Stochastic Relative Permeabilities Usually Have Neglectable Effect on Reservoir Performance

Abstract

During the last couple of years Norsk Hydro has developed a 3D model for simultaneous generation of stochastic absolute and relative permeabilities. By using core data containing relative permeability curves measured on a large number of core plugs from one single well in the North Sea, we have been able to model relative permeability curves (represented by endpoints and exponents) stochastically for four different depositional environments ranging from highly permeable mouthbar sands to low permeable tidal deposits.We show that for all the depositional environments, stochastic variation of the relative permeabilities have only marginal, if any, effect on the production characteristic, compared to keeping the relative permeabilities constant at their mean.Based on fractional flow theory, this paper summarizes the results from a theoretical and empirical statistical analysis of the correlation between the water shock front velocity and the absolute permeability for the different depositional environments, and we show that in specific cases this correlation can serve as an indication of the potential effects of stochastically varying relative permeability.curves.The main conclusion, which must be very' comforting to practicing engineers, is that in some situations stochastic modeling of the relative permeability curves is of minor importance, However, the choice of mean relative permeabilities may be crucial.

Quantitative Prediction Model for the Water–Oil Relative Permeability Curve and Its Application in Reservoir Numerical Simulation. Part 2: Application

“…On the basis of this research, Tjølsen et al summarized the correlation between the water shock front velocity and the absolute permeability for different depositional environments based on the fractional flow theory. Their further research showed that, when there was a positive correlation between the water shock front velocity and the absolute permeability, the breakthrough time became earlier, comparing the case of the varying relative permeability curve in each grid cell to the case of keeping the relative permeability curve constant in each grid cell. When there is a negative correlation, a later breakthrough time will be expected.…”

The Buckley--Leverett Equation with Spatially Stochastic Flux Function

“…There are also some papers on effective relative permeabilities; see [2]. Recently the authors of [16] have, by intensive use of reservoir simulation, shown that a spatially varying relative permeability can be replaced by the average relative permeability without changing the reservoir performance considerably. This paper will confirm the conclusion of [16] by a rigorous solution of the displacement in one dimension.…”