Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session L35: Porous Media Flows: Convection & CO2 SequestrationPorous

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Chair: Morris Flynn, University of Alberta Room: 301 
Monday, November 20, 2017 4:05PM  4:18PM 
L35.00001: Buoyant convective plumes in a layered heterogeneous porous medium Duncan Hewitt Convection in porous media, driven by either an isolated source of buoyancy or a distributed source along one boundary, can be encountered in a variety of geophysical settings, and has been widely studied in recent years because of its relevance to the longterm security of geologically sequestered CO$_2$ in saline aquifers. Such aquifers generally have a heterogeneous permeability structure, which is often dominated by thin, roughly horizontal layers of much lower permeability rock than the bulk rock. In this talk, we present simulations and theory of buoyant plumes spreading in the presence of such layers. The relative permeability and depth scale of the layer combine to give an effective impedance $\Omega$ of each layer, which, together with an effective Rayleigh number for the plume, govern its spread. If $\Omega$ is low, the plume is almost unaffected by the layer and spreads according to Wooding's [JFM;1962527544] similarity solution. For increasingly large values, the plume spreads as a `leaking' gravity current along the layer, which for sufficiently large values of $\Omega$ leaks only by diffusion across the layer. These regimes are explored in detail. The effect of a series of layers is explored, as is the extension to a line source buoyancy. [Preview Abstract] 
Monday, November 20, 2017 4:18PM  4:31PM 
L35.00002: The effect of sudden permeability changes in porous media filling box flows Morris Flynn We report on investigations of filling box flows in nonuniform porous media characterized by a sudden change in permeability. The medium consists of two layers separated by a horizontal permeability jump and is initially filled with light ambient fluid. A line source supplies dense contaminated fluid that falls toward the bottom of the domain. Two configurations are studied, i.e., a lowpermeability layer on top of a highpermeability layer and viceversa. In the former scenario, the flow dynamics are qualitatively similar to the case of a uniform porous medium. In the latter scenario, the flow dynamics are significantly different from those of the uniform porous medium case; after reaching the permeability jump, some fraction of the dense plume propagates horizontally as a pair of interfacial gravity currents. Meanwhile, the remaining fraction of the plume flows downward into the lower layer. Depending on the permeability ratio of the upper and lower layers and the source conditions, the gravity currents may become temporarily arrested after traveling some finite horizontal length. Predictions of the filling box time are made and compared against laboratory measurements. Positive agreement is typically found, especially when the lowerpermeability layer is located on top. [Preview Abstract] 
Monday, November 20, 2017 4:31PM  4:44PM 
L35.00003: Weakly nonlinear convection induced by the sequestration of CO$_2$ in a perfectly impervious geological formation Liet Vo, Layachi Hadji Linear and weakly nonlinear stability analyses are performed to investigate the dissolutiondriven convection induced by the sequestration of carbon dioxide in a perfectly impervious geological formation. We model this situation by considering a RayleighTaylor like base state consisting of carbonrich heavy brine overlying a carbonfree layer. We quantify the influence of carbon diffusion anisotropy, permeability dependence on depth and the presence of a first order chemical reaction between the carbonrich brine and host mineralogy on the threshold instability conditions and associated flow patterns. The weakly nonlinear analysis is performed using long wavelength asymptotics valid for small Damk\"{o}hler numbers. We derive analytical expressions for the solute flux at the interface. We delineate necessary conditions for the onset of the fingering pattern that is observed in laboratory and numerical experiments when the constant flux regime is reached. Using the derived interface flux conditions, we put forth differential equations for the time evolution and deformation of the interface as it migrates upward while the carbon dioxide is dissolving into the ambient brine. We solve for the terminal time when the interface reaches the top boundary and the shutdown regime begins. [Preview Abstract] 
Monday, November 20, 2017 4:44PM  4:57PM 
