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

Abstract

In this paper, we have proposed a new algorithm for pore network modelling of molecular diffusion in a single matrix block model. The block contains a volatile component adjacent to a gaseous lean component to mimic high capillarity-induced flow rates caused by either high liquid to gas mass transfer rates and/or small throat size of the porous medium. Various types of boundary conditions for liquid pressure calculation are formulated. Advantages and the range of applicability of this algorithm are compared against an existing algorithm. A threshold value for surface mass transfer coefficient is obtained above which the algorithms that are based on the rule that only one bond is invaded at each step of invasion are no longer applicable. Simultaneous multiple throat invasion in a single time step, unnecessity of liquid cluster identification, and possibility of throat refilling are the major advantages of the new pressure-based algorithm. While the phase distribution in the old approach is insensitive to surface mass transfer coefficient the proposed approach is severely dependent on the magnitude of this coefficient. The incident in which the liquid body is detached from the top surface in the proposed algorithm is also a strong function of surface mass transfer coefficient. The advantages of the new algorithm, however, come with a higher computational cost, especially for large network sizes.

Pore‐network modelling of combined molecular diffusion and gravity drainage mechanisms in a porous matrix block: The competitive role of driving forces

“…In continuation of the study presented by Mashayekhizadeh and Rasaei, [3,5] we apply some extensions to modelling the molecular diffusion mechanism in a matrix block near the fracture by considering the effect of gravity on the process of molecular diffusion. [3] As molecular diffusion and gravity drainage usually occur simultaneously, considering the force of gravity in the equations can be closer to the synchronous reality of molecular diffusion in fractured reservoirs.…”

“…Mass flux due to evaporation from throats adjacent to fractures is calculated from Equation (5). Despite the throats being far from model boundaries, the evaporation rate in near boundary throats depends on the liquid pressure.…”

“…The modelling technique used in this study is adopted from Mashayekhizadeh and Rasaei, [3,5] where they developed completely different algorithms, namely, a cluster-based approach (CBA) and a pressure-based approach (PBA). They showed that the two algorithms have close to the same results when modelling a simple molecular diffusion process.…”

“…In the literature, three methodologies: Bundle of capillary tube modelling, direct pore-scale modelling, and pore network modelling have been most frequently adopted in the investigation of the pore-scale mechanics of fluid-fluid and fluid-solid interactions in porous media by numerical simulation. [1] Molecular diffusion in porous media occurs in a wide range of processes such as geological carbon sequestration, [2] enhanced oil recovery, [3] drying processes, [4,5] and many others. [6] This mechanism is an important driving force for oil recovery from fractured reservoirs under nonequilibrium gas injection.…”

“…The modelling algorithm and governing equations used in this work are similar to that proposed by Mashayekhizadeh and Rasaei. [3,5] The differences are in the boundary conditions, the numerical method for solving the pressure matrix, and the introduction of a gravity term in the new modelling. To establish a basis for comparison of the magnitude and impact of forces and mechanisms, different scenarios, including diffusion-only and diffusion plus gravity cases, are examined in models with three different physical properties.…”