

17,951

Oil fields Gas fields

78 312

85 12,368

211 178

641 4135

57 22

145 594

347 511

871 17,098

All

390

12,453

389

4777

79

738

858

17,968

a

Price scenario I, II, III, IV, and V correspond to $40/bbl, $60/bbl, $80/bbl, $100/bbl, and $120/bbl for oil, and $4/Mcf, $6/Mcf, $8/Mcf, $10/Mcf, and $12/Mcf, respectively. Table 4 Present value of forecast production at 10% discount rate ($ million). Price scenarioa

North Oil

I

II

III

V

Oil

Offshore Gas

Oil

All Gas

Oil

Gas

Oil fields Gas fields

1,118 3,937

136 21,633

4,029 3,492

1,158 8,129

940 446

240 1256

6,087 7,875

1,534 31,018

All

5,055

21,769

7,521

9,287

1386

1496

13,961

32,552

Oil fields Gas fields

1,681 5,907

204 32,453

6,050 5,252

1,738 12,223

1506 678

387 1916

9,237 11,837

2,329 46,592

All

7,587

32,657

11,302

13,961

2184

2303

21,073

48,921

Oil fields Gas fields

2,244 7,876

273 43,272

8,070 7,013

2,318 16,317

2081 910

531 2574

12,395 15,798

3,121 62,163

10,120

43,545

15,083

18,635

2991

3104

28,193

65,284

2,806 9,845

341 54,091

10,090 8,772

2,898 20,408

2644 1141

672 3230

15,540 19,759

3,911 77,729

All

12,652

54,432

18,862

23,306

3785

3902

35,299

81,640

Oil fields Gas fields

3,369 11,814

409 64,910

12,110 10,532

3,478 24,499

3237 1372

820 3884

18,716 23,718

4,707

All

15,184

65,319

22,642

27,977

4609

4704

42,434

All IV

South Gas

Oil fields Gas fields

93,293 98,000

a Price scenario I, II, III, IV, and V correspond to $40/bbl, $60/bbl, $80/bbl, $100/bbl, and $120/bbl for oil, and $4/Mcf, $6/Mcf, $8/Mcf, $10/Mcf, and $12/Mcf, respectively.

7.4. Reserves valuation In Tables 4–6, the present value of expected production is depicted by price scenario in terms of a 10%, 20%, and 30% discount rate. At 10% discount (Table 4), oil reserves are valued between $14.0–$42.4 billion ($40/bbl–$120/bbl) and gas reserves are valued between $32.6–$98 billion ($4/Mcf–$12/Mcf). The valuations only consider commodity price and discount rate; they do not include royalties, taxes, operating and capital cost, or transportation expenses. Individually, these costs are usually small and represent less than 10% of the gross revenue, but collectively they are significant. Royalty rates on public lands often range between 12.5% and 25% gross revenue but on private lands they are whatever the market will bear. Tax rates depend on profits and operating costs. At 20% discount (Table 5), oil valuations vary between $8.7–$26.4 billion and gas valuations $20.5–$61.8 billion. At 30% discount (Table 6), oil and gas valuations vary between $6.3–$19.1 billion and $14.8–$44.5 billion, respectively. A graph of present value in terms of price scenario and discount rate is depicted in Fig. 23.

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Table 5 Present value of forecast production at 20% discount rate ($ million). Price scenarioa

I

II

III

IV

V

North

South Oil

Offshore Gas

Oil

All

Oil

Gas

Gas

Oil fields Gas fields

707 2050

89 13,216

2,683 2,340

757 5,441

615 302

159 867

Oil 4,004 4,692

Gas 1,005 19,524

All

2757

13,305

5,023

6,198

917

1026

8,697

20,529

Oil fields Gas fields

1062 3076

133 19,826

4,027 3,516

1,135 8,174

987 458

255 1320

6,076 7,050

1,523 29,319

All

4138

19,959

7,543

9,309

1445

1574

13,126

30,842

Oil fields Gas fields

1418 4101

178 26,435

5,370 4,693

1,514 10,907

1363 614

347 1771

8,151 9,408

2,039 39,113

All

5520

26,613

10,063

12,421

1977

2118

17,560

41,153

Oil fields Gas fields

1773 5127

222 33,045

6,714 5,869

1,893 13,639

1727 769

438 2220

10,214 11,765

2,553 48,904

All

6900

33,267

12,583

15,531

2496

2658

21,979

51,457

Oil fields Gas fields

2129 6152

267 39,654

8,058 7,045

2,271 16,371

2113 924

534 2668

12,299 14,121

3,072 58,692

All

8281

39,921

15,102

18,642

3037

3201

26,420

61,764

a

Price scenario I, II, III, IV, and V correspond to $40/bbl, $60/bbl, $80/bbl, $100/bbl, and $120/bbl for oil, and $4/Mcf, $6/Mcf, $8/Mcf, $10/Mcf, and $12/Mcf, respectively.

