Abstract
This contribution presents a strategy for programming mechanics simulations including particle methods on multi-core shared memory machines.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Tiab, D., Donaldson, E.C., Petrophysics: Theory and Practice of Measuring Reservoir Rock and Fluid Transport Properties, 2nd ed., Elsevier, San Diego, CA, 2003.
Johnson, E.F., Bossler, D.P., Naumann, V.O., Calculation of relative permeability from displacement experiments, petroleum transactions. AIME 216:370–372.8, 1959.
Taber, J.J., Dynamic and static forces required to remove a discontinuous oil phase from porous media containing both oil and water. SPE Journal 9:3–12, 1969.
Jones, S.C., Roszelle, W.O., Graphical techniques for determining relative permeability from displacement experiments. Journal of Petroleum Technology 30:807–817, 1978.
Kerig, P.D., Watson, A.T., Relative-permeability estimation from displacement experiments: An error analysis. SPE Reservoir Engineering 1:175–182, 1986.
Teige, G.M.G., Hermanrud, C., Thomas, W.H., Wilson, O.B., Nordgard Bolas, H.M., Capillary resistance and trapping of hydrocarbons: A laboratory experiment. Petroleum Geoscience 11:125–129, 2005.
Roberts, J.N., Schwartz, L.M., Grain consolidation and electrical conductivity in porous media. Physical Review B 31:5990–5997, 1985.
Schwartz, L.M.,Martys, N., Bentz, D.P., Garboczi, E.J., Torquato, S., Cross-property relations and permeability estimation in model porous media. Physical Review E 48:4584–4591, 1993.
Adler, P.M., Jacquin, C.G., Quiblier, J.A., Flow in simulated porous media. International Journal of Multiphase Flow 16:691–712, 1990.
Adler, P.M., Jacquin, C.G., Thovert, J.F., The formation factor of reconstructed porous media. Water Resources Research 28:1571–1576, 1992.
Hazlett, R.D., Statistical characterization and stochastic modeling of pore networks in relation to fluid flow. Mathematical Geology 29:801–822, 1997.
Yeong, C.L.Y., Torquato, S., Reconstructing random media. Physical Review E 57:495–506, 1998.
Yeong, C.L.Y., Torquato, S., Reconstructing random media. II. Three-dimensional media from two-dimensional cuts. Physical Review E 58:224–233, 1998.
Flannery, B.P., Deckman, H.W., Roberge, W.G., D’Amico, K.L., Three-dimensional x-ray microtomography. Science 237:1439–1444, 1987.
Dunsmuir, J.H., Ferguson, S.R., D’Amico, K.L., Stokes, J.P., X-ray microtomography: A new tool for the characterization of porous media. In: Proceedings of the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, pp. 22860-MS, 1991.
Spanne, P., Thovert, J.F., Jacquin, C.J., Lindquist, W.B., Jones, K.W., Adler, P.M., Synchrotron computed microtomography of porous media: Topology and transports. Physical Review Letters 73:2001–2004, 1994.
Coles, M.E., Hazlett, R.D., Spanne, P., Soll, W.E., Muegge, E.L., Jones, K.W., Pore level imaging of fluid transport using synchrotron x-ray microtomography. Journal of Petroleum Science and Engineering 19:55–63, 1998.
Schwartz, L.M., Auzerais, F., Dunsmuir, J., Martys, N., Bentz, D.P., Torquato, S., Transport and diffusion in three-dimensional composite media. Physics A 207:28–36, 1994.
Arns, C.H., Sheppard, A.P., Sok, R.M., Knackstedt, M.A., NMR petrophysical predictions on digitized core images. In: SPWLA 46th Annual Logging Symposium, Society of Petrophysicists and Well Log Analysts, p. MMM, 2005.
Arns, C.H., Sheppard, A.P., Saadatfar, M., Knackstedt, M.A., Prediction of permeability from NMR response: Surface relaxivity heterogeneity. In: SPWLA 47th Annual Logging Symposium, Society of Petrophysicists and Well Log Analysts, p. GG, 2006.
