Effect of heterogeneity on fluid flow. Stochastic modeling of absolute and relative permeabilities in oil reservoirs

摘要

This thesis contains 6 papers. The first paper presents a two-stage stochastic model that caters for the geological heterogeneities resulting from different rock types and the inherent spatial variability of rock properties. An example from a highly heterogeneous North Sea reservoir, deposited in an upper shore-face environment, illustrates the application of the model. This model is extended in paper 2, to model both static and dynamic saturation dependent properties (relative permeabilities) simultaneously. Hence, the main objective is to derive relationships between the petrophysical properties. The paper 3 addresses the simultaneous stochastic modeling of spatial variations of both absolute and relative permeability, with special emphasis on the impact on oil recovery from spatially varying relative permeability curves. The main conclusion is 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 profiles. In paper 4 the model described in paper 3 was applied to four different depostional environments, with large variation in the petrophysical properties and the interrelationships between the variables. The purpose of paper 5 is to describe a technique to scale up absolute permeability from a fine to a coarser grid, and to study how well this technique actually performs. The last paper describes a technique for stochastic simulation of permeability on a geological description grid, which will honour the observed core-plug measurements. Two or more steps are necessary. The technique handles the transition from core-plug to reservoir description scale correctly and consistently, provided some model assumptions are fulfilled. 168 refs., 54 figs., 17 tabs.