Distinguished Author Series

5PfE. /3q4b

Oil and Gas Reserves Classification, Estimation, and Evaluationby Forrest A. Garb, SPE Forrest A. Garb k president of the Gruy Companies and of H.J. GruY and Assocs. Inc., responsible for contracting and supenising evaluation and simulation pro~ects Before joining Gruy in 7957, ho worked for SoCony Mobil Oil Co., specializing in offshore drilling-fluid control and high-pressure cumplet;ons, and, later, in field and resewoir engineering for Mobilrs Venezuelan Div. G?rb re?ent/Y Presented Petroleum seminars to industv personnel in the Peoples Republic of China, and in 7979 was elected chairman of the Natl. Petroleum Commine? of the W.. council for W.China Trade. He is currently chairman of the D8@s SeCtiOn @n@@9 Educatio? Committee and was directorof that section during 1.978-79. Garb has revised the chapters on Estimation of Oil and Gas Resewes and Valuation of Oil and Gas Reserves for SPES 7985 revision of Petroleum Production Handbook. !

Introduction man has been The life-slyle of 2~-century influenced more by oil and gas than any other natural resource, and indications are that ofi and gas reiem= will increase in impintance the remainder of this century. Oil and gas production provides inexpensive portable energy and supplies feedstock to an international petrochemical indust~ that manufactures synthetic textiles and rnedlcines and supports world agriculture. Crops are planted, cultivated, treated with pesticides, fertilized, hqvested, moved to market, and cooked with oil apdlor gas. Wars have been fought to ensure petroleum availability, and reserve estimates have dic@ted actions of governments, entire industries, individual companies, lending institutions, and private investOrs. Many petroleum engineers spend a major part of their professional lives developing estimates of r~erves and production capabilities, along with new methods and techniques for improving ihese estimates. To understand the confidence levels and risks of tie estimates, a clear and consistent set of reserve classifications must be used. The confidence levels and the techniques implemented by the petroleum engineer depend on the quantity and ~e maturity of the d~ta available. The data quality, therefore, establmhes the classification assigned to the reserve estimates and indicates the confidence one should have in the reserve estimates. Abnost alf applications of oif and gas reserve estimates require, in the final analysis, an economic evaluation that considers the predicted production capacity and tie capital and operating cost estimates. The economic analysis is the thermometer used to indicate the health of the reserves owner and wiU becopyright 19S society of Petmle.m Engineers

representative and reliable only if the data, reserve estimaf+ng procedures, ~d r:se~e classificati%s ~e understood and applied properly. Reserve Ckiasification and Nomenclature The need for one universat classification and nomenclature system for petroleum reserves has long been recogriied by the vaious technical societies, professional organizations, gOvernment~ agencies, and the petroleum indus~. fn spite of the need for a standardization of definitions and concepts, differences in deftitions continue to cloud the absolute meaning of reserve definitions published by technical societies and regulatory bodies. The societies have established study groups to recommend a classification system, however, a upiversal system acce&ble to all estimators Wd users has not been agreed upon. A study group established in 1980, consisting of representatives of oil producing countiies, recommended a set of definitions and classifications. 1 A joint committee of SPE, AAPG, and API developed a set of definitions and a glossary of terms in 1981.2 These definitions, considered cOnsis!ent with U.S. DOE and Securities and Exchange Commission (SEC) definitions, ~: Present~ here afong with my co-rots On their us:. Proved Reserves. Proved reserves of cmd: oil, condensate, natural gas, or natural gas liquids are estimated quantities as ~f a specific date, which geological and engirieering data demonstrate with a reasonable certainty to be recoverable ~ the future from known resetioirs under existing economic conditions. (lvfost reservoir engineers consider 373

MASCH 1985

I .

projected economic conditions but hit reserve estimates to current technology.) Reservoirs are considered proved if economic producibility is supported by actual production or formation tests m if cbre ahlysis amioi log interpretation demonsmate economic producibility with reasonable certainty. (Most engineers require the formation tests.) The area of a reservoir considered proved includes (1) that portion delineated by drilling and defined by fluid contacts, if any, and (2) the adjoining portbns not yet drilled that reasonably can be judged economically productive on the basis of available geological and engineering data (frequently limited to direct offset locations). In the absence of data on fluid contacts, the lowest known structural occurrence of hydrocarbons contiols the lower proved liit of tie reservoir. Proved reserves are estimates of hydrocarbons to be recovered from a given date forward. They are expected to be revised as hydroc~bons axe produced and additional data become available. Proved natural gas resepes are composed of nonassociated gas and associated-dissolved gas. An appropriate reduction in gas reserves is required for the expected removal of natural gas liquids and the exclusion of nonhydrocarbon gases (if tiey occur in significant quantities) necessary for marketability. Reserves that can be produced economically through the application of established improved recovery techniques are included in the proved classification when two qualifications are met. 1. Successild testing by a pilot project or the operation of an installed program in the same reservoir or in one with similar rock and fluid properties provides support for the engineering analysis on wh]ch the project or program was based. 2. It is reasonably certain that tie project will proceed. Reserves to be recovered by improved recovery techniques that have yet to be established through repeated economically successful applications will be inclu&d in the proved category only after successful testing by a pilot project or after the operation of an installed program in the reservoir provides support for the engineering analysis on which the project or program was based. Proved Developed Reserves. A subcategory of proved reserves, proved developed reserves can be expected to be recovered throngh existing wells (including reserves behind-pipe, sometimes called proved developed nonpmducing) with proved equipment and operating methods. Improved recovery reserves can be. considered developed only after an improved recovery project has been installed. (Proved developed reserves do not require major capitaf expenditures to enable production.) Proved Undeveloped Reserves. Another subcategory of proved reserves, proved undeveloped reserves are expected to be recovered from (1) future drilling of374