Auzerais, F.M., Dunsmuir, J., Ferréol, B.B., Martys, N., Olson, J., Ramakrishnan, T.S., Rothman, D.H., Schwartz, L.M., Transport in sandstone: A study based on three dimensional microtomography. Geophysical Research Letters 23:705–708, 1996.
Ryu, S., Zhao, W., Leu, G., Singer, P.M., Cho, H.J., Keehm, Y., Numerical modeling of complex porous media for borehole applications. ArXiv e-prints. [Online] Available: http://adsabs.harvard.edu/abs/2009arXiv0908.1962R, 2009.
Zhan, X., Schwartz, L., Morgan, D., Smith, W., Toksöz, N., Numerical modeling of transport properties and comparison to laboratory measurements. Technical Report, Massachusetts Institute of Technology. [Online] Available: http://www-eaps.mit.edu/erl/Zhan_2008_final.pdf, 2008.
Arns, C.H., Knackstedt, M.A., Pinczewski,W.V., Garboczi, E.J., Computation of linear elastic properties from microtomographic images: Methodology and agreement between theory and experiment Geophysics 67:1396–1405, 2002.
Knackstedt, M.A., Arns, C.H., Sok, R.M., Sheppard, A.P., 3D pore scale characterization of carbonate core: Relating pore types and interconnectivity to petrophysical and multiphase flow properties. In: International Petroleum Technology Conference, pp. 11775-MS.
Knackstedt, M.A., Arns, C.H., Sheppard, A.P., Senden, T.J., Sok, R.M., Cinar, Y., Pinczewski, W.V., Ioannidis, M., Padhy, G.S., Archie’s exponents in complex lithologies derived from 3D digital core analysis. In: SPWLA 48th Annual Logging Symposium, Society of Petrophysicists and Well Log Analysts, p. UU, 2007.
Zhao,W., Picard, G., Leu, G., Singer, P.M., Characterization of single-phase flow through carbonate rocks: Quantitative comparison of NMR flow propagator measurements with a realistic pore network model. Transport in Porous Media 81:305–315, 2010.
Blunt, M.J., Jackson, M.D., Piri, M., Valvatne, P.H., Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow. Advances in Water Resources 25:1069–1089, 2002.
Sok, R.M., Arns, C.H., Knackstedt, M.A., Senden, T.J., Sheppard, A.P., Averdunk, H., Pinczewski, W.V., Okabe, H., Estimation of petrophysical parameters from 3D images of carbonate core. In: SPWLA Middle East Regional Symposium, Society of Petrophysicists and Well Log Analysts, 2007.
Ferréol, B., Rothman, D.H., Lattice-Boltzmann simulations of flow through Fontainebleau sandstone. Transport in Porous Media 20:3–20, 1995.
Kameda, A., Dvorkin, J., Keehm, Y., Nur, A., Bosl,W., Permeability-porosity transforms from small sandstone fragments. Geophysics 71:N11–N19, 2006.
Hazlett, R.D., Coles, M.E., Jones, K.W., Andrews, B., Dowd, B., Siddons, P., Peskin, A., Developments in synchrotron X-ray microtomography for application to flow in porous media. In: Proceedings of the 1996 Annual Technical Conference of the Society of Core Analysists, p. 9630, 1996.
Hazlett, R.D., Chen, S.Y., Soll,W.E.,Wettability and rate effects on immiscible displacement: Lattice Boltzmann simulation in microtomographic images of reservoir rocks. Journal of Petroleum Science and Engineering 20:167–175, 1998.
Chen, S., Doolen, G.D., Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics 30:329–364, 1998.
Zheng, H.W., Shu, C., Chew, Y.T., A lattice Boltzmann model for multiphase flows with large density ratio. Journal of Computational Physics 218:353–371, 2006.
Huang, J.J., Shu, C., Chew, Y.T., Lattice Boltzmann study of droplet motion inside a grooved channel. Physics of Fluids 21:022103, 2009.
Lucy, L.B., A numerical approach to the testing of the fusion hypothesis. Astronomical Journal 82:1013–1024, 1977.
