Transport in Porous Media

, Volume 112, Issue 1, pp 283–312 | Cite as

Numerical Simulation of Reactive Fluid Flow on Unstructured Meshes

  • Sarah Jane FowlerEmail author
  • Georg Kosakowski
  • Thomas Driesner
  • Dmitrii A. Kulik
  • Thomas Wagner
  • Stefan Wilhelm
  • Olivier Masset


Reactive transport simulation on unstructured meshes can provide fundamental insight into the effect that geometric complexity of geologic structures has on fluid flow and development of reaction fronts. When applied to conditions ranging from ambient to hydrothermal and combined with compressible flow, accounting for geometric complexity provides an advantage for applications such as enhanced geothermal systems, carbon dioxide sequestration, hydrothermal ore formation, and radioactive waste disposal. We introduce CSMP–GEMS, a thermo–hydro and chemical multicomponent reactive transport code based on coupling of the Complex System Modeling Platform (CSMP) transport modeling framework with the GEMS3K chemical speciation solver. GEMS3K features a comprehensive suite of non-ideal activity and equation-of-state models of solution phases (aqueous electrolyte, gas and fluid mixtures, solid solutions). Current features include transient, compressible, single-phase advective and/or dispersive fluid flow, mass transport, heat transport in saturated porous media, and geochemical reactions in subsurface hydrothermal systems. We present two one-dimensional numerical experiments to compare CSMP–GEMS with the reactive transport codes OpenGeoSys–GEM and TOUGHREACT. Each experiment simulates calcite dissolution and dolomite precipitation during advection and hydrodynamic dispersion. One experiment corresponds to an existing isothermal \((25\,^{\circ }\mathrm{C})\) benchmark; the second explores the applicability of the codes to non-isothermal problems. We also present a two-dimensional example that illustrates the application of CSMP–GEMS on unstructured meshes that can represent complex geologic relations. The results suggest that all three codes are well suited to predicting fluid circulation, heat transport, and mineral stability within hydrothermal systems relevant to enhanced geothermal systems and carbon dioxide sequestration in deep aquifers. Self-consistent accounting for kinetic processes is a major advantage of TOUGHREACT, but published applications are restricted to orthogonal meshes, potentially limiting the applicability of TOUGHREACT to geometrically less complex natural systems. OpenGeoSys–GEM can operate on unstructured meshes that may include multiple element types, facilitating the examination of non-orthogonal domains. However, due to its reliance on the groundwater equations, OpenGeoSys–GEM may be best suited for application to systems in which flow includes dispersion/diffusion and is not compressible. CSMP–GEMS does not currently calculate reaction kinetics, but may be useful for application to geometrically complex systems.


Reactive transport Numerical simulation Fluid–rock interaction Enhanced geothermal systems Hydrothermal systems 

List of symbols

\(\alpha _{l}\)

Longitudinal dispersivity (m)

\(\alpha _{t}\)

Transverse dispersivity (m)

\(\beta _{f}\)

Fluid compressibility (\(\hbox {Pa}^{-1}\))

\(\beta _{r}\)

Solid compressibility (\(\hbox {Pa}^{-1}\))

\(\nabla \)

Nabla operator (\(\hbox {m}^{-1}\))

\(\partial _t\)

Partial derivative with respect to time (\(\hbox {s}^{-1}\))

\(\partial _{P}\)

Partial derivative with respect to pressure (\(\hbox {Pa}^{-1}\))

\(\phi \)

Porosity (\(-\))

\(\mu \)

Fluid dynamic viscosity (Pa s)

\(\rho _{f}\)

Fluid density (\(\hbox {kg\,m}^{-3}\))

\(\rho _{r}\)

Rock density (\(\hbox {kg\,m}^{-3}\))

\(\omega \)

Mass fraction of a single solute species (\(-\))


Specific isobaric heat capacity for the fluid (\(\hbox {J kg}^{-1}\hbox { K}^{-1}\))


Specific isobaric heat capacity for the rock (\(\hbox {J kg}^{-1}\hbox { K}^{-1}\))


Pore diffusion coefficient (\(\hbox {m}^{2}\,\hbox {s}^{-1}\))


Hydrodynamic dispersion tensor (\(\hbox {m}^{2}\,\hbox {s}^{-1}\))


Effective diffusion coefficient (\(\hbox {m}^{2}\,\hbox {s}^{-1}\))


Gravitational acceleration (\(\hbox {m s}^{-2}\))


Total enthalpy (\(\hbox {J\,m}^{-3}\))


Fluid-specific enthalpy (\(\hbox {J kg}^{-1}\))


Rock-specific enthalpy (\(\hbox {J kg}^{-1}\))


Permeability (\(\hbox {m}^{2}\))


Thermal conductivity (\(\hbox {W\,m}^{-1}\,\hbox {K}^{-1}\))


Domain length (m)


Total fluid mass per pore volume (\(\hbox {kg\,m}^{-3}\))


Fluid pressure (Pa)


Source term


Temperature (\(^{\circ }\mathrm{C}\hbox { or K}\))


Darcy flux (\(\hbox {m s}^{-1}\))


Pore velocity (\(\hbox {m s}^{-1}\))


Domain width (m)

\(\Delta x\)

Horizontal grid discretization (m)


Depth (m)

\(\Delta z\)

Vertical grid discretization (m)








This work is a contribution from Module 4 of the GEOTHERM project, which has been funded by the Competence Center Environment and Sustainability (CCES) of the ETH Domain.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Sarah Jane Fowler
    • 1
    Email author
  • Georg Kosakowski
    • 2
  • Thomas Driesner
    • 3
  • Dmitrii A. Kulik
    • 2
  • Thomas Wagner
    • 4
  • Stefan Wilhelm
    • 5
  • Olivier Masset
    • 5
  1. 1.Division of GeologyKU LeuvenLeuvenBelgium
  2. 2.Laboratory for Waste ManagementPaul Scherrer Institut (PSI)VilligenSwitzerland
  3. 3.Institute of Geochemistry and PetrologyETH ZurichZurichSwitzerland
  4. 4.Division of Geology and Geochemistry, Department of Geosciences and GeographyUniversity of HelsinkiHelsinkiFinland
  5. 5.Groundwater Protection and Waste DisposalAF-Consult Switzerland Ltd.BadenSwitzerland

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