Sensitivity Analysis of Two-Phase Reservoir History Matching

Reducing the number of unknown reservoir properties (through a method like zonation) is generally recognized to be necessary to obtain accurate estimates from history matching; however, no reliable guidelines exist on how this can best be accomplished. Toward this end, the authors use a one-dimensional, incompressible, two-phase reservoir model to examine some of the fundamental issues in the estimation of spatially variable permeability and porosity from pressure data. Analytical expressions are developed that relate spatial variations in property values to perturbations in the measured pressure drop. Permeability and porosity are retained as functions so that the developed expressions are functional derivative sensitivity coefficients. Examination of these functions reveals the importance of the saturation distribution in regard to information about reservoir properties represented by pressure data. They determine that the rock properties ahead of the flood front cannot be determined from pressure data. Consequently, having more than a single zone for regions that have not undergone two-phase flow would be unwarranted on the basis of pressure data. Behind the flood front, the sensitivity of the pressure drop to variations in permeability and porosity, for M {le} 1, declines with time. Consequently, the reliability of forecasts may actually improve with time. Based more » on measures relating the relative variability of porosity and permeability functions, the contribution of permeability variations to pressure perturbations exceeds that of the porosity by more than a factor of five when M {le} 1. Thus, the representation of porosity with fewer zones than permeability is appropriate. « less