A solution for the transition zone isosats in two-phase primary drainage in the presence of gravity

Borehole resistivity simulations of oil-water transition zones with a 1.5D numerical solver

“…Determining the water saturation profile in the transition zone in a porous media to predict the recoverable oil saturated in the rock is a demanding task in petrophysics (see, e.g., [27][28][29]). However, sometimes, a saturation profile may be available from previously recorded data.…”

“…Moreover, we assume a homogeneous rock porosity equal to 20% and 25% for our first and second models, respectively. Using (29) and the resistivity values of Table 1, we obtain a set of resistivity values which are extended to the entire transition zone by using a cubic spline interpolation composed of three subintervals (see Figure 3). In this work, we approximate our formation as a sequence of three 1D models, which are described in Figures 4 and 5.…”

“…Despite the high efficiency of semi-analytic methods, they may sometimes lead to an unrealistic mapping of the reservoir since they have to consider piecewise constant resistivity profiles, and as a result, they often employ a sharp oil-water contact (OWC). However, in many realistic reservoir models, the OWC often appears as an oil-water saturated transition (OWT) zone with a variable resistivity profile (see Figure 2) [27][28][29][30]. To model this with a 1.5D semi-analytical code, it is necessary to approximate the real model in the OWT zone using multiple constant-resistivity layers, which increases the computational cost, implementation, modeling error, and complexity of computing derivatives needed by gradient-based inversion methods.…”