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

Abstract

Different functions describing matrix-fracture transfer were tested for countercurrent 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.

A Novel Multirate Dual-Porosity Model for Improved Simulation of Fractured and Multiporosity Reservoirs

“…The exchange of oil, gas, and water between the two domains is modeled by transfer func-tions (describing the physics of fluid exchange between fracture and matrix) and a shape factor (describing the geometry of the rock matrix). Much research has been dedicated to the appropriate use of transfer functions (Abushaikha and Gosselin 2008;Lu et al 2008;Al-Kobaisi et al 2009;Babadagli et al 2009;Balogun et al 2009;Ramirez et al 2009) and shape factors (Lim and Aziz 1995;Hassanzadeh and Pooladi-Darvish 2006;Rangel-German and Kovscek 2006;Gong et al 2008), whereas scaling groups have been developed to quantify the rate of oil recovery from matrix blocks and its dependence on rock and fluid properties (Ma et al 1997;Tavassoli et al 2005;Mason et al 2010;Schmid and Geiger 2012).…”

Free fall and controlled gravity drainage processes in fractured porous media: Laboratory and modelling investigation

“…[41][42][43][44] Other methods include recovery curves [45] and multiple interacting continuum (MINC). [23] The MINC method has been used to provide an accurate representation of matrix-fracture flow.…”

“…Several different methods have been proposed to model a fracture in fractured media, and the most common method is using shape factor and transfer functions in heterogeneous and fractured reservoir simulation. [41][42][43][44] Other methods include recovery curves [45] and multiple interacting continuum (MINC). [23] The MINC method has been used to provide an accurate representation of matrix-fracture flow.…”

An Analytic Solution for the Frontal Flow Period in 1D Counter-Current Spontaneous Imbibition into Fractured Porous Media Including Gravity and Wettability Effects

“…Although all the current expressions for predicting oil recovery from single matrix blocks (Aronofsky et al 1958;Kazemi et al 1992;Gupta and Civan 1994;Ma et al 1997;Viksund et al 1998;Civan 1998;Terez and Firoozabadi 1999;Babadagli et al 2009;Standnes 2010c) have one or more arbitrary parameters, the new expression is free of any arbitrary parameters. Furthermore, the presence of Lambert's W complex function in this new expression overcomes the issue of under and over estimation of oil recovery at early and late time, respectively, predicted by some of the current expressions available (Standnes 2010c).…”