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Numerical Heat Transfer, Part A: Applications
An International Journal of Computation and Methodology
Volume 69, 2016 - Issue 1
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Original Articles

Adaptive mesh refinement for non-isothermal multiphase flows in heterogeneous porous media comprising different rock types with tensor permeability

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Pages 31-50 | Received 20 Jul 2014, Accepted 15 Jan 2015, Published online: 23 Sep 2015

References

  • A. Bourgeat and A. Hidani, A Result of Existence for a Model of Two-Phase Flow in a Porous Medium Made of Different Rock Types, Appl. Anal., vol. 56, pp. 381–399, 1995.
  • A. Bourgeat and A. Hidani, Effective Model of Two-Phase Flow in a Porous Medium Made of Different Rock Types, Appl. Anal., vol. 58, pp. 1–29, 1995.
  • J. Jaffré, Flux Calculation at the Interface Between Two Rock Types for Two-Phase Flow in Porous Media, Transp. Porous Media, vol. 21, pp. 195–207, 1995.
  • M. J. Berger and J. Oliger, Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, J. Comput. Phys., vol. 53, pp. 484–512, 1984.
  • M. J. Berger and P. Colella, Local Adaptive Mesh Refinement for Shock Hydrodynamics, J. Comput. Phys., vol. 82, pp. 64–84, 1989.
  • D. S. Balsara, Divergence-Free Adaptive Mesh Refinement for Magnetohydrodynamics, J. Comput. Phys., vol. 174, pp. 614–648, 2001.
  • P. A. Durbin and G. Iaccarino, An Approach to Local Refinement of Structured Grids, J. Comput. Phys., vol. 181, pp. 639–653, 2002.
  • C. Pantano, R. Deiterding, D. J. Hill, and D. I. Pullin, A Low Numerical Dissipation Patch-Based Adaptive Mesh Refinement Method for Large-Eddy Simulation of Compressible Flows, J. Comput. Phys., vol. 221, pp. 63–87, 2007.
  • R. Venuturumilli and L. D. Chen, Numerical Simulation Using Adaptive Mesh Refinement for Laminar Jet Diffusion Flames, Numer. Heat Transfer B Fundam., vol. 46, pp. 101–120, 2004.
  • H. Luo, F. Laouafa, J. Guo, and M. Quintard, Numerical Modeling of Three-Phase Dissolution of Underground Cavities Using a Diffuse Interface Model, Int. J. Numer. Anal. Methods Geomech., vol. 38, pp. 1600–1616, 2014.
  • J. M. Alam, N. K.-R. Kevlahan, O. V. Vasilyev, and Z. Hossain, A Multiresolution Model for the Simulation of Transient Heat and Mass Transfer, Numer. Heat Transfer B Fundam., vol. 61, pp. 147–170, 2012.
  • Y. Li and J. Kim, Phase-Field Simulations of Crystal Growth with Adaptive Mesh Refinement, Int. J. Heat Mass Transfer, vol. 45, pp. 7926–7932, 2012.
  • N. Provatas, N. Goldenfeld, and J. Dantzig, Adaptive Mesh Refinement Computation of Solidification Microstructures Using Dynamic Data Structures, J. Comput. Phys., vol. 148, pp. 265–290, 1999.
  • J. A. Trangenstein, Multi-Scale Iterative Techniques and Adaptive Mesh Refinement for Flow in Porous Media, Adv. Water Resour., vol. 25, pp. 1175–1213, 2002.
  • M. Gerritsen, A. Kovscek, L. Castanier, J. Nilsson, R. Younis, and B. He, Experimental Investigation and High Resolution Simulator of In-Situ Combustion Processes: 1. Simulator Design and Improved Combustion with Metallic Additives, in Proc. SPE Int. Therm. Oper. Heavy Oil Symp. West. Reg. Meeting, California, SPE Paper 86962, 2004.
