Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological StorageReport as inadecuate

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Transport in Porous Media

, Volume 95, Issue 1, pp 25–54

First Online: 10 August 2012Received: 16 February 2010Accepted: 05 June 2012


We report a modeling and numerical simulation study of density-driven natural convection during geological CO2 storage in heterogeneous formations. We consider an aquifer or depleted oilfield overlain by gaseous CO2, where the water density increases due to CO2 dissolution. The heterogeneity of the aquifer is represented by spatial variations of the permeability, generated using Sequential Gaussian Simulation method. The convective motion of the liquid with dissolved CO2 is investigated. Special attention is paid to instability characteristics of the CO2 concentration profiles, variation of mixing length, and average CO2 mass flux as a function of the heterogeneity characterized by the standard deviation and the correlation length of the log-normal permeability fields. The CO2 concentration profiles show different flow patterns of convective mixing such as gravity fingering, channeling, and dispersive based on the heterogeneity medium of the aquifer. The variation of mixing length with dimensionless time shows three separate regimes such as diffusion, convection, and second diffusion. The average CO2 mass flux at the top boundary decreases quickly at early times then it increases, reaching a constant value at later times for various heterogeneity parameters.

KeywordsDensity-driven natural convection Porous media Heterogeneity CO2 Solubility Mass transfer List of SymbolsVariablesAAspect ratio of the domain H-L –

A0Amplitude of sinusoidal perturbation

cDimensionless concentration –

c′Concentration mol-m

DDiffusion coefficient m-s

f x, z Permeability variation function

FmAverage CO2 mass flux

gAcceleration due to gravity m-s

HHeight of the porous medium m

i and jIndex of the mesh points in x and z direction, respectively

kPermeability m

k0Mean permeability m

LLength of the porous medium m

PPressure Pa

RaRayleigh number –

tTime sec

tdDimensionless time –

uxDimensionless x-component velocity –

uzDimensionless z-component velocity –

uXx component velocity m-s

uZz component velocity m-s

wWidth of domain m

wtTotal dissolved CO2 concentration

xDimensionless distance in X coordinate

YLog-normal permeability distribution

zDimensionless distance in Z coordinate

Greek SymbolsαWave-number

βcThe volumetric expansion coefficient

\{\varepsilon}\Criteria for convergence

φPorosity –

λ0Wavelength of sinusoidal perturbation –

λCorrelation length scale m

μViscosity of fluid kg-ms

θMean of log permeability

ψStream function m  m  s

ρ0Pure liquid density kg-m

ρLiquid density kg-m

ΔρChange in density kg-m

σStandard deviation

τxHorizontal correlation length m

τzVertical correlation length m

AbbreviationSGSIMSequential Gaussian Simulation

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Author: Panneerselvam Ranganathan - Rouhollah Farajzadeh - Hans Bruining - Pacelli L. J. Zitha


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