Laplace-Transform Finite-Difference and Quasistationary Solution Method for Water-Injection/Falloff Tests

In this work, we present a method for efficiently and accurately simulating the pressure-transient behavior of oil/water flow associated with water-injection/falloff tests. The method uses the Laplace-transform finite-difference (LTFD) method coupled with the well-known Buckley-Leverett frontal-advance formula to solve the radial diffusivity equation describing slightly compressible oil/water two-phase flow. The method is semianalytical in time, and as a result, the issue of time discretization in the finite-difference approximation method is eliminated. Thus, stability and convergence problems caused by time discretization are avoided. Two approaches are presented and compared in terms of accuracy for simulating the tests with multiple-rate injection and falloff periods: One is based on solving the initial-boundary-value (IVB) problem with the initial condition attained from the end of the previous flow period, and the other is based on the conventional superposition on the basis of the single-phase flow of a slightly compressible fluid. The former is shown to always provide a more accurate and efficient solution. The method is quite general in that it allows one to incorporate the effect of wellbore storage and thick-skin and finite outer-boundary conditions. The accuracy of the method was evaluated by considering various synthetic test cases with favorable and unfavorable mobility ratios and by comparing the pressure and pressure-derivative signatures with a commercial black-oil simulator, and an excellent agreement was seen.