Accurate Fluid Interface Tracking of Interwell Tracer Flow by the Constrained Interpolation Profile Method

Abstract

Abstract An accurate numerical technique to follow tracer movement between sink and source is an invaluable tool in evaluating reservoir formation from interwell tracer test data. Tracer flow in porous media is modeled by the convective-dispersive equation. In case of convection-dominance over dispersion, the interface between tracer slug and tracer-free fluid becomes sharp and most finite difference techniques tend to cause numerical diffusion or non-physical oscillation. To overcome this difficulty, the constrained interpolation profile (CIP) method, a universal solver of hyperbolic equations, is employed for solving tracer flow problems in this study. In the CIP method, not only the tracer concentration but also its spatial gradients are simultaneously evaluated at each gridblock, so that more continuity conditions can be imposed to construct an interpolation function between neighboring gridblocks and the sharp interface can be tracked more accurately. The computation procedure is followed by a semi-Lagrangian scheme; the governing equations of both tracer concentration and its spatial gradients are decomposed into convective and non-convective phases. The convective phase is calculated by the CIP method, while the non-convective phase by the finite difference approximation. For one-dimensional test problems, the numerical results using the CIP method are almost in complete agreement with the analytical solutions, which verifies the accuracy of the developed method. Also the verification of the developed method for two-dimensional computation is provided by comparing the numerical results with semi-analytical solutions obtained using the complex variable boundary element method. Furthermore, from the numerical results of various two-dimensional example problems, such as staggered/direct line drive pattern floodings and flows in heterogeneous permeability fields, the developed method is found to be of use for practical purposes.