wells, (2) deepening of ex@ing wells to a different reservoir, or (3) the inst+ation of an improved recovery project. (Proved undeveloped reserves require major capital investment to enable production.) The probable and possible reserve definitions frequently used by industry do not enjoy offlci~ sanction by the SPE at the present time. The usual deftitions for these categories are as follows. ProbabIe Reserves. Probable reserves are quantities of recoverable hydrocarbons estimated on the basis of engineering and geological data that are similar to those used for proved reserves but that lack, for various reasons, the certainty required to classify the reserves as proved. Probable reserves are less certain to be recovered than proved reserves. In some cases, economic and regulatcny uncertainties may dictate the probable classification. Probable reserves include (1) reserves that appear to exist a reasonable distance beyond the proved liits of productive reservoirs, where water contacts have not been determiried, and proved limits are established only by the Iowest known structural occurrence of hydrocarbons; (2) r.+eryes in formations that appear to be productive from log characteristics only but lack definitive tests or core analyses data; (3) reserves in a portion of a formation that has be.& proved productive in other areas in a field but is separated from the proved area by sealing faults, provided that the geologic inte~retation indicates the probable area is related favorably to the proved potiion of the formation; (4) reserves obtainable by improved recove~ where an improved recove~ program, which has yet ~ be established through repeated economically successful operatio~, is planned but is not yet in operation and a successful pilot test has not been performed, but reservoir and. formstion characteristics appear favorable for its succesv (5) resewes in the same reservoir as proved reserves that would be recoverable if a more efficient recovery mechanism develops than was assumed in estimating the proved reserves; and (6) reserves that depend on a successfd workover, meatment, retreatment, change of equipment, or other mech@cal procedures for recovery, unless such procedures have been proven successful in wells exhibiting similar behavior in the same. reservoir. Possible Reserves. P9ssible reserves ae quantitk of recoverable hydrocarbons estimated on the basis of engineering and geological data that are less complete and less conclusive than the data used bJ estimates of probable reserves. Possible reserves are less certsin to be recovered than proved or probable resemes. In some cases, economic and regulatory uncertainties may dictate the possible classification. Possible reserves include (1) reserves that might be found if certafi geologic conditions exist that are JOUP.NALOF PETROLEUMTECHNOLOGY

indicated by structural extrapolation from developed ares, (2) reserves that might be found if reasonably definitive geophysical interpretations indkate a productive area larger than could be included within the proved and probable limits; (3) reserves that might be found in formations that have somewhat favorable log characteristics but leave a reasonable doubt ax to tkeir certainty; (4) reserves that might exist in untested fault segments adjacent to proved reservoirs where a reasonable doubt exists as to whether such fault segment contains recoverable hydrocarbons; and (5) reserves that might result from a planned improved recovery program that is not in operation and that is in a tield in which formation fluid or reservoir characteristics are such that a reasonable doubt exists as to its success. Several subcategories not recognized for regukitow or financial applications frequently nre used by companies intcmalfy to aid in their decision making. Subcategories such as shut in for market, awaiting workover, awaiting pipeline connection, or awaiting surface facilities are selfexplanatory. AddkionaJ definitions such as active secunday, future secondary, future tertiary, categories sometimes wifl be med. or total-all Prospective reserves are sometimes assigned for unexplored acreage or for deeper zones never penetrated. A number of terms are pertinent in defining resemes. Hydrocarbons injtilly in pface (oil and/or gas) refem to the original volume of hydrocarbons that occupied tic reservoir before production. Ultimate recove~ is the ultimate economically recoverable portion of the hydrocarbons initially in place (oil and/or gas). Reserve is the volume of hydro%rbons remaining to be recovered economically using proven technology as of a specified date. Crude oil is defined technically as a mixture of hydrocarbons that exist in the liquid phase in natural underground reservoirs and remain liquid at atmospheric pressure after passing through surface separating facilities. Volumes repofied as cmde oil include (1) Iiquids technically defined as crude oil and (2) smnll amounts of hydrocarbons that existed in the gaseous phase in natural underground reservoirs but are liquid at atmospheric pressure after being recovered from oilwell (casinghead) gas and lease separators. From a technicaf standpoint, these liquids are termed condensate. However, they frequently are commingled with a crude stream and are impractical to measure and report separately. Major condensate production is repurted as either lease condensate or plant condensate and is included in mtural gas liquids. Small amounts of nofiydrocabons produced with oil are sometimes measured and included in crude oil volumes. Natural gas is a mixture of hydrocarbons and !Wing quantiti= of nonbydrocmbons that exist either m the gaseous phase or in solution with cmde oil in MARCH 1985

