Pressure Analysis Of Heterogeneous Reservoir With Boundary Element Method

As a new numerical calculation method of the boundary type, boundary element method (BEM) manifests a lot of superiorities. Comparing to the domain type numerical schemes suche as finite difference method and finite element method, the flexibility in defining well situation, boundary geometry and boundary condition is the most notable feature when dealing with the problems of the reservoir engineering field. At present, most studies were still done on applying the BEM solving homogeneous reservoir. Only a little scholars put their eyes on heterogeneous reservoir, but the research on multiple wells reservoir with arbitrary shape, mixed boundary conditions and domain inhomogeneous regain needs to be improved .On this account, based upon the studies of our forerunners, according to the characteristics of the BEM, the whole reservoir is subdivided into several domains with different permeability in this paper. After the coefficient matrix equation groups of every sub-domain are obtained, all the unknowns on the boundary can be calculated by coupling all of the equation groups. Then, the reservoir pressure of every location and the flowing pressure of the well hole can be calculated. The main works done in this paper are as follows: First, the mathematical models of steady state flow and unsteady state flow in the reservoir with mixed boundary conditions, arbitrary shape and domain inhomogeneous regain were constructed. The fundamental solutions for the Poisson equations and modified Helmholtz equations were set up. And the applications of solving the two mathematical models with the domain discretization BEM are studied.Second, the steady state problem of fluid flowing in the reservoir with complex boundary and inhomogeneous regain was solved with the domain discretization BEM concretely. The method of calculating the pressure at any location in the reservoir and the flowing pressure of the well hole is set out.The correctness of the BEM is verified by comparing to the analytic solutions. The pressure contour maps and pressure profile maps of typical situations are drawn. By analyzing, it is found that the characteristics of boundary condition, heterogeneity and multiple well affecting the pressure field and the pressure behave of the well hole a lot, which provide rational reference for analyzing the pressure distribution and behave.At last, the unsteady state problem of fluid flowing in complex heterogeneous reservoir was solved with the domain discretization BEM detailed. The equations of calculating the flowing pressure and the pressure derivative of the well hole are worked out. By verifing against known analytic solutions, the accuracy of the BEM are verified. On the basis of drawing and studying the pressure behavior curves, the affects of the boundary condition, heterogeneity and multiple well to the pressure behavior curves are analyzed, which lay a foundation for the well test of complex heterogeneous reservoir.