A Lagrangian, stochastic modeling framework for multi-phase flow in porous media

Journal of Computational Physics

Volumn 227, Issue 13, 2008, Pages 6696-6714

  Tyagi, Manav ^a   Jenny, Patrick ^a   Lunati, Ivan ^b   Tchelepi, Hamdi A ^c  

^a ETH ZURICH   (Switzerland)

^b Laboratory of Environmental Fluid Mechanics   (Switzerland)

^c STANFORD UNIVERSITY   (United States)

Author keywords

Lagrangian approach; Multi phase flow; PDF method; Porous media; Stochastic particle method

Indexed keywords

FINITE VOLUME METHOD; FLOW OF FLUIDS; LAGRANGE MULTIPLIERS; RANDOM PROCESSES; STOCHASTIC MODELS; STOCHASTIC SYSTEMS;

FLOWS IN POROUS MEDIA; FLUID PHASIS; FLUID-PHASE; LAGRANGIAN APPROACHES; LAGRANGIAN STATISTICS; MULTI-PHASE FLOWS; PDF METHODS; POROUS MEDIUM; STOCHASTIC PARTICLE METHODS; STOCHASTICS;

POROUS MATERIALS;

EID: 44149102616     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.03.030     Document Type: Article

References (31)

1. M. Muskat Physical Principles of Oil Production 1949 McGraw-Hill London
2. M. Blunt M.J. King H. Scher Simulation and theory of 2-phase flow in porous media Physical Review A 46 1992 7680 7699
3. R. Lenormand E. Touboul C. Zarcone Numerical-models and experiments on immiscible displacement in porous-media Journal of Fluid Mechanics 189 1988 165 187
4. R. Hilfer P.E. Oren Dimensional analysis of pore scale and field scale immiscible displacement Transport in Porous Media 22 1996 53 72
5. S.W. Ahlstrom, H.P. Foote, R.C. Arnett, C.R. Cole, R.J. Serne, Multi-component mass transport model: theory and numerical implementation, Report. BNWL-2127, 1977.
6. T.A. Prickett, T.G. Naymik, C.G. Longquist, A random walk solute transport model for selected groundwater quality evaluations, Report. I-11, 1981.
7. W. Kinzelbach Numerische Methoden zur Modellierung des Transports von Schadstoffen im Grundwasser 1992 Oldenbourg Verlag
8. A.F.B. Tompson L.W. Gelhar Numerical simulation of solute transport in three-dimensional, randomly heterogenous porous media Advances in Water Resources 26 1990 2541 2562
9. D. Zhang L. Li H.A. Tchelepi Stochastic formulation for uncertainty analysis of two-phase flow in heterogeneous reservoirs SPE Journal 5 2000 60 70
10. D.W. Pollock Semianalytical computation of path lines for finite difference models Groundwater 26 1988 743 750
11. D.J. Goode Particle velocity interpolation in block-centered finite difference groundwater flow models Water Resources Research 26 1990 925 940
12. M.A. Celia T.F. Russell I. Herera R.E. Ewing An Eulerian–Lagrangian localized adjoint method for the advection–diffusion equation Advances in Water Resources 13 1990 187 206
13. L.F. Konikov, D.J. Goode, G.Z. Hornberger, A three-dimensional method of characteristics solute transport model (moc3d), Water Resources Investigation Report 96–4267, 1996.
14. T.F. Russel M.A. Celia An overview of research on Eulerian–Lagrangian localized adjoint methods (ELLAM) Advances in Water Resources 25 2002 1215 1231
15. H.K. Dahle M.S. Espendal R.E. Ewing O. Sævaried Characteristic adaptive subdomain methods for reservoir flow problems Numerical Methods for Partial Differential Equations 6 1990 279 309
16. H.K. Dahle R.E. Ewing T.F. Russell Eulerian–Lagrangian localized adjoint methods for a nonlinear advection–diffusion equation Computer Methods in Applied Mechanics and Engineering 122 1995 223 250
17. T.A. Hewett T. Yamada Theory for the semi-analytic calculation of oil recovery and effective relative permeabilities using streamtubes Advances in Water Resources 20 1997 279 292
18. J. Herzer W. Kizelbach Coupling of transport and chemical processes in numerical transport models Geoderma 44 1989 115 127
19. A. Abulaban J.L. Nieber D. Misra Modeling plume behavior for nonlinearly sorbing solutes in saturated homogeneous porous media Advances in Water Resources 21 1998 487 498
20. F. Delay Ph. Ackerer C. Danquigny Simulating solute transport in porous media or fractured formations using random walk particle tracking: a review Vadose Zone Journal 4 2005 360 379
21. A.C. Bagtzoglou A.F.B. Tompson D.E. Dougherty Projection functions for particle-grid methods Numerical Methods for Partial Differential Equations 8 1992 325 340
22. M.R. Thiele, R.P. Batycky, M.J. Blunt, A streamline-based field-scale compositional reservoir simulator, in: SPE Annual Technical Conference and Exhibition, San Antonio, TX, October 5–8, 1997, SPE 38889.
23. G. Dagan V. Cvetkovic Reactive transport and immiscible flow in geological media. I. General theory Proceeding of Royal Society London A 452 1996 285 301
24. V. Cvetkovic G. Dagan Reactive transport and immiscible flow in geological media. II. Applications Proceeding of Royal Society London A 452 1996 303 328
25. M.R. Thiele, H.A. Tchelepi, F.M. Orr, On particle tracking in multi-phase, multi-component flow, Unpublished work, 1992.
26. S.B. Pope Pdf methods for turbulent reactive flows Progress in Energy and Combustion Science 11 1985 119 192
27. P.E. Kloeden E. Platen Numerical Solution of Stochastic Differential Equations 1999 Springer
28. B. Rembold P. Jenny A multiblock joint PDF finite-volume hybrid algorithm for the computation of turbulent flows in complex geometries Journal of Computational Physics 220 2006 59 87
29. B.P. Leonard A stable and accurate convective modeling procedure based on quadratic upstream interpolation Computer Methods in Applied Mechanics and Engineering 19 1979 59 98
30. J. Xu S.B. Pope Assessment of numerical accuracy of PDF/Monte Carlo methods for turbulent reacting flows Journal of Computational Physics 152 1999 192 230
31. Q. Zhang K. Ichiki A. Prosperetti On the computation of ensemble of average for spatially non-uniform particle system Journal of Computational Physics 212 2006 247 267