Abstract
A three-dimensional analytical model is presented for predicting the performance of pressure and flow rate in anisotropic gas reservoirs. The model considers interference effects and restricted flow entry and uses the point-source solution to the equation that describes unsteady-state real-gas flow through porous media.
Introduction
The assumption of two-dimensional flow through isotropic porous media is frequently found in reservoir studies. Observed pressure behavior often can be matched using a two-dimensional flow model. However, there are some reservoirs for which matching would not be achieved, when reasonable values of the matching parameter are used, if three-dimensional and nonisotropic effects are not accounted for.
THEORY
It has been found that results obtained for linear or radial gas flow, regarding the gcg product fixed at its initial value, are good approximations to certain solutions that consider the pressure dependence of this product. To extend this treatment to problems of flow in three dimensions, the following development is presented.
The pseudopressure drop occurring at any point in a finite, uniform, anisotropic reservoir resulting from a constant real-gas flow rate at a point source is approximated by
24,865 q sc p sc T res m (x, y, z, t) = ------------------------ F......(1) Tsc kh
This equation is derived in Appendix A.
The fundamental assumption made in the derivation of Eq. 1 is that the viscosity-compressibility product is a constant. Generally, this is not true. However, for some reservoir problems where small changes in pressure are involved, such as those taking place in pressure are involved, such as those taking place in pulse testing and interference tests, this assumption pulse testing and interference tests, this assumption is reasonable.
The corresponding pressure drop is given by the following equation, which is derived in Appendix B:
iZi m p = ...................................(2) 2pi
EXAMPLE
Interference data from a hypothetical test are analyzed by a procedure similar to that proposed for two-dimensional flow in oil reservoirs. From these data, a representative value of the porosity in the region between the production well and the observation point is obtained. Three possible observation-point locations are considered to emphasize the influence of three-dimensional and nonisotropic effects. These locations are characterized by their vertical separation with respect to the midpoint of the well-completion interval. The information needed is given in Fig. 1 and Table 1;
y (ft) 9840 ---------------------------------------------
4920 ---- - ------ - ------ - -----* PRODUCING WELL 4592 ---- - ------ - ------ - --* OBSERVATION POINTS
0 ---------------------------------------------------->X (ft) 0 7544 8200 16400
Z(ft)
-------------------------------------------------- CASE 3 574 ---------------------------*
CASE 2 328 ---------------------------*
CASE 1 82 ---------------------------* * MIDDLE POINT OF THE COMPLETION INTERVAL 0 --------------------------------------------------
FIG. 1 LOCATION OF THE PRODUCING WELL AND THE OBSERVATION POINTS; INTERFERENCE-TEST EXAMPLE.
SPEJ
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