Pore network modelling of molecular diffusion in a single‐block model during lean gas injection, investigating the effect of throat sorting

Abstract

Based on analogy between isothermal drying of porous media and molecular diffusion in a single-block model containing a volatile liquid during lean gas injection, a detailed procedure is presented for two-dimensional quasi-static pore network modelling of diffusion. A modified invasion percolation algorithm is used to account for evaporation of liquid clusters formed during gas injection process. Diffusion in gas phase, capillaryinduced flow in liquid phase, and evaporation in gas-liquid interface were modelled to trace the movement of gas-liquid interface and desaturation profile. Using a set of throat sizes with normal distribution, 15 cases of a regular pore network model were proposed by rearranging throat positions in the model. Results of this study indicate that diffusion time, breakthrough time, vapour partial pressure gradient, liquid saturation gradient, liquid cluster frequency, gas-liquid interface frequency, and evaporation potential are strong functions of throat sorting. Correlation coefficient of throat size with position was used to capture the disorder of porous medium. It was shown that such a correlation coefficient is not capable of describing diffusion characteristics.

Pore network modelling of molecular diffusion in a single‐block model during lean gas injection, a comparative study on calculation approaches

“…Diffusion can potentially have mutual impact on such phenomena. The current work presents an alternative algorithm for pore network modelling of diffusion which confirms and improves findings of our previous work and reflects the reliability of the two approaches.…”

“…Throughout this article, we repeatedly refer to the algorithm presented in our previous work as the “cluster‐based approach” or CBA (an algorithm first introduced by Prat) and to an algorithm which will be presented in this work as the “pressure‐based approach” or PBA.…”

“…In a recent article, we took benefit of analogy between the drying and diffusion mechanisms in fractured reservoirs to develop a similar pore network model and investigated the effect of throat sorting on the characteristics of diffusion . That work was based on an algorithm for identification of the throat to be invaded in a time step.…”

“…The algorithm presented in our previous work for modelling the diffusion in a single block model is a first step towards understanding micro‐mechanisms occurring during non‐equilibrium gas injection in fractured reservoirs. It might be considered as a basis for implementation of more realistic assumptions and modelling of related phenomena in fractured reservoirs such as block to block and matrix‐fracture interactions, in future studies.…”

“…A proper set of equations as well as all boundary condition types are formulated here. In the “Comparison between PBA and CBA” section, we qualitatively compare our proposed algorithm in this work with the algorithm presented in our recent work and the benefits and limitations of each are discussed. The “Results” section deals with the comparison of results obtained from the two algorithms for a similar base case.…”