Gingold, R.A., Monaghan, J.J., Smoothed particle hydrodynamics: Theory and application to non-spherical stars. Monthly Notices of the Royal Astronomical Society 181:375–389, 1977.
Monaghan, J.J., Smoothed particle hydrodynamics. Annual Review of Astronomy and Astrophysics 30:543–574, 1992.
Hoover, W.G., Isomorphism linking smooth particles and embedded atoms. Physica A 260:244–254, doi: 10.1016/S0378-4371(98)00357-4, 1998.
Morris, J.P., Fox, P.J., Zhu, Y., Modeling low Reynolds number incompressible flows using SPH. Journal of Computational Physics 136:214–226, doi: 10.1006/jcph.1997.5776, 1997.
Monaghan, J.J., Smoothed particle hydrodynamics. Reports on Progress in Physics 68:1703–1759, 2005.
Tartakovsky, A.M., Meakin, P., Pore scale modeling of immiscible and miscible fluid flows using smoothed particle hydrodynamics. Advances in Water Resources 29:1464–1478, 2006.
Liu, G.R., Liu, M.B., Smoothed Particle Hydrodynamics: A Meshfree Particle Method, World Scientific, Singapore, 2007.
Bui, H.H., Fukagawa, R., Sako, K., Ohno, S., Lagrangian meshfree particles method (SPH) for large deformation and failure flows of geomaterial using elastic-plastic soil constitutive model. International Journal for Numerical and Analytical Methods in Geomechanics 32:1537–1570, 2008.
Randles, P.W., Libersky, L.D., Smoothed particle hydrodynamics: Some recent improvements and applications. Computer Methods in Applied Mechanics and Engineering 139:375–408, 1996.
Liu, M., Meakin, P., Huang, H., Dissipative particle dynamics simulation of pore-scale multiphase fluid flow. Water Resources Research 43:W04411, 2007.
Liu, M., Meakin, P., Huang, H., Dissipative particle dynamics simulations of multiphase fluid flow in microchannels and microchannel networks. Physics of Fluids 19:033302, 2007.
Tartakovsky, A.M., Meakin, P., Simulation of unsaturated flow in complex fractures using smoothed particle hydrodynamics. Vandose Zone Journal 4:848–855, 2005.
Tartakovsky, A.M.,Meakin, P.,Modeling of surface tension and contact angles with smoothed particle hydrodynamics. Physical Review E 72:1–9, 2005.
Hu, X.Y., Adams, N.A., A multi-phase SPH method for macroscopic and mesoscopic flowsl. Journal of Computational Physics 213:844–861, 2006.
Tartakovsky, A.M., Meakin, P., Ward, A.L., Smoothed particle hydrodynamics model of nonaqueous phase liquid flow and dissolution. Transport in Porous Media 76:11–34, 2009.
Tartakovsky, A.M., Meakin, P., A smoothed particle hydrodynamics model for miscible flow in three-dimensional fractures and the two-dimensional Rayleigh–Taylor instability. Journal of Computational Physics 207:610–624, 2005.
Tartakovsky, A.M.,Meakin, P., Scheibe, T.D.,West, R.M.E., Simulations of reactive transport and precipitation with smoothed particle hydrodynamics. Journal of Computational Physics 222:654–672, 2007.
Monaghan, J.J., Kocharyan, A., SPH simulations of multi-phase flow. Computer Physics Communications 87:225–235, 1995.
Cleary, P.W., Modelling confined multi-material heat and mass flows using SPH. Applied Mathematical Modelling 22:981–993, 1999.
Jiang, F., Sousa, A.C.M., SPH numerical modeling for ballistic-diffusive heat conduction. Numerical Heat Transfer, Part B. Fundamentals 50:499–515, 2006.
Rook, R., Yildiz, M., Dost, S., Modeling transient heat transfer using SPH and implicit time integration, Numerical Heat Transfer, Part B. Fundamentals 51:1–23, 2007.
Price, D.J., Modelling discontinuities and Kelvin–Helmholtz instabilities in SPH. Journal of Computational Physics 227:10040–10057, 2008.
Dolag, K., Bartelmann, M., Lesch, H., SPH simulations of magnetic fields in galaxy clusters. Astronomy and Astrophysics 348:351–363, 1999.
