A single-parameter fit correlation for estimation of oil recovery from fractured water-wet reservoirs

Spontaneous imbibition of water into the matrix blocks due to capillary forces is an important recovery mechanism for recovery of oil from fractured water-wet reservoirs. Such systems are usually modeled as a dual porosity system where the exchange rate of oil and water is described by so called transfer functions. A widely used correlation for predicting oil recovery from an individual matrix block is the Aronofsky model. In general this exponential decay rate function under predict early time recovery and overestimates late time oil recovery. Based on recent advances solving the Washburn equation, a new correlation for describing oil recovery vs. time for single matrix blocks is described. The correlation improves the fit to spontaneous imbibition data published in the literature. The correlation containing the Lambert's W function keeps the simplicity of the Aronofsky model as only one fit parameter is needed in order to predict oil recovery vs. time. Optimal fit to experimental data is obtained with a fit parameter value of 0.05 for the Aronofsky correlation whereas the value of 0.135 should be used in the improved correlation case.