L35.00004: Effect of dispersion on convective mixing in porous media Baole Wen, Marc Hesse We investigate the effect of dispersion on convection in porous media by performing direct numerical simulations (DNS) in a 2D RayleighDarcy domain. Scaling analysis of the governing equations shows that the dynamics of this system is not only controlled by the classical RayleighDarcy number based on molecular diffusion, $Ra_m$, and the domain aspect ratio, but also controlled by two other dimensionless parameters: the dispersive Rayleigh number $Ra_d = H/\alpha_t$ and the dispersivity ratio $r = \alpha_l/\alpha_t$, where $H$ is the domain height, $\alpha_t$ and $\alpha_l$ are the transverse and longitudinal dispersivities, respectively. For $Ra_m \ll Ra_d$, the effect of dispersion on convection is negligible; for $Ra_m \gg Ra_d$, however, the flow pattern is determined by $Ra_d$ while the mass transport flux $F\sim Ra_m$ at high$Ra_m$ regime. Our DNS results also show that the increase of the mechanical dispersion (i.e. decreasing $Ra_d$) will broaden the plume spacing and coarsen the convective pattern. Moreover, for $r \gg 1$ the anisotropy of dispersion destroys the slender columnar structure of the primary plumes at large $Ra_m$ and therefore reduces the mass transport rate. [Preview Abstract] 
Monday, November 20, 2017 4:57PM  5:10PM 
L35.00005: ABSTRACT WITHDRAWN 
Monday, November 20, 2017 5:10PM  5:23PM 
L35.00006: NonBoussinesq DissolutionDriven Convection and Pattern Formation in Confined Porous Media Mohammad Amin Amooie, Mohammad Reza Soltanian, Joachim Moortgat Geological carbon dioxide (CO2) sequestration in saline aquifers has been recognized as a technology to stabilize the atmospheric carbon concentrations. Solubility trapping as one of the storage mechanisms is associated with diffusiondriven slow dissolution of gaseous CO2 into the aqueous phase, followed by fast densitydriven convective mixing of CO2. We study the fluid dynamics of CO2 convection in the underlying single aqueousphase region. Two modeling approaches are presented: (i) constantconcentration condition for CO2 in aqueous phase at the top boundary, and (ii) sufficiently low, constant injectionrate for CO2 from top boundary. The latter allows for evolution of CO2 composition against the rate at which the dissolved CO2 convects. We model the full nonlinear phase behavior of brineCO2 mixture in a confined domain altered by dissolution and compressibility, while relaxing the common Boussinesq approximation. We discover new flow regimes and present quantitative scaling relations for global characters of spreading, mixing, and dissolution flux in two and threedimensional media. Our findings confirm the sublinear SherwoodRayleigh scaling for the constantconcentration case, while reconciling the classical linear scaling for the constantinjection model problem. [Preview Abstract] 
Monday, November 20, 2017 5:23PM  5:36PM 
L35.00007: Experimental characterization of 3dimensional gravitydriven fingering in a porous medium MarieJulie Dalbe, Ruben Juanes When water infiltrates a dry porous media, a gravitydriven instability can be observed. Water will penetrate the porous media along preferential paths, called fingers. This gravitydriven unstable multiphase flow has important implications for natural phenomena such as rainwater infiltration in soil and secondary oil migration in reservoir rocks. While several experimental and numerical studies have described the instability in 2dimensional (2D) settings, fundamental questions remain on the morphodynamics of gravity fingering in 3D. We developed a 3D experimental setup based on planar laserinduced fluorescence of indexmatched fluids that allows us to image this phenomenon dynamically. We study the impact of some crucial parameters such as rainfall rate or grain size on the finger size and velocity. In addition, experiments in stratified media reveal interesting dynamics of finger flow across material interfaces, an essential aspect towards the understanding of water infiltration in soils. [Preview Abstract] 
Monday, November 20, 2017 5:36PM  5:49PM 
L35.00008: RayleighTaylor convection in confined porous media Francesco Zonta, Marco De Paoli, Alfredo Soldati Motivated by the dissolution phenomena occurring during carbon sequestration processes, we analyze RayleighTaylor convection in isotropic porous media. In the RayleighTaylor configuration, a layer of dense fluid (CO2+brine) lyes on top of a layer of light fluid (brine). The velocity field is computed with the Darcy law, whereas the concentration field is determined by the advectiondiffusion equation. We used a pseudospectral scheme (Fourier discretization in periodic direction and Chebyshev polynomial in wallnormal direction) to run Direct Numerical Simulations (DNS) of the present system. We focused in particular on the behavior of the mixing length $h$ (the tiptorear finger distance), a fundamental quantity to characterize all the transfer phenomena (solute, convection and energy) occurring in the analyzed case. In particular, we observed that the time behavior of $h$ is twofold: during the initial transient evolution, $h$ has a self similar universal behavior; later, due to the presence of boundaries, the behavior becomes more complex and hard to predict. Physical implications of the present results on dissolution modeling approaches will be also addressed. [Preview Abstract] 
Monday, November 20, 2017 5:49PM  6:02PM 
