Scaling Up of Laboratory Relative Permeability Curves. An Advantageous Approach Based on Realistic Average Water Saturations

Abstract

Abstract Accordingly with Welge formulation, to obtain relative permeability curves at laboratory, all calculations are made on a selected point of the sample. Usually this point is located at the outlet face of the sample, where production rates are directly measured. As a result, relative permeability curves are reported as function of point saturations and not as function of average saturations. Laboratory curves are then adapted to reproduce reservoir behavior, usually through the derivation of pseudo functions. With usual methodologies, this pseudo curves are also expressed as function of point saturations and introduced in numerical simulators. In spite of this procedure, numerical simulators perform their calculations using the average water saturation at every grid block. Although point and average saturations are expected to be the same at infinitely small grid size, this is not the case with coarse areal simulation grids. In this paper, water-cut as a function of produced oil is analyzed for a linear case. Several cases are developed using relative permeability curves defined as function of point saturations for different grid sizes, and as a function of average water saturation. It is shown that only curves with average values give reliable data. As a result of this work, an advantageous methodology to transform laboratory measured curves into those consistent with numerical simulation approach is presented. It is also shown that the use of rock relative permeability curves, previously adapted to the particular geometry of the system under study, drastically reduces the number of grid blocks required and overcomes numerical dispersion. Introduction Relative permeability curves are of extreme importance during reservoir evaluations due to their ability of predicting fluid production during reservoir exploitation. They establish, for any particular phase, a functional dependence between phase saturation and the rock ability to produce it. These curves are determined in special core analysis laboratories through a sequence of measurements and calculations that can be summarized as follows:Measurement of global properties and parameters. These measurements includes geometrical parameters (length, area and poral volume of the sample), fluids properties (viscosities), displacement conditions (pressure difference or flow rate) and extreme point behavior.Displacement test. During the test, produced fluid volumes are recorded as a function of time. It should be mentioned that standard test conditions greatly diminish the influence of gravity and capillary forces. So, results of the test are assumed to be only function of viscous forces.Computation of relative permeability curves. The curves are calculated using some adaptations of frontal advance theory. As an example of steps 1 and 2 of the previous sequence, Jones y Roszelle1 experimental data set is shown in Tables 1 and 2, and in Fig. 1. This particular dataset was selected for the present study due to the fact that any interested reader can easily have access to the detailed sequence of measurements, but it should be pointed out that any laboratory set of data could have been used to fulfill this study's objectives. Computation of Relative Permeability Curves Before getting into the details of the usual computation of relative permeability curves during explicit calculation (JBN2 or JR1 methods), it is convenient to show that based on Tables 1 and 2 data, and through easy mathematics, it can be computed:The average water saturation of the sample. As long as the oil production is recorded at every time during the test, it is possibly to determine the average water saturation of the sample by performing a material balance.