Summary The purpose of this paper is to present case history studies that demonstrate methods of analyzing rate-time data to predict future production and to determine reservoir variables. Constant wellbore pressure analysis techniques are demonstrated, using pressure analysis techniques are demonstrated, using existing qDd - tDd type curves along with developing new qDd - tDd type curves from actual field data. Case histories for individual oil and gas wells are presented, along with groups of wells in a field and presented, along with groups of wells in a field and total field studies. The field studies include a one-well full water drive field, a low permeability solution gas drive field, and a field with both primary and secondary (waterflood) history. Field primary and secondary (waterflood) history. Field shutins and backpressure changes are shown to retrace the early time rate data as would be expected from superposition principles. Reservoir variables developed from a total field rate-time match are compared to early well pressure buildup analysis results. Comparisons are excellent. This work not only demonstrates the technique of analyzing rate-time data, it also presents a method whereby a reservoir or formation dimensionless type curve can be developed from rate-time field data. The resulting type curve can then be used to forecast wells or fields in the same reservoir or formation. Because such a type curve is dimensionless, changes in stimulation, spacing, and reservoir properties can also be accounted for. Introduction Since the original presentation in 1973 by Fetkovich of the paper "Decline Curve Analysis Using Type Curves", many successful applications have been made with declining rate-time data using the type curve approach. Case history studies of individual oil and gas wells, of groups of wells in a field, and of total fields are presented in this follow-up paper. Additional papers dealing with the constant wellbore pressure solution which also include the depletion period have since been published to aid analysis and understanding of what we published to aid analysis and understanding of what we now call "advanced decline curve analysis." In essence, decline curve analysis is a forecasting technique: rate-time data is first history matched on an appropriate type curve after which a forecast is made. Complex simulation studies proceed similarly. This paper demonstrates that by using basic reservoir engineering concepts and knowledge we know what direction to take, what type curve(s) to choose and where the rate-time data should fit. Decline analysis must work since it is founded on basic fluid flow principles, the same principles as used in pressure transient analysis. The problem most engineers have had and will continue to have with decline curve analysis is bad, erratic, or insufficient data. Careful attention to obtaining accurate flow rates, flowing pressures and downtime should help solve the problem. A good rate-time analysis will not only give the same results as conventional pressure transient analysis but will also allow a forecast to be made directly at no cost in lost production. For low permeability stimulated wells in particular, pressure buildup testing could be eliminated in many cases as being of little value or economically unjustifiable because of the resulting production loss when compared to what can be obtained from properly conducted constant wellbore pressure drawdown tests. pressure drawdown tests. RATE-TIME TYPE CURVE ANALYSIS CONCEPTS The Radial Flow Solution The fundamental basis of advanced decline curve analysis is an understanding of the constant wellbore pressure solutions and their corresponding log-log pressure solutions and their corresponding log-log type curve plots, which is the inverse of the constant rate solution. Fig. 1 is a composite of the analytical constant wellbore pressure solution and the Arps exponential, hyperbolic and harmonic decline curve solutions all on a single dimensionless type curve. The depletion stem values of b range between 0 (exponential) and 1 (harmonic) which are the normally accepted limits.