L35.00009: Threedimensional RayleighTaylor convection of miscible fluids in a porous medium. Tetsuya Suekane, Yuji Nakanishi, Lei Wang Natural convection of miscible fluids in a porous medium is relevant for fields, such as geoscience and geoengineering, and for the geological storage of CO2. In this study, we use Xray computer tomography to visualize 3D fingering structures associated with the RayleighTaylor instability between miscible fluids in a porous medium. In the early stages of the onset of the RayleighTaylor instability, a fine crinkling pattern gradually appears at the interface. As the wavelength and amplitude increase, descending fingers form on the interface and extend vertically downward; moreover, ascending and highly symmetric fingers form. The adjacent fingers are cylindrical in shape and coalesce to form large fingers. Fingers appearing on the interface tend to become finer with increasing Rayleigh number, which is consistent with linear perturbation theory. If the Péclet number exceeds 10, the transverse dispersion increases the finger diameter and enhances finger coalescence, strongly impacting the decay in finger number density. When mechanical dispersion is negligible, the fingerextension velocity, the masstransfer rate, and the onset time scale with Rayleigh number. Mechanical dispersion not only reduces the onset time but also enhances mass transport, which indicates that mechanical dispersion influences the longterm dissolution process of CO2 injected into aquifers. [Preview Abstract] 
Monday, November 20, 2017 6:02PM  6:15PM 
L35.00010: RayleighTaylor convection of immiscible fluids in threedimensional porous media Vlad Giurgiu, Marco De Paoli, Francesco Zonta, Alfredo Soldati The RayleighTaylor instability of two immiscible fluids is studied by means of a PhaseField Method (PFM). With this description, the fluidfluid interface is modeled as a thin transition layer where all the thermophysical properties vary rapidly but without discontinuities. This is achieved by introducing a phase indicator that is uniform in the bulk phases and varies across the thin separation interface between the two phases. This provides the accurate description of the interfacial dynamics, which is required to improve the current physical modeling of the transfer mechanisms between the two fluids in the present situation (not yet available). The fluid velocity is determined by the Darcy law, where the surface tension effects are also accounted for, whereas the concentration field is determined by the CahnHilliard equation. Current results obtained in the 3D configuration are also compared with results obtained in the 2D case to highlight the possible modifications of the flow topology coming from the coupled interaction between surface tension and gravity effects in a 3D environment. [Preview Abstract] 
Monday, November 20, 2017 6:15PM  6:28PM 
L35.00011: A phasefield method to analyze the dynamics of immiscible fluids in porous media Marco De Paoli, Alessio Roccon, Francesco Zonta, Alfredo Soldati Liquid carbon dioxide (CO2) injected into geological formations (filled with brine) is not completely soluble in the surrounding fluid. For this reason, complex transport phenomena may occur across the interface that separates the two phases (CO2+brine and brine). Inspired by this geophysical instance, we used a PhaseField Method (PFM) to describe the dynamics of two immiscible fluids in satured porous media. The basic idea of the PFM is to introduce an order parameter ($\phi$) that varies continuously across the interfacial layer between the phases and is uniform in the bulk. The equation that describes the distribution of $\phi$ is the CahnHilliard (CH) equation, which is coupled with the Darcy equation (to evaluate fluid velocity) through the buoyancy and Korteweg stress terms. The governing equations are solved through a pseudospectral technique (FourierChebyshev). Our results show that the value of the surface tension between the two phases strongly influences the initial and the long term dynamics of the system. We believe that the proposed numerical approach, which grants an accurate evaluation of the interfacial fluxes of momentum/energy/species, is attractive to describe the transfer mechanism and the overall dynamics of immiscible and partially miscible phases. [Preview Abstract] 
Monday, November 20, 2017 6:28PM  6:41PM 
L35.00012: Machine learning approach for predicting the effect of CO$_{\mathrm{2}}$ solubility on dissolution rate of calcite Mohammad Nomeli A machine learningassisted model is developed to predict the dissolution rate of calcite in saline solutions that are imbibed with dissolved CO$_{\mathrm{2}}$ over a broad range of both subcritical and supercritical conditions. This study focuses on determining the rate of calcite dissolution within a temperature range of 50100 C and pressures up to 600 bar, relevant for CO$_{\mathrm{2}}$ sequestration in saline aquifers. A general reaction kinetic model is used that is based on the extension of the standard Arrhenius equation with an added, solubility dependent, pH term to account for the saturated concentration of dissolved CO$_{\mathrm{2}}$. The kinetic model helps to obtain a predictive rate equation using machine learning methods to determine the dissolution of calcite as a function of temperature, pressure and salinity. The new rate equation helps us obtain good agreement with experimental data, and it is applied to study the geochemically induced alterations of fracture geometry due to calcite dissolution. [Preview Abstract] 
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