During the last few years, a two-stage stochastic model for 3-D modelling of reservoir architecure and absolute permeabilityl 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 developed 2 • 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 resultsReferences and figures at end of paper 345 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.

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.