Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage

Ranganathan, Panneerselvam; Farajzadeh, R.; Bruining, Hans; Zitha, Pacelli L.J.

doi:10.1007/s11242-012-0031-z

Cited by 72 publications

(33 citation statements)

References 41 publications

(51 reference statements)

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“…Similar to the instabilities induced by the viscosity difference between the fluids [47], instabilities induced by a density difference can lead to f ingering, channeling, and dispersive regimes depending on the degree of the permeability variance (Dykstra-Parsons coefficient) and the correlation length of the porous medium [15,37]. The dispersive regime (characteristic of flow in media with a high degree of heterogeneity) can be analytically modeled by choosing an effective dispersion coefficient in a diffusion-based model [20].…”

Section: Introductionmentioning

confidence: 99%

An empirical theory for gravitationally unstable flow in porous media

et al. 2013

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In this paper, we follow a similar procedure as proposed by Koval (SPE J 3(2): [145][146][147][148][149][150][151][152][153][154] 1963) to analytically model CO 2 transfer between the overriding carbon dioxide layer and the brine layer below it. We show that a very thin diffusive layer on top separates the interface from a gravitationally unstable convective flow layer below it. Flow in the gravitationally unstable layer is described by the theory of Koval, a theory that is widely used and which describes miscible displacement as a pseudo two-phase flow problem. The pseudo two-phase flow problem provides the average concentration of CO 2 in the brine as a function of distance. We find that downstream of the diffusive layer, the solution of the convective part of the model, is a rarefaction solution that starts at the saturation corresponding to the highest value of the fractional-flow function. The model uses two free parameters, viz., a dilution factor and a gravity fingering index. A comparison of the Koval model with the horizontally averaged concentrations obtained from 2-D numerical simulations provides a correlation for the two parameters with the Rayleigh number. The obtained scaling relations can be used in numerical simulators to account for the density-driven natural convection, which cannot be currently captured because the grid cells are typically orders of magnitude

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Section: Introductionmentioning

confidence: 99%

An empirical theory for gravitationally unstable flow in porous media

et al. 2013

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“…In this paper, the dissolution flux will be characterized by a generalization of the Sherwood number (see, e.g., [44,56]), which is a dimensionless measure of the convective flux across the upper boundary of the domain. We call this quantity the surface flux (S).…”

Section: Mathematical Model: Surface Flux In C-ed Processes In Porousmentioning

confidence: 99%

“…The governing equations used to describe the C-ED process are continuity (2), Darcy's law (3) and convection-di↵usion-reaction (4) (for more details see [44,56,58]):…”

Section: Mathematical Model: Surface Flux In C-ed Processes In Porousmentioning

confidence: 99%

“…Most of the literature on enhanced dissolution in CO 2 sequestration is concerned with the time evolution of the process and not with the analysis of the non-uniqueness of solutions, the corresponding bifurcation map and the stability of solutions. Moreover, in most of these works only molecular di↵usion is considered (e.g., [44]), chemical reaction is neglected (e.g., [28]) and the porous medium is taken as homogeneous (e.g., [26,56]). In this paper we target the problem of uncertainty quantification in the C-ED mechanism due to the medium heterogeneity, and taking into account dispersivity and chemical reaction, by considering possible stable (physically feasible) solutions on a bifurcation map, i.e., the long term evolution.…”

Section: Introductionmentioning

confidence: 99%

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Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Crevillén-García

Wilkinson

Shah

et al. 2017

Advances in Water Resources

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(2017) Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media. Advances in Water Resources, 99 . pp. 1-14. Permanent WRAP URL:http://wrap.warwick.ac.uk/85680 Copyright and reuse:The Warwick Research Archive Portal (WRAP) makes this work by researchers of the University of Warwick available open access under the following conditions. Copyright © and all moral rights to the version of the paper presented here belong to the individual author(s) and/or other copyright owners. To the extent reasonable and practicable the material made available in WRAP has been checked for eligibility before being made available.Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. A note on versions:The version presented here may differ from the published version or, version of record, if you wish to cite this item you are advised to consult the publisher's version. Please see the 'permanent WRAP url' above for details on accessing the published version and note that access may require a subscription. AbstractNumerical groundwater flow and dissolution models of physico-chemical processes in deep aquifers are usually subject to uncertainty in one or more of the model input parameters. This uncertainty is propagated through the equations and needs to be quantified and characterised in order to rely on the model outputs. In this paper we present a Gaussian process emulation method as a tool for performing uncertainty quantification in mathematical models for convection and dissolution processes in porous media. One of the advantages of this method is its ability to significantly reduce the computational cost of an uncertainty analysis, while yielding accurate results, compared to classical Monte Carlo methods. We apply the methodology to a model of convectively-enhanced dissolution processes occurring during carbon capture and storage. In this model, the Gaussian process methodology fails due to the presence of multiple branches of solutions emanating from a bifurcation point, i.e., two equilibrium states exist rather than one. To overcome this issue we use a classifier as a precursor to the Gaussian process emulation, after which we are able to successfully perform a full uncertainty analysis in the vicinity of the bifurcation point.