Thomas, L.K.; SPE, Phillips Petroleum Co. Phillips Petroleum Co. Dixon, T.N.; SPE, Phillips Petroleum Co. Phillips Petroleum Co. Evans, C.E.; SPE, Phillips Petroleum Co. Phillips Petroleum Co. Vienot, M.E.; SPE, Phillips Petroleum Co. Phillips Petroleum Co. Copyright 1987 Society of Petroleum Engineers Summary. This paper describes the evaluation of a waterflood pilot in the highly fractured Maastrichtian reservoir of the Ekofisk field in the Norwegian sector of the North Sea. A four-well pilot consisting of one water injector and three producers was initiated in Spring 1981 and was concluded in mid-1984. A total of 21 × 106 bbl [3.3 × 106 m3] of water was injected, and water breakthrough occurred in two of the production wells. Simulation of waterflood performance in the pilot was conducted with a three-dimensional (3D), three-phase dual-porosity model. Initial and boundary conditions were taken from a full 3D single-porosity model of the reservoir. The pilot was conducted to determine the following information for the Maastrichtian: water-cut performance vs. time, water imbibition characteristics, and anisotropy. Results from this work have been incorporated into a full-field waterflood study. Reservoir description included the determination of fractured areas, matrix block sizes, water/oil capillary imbibition, matrix permeability and porosity, and effective permeability. These data were derived from porosity, and effective permeability. These data were derived from fracture core analysis, pressure transient tests, laboratory water/oil imbibition studies, repeat formation pressure test results, and open- and cased-hole logs. An excellent match of waterflood performance was obtained with the dual-porosity model. Of particular interest are the imbibition characteristics of the Maastrichtian in the Ekofisk field and the character of the water-cut performance of the producing wells following injector shutdowns and startups. Introduction The Ekofisk field was discovered in Nov. 1969 in Block 2/4 of the Norwegian sector of the North Sea. The field is a north/south-trending anticline located about 160 miles [257 km] from land in about 240 ft [73 m] of water. In July 1971, production began from four subsea wells. These were later abandoned in 1974 when production began through permanent facilities. Field production peaked in Oct. 1976 at about 350,000 STB/D [55 600 stock-tank m3/d] and currently averages 110,000 STB/D [17 500 stock-tank m3/d]. Original oil in place (OOIP) in Ekorisk is estimated to be 6.7 × 109 bbl [1.1 × 109 m3]. The reservoir consists of about 600 ft [180 m] of productive limestone that can be divided into the Ekofisk productive limestone that can be divided into the Ekofisk formation (Danian Age), approximately 400 ft [120 m] thick, 50 to 90 ft [15 to 30 m] of dense limestone and a 200-ft [60-m] -thick section of highly fractured Tor formation (Maastrichtian Age). The reservoir rock is naturally fractured, with fracture intensity increasing with depth. The reservoir was overpressured initially and contained an undersaturated oil at an initial pressure of 7,120 psig at 10,400 ft [50 MPa at 3170 m] subsea. The psig at 10,400 ft [50 MPa at 3170 m] subsea. The bubblepoint pressure was approximately 5,545 psig [38 MPa] at a reservoir temperature of 268 deg. F [131 deg. C]. Initial solution GOR at producing separator conditions was 1,530 scf/STB [276 std m3/stock-tank m3]. Table 1 presents a summary of the Ekofisk reservoir parameters. The field was developed with three production platforms. Produced gas in excess of sales gas has been platforms. Produced gas in excess of sales gas has been reinjected into the Danian formation in the crest of the field. Oil produced from the field is sent by pipeline to Teesside, England, and gas production is transported by pipeline to Emden, Germany. As of Jan. 1, 1984, a total pipeline to Emden, Germany. As of Jan. 1, 1984, a total of 690 × 106 bbl [110 × 106 m3] of stock-tank oil and 2,263 Bcf [64 × 109 m3] of gas have been produced. Gas reinjection totals 621 Bcf [17.6 × 109 m3]. Primary oil recovery with excess gas injection is forecast to be about 1.2 × 109 bbl [190 × 106 m3] or 18% of the OOIP. A Maastrichtian pilot waterflood was initiated in the Ekofisk field in April 1981 to evaluate the performance of water injection in this highly fractured formation. The four wells that make up the heart of the pilot are B-16, of water injection well, and B-19, B-22, and B-24, the three closest Maastrichtian-only producers. Both model and laboratory studies were undertaken to assist in the evaluation and interpretation of waterflood results. The model study of water injection into the Ekofisk Pilot, which is located in the Platform B area of the field, Pilot, which is located in the Platform B area of the field, was conducted with a dual-porosity model. An analysis of available data was made to determine fractured zones in the pilot area, and only those areas were assigned dual porosities. History for this study consists of the period from Jan. 1, 1978, to April 1984 and includes a total pilot water injection of 21 × 106 bbl [3.3 × 106 m3]. pilot water injection of 21 × 106 bbl [3.3 × 106 m3]. During the injection period, 107 STB [1.5 × 106 stock-tank m3] of oil and 38.2 Bcf [1.1 × 109 m3] of gas were produced from the three pilot producers. produced from the three pilot producers. Initial conditions for the study were taken from a 3D history match of the field. The area selected for inclusion in the study is about 1,100 acres [445 ha] and includes five edge wells-B08, B-14, B-18, B-21, and B-23- in addition to the primary pilot wells. JPT P. 221
Field data indicate that in some instances significant afterflow occurs after a well is considered shut in. An analysis method for afterflow-dominated pressure buildup data is presented whereby the P D-t D model describing the transient behavior of the well can be directly obtained by matching a log-log plot of the rate-normalized pressure vs. time data to published type curves. The P D-t D model thus obtained allows a rigorous mathematical superposition analysis to be performed on the same data with results equivalent to those obtained from the normalized typecurve analysis.This work demonstrates that rate normalization must be based on total afterflow rates, confirming with field data Perrine's assumption that total rate should be used in multiphase flow analyses. Dramatic changes in character are seen between the rate-normalized pressure vs. time and the conventional pressure vs. time log-log data plots for low permeability stimulated wells. Several field examples demonstrate the application of this simple and effective technique.