Borve, S., Omang, M., Trulsen, J., Regularized smoothed particle hydrodynamics: A new approach to simulating magneto-hydrodynamic shocks. The Astrophysical Journal 561:82–93, 2001.
Holmes, D.W.,Williams, J.R., Tilke, P., An events based algorithm for distributing concurrent tasks on multi-core architectures. Computer Physics Communications 181:341–354, 2010.
Gropp, W., Lusk, E., Skjellum, A., Using MPI: Portable Parallel Programming with the Message-Passing Interface, MIT Press, Cambridge, 1999.
Eadline, D., MPI on multicore, an OpenMP alternative? Linux Magazine. [Online] Available: http://www.linux-mag.com/id/4608, 2007.
Leiserson, C.E., Mirman, I.B., How to Survive the Multicore Software Revolution (or at Least Survive the Hype), Cilk Arts, Cambridge, 2008.
Strikwerda, J.C., Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole, Pacific Grove, CA, 1989.
Chen, S., Doolen, G.D., Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics 30:329–364, 1998.
Zienkiewicz, O.C., Taylor, R.L, The Finite Element Method, 4th ed., McGraw-Hill, London, 1991.
Liu, H., Shi, P., Meshfree particle method. In: Proceedings of the Ninth IEEE International Conference on Computer Vision (ICCV’03), Vol. 1, IEEE Computer Society, Los Alamitos, CA, USA, pp. 289–296, 2003.
Koplik, J., Banavar, J.R., Willemsen, J.F., Molecular dynamics of fluid flow at solid surfaces, Physics of Fluids A. Fluid Dynamics 1:781–794, 1989.
Cundall, P.A., Strack, O.D.L., A discrete numerical model for granular assemblies. Geotechnique 29:47–65, 1979.
Williams, J.R., O’Connor, R., Discrete element simulation and the contact problem. Archives of Computational Methods in Engineering 6(4):279–304, 1999.
Williams, J.R., Perkins, E., Cook, B.K., A contact algorithm for partitioning N arbitrary sized objects, International Journal of Computer Aided Methods in Engineering – Engineering Computations 21(2–4):235–248, 2004.
Keaveny, E.E., Pivkin, I.V., Maxey, M., Karniadakis, G.E., A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows. The Journal of Chemical Physics 123:104107, 2005.
Hasimoto, H., On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. Journal of Fluid Mechanics 5(2):317–328, doi: 10.1017/S0022112059000222, 1959.
Zick, A.A., Homsy, G.M., Stokes flow through periodic arrays of spheres. Journal of Fluid Mechanics 115:13–26, doi: 10.1017/S0022112082000627, 1982.
Sangani, A.S., Acrivos, A., Slow flow through a periodic arrays of spheres. International Journal of Multiphase Flow 8(4):343–360, doi: 10.1016/0301-9322(82)90047-7, 1982.
Larson, R.E., Higdon, J.J.L., A periodic grain consolidation model of porous media. Physics of Fluids A 1(1):38–46, doi: 10.1063/1.857545, 1989.
Schwartz, L.M.,Martys, N., Bentz, D.P., Garboczi, E.J., Torquato, S., Cross-property relations and permeability estimation inmodel porous media. Physical Review E 48(6):4584–4591, doi: 10.1103/PhysRevE.48.4584, 1993.
Holmes, D.W., Williams, J.R., Tilke, P., Smooth particle hydrodynamics simulations of low Reynolds number flows through porous media. International Journal for Numerical and Analytical Methods in Geomechanics, 2010.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Williams, J.R., Holmes, D., Tilke, P. (2011). Parallel Computation Particle Methods for Multi-Phase Fluid Flow with Application Oil Reservoir Characterization. In: Oñate, E., Owen, R. (eds) Particle-Based Methods. Computational Methods in Applied Sciences, vol 25. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0735-1_4
Download citation
DOI: https://doi.org/10.1007/978-94-007-0735-1_4
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-0734-4
Online ISBN: 978-94-007-0735-1
eBook Packages: EngineeringEngineering (R0)