An Improved Streamline-Generating Technique That Uses the Boundary (Integral) Element Method

Abstract

The boundary element method (BEM) has been used to generate streamlines for homogeneous and sectionally homogeneous reservoirs having irregular boundaries. This technique is superior to earlier methods that use "image wells" to simulate the reservoir boundary, especially for cases where the reservoir boundary is irregularly shaped. It has wider applicability to different kinds of reservoirs and eliminates the need for trial-and-error solutions. The errors caused by discretization and numerical approximation arise on and adjacent to the boundaries only, therefore the pressures and pressure gradients on which the streamlines are derived can be calculated with very high accuracy in the interior of the reservoir. Thus, the streamlines generated with this method are expected to be more realistic and representative of the actual physical system.

Semianalytical Stream-Function Solutions on Unstructured Grids for Flow in Heterogeneous Media

“…Several authors have applied the BEM to difficult problems in petroleum reservoir engineering [18][19][20][21][22][23][24][25] . Numbere and Tiab 21 addressed the problem of streamline construction in homogeneous and sectionally homogeneous media.…”

Numerical Simulation of Unsteady-State Flow in Dual Porous Coalbed Methane Horizontal Wells with Complex Boundary Conditions

“…Coupling with the BEM [22], bottom-hole pressures and complicated flow characteristics under the condition of irregularly shaped area with mixed boundary could be calculated and analyzed. Numbere and Tiab [23] developed a streamline simulation with the BEM for homogeneous or partly homogeneous reservoirs with irregular boundary to make the simulation match physical model better. Kikani and Horne [24] employed the BEM to analyze the transient pressure response in reservoirs with arbitrary boundary and developed two formulas, namely, convolution formula and Laplace domain space formula, to solve transient fluid flow through porous medium in homogeneous reservoirs.…”

Petroleum Reservoir Engineering by Non-linear Singular Integral Equations

“…At the end of eight's Lafe and Cheng (1987) proposed a BEM for the solution of steady flows in heterogeneous solids. During the same period Masukawa and Horne (1988) and Numbere and Tiab (1988) applied boundary elements for steady state problems of streamline tracking.…”