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    A new lattice Boltzmann equation to simulate density-driven convection of carbon dioxide

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    Type
    Conference Paper
    Authors
    Allen, Rebecca
    Reis, Tim
    Sun, Shuyu cc
    KAUST Department
    Computational Transport Phenomena Lab
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Physical Science and Engineering (PSE) Division
    Date
    2013-02-18
    Online Publication Date
    2013-02-18
    Print Publication Date
    2013
    Permanent link to this record
    http://hdl.handle.net/10754/564659
    
    Metadata
    Show full item record
    Abstract
    The storage of CO2 in fluid-filled geological formations has been carried out for more than a decade in locations around the world. After CO2 has been injected into the aquifer and has moved laterally under the aquifer's cap-rock, density-driven convection becomes an important transport process to model. However, the challenge lies in simulating this transport process accurately with high spatial resolution and low CPU cost. This issue can be addressed by using the lattice Boltzmann equation (LBE) to formulate a model for a similar scenario when a solute diffuses into a fluid and density differences lead to convective mixing. The LBE is a promising alternative to the traditional methods of computational fluid dynamics. Rather than discretizing the system of partial differential equations of classical continuum mechanics directly, the LBE is derived from a velocity-space truncation of the Boltzmann equation of classical kinetic theory. We propose an extension to the LBE, which can accurately predict the transport of dissolved CO2 in water, as a step towards fluid-filled porous media simulations. This is achieved by coupling two LBEs, one for the fluid flow and one for the convection and diffusion of CO2. Unlike existing lattice Boltzmann equations for porous media flow, our model is derived from a system of moment equations and a Crank-Nicolson discretization of the velocity-truncated Boltzmann equation. The forcing terms are updated locally without the need for additional central difference approximation. Therefore our model preserves all the computational advantages of the single-phase lattice Boltzmann equation and is formally second-order accurate in both space and time. Our new model also features a novel implementation of boundary conditions, which is simple to implement and does not suffer from the grid-dependent error that is present in the standard "bounce-back" condition. The significance of using the LBE in this work lies in the ability to efficiently simulate density-driven convection of CO2 through water. From an implementation viewpoint, the locality of our algorithm exploits massively parallel modern computer architectures, including graphics processing units (GPUs), which would lead to very fast computations that scale linearly with the number of processors.
    Citation
    Allen, R., Reis, T., & Sun, S. (2013). A New Lattice Boltzmann Equation to Simulate Density-Driven Convection of Carbon Dioxide. SPE Reservoir Simulation Symposium. doi:10.2118/163658-ms
    Publisher
    Society of Petroleum Engineers (SPE)
    Journal
    SPE Reservoir Simulation Symposium
    Conference/Event name
    SPE Reservoir Simulation Symposium 2013
    ISBN
    9781627480246
    DOI
    10.2118/163658-ms
    ae974a485f413a2113503eed53cd6c53
    10.2118/163658-ms
    Scopus Count
    Collections
    Conference Papers; Environmental Science and Engineering Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computational Transport Phenomena Lab

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