During the last few years, a two-stage stochastic model for 3-D modelling of reservoir architecure and absolute permeability1 has been developed and utilized in field development studies. The scope of this paper is to present a new, important extension of this model: The possibility of generating relative permeability curves with stochastic spatial variation. Absolute permeability can be measured on cores as well as in analogue outcrops, using a field minipermeameter. Relative permeabilities, however, are in general time consuming and expensive to measure. For this reason, they are usually measured on a very limited number of core samples. Relationships or interdependendencies among petrophysical variables are required as input to the stochastic model. Based on a unique set of core data containing relative permeability curves measured on 85 core plugs from one single well in the North Sea, correlations between relative permeability curves (represented by endpoints and Corey-exponents), absolute permeability and depositional environment have been developed2 . Utilizing these correlations, the paper demonstrates a co-kriging procedure for simultaneously generating absolute and relative permeability fields.
An example based on data from a North Sea reservoir is given to illustrate the model and its application. To evaluate the effect of different relative permeability curves in each grid cell, flow simulations were performed. The same grid was used for the flow simulations as for the stochastic realizations, to avoid the problem of homogenization of the relative permeability curves. The results indicate that in the cases studied, the introduction of stochastic variation in the relative permeability curves has no significant effect on the shape of the production profile, when compared to the case with a constant relative permeability curve.