Renormalization calculations of immiscible flow

Oil reservoir properties can vary over a wide range of length scales. Reservoir simulation of the fluid flow uses numerical grid blocks have typical lengths of hundreds of metres. We need to specify meaningful values to put into reservoir engineering calculations given the large number of heterogeneities that they have to encompass. This process of rescaling data results in the calculation of effective or pseudo rock properties. That is a property for use on the large scale incorporating the many heterogeneities measured on smaller scales.For single phase flow, a variety of techniques have been tried in the past. These range from very simple statistical estimates to detailed numerical simulation. Unfortunately, the simple estimates tend to be inaccurate in real applications and the numerical simulation can be computationally expensive if not impossible for very fine grid representations of the reservoir. Likewise, pseudorelative permeabilities are time consuming to generate and often inaccurate.Real-space renormalization is an alternative technique which has been found to be computationally efficient and accurate when applied to single-phase flow. This approach solves the problem regionally rather than trying to solve the whole problem in one simulation. The effective properties of small regions are first calculated and then placed on a coarse grid. The grid is further coarsened and the process repeated until a single effective property has been calculated. This has enabled calculation of effective permeability of extremely large grids to be performed, up to 540 million grid blocks in one application.This paper extends the renormalization technique to two-phase fluid flow and shows that the method is at least 100 times faster than conventional pseudoization techniques. We compare the results with high resolution numerical simulation and conventional pseudoization methods for three different permeability models. We show that renormalization is as accurate as the conventional methods when used to predict oil recovery from heterogeneous systems.