Using Direct Numerical Simulation of Pore-Level Events to Improve Pore-Network Models for Prediction of Residual Trapping of CO2

Direct numerical simulation and pore-network modeling are common approaches to study the physics of two-phase flow through natural rocks. For assessment of the long-term performance of geological sequestration of CO2, it is important to model the full drainage-imbibition cycle to provide an accurate estimate of the trapped CO2. While direct numerical simulation using pore geometry from micro-CT rock images accurately models two-phase flow physics, it is computationally prohibitive for large rock volumes. On the other hand, pore-network modeling on networks extracted from micro-CT rock images is computationally efficient but utilizes simplified physics in idealized geometric pore elements. This study uses the lattice-Boltzmann method for direct numerical simulation of CO2-brine flow in idealized pore elements to develop a new set of pore-level flow models for the pore-body filling and snap-off events in pore-network modeling of imbibition. Lattice-Boltzmann simulations are conducted on typical idealized pore-network configurations, and the interface evolution and local capillary pressure are evaluated to develop modified equations of local threshold capillary pressure of pore elements as a function of shape factor and other geometrical parameters. The modified equations are then incorporated into a quasi-static pore-network flow solver. The modified model is applied on extracted pore-network of sandstone samples, and saturation of residual trapped CO2 is computed for a drainage-imbibition cycle. The modified model yields different statistics of pore-level events compared with the original model; in particular, the occurrence of snap-off in pore-throats is reduced resulting in a more frontal displacement pattern along the main injection direction. Compared to the original model, the modified model is in closer agreement with the residual trapped CO2 obtained from core flow experiments and direct numerical simulation.

Foam Generation in the Presence of Residual Oil in Porous Media

This paper studies the effect of trapped, emulsified oil on the requirement for the geometrical Roof snap-off for foam generation in a porous medium. We extend an existing hydrodynamic pore-level model to describe the liquid accumulation in an appropriately-sized pore in the presence of oil. The effect of oil is simulated by adjusting the pore shape to be asymmetrical as observed in microfluidic experiments with residual oil. We alter the boundary and initial conditions of the problem to test various scenarios. Specifically, four cases are presented. The liquid accumulation is presented when the amount of wetting liquid volume connected to the pore is altered through changing the boundary conditions (cases 1 and 2). Moreover, the effect of drier surrounding medium and/or drier pores is also tested by increasing either the capillary pressure surrounding the pore or the capillary pressure of the pore itself (cases 3 and 4). We find that the presence of residual oil affects the liquid accumulation times when there is no external liquid pressure gradient applied. Additionally, residual oil presence makes the Roof snap-off criterion for liquid accumulation stricter. To augment our pore-level study, we use a statistical pore network to observe the effect of the microscopic changes observed in our pore-level model macroscopically. Our results indicate that a stricter Roof snap-off criterion leads to fewer germination sites for lamellae generation. Our pore network analysis computes the generation rate constant to be as much as four times larger in the absence of oil than in its presence. Results suggest that changes to the shape of pore constrictions by emulsified oil reduce the effectiveness of foam generation.

Porous Flow with Diffuse Interfaces

This chapter presents a model developed by the author, in publications dated from 2002 to 2016, on flow in porous media assuming diffuse interfaces. It contains five sections. Section 1 is an Introduction, tracing the origin of the diffuse interface formalism. Section 1 also presents the traditional compositional model, pointing out its emphasis on phases and questioning the concept of relative permeabilities. Section 2 presents the mass, momentum, and energy balance equations, for a multicomponent continuous fluid, in their most general form, at the pore level. The existence of constitutive equations with phase-inducing terms is mentioned, but the equations are not introduced at this level, and phases are not an explicit concern. Section 3 is about the averaging of the pore level equations inside a region containing many pores. There is no explicit mention of phases and therefore not of relative permeabilities. Section 4 is the technical basis from which the constitutive equations of the model arise, and it is shown that many models can exist. Section 5 introduces constitutive equations and presents a minimal model for multicomponent, multiphase, and thermal flow in neutrally wetting porous media, i.e., a model with a minimal amount of phenomenological parameters.