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 incorpo rating the many heterogeneities measured on smaller scales. For single phase flow, a variety of techniques have been tried in the past. Thes e range from very simple statistical estimates to detailed numerical s imulation. Unfortunately, the simple estimates tend to be inaccurate i n real applications and the numerical simulation can be computationall y expensive if not impossible for very fine grid representations of th e reservoir. Likewise, pseudorelative permeabilities are time consumin g to generate and often inaccurate. Real-space renormalization is an a lternative technique which has been found to be computationally effici ent and accurate when applied to single-phase flow. This approach solv es the problem regionally rather than trying to solve the whole proble m in one simulation. The effective properties of small regions are fir st calculated and then placed on a coarse grid. The grid is further co arsened and the process repeated until a single effective property has been calculated. This has enabled calculation of effective permeabili ty of extremely large grids to be performed, up to 540 million grid bl ocks in one application. This paper extends the renormalization techni que to two-phase fluid flow and shows that the method is at least 100 times faster than conventional pseudoization techniques. We compare th e results with high resolution numerical simulation and conventional p seudoization methods for three different permeability models. We show that renormalization is as accurate as the conventional methods when u sed to predict oil recovery from heterogeneous systems.