Evaluation of Matrix-Fracture Transfer Functions for Counter-Current Capillary Imbibition

Abstract

Different functions describing matrix-fracture transfer were tested for counter-current capillary imbibition interaction. The recovery curves obtained from capillary imbibition experiments were used to fit the transfer functions. The exponential coefficients yielding the best fit to the experimental data were obtained and correlated to the effective parameters such as viscosity, IFT, matrix length and diameter, matrix permeability and porosity, and wettability using multivariable regression analysis. In order to obtain the recovery curves, experiments were conducted on Berea sandstone and Indiana limestone samples. Cylindrical samples with different shape factors were obtained by cutting the plugs 1, 2.5, and 5 cm in diameter and 2.5, 5, and 10 cm in length. All sides were coated with epoxy except one end. More than fifty static imbibition experiments were carried out on vertically and horizontally situated samples where the imbibition took place upward and lateral directions, respectively. Brine–air, brine–kerosene, brine–mineral oil, and surfactant solution–mineral oil pairs were used as fluids. For many matrix shape factors (especially longer and small diameter ones), dividing the recovery curve into three parts were needed as the early, intermediate, and late times, which are typically distinguished by the time required for the imbibition front to reach the closed boundary at the end of the core. Correlations among the exponential coefficients and rock/fluid properties were developed. It was observed that different rock/fluid properties and transfer mechanisms (capillary imbibition and gravity drainage) govern the process for each part. Hence, the analyses done in this study were useful not only for developing explicit transfer functions but also identifying the physics of the counter-current imbibition recovery.