Density Functional Hydrodynamics in Multiscale Pore Systems: Chemical Potential Drive

Abstract

We use the method of density functional hydrodynamics (DFH) to model compositional multiphase flows in natural cores at the pore-scale. In previous publications the authors demonstrated that DFH covers many diverse pore-scale phenomena, starting from those inherent in RCA and SCAL measurements, and extending to much more complex EOR processes. We perform the pore-scale modelling of multiphase flow scenarios by means of the direct hydrodynamic (DHD) simulator, which is a numerical implementation of the DFH. In the present work, we consider the problem of numerical modelling of fluid transport in pore systems with voids and channels when the range of pore sizes exceed several orders of magnitude. Such situations are well known for carbonate reservoirs, where narrow pore channels of micrometer range can coexist and interconnect with vugs of millimeter or centimeter range. In such multiscale systems one cannot use the standard DFH approach for pore-scale modeling, primarily because the needed increase in scanning resolution that is required to resolve small pores adequately, leads to a field of view reduction that compromises the representation of large pores. In order to address this challenge, we suggest a novel approach, in which transport in small-size pores is described by an upscaled effective model, while the transport in large pores is still described by the DFH. The upscaled effective model is derived from the exact DFH equations using asymptotic expansion in respect to small-size characterization parameter. This effective model retains the properties of DFH like chemical and multiphase transport, thus making it applicable to the same range of phenomena as DFH itself. The model is based on the concept that the transport is driven by gradients of chemical potentials of the components present in the mixture. This is a significant generalization of the Darcy transport model since the proposed new model incorporates diffusion transport in addition to the usual pressure-driven transport. In the present work we provide several multiphase transport numerical examples including: a) upscaling to chemical potential drive (CPD) model, b) combined modeling of large pores by DFH and small pores by CPD.

Incorporation of Sub‐Resolution Porosity Into Two‐Phase Flow Models With a Multiscale Pore Network for Complex Microporous Rocks

“…For materials, such as carbonate rocks, with a significant fraction of the pore space that is unresolved by micro-CT imaging, which are the subject of the current study, multiscale image-based models must be developed, validated, and tested. Two common approaches that can be implemented to predict behavior across different scales are multiscale direct numerical simulation (DNS) and multiscale pore network models (PNMs) (Bijeljic et al, 2018;Brinkman, 1949;Carrillo & Bourg, 2019;Dinariev et al, 2020;Guo et al, 2018;Lesinigo et al, 2011;Meakin & Tartakovsky, 2009;Raeini et al, 2012;Sadeghnejad et al, 2021;Wu et al, 2022). In contrast to DNS, pore network modeling is more computationally efficient (Bultreys et al, 2018;Foroughi et al, 2020Foroughi et al, , 2021Giudici et al, 2023;Øren et al, 2019;Raeini et al, 2019).…”

Incorporation of Sub-Resolution Porosity into Two-Phase Flow Models with a Multiscale Pore Network for Complex Microporous Rocks

“…For materials, such as carbonate rocks, with a significant fraction of the pore space that is unresolved by micro-CT imaging, which are the subject of the current study, multiscale image-based models must be developed, validated, and tested. Two common approaches that can be implemented to predict behavior across different scales are multiscale direct numerical simulation (DNS) and multiscale pore network models (PNMs) [Sadeghnejad et al, 2021;Brinkman, 1949;Bijeljic et al, 2018;Lesinigo et al, 2011;Guo et al, 2018;Carrillo and Bourg, 2019;Dinariev et al, 2020;Wu et al, 2022;Meakin and Tartakovsky, 2009;Raeini et al, 2012]. In contrast to direct numerical simulation, pore network modeling is more computationally efficient [Øren et al, 2019;Foroughi et al, 2020Foroughi et al, , 2021Bultreys et al, 2018;Raeini et al, 2019;Giudici et al, 2023].…”

A Simulation Approach Including Underresolved Scales for Two-Component Fluid Flows in Multiscale Porous Structures

“…These studies, however, mainly focused on single-component fluid flow and did not extend to multicomponent fluid flow. A few recent studies [17,18] have discussed multicomponent fluid flow in multiscale porous structures. In reference [17], the relative permeability from underre-solved PM regions was computed by solving the transport equation for the total energy, Helmholtz free energy and kinetic energy, without referring to physical properties such as the capillary pressure curves.…”

“…A few recent studies [17,18] have discussed multicomponent fluid flow in multiscale porous structures. In reference [17], the relative permeability from underre-solved PM regions was computed by solving the transport equation for the total energy, Helmholtz free energy and kinetic energy, without referring to physical properties such as the capillary pressure curves. In reference [18], the precomputed capillary pressure and the effective flow resistance in the resolved PM were applied to derive a force balance analysis at the capillary equilibrium state using recursive methods.…”