Table 6 Present value of forecast production at 30% discount rate ($ million). Price scenarioa

North Oil

I

II

III

IV

V

South Gas

Oil

Offshore Gas

Oil

All Gas

Oil

Gas

Oil fields Gas fields

519 1316

66 9,301

2,015 1,763

563 4,094

456 228

119 661

2,990 3,307

748 14,057

All

1835

9,367

3,778

4,657

684

780

6,297

14,805

Oil fields Gas fields

780 1974

100 13,953

3,024 2,648

845 6,148

735 345

189 1006

4,539 4,967

1,134 21,107

All

2754

14,052

5,672

6,993

1080

1196

9,506

22,242

Oil fields Gas fields

1041 2632

133 18,604

4,033 3,534

1,127 8,204

1014 463

258 1349

6,089 6,629

1,518 28,157

All

3673

18,737

7,567

9,331

1477

1607

12,717

29,675

Oil fields Gas fields

1302 3290

166 23,255

5,042 4,419

1,409 10,257

1283 580

325 1691

7,627 8,289

1,900 35,204

All

4592

23,421

9,461

11,667

1863

2016

15,916

37,104

Oil fields Gas fields

1563 3948

199 27,907

6,051 5,304

1,691 12,311

1569 696

396 2031

9,183 9,948

2,286 42,249

All

5511

28,106

11,355

14,002

2265

2427

19,131

44,535

a

Price scenario I, II, III, IV, and V correspond to $40/bbl, $60/bbl, $80/bbl, $100/bbl, and $120/bbl for oil, and $4/Mcf, $6/Mcf, $8/Mcf, $10/Mcf, and $12/Mcf, respectively.

Oil and gas prices in the US are not strongly correlated since they are traded in separate markets and have different demand drivers and are subject to different seasonal impacts. The price scenarios are independent and can be mixed according to the beliefs of the user to represent a more realistic view of price dynamics. For example, at 10% discount, liquid production is valued at $28.2 billion at $80/bbl oil and gas production is worth $32.6 billion at $4/Mcf gas. The present value of reserves at $80/bbl oil and $4/Mcf gas is thus valued at $60.8 billion. 8. Conclusion When well production is aggregated at the field level, profiles often exhibit dramatic changes and volatile characteristics that are not amenable to traditional decline curve analysis. To handle the variety of profiles observed, a structured algorithmic framework was outlined where similar profiles were grouped within the same class for forecasting and proved

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Fig. 23. Present value of gross revenues per hydrocarbon price and discount rate scenario.

reserves estimation. Inherent limitations exist on the ability of empirical methods to capture variability and to predict future performance. Our approach combined standard decline curve techniques with heuristic methods to mimic individual field performance. Our estimates of proved reserves are lower than EIA estimates for oil reserves (343 vs. 388 MMbbl), but greater for gas reserves (17.9 vs. 11.6 Tcf) and gas liquid reserves (510 vs. 300 MMbbl). We estimate that the total value of oil and gas production from producing fields range between $46.6 and $140.4 billion depending on the future price scenario. Most oil reserves are located in the South while the North has the majority of gas and gas liquid reserves. Gas revenue from conventional fields is expected to be dominated by production in the North, and as the Haynesville Shale play becomes fully established, unconventional gas will eventually dominate hydrocarbon production in the state. Acknowledgments This paper was prepared on behalf of the US Department of the Interior, Bureau of Ocean Energy, Management and Enforcement (BOEMRE), Gulf of Mexico OCS region, and has not been technically reviewed by the BOEMRE. The opinions, findings, conclusions, or recommendations expressed in this paper are those of the authors, and do not necessarily reflect the views of the Bureau of Ocean Energy, Management and Enforcement. Funding for this research was provided through the US Department of the Interior and the Coastal Marine Institute, Louisiana State University. Appendix A. Cumulative GOR trend analysis There are three options in production forecasting:

