On the use of Darcy's law and invasion‐percolation approaches for modeling large‐scale geologic carbon sequestration

Abstract

Most large‐scale flow and transport simulations for geologic carbon sequestration (GCS) applications are carried out using simulators that solve flow equations arising from Darcy's law. Recently, the computational advantages of invasion‐percolation (IP) modeling approaches have been presented. We show that both the Darcy's‐law‐ and the gravity‐capillary balance solved by IP approaches can be derived from the same multiphase continuum momentum equation. More specifically, Darcy's law arises from assuming creeping flow with no viscous momentum transfer to stationary solid grains, while it is assumed in the IP approach that gravity and capillarity are the dominant driving forces in a quasi‐static two‐phase (or more) system. There is a long history of use of Darcy's law for large‐scale GCS simulation. However, simulations based on Darcy's law commonly include significant numerical dispersion as users employ large grid blocks to keep run times practical. In contrast, the computational simplicity of IP approaches allows large‐scale models to honor fine‐scale hydrostratigraphic details of the storage formation which makes these IP models suitable for analyzing the impact of small‐scale heterogeneities on flow. However, the lack of time‐dependence in the IP models is a significant disadvantage, while the ability of Darcy's law to simulate a range of flows from single‐phase‐ and pressure‐gradient‐driven flows to buoyant multiphase gravity‐capillary flow is a significant advantage. We believe on balance that Darcy's law simulations should be the preferred approach to large‐scale GCS simulations. © 2015 Society of Chemical Industry and John Wiley & Sons, Ltd

Modeling CO2 plume migration using an invasion‐percolation approach that includes dissolution

“…CO 2 is either invading or back‐filling cells to establish a fluid column high enough to overcome the capillary resistance. The simplicity of the governing equations is the key behind the computational efficiency of MIP 16,23 . Note that MIP is a quasi‐static fluid displacement model where the system evolution is described by pore‐by‐pore advancement of one fluid immiscibly displacing another in a porous medium assuming a constant rate of displacement 14,65 .…”

“…On the other hand, Darcy‐based approaches solve a set of partial differential equations to estimate the temporal and spatial distribution of the pressure and saturation of either phases (black‐oil simulation, BOS) or components (compositional simulation) 15 . Oldenburg et al 16 . reviewed and compared these approaches in the context of Navier–Stokes equations.…”

“…In 2014, Cavanagh and Nazarian 22 proposed a comprehensive benchmark for the Sleipner project where better results are observed in the case of BOS only when the pressure field is dissipated (after running the simulation for more than 90 years). In addition, the computational efficiency of MIP simulations has been discussed in several studies 16, 23, 24 . In conclusion, Cavanagh et al 25 .…”

Thermodynamics‐related processes during the migration of acid gases and methane in deep sedimentary formations

“…All these processes are simulated at basin scale and for geological times. At this respect, it is worth mentioning a review of the use of Darcy's law and invasion-percolation (IP) approaches recently published by Oldenburg et al 4 focused on the modeling of large-scale geologic carbon sequestration. The simulation of migration of liquid hydrocarbons and gases through sedimentary units toward structural traps is more complex and, even if a complete mathematical formulation is available (multiphase Darcy's law), a more simplified approach is often used involving ray-tracing and percolation theory.…”

“…2,3 The simplification is due to the computational demand required for a more accurate solution of the problem, but questions arise about the real capability of these simplified methods to capture the whole spectrum of movements of fluids in porous media. At this respect, it is worth mentioning a review of the use of Darcy's law and invasion-percolation (IP) approaches recently published by Oldenburg et al 4 focused on the modeling of large-scale geologic carbon sequestration. After evaluating strengths and weaknesses of Darcy's law and IP approaches, they conclude that Darcy's law has a wider application field than IP and is more suitable for the modeling of processes of concern for geological carbon sequestration.…”