Publications

Including the effects of reservoir heterogeneity on the prediction of fluid flow processes in underground reservoirs is a central problem in reservoir engineering. Whilst advances in reservoir characterization and geostatistics have increased the understanding of the nature of the spatial distribution of these heterogeneities, these methods have generally been responsible for the use of finer scale models for the multi-phase flow conditions where the concept of relative permeability dominates fluid movement. The use of finer scale models can lead to excessive demands for the computer storage and execution run-time which can quickly become prohibitive as the number of grid blocks and simulation dimensions increase.In order to alleviate this problem the concept of upscaling, in the form of pseudofunctions, such as pseudo relative permeabilities, are often employed. These functions are based on finer grid models yet are applied to much coarser scale models which often have reduced dimensions. Correctly specified, a coarse pseudofunction model should predict the same overall recoveries and fluid production histories as the finer one it is attempting to represent. Whilst the use of pseudofunctions is widespread, detailed comparison, using analytical as.well as simulation models, shows that many of the previously published pseudofunction techniques suffer from poor performance when used in up-scaled models. Significant errors in the predicted production profiles or the in-situ fluid distributions are frequently observed particularly at non-unit mobility displacement conditions and in flows exhibiting large permeability layering effects.This paper reviews the underlying reasons responsible for poor pseudofunction performance in the previously published methods and finds that the main reason is that previous methods failed to recognize the inherent non-linear, or curved characteristic, behavior of saturation velocities. Methods employing the VIIelge construction, or the Buckley-Leverett assumption of constant saturation velocities fail to incorporate these non-linear effects.By considering the use of several simulation models such as: a) a viscous dominated layered models, and b) complex simulation models displaying different viscous/gravity/capillarity effects, methods are developed which take into account the conccpt of length-dependency of saturation velocities in prescribing up-scaled representations. Such methods are based on the underlying characteristic curves in x-t space to analyze the displacement process prior to segmenting the flow path into idealized zones, where the assumption of local linearity of the characteristics is made.It is found that the proposed pseudofunction rnethod is able to accurately reproduce the dynamics of a finer scale model in each case. With further work, such methods can be directly incorporated into the current simulation practice.