An improved procedure for generating pseudorelative permeabilities for water flooding in stratified reservoirs

This paper presents an improved procedure for generating pseudorelative permeability curves for stratified water flooding using either constant pressures or constant flux at the reservoir/grid block boundaries. The concept of pseudorelative permeability reflects the generation of a relative permeability curve that can be used to represent the entire reservoir thickness, rather than a specific layer during reservoir simulation, thus saving computational time. In this paper, fractional flow theory is applied to the generation of pseudorelative permeability curves for (1) constant flow rate and (2) constant pressure boundary conditions. Previously, pseudorelative permeability curves were generated for constant flow rate only, since the analytical solutions for constant pressure boundaries were non-existant. In this paper, this restriction has been removed based on novel analytical solutions for constant pressure boundaries. The method within this paper also differs from previous methodologies and studies, which are all based on an approximation using piston-like displacement for water flooding. Instead, this new model uses fractional flow theory to its fullest extent to generate pseudorelative permeability curves that are physically more realistic. The solution is extended to generate pseudorelative permeability curves for waterflooding of a reservoir under the assumption of constant pressure boundaries which is an equally realistic assumption in comparison to constant flow rate. The generated pseudorelative permeability curves are used in a 2D areal reservoir model in a standard reservoir simulator to predict the behavior of the fully layered 3D reservoir model. It is found that there is considerably better agreement between the results obtained with this new method and the fully layered reservoir model compared to previous methods.