• Forecast the individual oil and gas streams separately. • Forecast the primary product stream and infer secondary production. • Forecast the combined BOE stream and then decompose into separate oil and gas components. There are advantages and disadvantages of each approach. Forecasting oil and gas individually is problematic because the two streams are treated as independent when in fact they are related and often correlated. If the combined BOE stream is forecast, an assumption on future GOR is necessary to decompose the BOE stream back into oil and gas components. Forecasting on the primary product is reasonable if the oil and gas streams are correlated and the correlation is expected to hold in the future.12 For oil fields, a log–log plot of cumulative gas vs. cumulative oil production is often utilized to project associated gas production. Cumulative gas vs. cumulative oil will plot as a straight line until the reservoir pressure falls below the bubble point, at which point an inflection will occur and the slope will increase. At the inflection point, gas production begins to increase relative to oil production. For gas fields, an analogous plot of cumulative oil vs. cumulative gas production can be utilized to project condensate production. To determine which product stream to apply, we regress cumulative gas and cumulative oil production on a log–log scale with unknown parameter {A} and select A to best-fit the relation: log(Cumulative Gas + A) = log(Cumulative Oil).

12 For example, black oil often has low reservoir pressure, low GOR, and experience high water cuts later in field life. In solution gas drive reservoirs at or above the bubble point the GOR is relatively constant. Below the bubble point, the GOR increases which is reflected in a change in slope of cumulative gas vs. cumulative oil production [30].

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Fig. B.1. Production class template — Young.

Parameter A is varied to maximize the model-fit R2 and the final value of R2 is used at the decision node. If R2 ≥ 0.98, the primary product stream is used in subsequent analysis; if R2 < 0.98, the BOE stream is used. After A is determined, the equation is represented by log(Cumulative Gas + A) = B ∗ Cumulative Oil + C . Parameters {A, B, C} define the functional form of the cumulative GOR trend analysis and relate the primary product stream to the secondary product. Appendix B. Production class models Young (Fig. B.1) The Niblett Canal field was discovered in South Louisiana in 2004. At the time of evaluation in 2009 the field only produced for five years, and so Niblett is classified as a young field and its BOE stream is used to match its cumulative production against similar fields. Through 2008, Niblett Canal produced 703 Mbbl oil and 734 MMcf gas and had a cumulative GOR = 1043. The

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585

Fig. B.2. Production class template — Peak.

Niblett BOE production profile was compared against the profiles of terminated oil fields in South Louisiana. Subcategory 4 average profile has a five-year cumulative BOE production of 787,042 BOE which is the closest to the Niblett Canal field production in year five. Subcategory 4’s production profile is used as the reference profile and adjusted by the factor α = 825,502/787,042 = 1.05. The BOE adjusted production profile for subcategory 4 is used to forecast the production for Niblett Canal. After the adjusted BOE profile is constructed, oil and gas are estimated assuming a constant CGOR = 1043. The economic limit threshold of the field is estimated to be $83,000, and when gross revenue achieves this value, production terminates. Proved oil and gas reserves are estimated at 776 Mbbl and 812 MMcf. Peak (Fig. B.2) Cameron Canal was discovered in 1979 in South Louisiana. After 16 years of continuous production, operations stopped for a decade until 2005 when new wells were drilled and production resumed at levels that exceeded previous rates. Cameron Canal is unusual in its long period without production. Cumulative GOR = 16,820 indicates a gas field. At the time of analysis, the field was 30 years old and peak production was less than five years. Hence, the Cameron Canal field is classified as a peak producer. Cumulative GOR trend analysis yields parameters {A, B, C} = {3.9E6, 5.6E−09, 6.6} and R2 = 0.99. Since R2 ≥ 0.98, the primary product (gas) stream is used in forecasting. Field production peaked in 2007 and because there are only two years data after peak, we assume that gas production will follow an exponential curve at the

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Fig. B.3. Production class template — Normal.

decline rate d = 0.10. The following equations are adapted for forecasting: qg (f , t ) = qg e−0.1t ; qo (f , t ) = Q o (f , t ) − Q o (f , t − 1); where Q o (f , t ) = 10BQ (f ,t )+C − A. The field is expected to terminate in 2045 at the economic limit $236,000. In 2009, proved reserves at Cameron Canal are estimated to be 9.49 Bcf gas and 592 Mbbl oil. g