natural underground reservoirs. Naturul gas has two subclasses. Asmciazed gas is naturnl gas found in coniact with crude oil in the reservoir. Associated gas may consist of free gas, commonly called gas-cap gas, ador dissolved gas in solution in the crude oil. Nonassociated gas is natural gas found in reservoirs that do not contain significant quantities of crude oil. DissoIved gas and gin-cap gas may be produced concurrently from the same wellbore. In such situations, it is not feasible to measure the production of dissolved gas and gas-cap gas separately. Therefore, production usually is reported under casinghead gas. Reserves and producing capacity estimates for associated and dissoIved gas usually are reported as a combined total. Natural gas liquids (NGLs) are those portions of reservoir gas that are liquefied at the surface in lease separators, field facilities, or gas processing plants. NGLs include, but are not limited to, etbnne, propanes, butanes, pentanes, natural gasoliie, nnd condensate. Improved recovery comprises alf methods for supplementing naturaI reservok forces and energy, or otherwise increasing ultimate recovery from a reservoir, including (1) pressure maintenance, (2) cycling, (3) waterflooding, and (4) aIIY omer secondary recovery technique. Improved recovexy ASO includes recovery techniques called enhanced recovery methods, such as thermal recovery, chemical flooding, steam injection, in-situ combustion, and use of miscible and immiscible dkplacement fluids. These classifications and definitions ae useful for defining stages of development, maturity of data, and the risk associated in accurately estimating the vohtmes and producibility of the reserves. The classifications are used to assign rixk-adjustment factors for fmncinl evacuation of the reserve quantities; therefore, it is obvious that a universal set of definitions should be used by both the petroleum and financiaf communities. Reserve Classification Sununnry

Reserves have five baaic classifications, which may be expanded to meet individual company needs. 1. Classification by ownership MD be subdivided into gross reserve (100 % of well, lease, or reservoir) and net reseme (net to interests evakated after M royalties, overrides, production payments, or reversinnmy interests). 2. ClasWlcation by energy source includes primary and improved recovery. 3. Classification by degree of proof includes proved, probable, possible, and prospective reserves. 4. Classification by development status is divided into developed and undeveloped reserves. 5. Classification by producing status subdivides reserves into producing or nonprnducing. 375 .

Prcdm!bn 1

Pram

W,

1.,0,,8,, ,mad

&

Fig. 1Range in estimates of ultimate recovery during the life

of a reservoir.

Estimating

Reserve

VoIumes

A total treatment forestimating reserves under any possible circumstance of reservoir character or data quality is beyond thescope ofthis paper. Expansion of the subject materizd may be found in Chaps. 37 and 38 of Ref. 3 and Chaps. 40 and 41 of Ref. 4. Discussion. Managements decisions are dictated..by anticipated investment results. In the case of oil and gas, the petroleum engineer compares the estimated costs in dollars for some investment opportunity vs. the cash flow resulting from production of barrels of oil or cubic feet of gas. This analysis may be used in formulating policies for (1) exploration and development of oil and gas properties, (2) design and construction of plants, gathering systems, and other surface facilities, (3) determining the division of ownership in unitized projects, (4) determining the fair market value of a property to be bought or sold, (5) determining the collateral value of producing properties for loans, (6) establishing sales contracts,376 _..

rates, and prices, and (7) obtaining SEC or other regulatory body approvals. Reserve estimates are just that-estimates. They can be no better than the data on whlcb they are based and are subject to the experience of the estimator. Unfortumtely, reliable reserve figures are most needed during the early stages of a project, when only a minimum amount of information is available. Because the information base is cumulative during. the life of a property, the resetwoti engineer has an increasing amount of data with which to work as a project matures, and this increase in data not onfy changes the procedures for estimating reserves but, correspondingly, improves the confidence in the estimates. Reserves frequently are estimated (1) before drilling or any subsurface development, (2) during the development drilling of the field, after some performance data are available, and (3) after performance trends are well established. Fig. 1 demonswates (1) the various periods in the life of an imaginary oil property, (2) the sequence of appropriate recovery estimating methods, (3) the impact on the range of recovery estimates that ttsually results as a property ages and more data become available, (4) a hypothetical production profile, and (5) the relative risk in using the recovery estimates. Tme is shown on the horizontal axis. No particular units are used in thk chart, and it is not drawn to any specific scale. Note that, while the tdtimate recove~ estimates may become accurate at some point in the late. fife of a reservoir, the reserve estimate at that time still may have significant risk. During the last week of production, if one projects a reserve of 1 bbl [0.15 m3] and 2 bbl [0.3 m3] are produced, the reserve estimate was 100 % in error. Reserve estimating methods usually are categorized into three famifies: (1) analogy, (2) volumetric, and (3) performance techniques. The performance technique met30ds usually are subdivided into simulation stttdies, material-balance calculations, and deciine trend amdyses. The relative periods of application fOt these several techniques are shovm on Fig. 1. During Period AB, before any wells ae drilfed on the prope~, any recovery estimates will be of a very general nature based on experience from similar pools or wells in the same area. Thus, reserve estimates during this period are established by anafogy to other production and usually are expressed in barrels per acre. The second period, BC, follows after one or more weUs are drifled and found productive. The welf logs provide subsurface information, which allows an acreage and thickness assignment or a geologic interpretation of the reservoir. The acre-foot volume considered to hold hydrocarbons, calculated oif or gas in place ,per acre-foot, and a recovery factor allow closer liits for the recovery estimates than were possible by analogy alone. Volumetric amdysis data may include well logs, core analyses data, bottomholeJOURNAL OF PETROLEUM TECHNOLOGY

TABLE IULTIMATE RECOVERY DISTRIBUTION SAMPLE FIELD Estimated Ultimate RecoveT (10 bbl) -

