Solving Biot poroelasticity by coupling OPM Flow with the two-point stress approximation finite volume method

TL;DR

This work presents a cell-centered coupling of Two-Point Stress Approximation (TPSA) elasticity with an established finite-volume reservoir flow solver (OPM Flow) using a fixed-stress splitting. By reformulating Biot poroelasticity and exploiting the same grid for flow and mechanics, the method exchanges only one scalar value per cell per iteration and reuses TPFA preconditioners, enabling efficient large-scale simulations. The authors develop rescaling and block-triangular AMG-based preconditioning to solve the resulting TPSA system, and demonstrate quadratic convergence and practical effectiveness through analytical and realistic test cases, including a sealing barrier and the Norne reservoir. The study highlights that poroelastic coupling can connect compartmentalized flow regions and significantly alter pressure evolution, underscoring the importance of including solid mechanics in reservoir models. The approach provides a scalable, non-invasive framework for integrated poroelastic reservoir simulation with readily reusable solvers and preconditioners.

Abstract

Finite volume methods are prevalent in reservoir simulation due to their mass conservation properties and their ability to handle complex grids. However, a simple and consistent finite volume method for elasticity was unavailable until the recently developed two-point stress approximation finite volume method (TPSA). In this work, we show how to couple TPSA to an established flow simulator, using OPM Flow as our primary example. Due to this choice of numerical methods, the coupling is naturally handled at the cell centers, without requiring interpolation operators. We propose a fixed stress coupling scheme and reuse algebraic multi-grid preconditioners, which are known to be effective for two-point flux finite volume methods. Numerical examples illustrate the flexibility of the approach and we showcase how the introduction of solid mechanics impacts the behavior of compartmentalized flow systems.

Figures (5)

• Figure 1: (a) The error converges quadratically with respect to the mesh size $h$ in all variables. (b) Convergence of the iterative solver BiCGStab for the TPSA system using the preconditioner \ref{['eq: preconditioner']} on the four finest grids.
• Figure 2: (a) The second test case includes a sealing barrier that divides the domain into two subdomains, $\Omega_1$ in red and $\Omega_2$ in blue, respectively. (b) The fluid pressure, averaged over the subdomains. The pressure increases due to an injection well in $\Omega_1$, which only affects the pressure in $\Omega_2$ if poroelasticity effects are included in the model.
• Figure 3: Comparison between the different splitting schemes for the test case of \ref{['sub:a_sealing_barrier']}. We observe that Anderson acceleration is particularly effective for this simple problem.
• Figure 4: (a) Deviation in fluid pressure $\Delta p_f$ and (b) the vertical displacement $u_z$ for the third test case on the Norne reservoir. At the injection well in the lower left of the region, the fluid pressure increases, causing the porous medium to expand. Conversely, a decrease in pressure makes the reservoir contract at the extraction well in the rear.
• Figure 5: (a) The proposed preconditioner \ref{['eq: preconditioner']} allows BiCGStab to converge within 16 iterations for the majority of time steps. (b) The fixed stress schemes outperform the Lagged coupling from the second iteration onwards. The convergence improves if Anderson acceleration is applied.

Theorems & Definitions (2)

• Remark 1
• Remark 2: Gravity