Interpretation of Two-Phase Oil-Water Injectivity and Falloff Testing in a Vertical Injection Well Using Laplace-Transform Finite-Difference Method
Injection and falloff tests have a number of advantages over the production well testing methods in terms of efficiency and HSE concerns. However, the injectivity well test interpretation is complicated due to various reasons. Injection of water into a reservoir changes the system from a single-phase flow to a two-phase oil-water flow governed by relative permeabilities. Also, the inclusion of parameters such as skin, wellbore storage, boundary conditions and saturation gradient behind the front complicates the interpretation further. In this work, we have focused on injection well testing of a vertical well in a single layer homogeneous oil reservoir. We have compared the solutions from numerical and Laplace-Transform Finite-Difference (LTFD) models for injection and falloff periods under different conditions. LTFD method is a semi-analytical method that could not only simplify the two-phase water injection problem making it easier to solve unlike the analytical methods, but also eliminate the issue of time discretization, thereby resolving the instability, convergence issues and problematic time iterations encountered in numerical methods. The LTFD method showed great agreement with the numerical simulation results for different scenarios. The validated results were used to analyse the pressure behaviour associated with injection and falloff periods. Furthermore, the influence of parameters such as wellbore storage, skin and outer boundary conditions in the interpretation of pressure behaviour during the injection and falloff periods were examined in detail. It was observed that during the injection period, the effect of wellbore storage on the pressure derivative curve was only during the early times. However, the impact of skin was consequential that it could considerably delay the desired reservoir response from the zero-skin zone requiring longer injection periods. During the falloff period, the effect of skin and wellbore storage on the pressure derivative curve was insignificant except for early times. Also, substantial effects of skin and wellbore storage were encountered for unfavourable endpoint mobility ratios.