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“…The density of the formation water increases about 0.1 to 1%, depending on its salinity, when CO 2 is dissolved [Pruess and Zhang, 2008;Pau et al, 2010]. There are many expressions available in the literatures to compute the change of the density Yang and Gu, 2006;Farajzadeh et al, 2007;Hassanzadeh et al, 2007;Allen and Sun, 2012;Ranganathan et al, 2012]. In this work, we refer to Allen and Sun [2012] for the density change formulation (14) where is the mixture density between the formation water and the dissolved CO 2 , is the pure density of the unsaturated formation water, is the density difference between the formation water and the CO 2 -saturated formation water.…”

Section: Governing Equationsmentioning

confidence: 99%

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

2014

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Carbon dioxide (CO 2 ) sequestration in saline aquifers is considered as one of the most viable and promising ways to reduce CO 2 concentration in the atmosphere. CO 2 is injected into deep saline formations at supercritical state where its density is smaller than the hosting brine. This motivates an upward motion and eventually CO 2 is trapped beneath the cap rock. The trapped CO 2 slowly dissolves into the brine causing the density of the mixture to become larger than the host brine. This causes gravitational instabilities that is propagated and magnified with time. In this kind of density-driven flows, the CO 2 -rich brines migrate downward while the brines with low CO 2 concentration move upward. With respect to the properties of the subsurface aquifers, there are instances where saline formations can possess anisotropy with respect to their hydraulic properties. Such anisotropy can have significant effect on the onset and propagation of flow instabilities. Anisotropy is predicted to be more influential in dictating the direction of the convective flow. To account for permeability anisotropy, the method of multipoint flux approximation (MPFA) in the framework of finite differences schemes is used. The MPFA method requires more point stencil than the traditional two-point flux approximation (TPFA). For example, calculation of one flux component requires 6-point stencil and 18-point stencil in 2-D and 3-D cases, respectively. As consequence, the matrix of coefficient for obtaining the pressure fields will be quite complex. Therefore, we combine the MPFA method with the experimenting pressure field technique in which the problem is reduced to solving multitude of local problems and the global matrix of coefficients is constructed automatically, which significantly reduces the complexity. We present several numerical scenarios of density-driven flow simulation in homogeneous, layered, and heterogeneous anisotropic porous media. The numerical results emphasize the significant effects of anisotropy in driving the migration of dissolved CO 2 along the principal direction of anisotropy even if the porous medium is highly heterogeneous. Furthermore, the impacts of the increase of density difference between the brine and the CO 2 -saturated brine with respect to the onset time of convection, the CO 2 flux, and the CO 2 total dissolved mass are also discussed in this paper. Motivation and backgroundNowadays, global warming issue has become the world-widely discussed topic due to the change of climate on the Earth. One of the causes of the global warming is the greenhouse gasses emission, i.e., the release of CO 2 into the atmosphere due to the use of fossil fuels in the industry activities such as power plant, refineries, petrochemical industries, oil and gas processing, etc. The amount of CO 2 concentration in the atmosphere has steadily increased particularly in the last century, from 280 ppm (prior to the industrial revolution) to 390 ppm (at the current time) with annual increase of 1 to 2 ppm [Firoozabadi ...

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Numerical Simulation of Natural Convection in Heterogeneous Porous media for CO2 Geological Storage

Cited by 72 publications

References 41 publications

An empirical theory for gravitationally unstable flow in porous media

An empirical theory for gravitationally unstable flow in porous media

Gaussian process modelling for uncertainty quantification in convectively-enhanced dissolution processes in porous media

Density-Driven Flow Simulation in Anisotropic Porous Media: Application to CO2 Geological Sequestration

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