Normal (Fig. B.3) The Houston River field was discovered in 1997 in South Louisiana and at the time of evaluation produced a total of 1.73 MMbbl oil and 1.07 Bcf gas. CGOR = 600 indicates that the field is primarily an oil producer. Since the field is 12 years old and more than five years past peak production, we compute the cumulative GOR trend parameters {A, B, C} and R2 to yield {3.15E05, 6.81E−08, 6.5} and R2 = 0.99. Since R2 ≥ 0.98, we use the primary product stream (oil) for forecasting. Field production peaked in 1999 and because at least 10 observations are available, regression was performed yielding R2 = 0.98 and a hyperbolic profile (c = 0.02, n = 4.6). Since R2 ≥ 0.90 the profile is classified as normal and used to forecast oil production. From the oil production forecast, the secondary stream (gas) is projected using the CGOR trend analysis parameters. The Houston River field will stop production at its economic limit in 2028 at which time it is estimated to have produced an additional 212 Mbbl oil and 142 MMcf gas.

M.J. Kaiser / Mathematical and Computer Modelling 55 (2012) 564–589

587

Fig. B.4. Production class template — Chaotic I.

Chaotic I (Fig. B.4) The Jennings field is the oldest producing field in Louisiana. From 1977, cumulative production totaled 7.6 MMbbl oil and 4.8 Bcf gas. Cumulative GOR = 629 indicates black oil production. Cumulative GOR trend analysis yields R2 = 0.96 < 0.98, and so the BOE product stream is applied. BOE production peaked in 1985, and since there are at least five years after peak production, the data is regressed to yield R2 = 0.85 < 0.90. The Jennings field is thus classified as a chaotic producer. Since there are 24 years production after peak, the profile is truncated to 1998 (= 1986 + 12). There are 11 years after the new peak, and the best-fit decline curve yields an exponential model with decline rate d = 0.14 and model fit R2 = 0.92, a chaotic I producer. In 2009, Jennings is estimated to hold remaining proved reserves of 457 Mbbl oil and 287 MMcf gas. Production is estimated to terminate in 2037. Chaotic II (Fig. B.5) The McKenzie field in North Louisiana was discovered in 1980 and has produced continuously throughout this period. Cumulative GOR = 16,570 indicates that the field is primarily a gas producer. Production peaked in 1992 so it is neither a young nor a peak model class. Cumulative GOR trend analysis yields R2 = 0.97 and so the BOE product stream is adopted. Using BOE production, the best-fit curve is an exponential model with R2 = 0.70 < 0.90, and so the field is a chaotic producer. Production after peak is truncated and because there are only two observations after peak, the curve is modeled as a chaotic II producer. McKenzie’s five-year average production is computed as 127,432 BOE. We assume that the BOE stream will decline along an exponential curve at a 10% decline rate beginning from the five-year average production. The BOE

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M.J. Kaiser / Mathematical and Computer Modelling 55 (2012) 564–589

Fig. B.5. Production class template — Chaotic II.

production forecast is performed and the oil and gas stream is decomposed from the BOE stream. The last year of production will occur in 2054. McKenzie’s proved reserves are estimated to be 5.28 Bcf gas and 319 Mbbl oil. References [1] Jennings field – The birthplace of Louisiana oil industry. Public Information Series No. 9. Louisiana Geological Survey. Baton Rouge, September 2001, LA. [2] R. Gramling, Oil on the Edge, State University of New York Press, Albany, NY, 1996.