Well 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Cumulative (oh) . 5 10 15 20 25 30 35

8,09.0 9.5

10.011.0 14.5 16.2 24.0 34.0 35.7 4a.1 43.2 52.0 65.0 66.0 78.0

4045 50 55 60 65 70 75 80 85 90 95 100

Fig. 2Ukimate

recovery distribution of a sample field

101.0112.2 128.5 131.9 .. 989.8

Average =989,8/20 =49.5 x 10s bbl [78.7x 103 m] Median recovery = 68.7% average recovery.

instmummts have enabled good calculations after no more thao 5 or 6% of the hydrocarbons in place have been produced. Reserve estimates based on extrapolation of established performance trends, such as during Period DEF, we considered the estimates of highest confidence. Reserve Estimation Methods

mapping. with observed pressure behavior during early production periods, olso msy indicate the type of producing mechanism to be expected for the reservoir. The third period, CD, represents he period after delineation of the reservoir. At tiis time, usually there are performance data adequate to enable reseme estimates to be derived using numerical simulation model studies. Model studies cm yield very useful reserve estimates for a spectrum of operating 0ption3 if sufficient information is available to describe the geometry of the reservoir, any spatial distribution of the rock and fluid characteristics, and the reservoir producing mechanism. Because numerical simulators depend on matching history for calibration to ensure the model is representative of the actual reservoir, numeric6f simulation models performed in the early life of a reservoir may not be considered m have high confidence. Doring Period DE, as performance data mature, the material-balance method may he implemented to check the previous estimates of hydrocarbons initially in place. The pressure behavior studied through the materkd-balance calculations also may offer vakble clues regarding the type of production mechanism existent in the reservoir. Confidence in the material-balance calculations depends on the precision. of the reservok pre3surcs recorded for the reservoir and the engineers ability to determine the tree average pressure at the dates of study. Frequent pressure surveys taken with precisionInterpretation of these data, along MARCH 1935

sample information,

and subsurface

Anafogy. Before a reservoir is drilled, prospective reserves usually are estimated on the basis of analogy. In geologic provinces where production from thetarget formation in other entrapments exists, statistical analyses of the older wells to determine the meao or median reserves can provide useful intoruw.tion. Iflittle ornopmduction from the target formation exists, then statistical damfromw elk completed in formations having characteristics anticipated for the target zone are used. Because no factwd information from the reservoir being stodied is included in the ana.lo=q approach, reseme estimate6 w derived have the lowest confidence and ususlly are expreksed in a minimum to maximum range. When performing a statistical analysis for analogy porposes, a simple average is adeqoate only if the ukimate recovery values found for the wells stodied are reasonably constant. 3f a wide variance is observed, then a statistical dktribution must be prepared to establish a median recovery value. Table 1 presents a sample oltimate reserve distribution for 20 shaJIow oif wells found in the vicinity of a proposed drilling program. Ultinmte recovery ~ estimates for each of the 20 wells were prepared by extrapolation of their per fornwmce trends. These reserves then were arranged in ascendhg order, as shown on the table. The reserve estimates plowed vs. the cumulative percent of the samples is shown on Fig. 2. A smooth cuwe passed through the data point3 indicates a median reserve of approximately 377

OIL-WATER CONTACT -7450 GAS-OIL

-mE ~ x -7350 k x ,?, -74C0 !$ -7450

-7450-75C0

Fig. 3Geological reservoir,

map on top (

) and base ()

of a

k. ~2,4 4~ +$.< 88 Ross L EARING AND WME ~ [(88-4?+ 378 -Z42)+41209-106,] :9~ ACRE FE,, J%., :::,,,. ,W,*., . . ~hND ~ASE?. 242 +;36 37s ,W -. 009 : BCRES .5REb2E&OS;?BY 4c05c1 CONTWR Fig.

24

~A,.o,LcoN,KT

4Acre-feet

diagram.

34,000 bbl [5406 m3 ] per well. The average reserve for the same sampIing is 49,500 bbl [7870 m3]. For this example, the median or most expected well is otdy 68.7% of the average reserve for the group of wells. If only a small drilling program is proposed, tie possible reserve per well should be based on the median. If the drilling program approaches the number of wells analyzed in the distribution, then the use of the average reserve becomes defensible. Similar dktribution analyses of initial producing rates and expected well life derived from the study of existing wells will aid the engineer in time rating the most appropriate reserve estimate. Volumetric Methods. A geologic. interpretation of a reservoir cannot be prepared until sufficient wells have been drilled to delineate its areal geometry and thickness. After completion of the tirst well, reservoir engineers frequently assign a reasonable drainage area and produce thk mea by the net pay thickness indicated by the electric well log. This acre-feet assignment is used only until sufficient subsurface control is available to enable geologic mapping. The computation of reservoir volume, based on geologic mapping, has been presented in several SPE publications, 3,4 which present a sample subsurface geologic map (Fig. 3) contoured on the subsea depth of the top of the sand (solid lines) and on the subsea. depth of the base of the sand (dashed lines). The total area enclosed by each contour is planimetered and. plotted as the abscissa on an acre-feet diagram (Fig. 4) against the corresponding subsea depth as the ordinate. Tbe ga,-oil and oil-water contacts, as determined by core, log, or test data, are shown as horizontal lines on the acre-feet diagram. After connecting the observed points, the combined gross volume of tie oil- andlor gas-bearing zone may be detertnfned by using several methods. 3s4 1. Volume can be calculated by planimetering from the acre-feet diagram. 2. If the number of contour intervals is even, volume can be computed by Simpsons rule:378

