Multiblock Pore-Scale Modeling and Upscaling of Reactive Transport: Application to Carbon Sequestration


In order to safely store CO2 in depleted reservoirs and deep saline aquifers, a better understanding of the storage mechanisms of CO2 is needed. Reaction of CO2 with minerals to form precipitate in the subsurface helps to securely store CO2 over geologic time periods, but a concern is the formation of localized channels through which CO2 could travel at large, localized rates. Pore-scale network modeling is an attractive option for modeling and understanding this inherently pore-level process, but the relatively small domains of pore-scale network models may prevent accurate upscaling. Here, we develop a transient, single-phase, reactive pore-network model that includes reduction of throat conductivity as a result of precipitation. The novelty of this study is the implementation of a new mortar/transport method for coupling pore networks together at model interfaces that ensure continuity of pressures, species concentrations, and fluxes. The coupling allows for modeling at larger scales which may lead to more accurate upscaling approaches. Here, we couple pore-scale models with large variation in permeability and porosity which result in initial preferential pathways for flow. Our simulation results suggest that the preferential pathways close due to precipitation, but are not redirected at late times.

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k 1 :

Reaction rate of bicarbonate dissociation (M/L 3 T)

k 2 :

Reaction rate of calcite precipitation (1/T)

q ij :

Flow rate within pore throat connecting pores i and j (L 3/T)

R ij :

Radius of pore throat connecting pores i and j (L)

μ :

Viscosity (M/LT)

L ij :

Length of pore throat connecting pores i and j (L)

P i :

Pressure of pore i (M/LT 2)

c HCO 3 :

Bicarbonate concentration (M/L 3)

\({{c}_{{\rm H{\rm CO}_{3}}^{-}}^{{\rm eq}}}\) :

Bicarbonate concentration at equilibrium (M/L3)

t :

Time (T)

V p,i :

Volume of pore i (L 3)

ρCaCO3 :

Calcite density (M/L 3)

Δt :

Time step (T)

ΔV p,i :

Change in volume of pore i (L 3)

Δc :

Change in concentration (M/L 3)

Q :

Overall flow rate through the domain (L 3/T)

V p,0 :

Initial pore volume of entire domain (L3)

J :



Lagrange multiplier of interface basis functions

F :

Jump in interface flux vector

\({\bar{c}}\) :

Average projected concentration over a bundle (M/L3)

u :

Darcy velocity (L/T)

Da :

Damkohler number, rate of precipitation to rate of convection

α :

Rate of calcite precipitation to rate of bicarbonate dissociation

c * :

Dimensionless concentration

t * :

Dimensionless time (pore volume throughput = Qt/V p,0)


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Correspondence to M. T. Balhoff.

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Mehmani, Y., Sun, T., Balhoff, M.T. et al. Multiblock Pore-Scale Modeling and Upscaling of Reactive Transport: Application to Carbon Sequestration. Transp Porous Med 95, 305–326 (2012).

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  • Pore-scale modeling
  • Mortar coupling
  • Reactant transport
  • Carbon sequestration
  • Upscaling
  • Multiscale modeling