An Adaptive Multiphysics Model Coupling Vertical Equilibrium and Full Multidimensions for Multiphase Flow in Porous Media

Abstract

Efficient multiphysics (or hybrid) models that can adapt to the varying complexity of physical processes in space and time are desirable for modeling fluid migration in the subsurface. Vertical equilibrium (VE) models are simplified mathematical models that are computationally efficient but rely on the assumption of instant gravity segregation of the two phases, which may not be valid at all times or at all locations in the domain. Here we present a multiphysics model that couples a VE model to a full multidimensional model that has no reduction in dimensionality. We develop a criterion that determines subdomains where the VE assumption is valid during simulation. The VE model is then adaptively applied in those subdomains, reducing the number of computational cells due to the reduction in dimensionality, while the rest of the domain is solved by the full multidimensional model. We analyze how the threshold parameter of the criterion influences accuracy and computational cost of the new multiphysics model and give recommendations for the choice of optimal threshold parameters. Finally, we use a test case of gas injection to show that the adaptive multiphysics model is much more computationally efficient than using the full multidimensional model in the entire domain, while maintaining much of the accuracy.

An Adaptive Hybrid Vertical Equilibrium/Full‐Dimensional Model for Compositional Multiphase Flow

“…For the injection case, Figures 6a and 6b show snapshots of the values of the relative permeability criterion, as calculated in Equation 15, in the whole domain for three times, and the behavior of the criterion values over dimensionless time for two different locations along the horizontal axis. Similarly, as observed for two incompressible, immiscible phases by Becker et al (2018), the criterion values show a high peak around the injection region, indicating that the phases here are not in equilibrium due to injected gas-phase moving continuously upward. Toward the tip of the gas-phase plume, the criterion values increase again, indicating that brine phase drains out of the advancing gas-phase plume.…”

“…A threshold value of 0.07 for the relative permeability criterion was chosen, starting with a higher value which is reduced until a stable solution is reached, as suggested by Becker et al. (2018). Hydrogen is injected and extracted in the center of the radially symmetric aquifer, through a large‐diameter well (0.53 m) that is perforated in the top 5 m of the aquifer.…”

“…The aquifer is discretized into a radially symmetric grid with horizontal resolution of 5 m and vertical resolution of 0.94 m (for full-dimensional model and full-dimensional subdomains of the hybrid model). A threshold value of 0.07 for the relative permeability criterion was chosen, starting with a higher value which is reduced until a stable solution is reached, as suggested by Becker et al (2018). Hydrogen is injected and extracted in the center of the radially symmetric aquifer, through a large-diameter well (0.53 m) that is perforated in the top 5 m of the aquifer.…”

“…Thus, relative permeability profiles are a natural choice to determine applicability of VE models. To receive the criterion, the difference between the simulated profile in a full-dimensional column to a hypothetical VE profile is calculated as the area between the profiles, and normalized with the thickness of the mobile gas-phase plume in the hypothetical VE profile (Becker et al, 2018). The equation to calculate the criterion values thus follows as:…”

On the limit of a two‐phase flow problem in thin porous media domains of Brinkman type

“…We also refer to the multiscale model approach in Guo et al 9 A comparative study on the accuracy and efficiency of the asymptotic approach over the others is preformed in Armiti‐Juber and Rohde, 7 where also an equivalence result with the multiscale approach is proved. A recent approach suggests an adaptive algorithm that couples the dimensional reduction approach with the full model 10 . It is based on a local criterion that determines the applicability of the reduced model.…”