Yq =v3h[(yo+yn)+4(yl +z(y~ +y~+

+Ys + +yn-z)],

+yn-l)

where VR = reservoir volume, acre-tl [m 3], h = contour interval, feet [m], YO = area on top of sand minus area on base of sand at highest contour, and Y = area on top of sand minus area on base of sand at lowest contour. Using this rule, the example calculation reservoir Yolume of: yields a

VR = ;[0+(378

242) +4 X (24 O) + (209 106)

+2 x(88-42)]

,

=;[(136)+4x(24+

103)+(2x46)],

= 12,267 acre- ft. 3. The volume may be computed with somewhat less accuracy by the Trapezoidal rule vR=h[%(yo+yn)+y, The sample problem VR=50[M(O+136)+ = 12,050 acre-ft. Because the acre-feet diagram shown in Fig. 4 usually is prepared on the top and base of formation porosity, this gross volume must be reduced to JOURNAL OF PETROLEUMTECHNOLOGY .+y~+ .+yn_, ].

when solved by this rule yields: (24+46+103)]

account for any shale stringers or impermeable sections within the formation itself. OZI the basis of a study of the individual well logs or core datx, the engineer must determine what fraction of the gross sand section is expected to contain producible hydrocarbons. This fraction times the gross sand volume yields the net pay volume. If, for example, in the illustrated case it is found that 15% of the gross section consisted of evenly distributed shale or dens: impervious stzenls, the net hydrocarbon pay volumes wovld then reduce to 85% of the gross sxnd volume (10,427 net acre-ft). In contrast to Fig. 3, separate strnchrre maps for the tOP ~d base porosity usually aie prepared. If the mture of the porosity for a zone varies substantially from well to well, or if there is a widely varying water saturation, it is sometimes justified to prepare a hydrocarbon tilckness map, termed an isovol map, based on the pay tilcfmess determined at each well multiplied by the porosity at tfrxt location and by the hydrocarbon saturation [isovol =h x ~ x (1 .9W)]. This computes tbe total void space for hydrocsrbona at each weU point. A map contoured on the hydrocarbon pore t.fichess is pxrticub.dy useful for representing thick sectiom having porosity lerises or Iarnioa, which we diftlcult to correlate between wells and are believed to be irr communication, forming a single reservoir. Computation of Oil or Gas in Place. Once the size of the reservoir is known, along with its lithologic characteristics and the properties of &e reservoir fluids, then the amount of oif or gas initially in place may be computed with the foflowing foqmdas. ~ree Gas or Gas-Cap Present). 43,560 vg4(lG= ZTIZ,

units of thousand cubic feet, this equation ia G= 43,560 V8@(l SW)P(460+60) zT(14.65)1>000 l,546V#(l ZT If S1 units are used for gas volume measured meters the 1,546 ia replaced by 2.85. Oil irr the Reservoir Saturated Potion). ~= 7,758V04(I B. where N = reservoir oil initially in place, STB [stock-tamk m3], 7,758 = number of bamels per acre-foot, V. = o~-bearing volume of reservoir, acre-ft [m3], and B. = oil formation volume factor, RBISTB [res m3/stock-tank m3]. The 7,758 is omitted if S1 units me used. Sol@on Gas in an Oil Reservoir Present). 7,758 VJJ(1 SW)R$ G.= B. where R, is the solution gas-oil ratio, scf/bbl [std m3 /m3 ] and G, is tle solution gas, scf [std m3 ]. The volumetric method for estimating reservoir size resuka in an estimate of hydrocarbon volumes initially in place. The ultimate recovery of the reserves requires rluther estimation of the percentage recovery. This recovery factor usually is based on empirical correlations or on experience. Performance Techniques (No Free Gas in cubic SW)P ,.

(No Free Gas Present fn the Oil

-SW)

Gas (No Residual

Oil

sw)pT,

G = free reservoir gas in place, Vg = free gas-bearing vohrne of reservoir, acre-ft [m3 ], b = formation porosity, fraction, SW = interstitial water sanrration, psia [kPa],p, = skm~rd pressure base, psia ma], T = reservoir temperature, degrees absoIute, T, = standard temperature base, degrees absolute, and z = gas deviation factor at reservoir conditions.

The 43,560 is omittecj if S1 units are used. For standard conditions of 14.65 psia [101 kFa] and 60 F [15 C], and for gas volumes measured inMARCH 1985

NurrmricaJ Sirzrufation Models. The first efforts to sirmkte reservoir performance were laboratory experiments using sandpack and, later, electrical network These models were designed (1) to clarify the physical phenomena controlling petroleum reservoir performance, (2) to model reservoir performance under different produc~ng condhions, and (3) to aid in selecting the optimum producing procedure for the reservoir. A field can be produced only once, and if an error is made, any opportunities to improve recovery may be lost forever. A model can be produced or run rnnny times to study the field performance under natural depletion vs. improved recovery or the effects of weU l~cations and spacing. The runs can yield relative information on recoveries, 379 .

