Nonlinear Simulation Methods for Multiphase Flow in Porous Media

Accurate numerical simulation of multiphase flow in porous media underpins advances in hydrocarbon recovery, carbon capture and storage, and groundwater management. The governing equations combine Darcy’s law for flow with mass conservation and nonlinear constitutive relations for phase relative permeability and capillary pressure. The resulting system of nonlinear partial differential equations poses challenges of stiffness, strong coupling and heterogeneity across scales. Traditional sequential approaches decouple pressure and saturation but often require small time steps for stability, while fully implicit schemes improve stability at the cost of solving large nonlinear systems. Recent developments have focused on enhancing robustness and efficiency through tailored nonlinear solvers, preconditioning techniques and multilevel algorithms. Domain decomposition and additive Schwarz preconditioners address local nonlinearities, nonlinear multigrid methods exploit coarse-scale corrections for rapid convergence, and hyperbolic reformulations enable explicit, locally conservative schemes suitable for parallel implementation. These innovations collectively allow larger time steps, handle highly heterogeneous geological models and reduce computational expense, thereby extending the predictive reach of multiphase flow simulators in practical subsurface applications.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Nonlinear Simulation Methods for Multiphase Flow in Porous Media publication trend

The graph below shows the total number of articles in nonlinear simulation methods for multiphase flow in porous media across all publications each year (not limited to Nature Index journals).

Technical terms

Darcy’s law: Empirical relation describing flow velocity through a porous medium under an applied pressure gradient.

Fully implicit method: Time-stepping scheme where flow and transport equations are solved in a coupled, single nonlinear system at each step.

Nonlinear preconditioner: Operator applied to improve convergence of Newton’s method by addressing local nonlinearities before global updates.

Multigrid method: Hierarchical solver that accelerates convergence by transferring corrections across multiple spatial scales.

Hyperbolic conservation law: Formulation of transport equations emphasising wave propagation and local fluxes for explicit solution strategies.

References

1. A numerical study of the additive Schwarz preconditioned exact Newton method (ASPEN) as a nonlinear preconditioner for immiscible and compositional porous media flow. Computational Geosciences (2021).
2. An aggregation-based nonlinear multigrid solver for two-phase flow and transport in porous media. Computers & Mathematics with Applications (2022).
3. Tightly coupled hyperbolic treatment of buoyant two-phase flow and transport in porous media. Journal of Computational Physics (2023).