Summary This work presents the conversion of the shape factor, CA, to a pseudosteady-state skin term, sCA. When the shape factor is expressed as a skin term, it becomes easier to see the effect that a well placement in a given drainage area will have on the wells performance. Skin factors for published drainage shapes and well locations are given. Discussion In attempting to calculate interference effects of well locations on production forecasts, it was found very convenient to express the shape factor, CA, as a pseudosteady-state skin term, sCA. When using pseudosteady-state flow pseudosteady-state skin term, sCA. When using pseudosteady-state flow equations, the effect of a well not located in the center of a radial or square drainage area becomes immediately apparent when the shape factor is expressed as a skin term. The general pseudosteady-state equation in terms of CA for oil, gas, or water can be written as ..........................................(1) By using an effective drainage radius, r,', to maintain an equivalent reservoir volume ..........................................(2) and the shape factor for a well at the center of a circular drainage area (CA =31.62), we can obtain the familiar radial flow pseudosteady-state equation ..........................................(3) Introducing a reference shape factor term, we can write ..........................................(4) ..........................................(5) Defining a pseudosteady-state skin factor, sCA, as ..........................................(6) we have, referencing to the center of a circle (the classic analytical solution) with CA, ref = 31.62, ..........................................(7) or, referencing to the center of a square (field and model situations) with CA, ref = 30.8828, ..........................................(8) Values of scA referenced to the center of a circle or square are tabulated in Table 1. Values of CA in Table 1 were obtained from Ref. 1 Constant wellbore pressure production forecasts for wells not in the center of a circle are made conveniently by using the concept of effective wellbore radius with and from Ref. 2 and . Nomenclature A = drainage area, ft2 [M2] B = formation volume factor CA = shape factor D = nondarcy flow constant JPT February 1985 p. 321
This paper presents a detailed case history studyIn solution gas drive reservoirs, decline curve of a low permeability volatile oil field located analysis of rate-time data for predicting future in Campbell County, Wyoming. The field was anal--production and determining recoverable reserves for yzed on an individual well basis using advanced a fairly large number of wells is conwnonlydone decline curve analysis for 40 individual well com-using the Arpsl empirical equations and a compupletions. Well permeabilities, skins and original terized statistical approach to arrive at answers oil in place are calculated for each well from rate-fairly quickly. For wells in high permeability time analysis using constant wellbore pressure type reservoirs producing essentially wide-open$ wfthout curve analysis techniques. future backpressure changes and without future stimulation treatments, the results obtained should Original oil in place values calculated from rate-be reasonably good providing the limits of thedetime analysis for individual wells are used with cline exponent b of between O and 1.0 are honored. recoverable reserve projections from the decline analysis to obtain fractional recoveries for each At the other extreme in analyzing rate-time data well. Gas-oil ratios versus fractional recovery for predicting future production and recoverable curves are also made for each well using historical reserves, a reservoir simulation study could be cumulative production and the calculated oil in undertaken. However, this approach could take as place values. Ultimate fractional recovery numbers much as a year to accomplish and normally would not and GOR vs fractional recovery curves, plotted for be considered acceptable, particularly for timeeach well, are shown to suggest different rock types constrained property acquisition or sales situations and reservoir fluids. Multi-well decllne curve where few of the detailed reservoir parameters analysis shows the validity of the varfables s necessary for a simulation study are available. (skin), k, OOIP, ultimate fractional recovery and GOR vs fractional recovery evaluated from each Many of the newer oil and gas fields being discovwell's type curve evaluation. These variables must ered and produced are in the low permeability classall give consistent and reasonable numbers when ification, where transient behavior can last for compared with each other. A single well analysis years, and therefore are not amenable to analysis can easily give results that are not recognized as using the Arps equation alone. Also, a model study being invalid unless compared with other wells in of such low permeability reservoirs would require a the field. very fine grid system to correctly simulate and match the early transient rate-time decline data. The study also illustrates flowing and pumping well backpressure changes in a well's decline, the method An approach to the problem of analyzing low petmeof handling such changes, and their effect on ulti-ability wells and total field rate-time decline has ...
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