prodttcing rates, and capital expenses, thus indicating the method hat will optimize the reservoir. The early physical models, however, were expensive, time consuming to conztict, and unique to the fields that they represented. In addition, variation in field geometry or characteristics were dit%ctdt to alter if production hktory suggested that modifications were necessary. The development of high-speed digit~ computers led to mathematical models with more universal aPP~@iOn. M:tbematica! models cotid be applied to a wide variety of reservoirs by simply changing data, and modifications to. a reservoir could be efficiently implemented. The numerical simulation model, which now is a standard tool of industry, evolved from the materialbalance concepts fust presented by Schilthuia5 in 1936. The material balance, however, treats a reservoir as a single homogeneous tank with no areal or vertical distribution of reservoir rock or fluid characteristics. A numerical simulator reduces the material-bakmce tank to a very small element and considers tiis element to be just one of many within the boundaries of a reservoir. Each element is considered contiguous and in communication with the others surmundhtg it; elements may be arrWged weally and vertically to represent the physical geometry of the reservoir to be studied. Rock and fluid characteristics may be varied within each element to represent any heterogeneities of an anisotiopic reservoir. Reservoirs may be described quite accurately by using very small elements or blocks. Many very small blocks, of course, increase computer time and spatial reservoir definition requirements. Once a reservoti representation has been prepared in the individual element form, the numerical simulation model executis for each of a series of timeateps a collection of material-balance equations for all of the blocks until the dynamic .effect.s of fluid movement, caused by either production or injection into one or more blocks, is balanced. These executio~ are performed in small enough timesteps to indicate the per form?.nce of the reservoir in general and for each producing well considered by the model. Because flow is permitted across the interior block boundaries, fluid front movements can be tracked with numericaJ simulators to monitor changes in g+soil or oil-water contacts. Models also can present the dynamic changes in pressure and changes in rese~oir saturation dktributions. Numerical simulators frequently are executed for two or three dimensions in space and for one, two, or three phases of rezervoir fluids. 6 The sim~ators usually are classified according to the. type of reservoir they are designed to simulate. They may be divided generally into three classifications: (1) gas reservoir simulators, (2) black oil rtxervoir simulators, and (3) compositional rcsemok3S0

simulators. Gas simulators may be one- or two-phase models, depending on whether or not mobile water is to be considered. A black oil model usually is capable of simulating systems where gas, oil, and water are present in any proportion. Models usually include the ablity to consider gas going in or c@pg out of solution in the oil. The data required for numerical simulation ue much the same as for a material balance. However, the spatial variations must be definable. Each element is identified in an x, y, and, perhaps, z coordinate, while the tital aiea studied is considered to be sealed at the outer bounds.g. To each block or ceil, rock data such as specific permeability and porosity must be assigned. Permeability frequently is assigned iztdependently to the x, y, or z direction. The gmmetricd data consist of the cell dimensions and the cell elevation relative to some datum. Most black oil models requize that an initial phase saturation be provided for each block and, sometimes, block pressures may be assigned. Relative permeabtity, capifbwy pressure, and fluid PVT data also must be provided for each specific problem. Condensate and volatile oil reservoirs usually requize different simulators that can account for the compositional behavior between the individual hydmcxbon components in the gas and liquid phases. This is because PVT infornwtion does not describe fluid behavior adequately for condensate and volatile oits. Transfer of mass between each of the elements is calculated in mole fractions of eit4zer individual components or pseudocornponents combining two or more of the individual hydrocarbon components. Fractured carbonate reservoirs are difficult to simulate because of mtdtipezmeability considerations. Simultaneous flow through a matrix and fracture penneabflities complicate the mathematic.d representations for fluid flow. At this writing, mukipermeabilhy compositional simulators are the frontier. Special reservoir simulators have been developed t? represent reservoir phenomena, such as weUbore coning, gravity segregation, or crossflow between stzingers, as well as tbergd recovew processes, miscible displacement, and other @proved recovev methods. Because any numerical simulation model is made from very limited spati~ distribution information, the model is apt to be inaccurate. Cahbration of the model, however, may be achieved through history matching procedures. The numerical simulator is executed first, using the best data available. The computed results are compared with the obsewed field hktory, and if agreement is not satisfactory, areal data SUChas permeability, relative permeability, or porosity values are varied between computer runs until a satisfactory match is achieved. The simulator then is used to predict performance on the basis of the operating options for the reservoir.JOURNAL OF PETROLEUM TECHNOLOGY