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589

[3] E.R. Bartley, The Tidelands Oil Controversy: A Legal and Historical Analysis, University of Texas Press, Austin, TX, 1953. [4] US Department of Energy, Energy Information Administration, Crude Oil Production. Washington, DC, 2010. Available at: http://tonto.eia.doe.gov/ dnav/pet/pet_crd_crpdn_adc_mbbl_m.htm. [5] US Department of Energy, Energy Information Administration, Natural Gas Gross Withdrawals and Production. Washington, DC, 2010. Available at: http://tonto.eia.doe.gov/dnav/ng/ng_prod_sum_dcu_rusf_a.htm. [6] US Department of Energy, Energy Information Administration, US Crude Oil, Natural Gas, and Natural Gas Liquids Proved Reserves, 2008, Washington, DC, October 29, 2009. Available at: http://www.eia.doe.gov/oil_gas/natural_gas/data_publications/crude_oil_natural_gas_reserves/cr.html. [7] SPE/WPC/AAPG/SPEE, 2007. Petroleum Resources Management System. Available at: http://www.spe.org/industry/docs/Petroleum_Resources_ Management_System_2007.pdf#redirected_from=/industry/reserves/prms.php. [8] US Securities and Exchange Commission, (US SEC) 2008, Modernization of the Oil and Gas Reporting Requirements. Confirming version (proposed rule), 17 CFR Parts 210, 211, 229, and 249, Release Nos. 33-8995; 34-59192; FR-78; File No. S7-15-08, RIN 3235-AK00. Available at: http://www.sec.gov/rules/final/2008/33-8995.pdf. [9] R. Barry, The Management of International Oil Operations, PennWell Publishing Company, Tulsa, Oklahoma, 1993. [10] B.G. Dharan, 2004, Improving the Relevance and Reliability of Oil and Gas Reserves Disclosures, Prepared/Written testimony for the US House Committee on Financial Services,108th Congress, Second Session (21 July 2004). Available at: http://archives.financialservices.house.gov/media/pdf/ 072104bd.pdf. [11] R. Harrel, C. Cronquist, Estimation of primary reserves of crude oil, natural gas, and condensate, in: E. Holstein (Ed.), in: Reservoir Engineering and Petrophysics, vol. V(B), SPE, Richardson, TX, 2007, pp. 1480–1570. (Chapter 16). [12] J.R. Etherington, Managing your business using integrated PRMS and SEC standards, SPE 124938, SPE Annual Technical Conference and Exhibition, 4–7 October 2009, New Orleans, Louisiana, 2009. [13] W.J. Lee, Modernization of the SEC oil and gas reserves reporting requirements, Paper SPE 123793, SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 4–7 October 2009. [14] M.A. McLane, Reserve Overlooking — The problem no one wants to talk about, Paper SPE 68580 presented at the SPE Hydrocarbon Economics and Evaluation Symposium, Dallas, Texas, 2–3 April, 2001. [15] G.T. Olsen, W.J. Lee, T.A. Blasingame, Reserves overbooking: the problem we’re finally going to talk about, SPE 134014, SPE Annual Technical Conference and Exhibition, Florence, Italy, 20–22 September 2010. [16] Field Naming Handbook, Minerals Management Service, New Orleans, LA, 2006. [17] M.B. Kumar, Delineation of petroleum reservoir boundaries for unitization in Louisiana: an overview of practices and trends, The Professional Geologist, May, pp. 2–4, 2002. [18] M.B. Kumar, Geological aspects of unitization in the petroleum fields of Louisiana: a brief overview, The Professional Geologist, November/December, 2007, pp. 30–32. [19] J.H. Schuenemeyer, E.D. Attanasi, Forecasting rates of hydrocarbon discoveries in a changing environment, Marine and Petroleum Geology 14 (3) (1985) 313–318. [20] P.R. Rose, Risk Analysis and Management of Petroleum Exploration Ventures, AAPG Methods in Exploration No. 12, 2001. [21] M.J. Kaiser, Economic limit of field production in Louisiana, Energy 35 (2010) 3399–3416. [22] D.M. Anderson, G.W.J. Stotts, L. Mattar, D. Ilk, T.A. Blasingame, Production data analysis — challenges, pitfalls, diagnostics, SPE 102048, SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 24–27 September 2006. [23] D. Ilk, C.D. Jenkins, T.A. Blasingame, Production analysis in unconventional reservoirs — diagnostics, challenges, and methodologies, North American Unconventional Gas Conference and Exhibition, The Woodlands, Texas, 14–16 June 2011. [24] D.R. Harrell, J.E. Hodgin, T. Wagenhofer, Oil and gas reserves estimates: recurring mistakes and errors, SPE 91069, SPE Annual Technical Conference and Exhibition, Houston, Texas, 26–29 September 2004. [25] M.J Kaiser, Hydrocarbon production forecast for committed assets in the shallow water outer continental shelf of the Gulf of Mexico, Energy 34 (11) (2009) 1813–1825. [26] M.J. Kaiser, Marginal production in the Gulf of Mexico – II. Model framework and results, Applied Energy 87 (10) (2010) 2526–2534. [27] Strategic Online Natural Resources Information System, Louisiana Department of Natural Resources. Available at: http://sonris-www.dnr.state.la.us/ www_root/sonris_portal_1.htm. [28] SPE, 2001, Standards pertaining to the estimating and auditing of oil and gas reserves information, Approved by SPE Board of Directors, June 2001. Article 5.7 Estimating Reserves by Analogy to Comparable Reservoirs. [29] S.W. Poston, B.D. Poe Jr., Analysis of Production Decline Curves, Society of Petroleum Engineers, Richardson, TX, 2008. [30] J. McCain, Petroleum Fluids, 2nd ed., PennWell, Tulsa, OK, 2001.