  • H. Luo, X. Wang, and M. Quintard, Adaptive Mesh Refinement for One-Dimensional Three-Phase Flows in Heterogeneous Fractured Porous Media, Numer. Heat Transfer B Fundam., vol. 54, pp. 476–498, 2008.
  • M. Mamaghani, G. Enchéry, and C. Chainais-Hillairet, Development of a Refinement Criterion for Adaptive Mesh Refinement in Steam-Assisted Gravity Drainage Simulation, Comput. Geosci., vol. 15, pp. 17–34, 2011.
  • Y. Chen and L. J. Durlofsky, A Coupled Local-Global Upscaling Approach for Simulating Flow in Highly Heterogeneous Formations, Adv. Water Resour., vol. 26, pp. 1041–1060, 2003.
  • J. A. Trangenstein and Z. Bi, Large Multi-Scale Iterative Techniques and Adaptive Mesh Refinement for Miscible Displacement Simulation, in Proc. SPE/DOE Improved Oil Recovery Symp., Oklahoma, SPE Paper 75232, 2002.
  • N. H. Darman, G. E. Pickup, and K. S. Sorbie, A Comparison of Two-Phase Dynamic Upscaling Methods Based on Fluid Potentials, Comput. Geosci., vol. 6, pp. 5–27, 2002.
  • T. Arbogast, Implementation of a Locally Conservative Numerical Subgrid Upscaling Scheme for Two-Phase Darcy Flow, Comput. Geosci., vol. 6, pp. 453–481, 2002.
  • Y. Gautier and B. Noetinger, Preferential Flow-Paths Detection for Heterogeneous Reservoirs Using a New Renormalization Technique, Transp. Porous Media, vol. 6, pp. 1–23, 1997.
  • X. Wang, M. Quintard, and G. Darche, Adaptive Mesh Refinement For One-Dimensional Three-Phase Flow with Phase Change In Porous Media, Numer. Heat Transfer B Fundam., vol. 50, pp. 231–268, 2006.
  • M. G. Edwards and C. F. Rogers, A Flux Continuous Scheme for the Full Tensor Pressure Equation, in Proc. 4th Eur. Conf. Math. Oil Recovery, Norway, vol. D, pp. 15, 1994.
  • I. Aavatsmark Multipoint Flux Approximation Methods for Quadrilateral Grids, in Proc. 9th Int. Forum Reservoir Simul., Abu Dhabi, 2007.
  • I. Aavatsmark, An Introduction to Multipoint Flux Approximations for Quadrilateral Grids, Comput. Geosci., vol. 6, pp. 405–432, 2002.
  • M. G. Edwards, Unstructured, Control-Volume Distributed, Full-Tensor Finite-Volume Schemes with Flow Based Grids, Comput. Geosci., vol. 6, pp. 433–452, 2002.
  • H. A. Friis and M. G. Edwards, A Family of MPFA Finite-Volume Schemes with Full Pressure Support for the General Tensor Pressure Equation on Cell-Centered Triangular Grids, J. Comput. Phys., vol. 230, pp. 205–231, 2011.
  • I. Aavatsmark E. Reiso, H. Reme, and R. Teigland, MPFA for Faults and Local Refinements in 3D Quadrilateral Grids with Application to Field Simulations, in Proc. 2001 SPE Reservoir Simul. Symp., Houston, SPE Paper 66356, 2001.
  • I. Aavatsmark, E. Reiso, H. Reme, and R. Teigland, Control-Volume Discretization Method for Quadrilateral Grids with Faults and Local Refinements, Comput. Geosci., vol. 5, pp. 1–23, 2001.
  • R. M. Bulter, Thermal Recovery of Oil and Bitumen, chap. 5, Prentice Hall, Englewood Cliffs, NJ, 1991.
  • J. Bear, Dynamics of Fluids in Porous Media, pp. 106–107, American Elsevier, New York, 1972.
  • K. Mehrotra, A Generalized Viscosity Equation for Pure Heavy Hydrocarbons, Ind. Eng. Chem. Res., vol. 30, pp. 420–427, 1991.
  • K. Aziz, A. B. Ramesh, and P. T. Woo, Fourth SPE Comparative Solution Project: A Comparison of Steam Injection Simulations, J. Pet. Technol., vol. 39, pp. 1576–1584, 1987.

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