When a hkto~ match has been achieved, the engineer has determined a combination of reservoir variables that may not be tutique and may not represent reservoir conditions precisely. In general, however, the longer the matched hktory period, the more reliable the predicted per fommnce will be. Material-Bafance Method. If sufficient pressure production performance data are recorded and PVT data describing the reservoir, fluid behavior are available, the amount of oil or gas in place in a reservoir sometimes may be computed by the materid-balapce method. 5 This method is based on the premise that the pore volume (PV) of a reservoir remains constant or changes in a predictable manner with the reservoir pressure drop, as oil, gas, andlor water are produced. .If the reservoir PV remains near constant, then as reservoir fluids are produced ~d rese~ok pressure falls,, the fluids remaining in the reservoir must expand to occupy tie PV. The reservoir fluid unit expansion per pound of pressure loss isdefined bylaboratory PVT analyses. Periodic survey data indicate the loss in reservoir pressure corresponding to withdrawals. The material balance calctdates the volume of reserioir fluids that would berequired toexhiblt anexparision for the observed pressure drop, which would equal the witbdrawxs. Calculations at severul pressure withdrawal points yielding consistent results usually are required. an Successful application of &is method rqdres accurate history of the a~erage pressure of the reservoir, reliable oil, gas, and water production data, and PVT dam on the reservoir fluids. The results from atnaterial-balance culcttlation may be quite erratic, especially when there are unknowns other than the amount of oil in place, such as the size of a free gaacapor the presence of waterdrive. Table2 presents the most frequently used. material-balance equations. It is beyond the scope of this paper to treat each of them. The material bakmce cum be rearranged to solve any of. theunknowm if sufficient dam are known or if arange OFprobable data can be identified. Applications by Schilthuis, 5 Muskat,,6 Taquer, 7 Babson, s and others have been published und arc accepted by indus~. Innovative applications for using the miterial balunce to solve simukaneuusly for oil in place and aquifer activities have been published by Odeh and Havlena9 and McEwen. 10 Materid-bskmce calculations also may be desiSned to extend the observed per fomtance of a reservoir into the future. These predictive tools assume a homogeneous reservoir and require application of relative permeability concepts. The concept of relative pcrmeab:lity is one of the most critical as~cts of rnaterial,b.alance and numerical simulation calculations. Industry accepts that the permeability of porous media to a ,flowing tluid varies with tAe saturation of that fluid, but the change is difficult to predict in advance. CoreMARCH 1985

analyses presenting relative permeability curves for a tiny sample of the reservoir sometimes simply are not representative of the tiful r.&emoti system. Although ~eld-derived relative permeabili~, curves solved from obseryed production are highly desirable, the need for the relative permeability curve often precedes having enough data to prepare one from field inforgmtion. The accuracy of a material bulance ulso is hindered by the fact that most calculations assume gas released from solution in the resewoir to be dktributed homogeneously. This average saturation is used to conclude relative permeability values for the calculation. If the reservoir has good vertical permeability, then fluid segregation resulting from gravity @fects may cause the reservoir to perform differently than the material bakmce wotdd $aIculate. When au engineer is forced to assume a relative perineability curve, the engineer assumes a vuriable that will control the results of the materti-baknce calculation. However, relative permeability curves can be estimated to a reasonable degree of accuracy if lithologic conditions are weII known and if sufficient laboratory curves have been prepired during core analyses. Improved Recowy. SpeciuI calculations designed to treat secondaty or improved recovery procedures, such aa the Bucldey-Leverett, 11 Stiles, 12 and have become Pafl Of Dykstra-Parsons 13 ~~c~atiom, the resefioir engineers standard tools. Th&e calculations are greatly enhanced through the use of computers, arid computer programs have been published for application of these standard procedures. 14 Production DecIine Curves. Tbe highest confidence estimates of ultimate recovery result by extrapolation of performance trends. Because the engineer usually wishes to determine the remaining oil reserves and the remaining productive life, the cumulative production and time normally are selected as independent variables and are plotted as abscissus. A vaIYing characteristic of the well performance that can be measured easily is selected as a variable to produce a trend curve. For exmapolation purposes, titk variable (such as rate, pressure, or water cut) must be a continuous function of the independent variable and change in, some uniform, definable mumter. By plotting the vaks of this continuously changing dependent variable as ordmtes against the values of the independent variable as abscissas, and graphically or mathematically extrapolating the aPP~en~ ttend until a ~own endpoint is reached, one may estimate the rematning reserves or the remuining life for a reservoir. For oil reserves, these plbts are usually the Iogurhftm of the producing rate vs. time. For gas reservoirs, similar production curves sometimes are used,, or pressure divided by the compressibility factor for the gas may be plotted vs. cumulative production to derive estimates of initial gas in place.381

TABLE 2CLASS1FICATION Reservoir Type

OF MATERIAL-BALANCE Material.Balance

EQUATIONS Unknowns - WP) N, We, m Equation

Equation-

NP[B, +0.1781 Bg(RP -R$;)]-(We Oil resewoir with gas cap ad active water drive N= 5 m80r ~ () B@ +(Eft -Bo,)

11

NP[Et +0.1781 .9Q(RP -R*)]+ Oil reservoir with gas can no active water drive (we =0) N= B mBd ~-l () B g; +(Et-Bd)

WP N, m 12

Initially undersaturated oil reservoir with active water drive (m =o& 1, Above bubblepoint

NP(l +APc,J N= [

w. -w. - y .,

1-orJ1

(1 - SW) N, We 13

APIco +c, -sv/(co

~= 2. Below bubblepoint

NP[B, +0.1781 Bg(RP -R~l)]-(W~B,-Ed

WP)

N, We

14

Initially undersaturated oil reservoi~ no active water drive (m= O), (W. = O): 1. Above bubblepoint

NJ! [ N=

+A/)CO)+

~ d

1-R4)]+

(1 -SW) N 15

APIco +c, -Sw(Co

-cw/)1W,

2. Below bubblepoint

~=

NPIBC+0.1781B,(RP s! 6., GPf3g -5.615(Wa

N

16

- W,) G,W 17

Gas reservoir with active water drive

GP =

B, - B,, GPBg +5,615WP

Gas resewoic

no active water drive (Wa = O)

GR = Bg-BgI

G

18

where Bg = gas FVF, vol/vol, BO = oil FVF, RBISTB [res m3/stock.tank

m3],

B, = two-phase FVF for oil,. RBISTB [res m31sfock-tank ins], C, = comPressibiliW factor for reservoir rock, vollvcdlpsi, c. = compressibility factor for oil, vollvollpsi, c. = c0mpres5ibility factor for water, KWw31/pSi, GR GP i m N NP RP R, = = = = = ; = = reservoir gas in place, scf [std m3j, cumulative gas produced, scf [std m3], initial conditions, ratio of gascap volume to oil zone olume, reservoir oil in place, STB [stock-tank ins], cumulative oil produced, STB [stock-tank ins], cumulative produced GOR, scf/STB [std m3/stock-tank solution gas ratio, scf/STB [std mslstock-tank m3],

rn3],

SW = interstitial water saturation, fraction of pore space, We = c.mlative water influx, bbl [rn3], ad WP = cumulative water produced, bbl [m3]. .1{S!M are used, 5.8,s and 0,,75, should be amli,ed.

