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Keywords: constant rate

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Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Permian Basin Oil and Gas Recovery Conference, March 8–9, 1990

Paper Number: SPE-20111-MS

... method is discussed by Cullender. Previous simulation work by Sullivan and Poston has shown isochronal, transient pressure tests Poston has shown isochronal, transient pressure tests under

**constant****rate**conditions may be used to determine gas reserves with a good degree of accuracy. The method permits...
Abstract

SPE Members Summary Static reservoir pressures are required for all gas material balance calculations. There are no techniques currently available for using isochronal, transient pressure buildup tests to estimate original gas in place. A method to extrapolate the slope of a line generated from two or more isochronal or short-term pressure buildup tests to initial conditions to estimate gas pressure buildup tests to initial conditions to estimate gas reserves has been developed. Simulation as well as theoretical studies prove the technique may be applied to gas reservoirs with a permeability of one md or greater. However, the extrapolations become skewed for gas reservoirs displaying a permeability of less than one md. The isochronal test method may not be used with a high degree of accuracy for these low permeability reservoirs. The divergence of the extrapolations was found to be caused by the c product term evaluated at a subsequent pressure differing significantly from the c product term pressure differing significantly from the c product term evaluated at static conditions. This pressure drawdown effect was found to only be significant in reservoirs displaying a permeability of less than 1 md. Analysis of the fundamental concepts has formulated a relationship between the diffusivity equation and the material balance equation to account for changing fluid properties during pressure buildup. A method has been developed from these relationships to adjust the real time isochronal interval for the changing gas fluid properties. The adjustment technique permits the transient pressure, isochronal method to be applied to very low permeability reservoirs as long as the pressure is 1,000 psia or greater. Introduction Material balance or reservoir simulation models are used to estimate reserves and predict future producing characteristics for gas reservoirs. The pressure-fluid properties-production history relationships established in properties-production history relationships established in the material balance equations are assumed to be a function of average reservoir pressure. These pressures must be measured at static or stabilized conditions. Attaining static conditions in very low permeability or extremely heterogeneous reservoirs is often a practical impossibility because shut-in times may extend for several months. Shut-in times for moderate to high permeability reservoirs are of a much lesser interval. In any case. revenue is lost when a gas well is closed in for measurement of a static bottomhole pressure. The potential loss of income resulting from shutting a well in potential loss of income resulting from shutting a well in often inhibits operators from obtaining static bottomhole pressures. pressures. Short term, pressure testing to determine the gas well deliverability is a current industry standard for reducing total test time to estimate well potential. Different shut-in times reflect different reservoir radii of investigation. The isochronal test method is discussed by Cullender. Previous simulation work by Sullivan and Poston has shown isochronal, transient pressure tests Poston has shown isochronal, transient pressure tests under constant rate conditions may be used to determine gas reserves with a good degree of accuracy. The method permits extending the constant line slopes generated from permits extending the constant line slopes generated from short-term buildup pressures measured over at least two different periods to the initial p /z value on the vertical axis of a p/z vs. Gp plot. The line then is extended to the intersection of the x axis where original gas in place is determined. An estimate of cumulative gas produced at any subsequent pressure may then be made from the plot. Fig. 1 shows the mechanics of the old and new p/z vs.G plot concepts. plot concepts. Additional theoretical and simulation work has shown the isochronal, transient pressure analysis method requires the well or reservoir to be in a constant producing or a constant bottomhole flowing pressure condition. A different type of plot must be generated for either producing situation. The p /z plot for the constant pressure producing situation. The p /z plot for the constant pressure case intersects the static pressure p/z plot at the point where p /z equals the static p/z value. Fig. 2 shows the mechanics of the constant pressure process. The present paper extends our knowledge of the isochronal, transient paper extends our knowledge of the isochronal, transient pressure concept and presents an analysis of the pressure concept and presents an analysis of the fundamentals underlying the reserves estimation method.

Proceedings Papers

Publisher: Society of Petroleum Engineers (SPE)

Paper presented at the Permian Basin Oil and Gas Recovery Conference, March 13–15, 1986

Paper Number: SPE-15028-MS

... reservoir shape factor spe 15028 circular reservoir shape factor reservoir drillstem testing drillstem/well testing

**constant****rate**rate change upstream oil & gas earlougher infinite series average reservoir pressure drainage area compressibility new method equation society...
Abstract

SPE Members Abstract This paper presents a new method of estimating drainage area size and shape from production data (bottom-hole pressures and flowrates). The method is a rigorously derived approximation for variable-rate flow in a closed reservoir. This method requires a graph of Ap/qm vs. the superposition plotting function (which is easily calculated by plotting function (which is easily calculated by hand). The slope and intercept of the graph are used to provide the desired estimates of drainage area size and shape. The method that we propose is an approximation, however it has been proved to be very accurate for the constant rate, constant pressure, exponential rate, logarithmic rate, hyperbolic rate, sinusoidal rate, and discrete rate cases. The method also gives acceptable results for square wave rate and random rate cases. The new method is derived for the time after the initial pressure transient has reached the outer boundary. The changes in flowrate cause additional transients, but we assume that this effect is negligible when compared to the influence of the outer boundary. Therefore, if the change in flowrate does not dominate the influence of the outer boundary, the new method should give acceptable results. Also, at present, this method is only derived for single-phase flow of a liquid of small and constant compressibility. Introduction The purpose of this paper is to present a simple, but accurate method of predicting reservoir drainage area size and shape from variable-rate production data. Previous works have dealt with production data. Previous works have dealt with constant or cyclically constant rate and constant bottom-hole pressure production. A summary of these methods is shown graphically in Figure 1. Earlougher defined the cyclically constant or square wave rate case in Figure 2. Rather than focus on a particular rate scheme, we develop a general variable-rate approximation that should give accurate results for typical production situations. Without a variable-rate solution we would have use the more tedious material balance methods that require average reservoir pressures to estimate reservoir pore volume. This would require the well to be shut-in, which results in lost revenue. However, with the new method, the reservoir pore volume and shape can be estimated directly from the production data, without shutting-in the well. production data, without shutting-in the well. The problem of variable-rate flow in bounded systems isolimited in the literature t work by Earlougher-' and the "stabilized flowing,- U methods (which use average reservoir pressures). Though both approaches give acceptable results for their specific application, Earlougher's case is not realistic and the "stabilized flow" methods again require the well to be shut-in for average reservoir pressure determinations. This suggests the need for a general solution for variable-rate flow in a bounded reservoir. In the "Description of the New Method" section we will present the general variable-rate solution and the reservoir characteristics which can be derived from it. Also, we will verify the general variable-rate equation (Eq.(2)) using analytical and finite-difference simulation. Then a step-by-step procedure for applying our method and a complete example will be shown in the "Method of Application" section. Finally, we will present the derivation of the exact solution for variable-rate flow in a bounded circular reservoir and the approximate solution for variable-rate flow in any shape reservoir in the Appendix of this report. P. 361