Perturbation Solution for One-Dimensional Flow to a Constant-Pressure Boundary in a Stress-Sensitive Reservoir

Abstract

Most analyses of fluid flow in porous media are conducted under the assumption that the permeability is constant. In some “stress-sensitive” rock formations, however, the variation of permeability with pore fluid pressure is sufficiently large that it needs to be accounted for in the analysis. Accounting for the variation of permeability with pore pressure renders the pressure diffusion equation nonlinear and not amenable to exact analytical solutions. In this paper, the regular perturbation approach is used to develop an approximate solution to the problem of flow to a linear constant-pressure boundary, in a formation whose permeability varies exponentially with pore pressure. The perturbation parameter αD is defined to be the natural logarithm of the ratio of the initial permeability to the permeability at the outflow boundary. The zeroth-order and first-order perturbation solutions are computed, from which the flux at the outflow boundary is found. An effective permeability is then determined such that, when inserted into the analytical solution for the mathematically linear problem, it yields a flux that is exact to at least first order in αD. When compared to numerical solutions of the problem, the result has 5% accuracy out to values of αD of about 2—a much larger range of accuracy than is usually achieved in similar problems. Finally, an explanation is given of why the change of variables proposed by Kikani and Pedrosa, which leads to highly accurate zeroth-order perturbation solutions in radial flow problems, does not yield an accurate result for one-dimensional flow. Article Highlights Approximate solution for flow to a constant-pressure boundary in a porous medium whose permeability varies exponentially with pressure. The predicted flowrate is accurate to within 5% for a wide range of permeability variations. If permeability at boundary is 30% less than initial permeability, flowrate will be 10% less than predicted by constant-permeability model.

Effect of Effective Pressure on the Permeability of Rocks Based on Well Testing Results

“…The mathematical model presented in [27] and based on pressure build-up curves makes it possible to predict the change in the permeability during the hydrocarbon production. The authors in [28][29][30][31][32][33] also study the nature of changes in fluid filtration in a reservoir as a result of changes in effective pressure and permeability and its relationship with the results of pressure build-ups. In these works, the same approach was used, although the method used is universal but it does not take into account the reservoir properties, the values of the coefficients in the equations are individual for each rock and, possibly, depend on its properties, therefore, additional research is needed in order for this method to be used for predicting permeability of formations with different properties.…”

The Pressure Buildup Well Test Analysis considering Stress Sensitivity Effect for Deepwater Composite Gas Reservoir with High Temperature and Pressure

“…At present, many researchers have studied the influence of stress sensitivity effect on well test curves. However, the influence on the pressure drawdown well test is mainly discussed in these studies [19][20][21][22][23][24][25][26][27][28][29][30]. For practices in oilfields, the quality of pressure data from the drawdown stage of well test is poor due to the influence of production fluctuation.…”