382

JOURNAL OF PETROLEUM

TECHNOLOGY

The extrapolation procedure is of m empirical nature but represents the, system being nm?lyzed. If the system is not imbulanced because of a change in operations, then the extrapolation should be a reasonable representation of the future reservoir performance. Among the dependent variables usually extrapolated, the logarithm of the rate of production is by far the most POPULWbut only when production is not restricted. Because the volumes of oil andlor gas usually are sold, this dependent variable has the adwmtage of being readily available and accurately recorded. The endpoint of any rate extrapolation is normally the economic limit rate, nnd since actual or estimated operating costs nre usually available, thk endpoint is not dlfticult to determine. Extrapolation of performance curves should be performed carefully to ensure that any established decliie in producing trend is not the result of proration, mechanical wear of lifting equipment, physical changes in or around the wellbore (such as deposition of wax, salt, or asphaltenes), or from loose sand, silt, mud, or cave-ins into tie wellbore, Any changes around the wellbore as the result of gas-cap or water encroachment also must be considered. The engineer extrapolating oilwell perfommnce data dso should determine if the data represent production above or below bubblepoint pressure. Extending an oif perfommnce curve through the bubblepoint is invalid, gas released from solution below bubblepoint pressure will add energy to the producing system, which will alter reservoir saturations and relative permeabilities and change the nature and slope of the decliie curve. Snperpressured reservoirs also require special cxre because projecting datn recorded at above-normal pressure grxdients mny prove nonrepresentative of performance at nnd bdow normal pressure ranges. Extrapolation of a performance trend assumes that the operations in effect during the trend period wifl continue. Inffl ckilIing, gas, steam, or water injection, or any operational change may render the extrapolation invalid. Types of Production Decline Curves. Production decline curves usually plot production rate vs. time or vs. cumulative production. Because productionratehime curves have found more acceptance, the folfowing discussion will focus on this type of plot. There are two dedine terms used in equations describ@ rate-time cumes. The nominal decline rate, a, is defined as the negative slope of the curve representing the natural logarithm of the production rate, q, vs. time, t, or: dlnq dt dqldt . _ . q

mainly in the derivation of the vaious mathematical equations. The effective decline rate, d, is a step function more commonly used in practice and is the drop in production rate from m initial to a final rate for a period of time divided by the production rate at the beginning of the period d= , 92 ql E71 The time period may be 1 month or 1 year for effective monthly or annual decline rates, respectively. Three types of production decline curves commonly Arps, 15,16 in his extensive have been recognized. treatments of decline curves, published the impottnnt relati.onshipi for constant percen~ge (exponential), hyperbolic, and harmonic decline curves. Fig. 5 presents those relationships along with the curve appearmce for rate-time snd rate-cumulative plots for the thee types of curves when plotted on regular coordinate paper, semilog paper, and log-log paper. h analysis of a large number of acmal production decline curves by Cutler 17 indicated that most decline curves demonstrated a hyperbolic shape, with values for the,exponent n fall@ between 0.0 and 0.7, witi the majority falling between 0.0 and 0.4. Gravity drainage production under certain conditions was reported by the API Is to have an exponent n equ~ 0 0.5. The occurrence of harmonic declines (n= 1) is apparently very rare. The constant percentage or exponential decline curve is a straight line on semilog paper. The ratecumtiative curve is a stm.ight line on regular coordinate paper. In either case, the tangent of the xwzle of slope is equal to the nominal decline fr;ction. In the cnse of the hyperbolic-type decline curve, the rate-time relationship.., as well as the rate-cumulative relationship, requires shifting on log-log paper to yield a straight line. Before the development of digital computers, shitiing of curves was a ccamnoa practice, but computer regression procedures have made thk unnecessary. Performance histories can be regressed with computer pro=wmns to identitj the Ieast-squares best fit through historical production information, and the equations thus solved can be extrapolated for predictions of future performance. Because hyperbolic decline cunes asymptotically approach a horizontal line, very long extrapolation of hyperbolic curves can result in optimistic projections. Knowledge of rhe decline rate observed for sfiila aPP~ent *IUUM wefls having more hktory sometimes enables the reservoir engineer to decide at whnt point in the projection the hyperbolic extrapolation should be replaced with an exponential extension to the economic limit. 3s3

~=.

.

Nomirwd decline is a continuousMARCH 1985

function and is used

WCLIW

VPE

Constant-Percentage

Decline

Harmonic Decline decline is proportional to production rate =1 D=Kq=~ forinitial conditions

Basic Characteristic

decline is constant =0

-Dt=log.:

q,Rate.Time Relationship q, =qje-or Q