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.
