Determination of the throat size distribution of a porous medium as an inverse optimization problem combining pore network modeling and genetic and hill climbing algorithms

Abstract

The pore size distribution of a porous medium is often estimated from the retention curve or the invading fluid flow rate curve using simple relationships more or less explicitly based on the consideration that the porous medium is made of a bundle of cylindrical parallel tubes. This type of determination is tested using pore network simulations. Starting from two-or three-dimensional networks, the characteristics of which are known apriori, the estimation of the throat size distribution (TSD) is performed using the standard methods in the case of drainage. Results show a significant discrepancy with the input data. The disagreement is more pronounced when the fluid flow rate curve is employed together with the parallel tubes assumption. The physical origins of these shortcomings are identified. A method, based on pore network simulations combined with a genetic algorithm and the hill climbing algorithm, is then designed, which makes simultaneous use of the nonwetting fluid flow rate curve and the retention curve of the medium. Very significant improvement is achieved in the estimation of the TSD using this procedure.

Identification of local contact angle distribution inside a porous medium from an inverse optimization procedure

“…As considered in Ref. [29] in the case of the throat size distribution (TSD) determination problem, it is possible to perform the optimization procedure considering only one datum, either the capillary-pressure curve or the relative permeability curve. For the TSD problem, it was found that considering both data led to the best results and that the consideration of the capillary-pressure curve alone led to better results than the relative permeability curve alone.…”

“…The capillary-pressure curve P c (S), where S is the saturation of the displaced fluid, is computed using an algorithm similar to the one presented in Refs. [29,39], but takes into account here the presence of hydrophilic elements. This algorithm mimics the commonly used experimental procedure [25].…”

“…As in Ref. [29], only the relative permeability for the invading (liquid) phase is computed and the reader is referred to this article for the reasons motivating this choice. An equilibrium liquid gas distribution in the network is obtained for each value of the capillary pressure, P c , under consideration.…”

“…The invading phase relative permeability is determined from the computation of the invading fluid viscous flow through the network for each equilibrium phase distribution, that is for each point of the capillary-pressure curve. The computation of the displacing fluid flow rate, Q i , is performed as follows [29,39]. At each saturation equilibrium, i, a pressure difference, P, much smaller than the capillary pressure characterizing this equilibrium, is applied in the displacing fluid between the network inlet and outlet.…”

“…This characterization is addressed as an inverse optimization problem, which includes two-phase flow simulations within the microstructure and an optimization procedure combining a genetic algorithm [26,27] and the hill-climbing algorithm [26,28]. This type of approach has shown promising results for the identification of the pore size distribution from macroscopic flow data such as the capillary-pressure curve and/or normalized flow curves [29]. Contrary to this previously reported work where the objective was to identify the pore size distribution assuming a spatially uniform wettability throughout the pore space, the objective here is to identify the internal contact angle spatial distribution, knowing the microstructure geometry and thus the pore size distribution.…”