Pore-network modeling to calculate transport properties from small-scale data

Abstract

Paper description: Modeling of two or three-phase flow in porous media is of prime importance in estimating the contamination of soils by liquid organic pollutants and in designing remediation solutions. For an accurate prediction of the transport properties of a porous medium, small-scale data on the pore space geometry and topology are needed. Although the small-scale structure is closely related to the capillary properties of the porous medium, it has been shown (Laroche and Vizika, 2005) that the information derived from a mercury invasion Pc curve is not sufficient to characterize transport properties. The objective of the present work is to evaluate the prediction accuracy of network modeling to calculate transport properties of porous media. The construction of the numerical porous media is based on the interpretation of mercury invasion capillary pressure curve and a relationship between laboratory measurements of formation factor and permeability. A pore-network modeling approach is used to model the multi-phase flow and to calculate the gas/oil relative permeabilities in presence of irreducible water for homogeneous (Fontainebleau) sandstone. The characteristics of the pore-network are defined with the requirement that it satisfactorily reproduces the capillary pressure curve, the porosity, the formation factor and the permeability determined experimentally. Results-Observations: A formula relating permeability and formation factor to the mean throats radius and its standard deviation has been developed. The calculations are based on simple representation of the pore-throats by a bundle of capillary tubes with a size distribution characterized by the man pore radius and its standard deviation. A sensitivity study on the effect of the input parameters on the prediction of capillary pressure and gas/liquid relative permeability curves is presented. The simulations show that different input parameters can lead to similarly good reproductions of the experimental capillary pressure, although the predicted relative permeabilities are somewhat widespread. This means that the information derived from a mercury invasion capillary pressure curve is not sufficient to characterize transport properties even in a homogeneous porous medium. Information on the formation factor ensures a correct interpretation of the capillary pressure curve and leads to more realistic predictions of the relative permeabilities.