Principles of reactive flow modelling: why they are important for Carbon Capture and Storage (CCS) activities

A major aim of reactive flow models in CCS activities is to understand and predict the evolution of the CO₂ plume injected in the reservoir for planning and monitoring purposes (e.g. Jenkins et al., 2015). They can also be used to support the evaluation of the risks of leakage through the caprock and the fate of the fluids in the overburden. It is therefore also an essential tool to help constrain the risks of contamination of usable groundwater (Li et al., 2018) or of surface carbon emissions (Directive 2009/31/EC). In any case, accurate modelling of the evolution of CO₂ fluids in the subsurface faces several challenges which are related, amongst others, to the complexity of the physical and chemical processes involved (Kelemen et al., 2019). For this reason, multiphysics reactive flow numerical models are well-suited to simulate such complex systems.

A model is a simplified version of reality to understand a problem of interest, based on a balance between realism and practicality (Bethke, 2022). Geochemical modelling uses chemical thermodynamics and/or kinetics to analyse the chemical reactions that affect geochemical systems. In reactive flow models, chemical reactions and physical transport of fluids are simulated simultaneously. Multiphysics reactive flow models integrate additional physical processes beside fluid flow within the single simulation environment (e.g., heat transfer, mechanical deformation, …). Discretised numerical models are necessary to solve such complex problems computationally: the system (“domain”) is divided into smaller elements, using methods such as, e.g. Finite Difference Method (FDM) or Finite Volume Method (FVM).

Geochemical modelling implies, first, the conceptualisation of the system or process of interest in a useful way (Bethke, 2022). An example relevant for CCS could be assessing how geochemical interactions between the CO₂ plume and the rock/sediments drive porosity and permeability changes in a reservoir of variable lithologies. The system includes one or more phases (solid, liquid, gas, supercritical) and species (molecular entities that exist within a phase). It must remain in equilibrium throughout the calculations, i.e., mass, energy and momentum must be preserved within the system (Figure 1).

Figure 1: Schematic diagram of a reaction model (modified from Bethke, 2022)

A mathematical model is then built to translate the processes of the conceptual model into equations (Figure 2).

Figure 2: An example of relationships used to express mass, energy and momentum conservation in a FVM.

A set of governing equations is defined to fully describe the equilibrium state of the geochemical system (e.g. Jiang, 2011). Solving the governing equations requires iterative computing methods in which the values that satisfy the equations to within a small tolerance are achieved through a sequence of improving approximate solutions.

Multiphysics reactive flow models have already been used extensively to predict or monitor the development of CO₂ injected in the subsurface (e.g., Ahusborde et al., 2021; Lyu and Voskov, 2023) although there is still need for improved modelling tools (Nordbotten et al., 2012).

References:

Ahusborde, E., Amaziane, B. & Moulay, M.I. High performance computing of 3D reactive multiphase flow in porous media: application to geological storage of CO₂. Computing Geoscience 25, 2131–2147 (2021). https://doi.org/10.1007/s10596-021-10082-x

Bethke, C. (2022). Geochemical and biogeochemical reaction modeling. Cambridge University Press, 502 pp.

Directive 2009/31/EC of the European Parliament and Council on the geological storage of carbon dioxide. Directive - 2009/31 - EN - EUR-Lex (europa.eu). 

Jenkins, C., Chadwick, A., and Horvorka, S. D. (2015). The state of the art in monitoring and verification – ten years on. International Journal of Greenhouse Gas Control 40, 312-349.

Jiang, X. (2011). A review of physical modelling and numerical simulation of long-term geological storage of CO₂. Applied Energy 88(11), 3557-3566, ISSN 0306-2619,https://doi.org/10.1016/j.apenergy.2011.05.004.

Kelemen, P., et al. (2019). An overview of the status and challenges of CO₂ storage in minerals and geological formations. Frontiers in Climate Review, November 2019, Vol. 1, Article 9, 20pp.

Li, Z., Fall, M., and Ghirian, A. (2018). CCS risk assessment: Groundwater contamination caused by CO₂, Geosciences 2018, 8, 397.