Microcontinuum approach to multiscale modeling of multiphase reactive flow during mineral dissolution

Image-based modeling of mineral dissolution poses challenges due to its multiscale nature, requiring the consideration of multiphase reactive flow and transport at both the resolved pore scale (macropores/fractures) and the unresolved Darcy scale (micropores). The existing hybrid-scale simulation methods pose difficulties in handling the multiscale fluid-rock interactions and temporal structural evolution. In this study, we propose a multiscale compressive continuum species transfer (MC-CST) scheme to address the limitations of the standard CST scheme, which exhibits numerical diffusion issues at the gas-liquid interface and thereby suffers from inaccuracies in reactive transport simulations. The proposed scheme incorporates an additional compressive term derived from volume-averaging principles for the advection and diffusion fluxes in a single-field framework. To ensure the impermeable species transport condition at the solid boundary, a concentration extrapolation algorithm is developed. Four validation cases are conducted to demonstrate the model's capability in accurately simulating multiphase reactive flow and transport at various scales, including pore scale, continuum scale, and hybrid scales. Special attention is given to accurately modeling the thermodynamic conditions at the gas-liquid interface, particularly with respect to the concentration jump under conditions of large local Péclet numbers. Furthermore, we present a case study simulating calcite dissolution in a porous medium to underscore the importance of multiscale fluid-rock interactions for an in-depth comprehension of the dissolution regime.

Figure 1

Graphic representation of the concentration gradient at the solid surface: (a) the pore-scale approach; (b) noncorrected concentration gradient vectors in the multiphase multiscale model; (c) illustration of the concentration extrapolation from the fluid region to the solid region at the fluid/solid interface and the resulting corrected concentration gradient vectors in the multiphase multiscale model.

Figure 2

Flowchart of the microcontinuum model of the multiphase reactive flow.

Figure 3

Comparisons of the analytical solution and numerical results by the standard CST and MC-CST models for the diffusion-dominated flow for very early physical times (zoom in).

Figure 4

Comparisons of analytical solutions and numerical results from the standard CST and MC-CST models for the advection-dominated flow case. Solid lines represent the analytical solutions, dashed lines are saturation profiles, and markers depict numerical results.

Figure 5

Concentration contours near the gas-liquid interface for the advection-dominated flow obtained using (a) CST and (b) MC-CST models. The white dashed line is the gas-liquid interface.

Figure 6

Darcy-scale simulation configuration of the absolute permeability field and boundary conditions for oil drainage.

Figure 7

Simulation results of liquid saturation solved by (a) hybridPorousInterFoam, and (b) the present model. The white line delineates the oil-water interface.

Figure 8

Simulation results of solute concentration solved by the present model for different Henry's constant: (a) $H=1$, (b) $H=2$, (c) $H=5$. The white line delineates the oil-water interface.

Figure 9

Simulated concentration profile along the horizontal line at $y=0.06\mathrm{m}$ for different Henry's constants. The horizontal line is labeled in Fig. 8.

Figure 10

Simulation domain and results of the solid tube case: (a) domain configuration, (b) liquid saturation field $(t=0.3\mathrm{s})$, and concentration fields $(t=0.3\mathrm{s})$ solved using (c) the CST model without boundary correction, (d) the CST model with boundary correction, (e) the MC-CST model without boundary correction, and (f) the MC-CST model with boundary correction.

Figure 11

Simulation domain and results of the porous tube case: (a) domain configuration, (b) liquid saturation field $(t=0.3\mathrm{s})$, and concentration fields $(t=0.3\mathrm{s})$ solved by the MC-CST model with various Henry's constants of (c) $H=1$, (d) $H=2$, (e) $H=5$, and (f) $H=10$.

Figure 12

Simulation results for temporal evolutions of fluid saturation and calcite structure during the multiphase dissolution.

Figure 13

Comparisons of the residual normalized mass of the calcite grain between numerical results and experimental measurement [17].

Figure 14

Snapshots of (a) computational domain, (b) liquid saturation, and (c) velocity magnitude fields at $t=20\mathrm{s}$ solved for the multiphase dissolution of solid grains. Black irregular particles represent the solid calcite grains, while the white solid line delineates the fluid-solid interface (${\varepsilon }_{\mathrm{f}}=0.85$ isosurface). The white dashed line delineates the preferential flow pathway.

Figure 15

Snapshots of concentration fields at $t=20$ and 50 s in fluid regions for the multiphase dissolution of (a) solid grains, and porous grains with porosity of (b) ${\varepsilon }_{\mathrm{f}}=0.1$, (c) ${\varepsilon }_{\mathrm{f}}=0.2$, and (d) ${\varepsilon }_{\mathrm{f}}=0.3$. The white dashed line delineates the preferential flow pathway. The color ranging from white to black within the solid grains corresponds to the volume fraction of the solid phase, varying from 0 to 1.

Figure 16

Snapshots of concentration fields at $t=20$ and 50 s within solid and porous regions for the multiphase dissolution of (a) solid grains, and porous grains with porosity of (b) ${\varepsilon }_{\mathrm{f}}=0.1$, (c) ${\varepsilon }_{\mathrm{f}}=0.2$, and (d) ${\varepsilon }_{\mathrm{f}}=0.3$. The red dashed line delineates the preferential flow pathway. The white represents the fluid regions, and the gray area represents the gas phase. The black solid line represents calcite at $t=0\mathrm{s}$.

Figure 17

Normalized mass of solid grains and porous grains with the porosity of ${\varepsilon }_{\mathrm{f}}=0.1,0.2,0.3$. The capillary effect in the subresolution porous medium is not considered.

Figure 18

Profiles of normalized mass along the $x$ direction at 20 and 50 s of solid grains and porous grains with a porosity of ${\varepsilon }_{\mathrm{f}}=0.1,0.2,0.3$. The slope is calculated by linear regression of the normalized mass of calcite and the dimensionless length of the $x$ direction.