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    Lattice Boltzmann flow simulations with applications of reduced order modeling techniques

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    Type
    Conference Paper
    Authors
    Brown, Donald
    Li, Jun
    Calo, Victor M. cc
    Ghommem, Mehdi
    Efendiev, Yalchin R. cc
    KAUST Department
    Applied Mathematics and Computational Science Program
    Biological and Environmental Sciences and Engineering (BESE) Division
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Earth Science and Engineering Program
    Environmental Science and Engineering Program
    Numerical Porous Media SRI Center (NumPor)
    Physical Science and Engineering (PSE) Division
    Date
    2014-01-19
    Online Publication Date
    2014-01-19
    Print Publication Date
    2014
    Permanent link to this record
    http://hdl.handle.net/10754/564846
    
    Metadata
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    Abstract
    With the recent interest in shale gas, an understanding of the flow mechanisms at the pore scale and beyond is necessary, which has attracted a lot of interest from both industry and academia. One of the suggested algorithms to help understand flow in such reservoirs is the Lattice Boltzmann Method (LBM). The primary advantage of LBM is its ability to approximate complicated geometries with simple algorithmic modificatoins. In this work, we use LBM to simulate the flow in a porous medium. More specifically, we use LBM to simulate a Brinkman type flow. The Brinkman law allows us to integrate fast free-flow and slow-flow porous regions. However, due to the many scales involved and complex heterogeneities of the rock microstructure, the simulation times can be long, even with the speed advantage of using an explicit time stepping method. The problem is two-fold, the computational grid must be able to resolve all scales and the calculation requires a steady state solution implying a large number of timesteps. To help reduce the computational complexity and total simulation times, we use model reduction techniques to reduce the dimension of the system. In this approach, we are able to describe the dynamics of the flow by using a lower dimensional subspace. In this work, we utilize the Proper Orthogonal Decomposition (POD) technique, to compute the dominant modes of the flow and project the solution onto them (a lower dimensional subspace) to arrive at an approximation of the full system at a lowered computational cost. We present a few proof-of-concept examples of the flow field and the corresponding reduced model flow field.
    Citation
    Brown, D. L., Li, J., Calo, V. M., Ghommem, M., & Efendiev, Y. (2014). Lattice Boltzmann Flow Simulations With Applications of Reduced Order Modeling Techniques. International Petroleum Technology Conference. doi:10.2523/17457-ms
    Publisher
    Society of Petroleum Engineers (SPE)
    Journal
    International Petroleum Technology Conference
    Conference/Event name
    International Petroleum Technology Conference 2014: Unlocking Energy Through Innovation, Technology and Capability, IPTC 2014
    DOI
    10.2523/17457-ms
    ae974a485f413a2113503eed53cd6c53
    10.2523/17457-ms
    Scopus Count
    Collections
    Conference Papers; Biological and Environmental Science and Engineering (BESE) Division; Environmental Science and Engineering Program; Applied Mathematics and Computational Science Program; Physical Science and Engineering (PSE) Division; Earth Science and Engineering Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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