This paper demonstrates that decline curve analysis not only has a solid fundamental base but also provides a tool with more diagnostic power than has been suspected previously. The type curve approach provides unique solutions on which engineers can agree or shows when a unique solution is not possible with a type curve only. Introduction Rate-time decline curve extrapolation is one of the oldest and most often used tools of the petroleum engineer. The various methods used always have been regarded as strictly empirical and generally not scientific. Results obtained for a well or lease are subject to a wide range of alternate interpretations, mostly as a function of the experience and objectives of the evaluator. Recent efforts in the area of decline curve analysis have been directed toward a purely computerieed statistical approach, its basic objective being to arrive at a unique "unbiased" interpretation. As pointed out in a comprehensive review of the literature by Ramsay,1 "In the period from 1964 to date (1968), several additional papers were published which contribute to the understanding of decline curves but add little new technology." A new direction for decline curve analysis was given by Slider2 with his development of an overlay method to analyze rate-time data. Because his method was rapid and easily applied, it was used extensively by Ramsay in his evaluation of some 200 wells to determine the distribution of the decline curve exponent b. Gentry's3 Fig. 1 displaying the Arps4 exponential, hypbolic, and harmonic solutions all on one curve also could be used as an overlay to match all of a well's decline data. However, he did not illustrate this in his example application of the curve. The overlay method of Slider is similar in principle to the log-log type curve matching procedure presently being employed to analyze constant-rate pressure buildup and drawdown data.5–9 The exponential decline, often used in decline curve analysis, readily can be shown to be a long-time solution of the constant-pressure.10–13 It followed then that a log-log type curve matching procedure could be developed to analyze decline curve data.

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.

The purpose of this paper is to give engineers responsible for making forecasts and determining reserves for numerous operated or nonoperated wells some guidelines and fundamental concepts to allow them to make these forecasts and determinations more quickly and accurately.

This paper presents the results and methods of analyzing isochronal and flow after flow multipoint back-pressure tests conducted on oil wells. Tests were conducted in reservoirs with permeabilities ranging from 6 MD to >1000 MD. Reservoirs in which oil well multipoint back-pressure tests were obtained ranged from highly undersaturated, to saturated at initial reservoir pressure, to a partially depleted field with a gas saturation existing above the critical. Each of these three reservoir fluid states can result in different interpretation methods. Back-pressure tests were run to pseudo-steady state in the field where the saturation was above the critical gas saturation. In all cases, oil well back-pressure tests curves were found to follow the same general form as that used to express the rate-pressure relationship of a gas well:Equation From some 40 oil well back-pressure tests examined, the exponent n was found to lie between 0.568 and 1.000, very near the limits commonly accepted for gas well back-pressure curves. Flow point alignment to establish an oil well back-pressure curve on the customary log qo vs. log Î"(p2) plot is considered to be as good as that obtained on gas well back-pressure tests. This paper demonstrates that gas wells and oil wells behave very similarly and should be tested and analyzed using the same basic flow equations. Introduction Multipoint back-pressure testing of gas wells is an accepted procedure for establishing a gas well's performance curve. Flow after flow1 and isochronal2 testing are the two basic methods commonly used. In high permeability reservoirs, either method can be employed. In low permeability reservoirs, the Isochronal method of testing eliminates the transient effects that can severely distort the results obtained from a flow after flow test. Methods for analyzing and calculating gas well performance curves have been the subject of numerous investigations. The bulk of these investigations have examined non-Darcy flow behavior, the primary reason that multipoint tests are conducted.

This approach to water influx calculations offers a useful and flexible method of forecasting and analyzing the performance of water drive reservoirs. The separation of the water influx problem into a rate equation and a material balance equation, not requiring superposition, makes the concepts and calculations quite simple and easy to apply. Introduction All gas and oil reservoirs are associated to varying extents with formation waters. The inclusion of the effects of expansion or invasion of this water into oil and gas reservoirs has taken many forms, from recognizing the effects of the expansion of the connote water within the gas or oil reservoir itself, to calculating water influx or efflux across a boundary (with the boundary usually being that of an oil or gas reservoir). There are four currently popular methods used for calculating water influx into reservoirs. They are:Schilthuis, steady stateHurst Simplified, unsteady stateResistance or Influence Function, unsteadystatevan Everdingen-Hurst Radial, unsteady state The first three methods have proved useful for predicting water drive performance after sufficient predicting water drive performance after sufficient historical data have been obtained to fix the necessary influx constants. With what some consider to be disappointing results, the van Everdingen-Hurst Radial method is often used with geological and core data when little or no performance history is available. It has also been used to predict reservoir performance after enough historical data have been accumulated to develop values of the influx constants, tD and C. In an attempt to include geometries other than radial, derivations for both limited and infinite systems have been made to cover linear spherical, elliptical, thick-sand, and wedge-shaped reservoir-aquifer models. The many rigorous geometrical representations that have been developed cannot readily handle the effect of interference between reservoirs. Electric analyzer studies of the Smackover Limestone aquifer in Arkansas by Bruce, of the Woodbine aquifer in East Texas by Rumble et al., and of the Ellenberger in West Texas by Moore and Truby have shown that reservoirs sharing a common aquifer can severely interfere with each other, and that, for individual reservoirs in a common aquifer, water drive performance calculations that do not consider interference performance calculations that do not consider interference can be greatly in error. Mortada developed a mathematical method with which to handle interference in a basically infinite radial aquifer system. The method has been applied to field cases. Coats concluded from his own study that, "In predicting the pressure-volume behavior of gas reservoirs situated on the common aquifer the effect of interference from other reservoirs on the common aquifer must be accounted for." Another aquifer problem more recently presented in the literature is that of flank water injection for pressure maintenance, either to initiate or to pressure maintenance, either to initiate or to supplement edge-water influx. A case history shows that we need to be able to study the effects of injecting water into the aquifer instead of merely including it in the hydrocarbon material balance equation. JPT P. 814