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.
Oldenburg, Curtis M., et al. "On the use of Darcy's law and invasion-percolation approaches for modeling large-scale geologic carbon sequestration." Greenhouse Gases: Science and Technology, vol. 6, no. 1, Nov. 2015. https://doi.org/10.1002/ghg.1564
Oldenburg, Curtis M., Mukhopadhyay, Sumit, & Cihan, Abdullah (2015). On the use of Darcy's law and invasion-percolation approaches for modeling large-scale geologic carbon sequestration. Greenhouse Gases: Science and Technology, 6(1). https://doi.org/10.1002/ghg.1564
Oldenburg, Curtis M., Mukhopadhyay, Sumit, and Cihan, Abdullah, "On the use of Darcy's law and invasion-percolation approaches for modeling large-scale geologic carbon sequestration," Greenhouse Gases: Science and Technology 6, no. 1 (2015), https://doi.org/10.1002/ghg.1564
@article{osti_1474916,
author = {Oldenburg, Curtis M. and Mukhopadhyay, Sumit and Cihan, Abdullah},
title = {On the use of Darcy's law and invasion-percolation approaches for modeling large-scale geologic carbon sequestration},
annote = {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.},
doi = {10.1002/ghg.1564},
url = {https://www.osti.gov/biblio/1474916},
journal = {Greenhouse Gases: Science and Technology},
issn = {ISSN 2152-3878},
number = {1},
volume = {6},
place = {United States},
publisher = {Wiley},
year = {2015},
month = {11}}