A parallel FE-FV scheme to solve fluid flow in complex geologic media

Computers and Geosciences

Volumn 34, Issue 12, 2008, Pages 1697-1707

  Coumou, Dim ^a   Matthäi, Stephan ^b   Geiger, Sebastian ^c   Driesner, Thomas ^a  

^a ETH ZURICH   (Switzerland)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

^c HERIOT WATT UNIVERSITY   (United Kingdom)

Author keywords

Computational geoscience; CSMP; MPI; Multi phase fluid flow; Parallel computing; Porous media

Indexed keywords

ADVECTION; CHLORINE COMPOUNDS; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; FINITE ELEMENT METHOD; FLOW OF FLUIDS; GRAPHIC METHODS; MATHEMATICAL OPERATORS; MESH GENERATION; NUMERICAL ANALYSIS; POROUS MATERIALS; TURBULENT FLOW;

APPLICATIONS.; COMPLEX SYSTEMS; COMPUTATIONAL GEOSCIENCE; COMPUTATIONAL TIME; CSMP; DOMAIN PARTITIONING; FIELD DATA; FINITE ELEMENT; FINITE ELEMENT MESHING; FINITE VOLUMES; FINITE-ELEMENT METHODS; FLUID FLOWING; GEOLOGIC MEDIA; HETEROGENEOUS POROUS MEDIUM; LINUX CLUSTERING; MATHEMATICAL COMPLEXITY; MPI; MULTI PROCESSORS; MULTI-PHASE FLUID; MULTI-PHASE FLUID FLOW; MULTI-PHYSICS CODE; NUMERICAL ACCURACY; OPERATOR-SPLITTING APPROACH; ORDERS-OF-MAGNITUDE; PARALLEL COMPUTING; PARALLEL SCHEME; PARALLELIZATION; POROUS MEDIA; PRESSURE DIFFUSION; RUN-TIME; SINGLE PROCESSORS; SPACE AND TIME; SUB-DOMAINS; TEMPORAL SCALING; TIME PERIODS;

FINITE VOLUME METHOD;

ACCURACY ASSESSMENT; ADVECTION-DIFFUSION EQUATION; CLUSTER ANALYSIS; COMPUTER SIMULATION; DATA PROCESSING; FINITE ELEMENT METHOD; FINITE VOLUME METHOD; FLUID FLOW; POROUS MEDIUM; TESTING METHOD;

EID: 38349120316     PISSN: 00983004     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cageo.2007.11.010     Document Type: Article

References (58)

1. Ashby S., Bosl W., Falgout R., Smith S., and Tompson A. A numerical simulation of groundwater flow and contaminant transport on the Cray T3D and C90 supercomputers. International Journal of High Performance Computing Applications 13 1 (1999) 80-93
2. Aziz K., and Settari A. Petroleum Reservoir Simulation (1979), Elsevier Applied Science Publisher, London, UK 476pp
3. Baliga B., and Patankar S. A new finite-element formulation for convection diffusion problems. Numerical Heat Transfer 3 (1980) 393-409
4. Barnard, S., Simon, H., 1993. A fast multilevel implementation of recursive spectral bisection for partitioning unstructured problems. In: Proceedings of the Sixth SIAM Conference on Parallel Processing for Scientific Computing, Norfolk, Virginia, USA, pp. 711-718.
5. Belayneh, M., 2003. Analysis of natural fracture networks is massive and well-bedded carbonates and the impact of these networks on fluid flow in dual porosity medium. Ph.D. Dissertation, Imperial College, London, UK.
6. Belayneh M., Geiger S., and Matthai S. Numerical simulation of water injection into layered fractured carbonate reservoir analogs. AAPG Bulletin 90 10 (2006) 1473-1493
7. Bhogeswara, R., Killough, J., 1982. Parallel linear solvers for reservoir simulation: generic approach for existing and emerging computer architectures. In: Proceedings of 12th SPE Symposium on Reservoir Simulation, New Orleans, LA, SPE, pp. 71-82.
8. Calahan, D., 1982. Vectorized direct solvers for 2-d grids. In: Proceedings of Sixth SPE Symposium on Reservoir Simulation, New Orleans, LA, SPE, pp. 489-497.
9. Coumou D., Driesner T., Geiger S., Heinrich C., and Matthai S. The dynamics of mid-ocean ridge hydrothermal systems: splitting plumes and fluctuating vent temperatures. Earth and Planetary Science Letters 245 (2006) 218-231
10. NaCl. Acta Minerarology and Petrology Abstracts, Series 2 (2003) 55-56
11. Durlofsky L. Accuracy of mixed and control volume finite element approximations to darcy velocity and related quantities. Water Resources Research 30 (1993) 965-973
12. Elmroth E., Ding C., and Wu Y. High performance computations for large scale simulations of subsurface multiphase fluid and heat flow. Journal of Supercomputing 18 (2001) 235-258
13. Faust C., and Mercer J. Geothermal reservoir simulation 2. Numerical solution techniques for liquid-dominated and vapor-dominated hydrothermal systems. Water Resources Research 15 1 (1979) 31-46
14. Fontaine F., and Wilcock W. Dynamics and storage of brine in mid-ocean ridge hydrothermal systems. Journal of Geophysical Research 111 B06102 (2006)
15. Forsyth P. A control volume finite element approach to napl groundwater contamination. SIAM Journal of Scientific Computing 12 (1991) 1029-1057
16. 2O. Transport in Porous Media 63 3 (2004) 399-434
17. Geiger S., Roberts S., Matthai S., Zoppou C., and Burri A. Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media. Geofluids 4 (2004) 284-299
18. 2O fluid convection in the Earth's crust. Journal of Geophysical Research 110 B07101 (2005)
19. Gropp W., Huss-Lederman S., Lumsdaine A., Lusk E., Nitzberg B., Saphir W., and Snir M. MPI-The Complete Reference: Volume 2: The MPI Extensions (1996), The MIT Press, Cambridge, MA, USA, London, UK 344pp
20. Gropp W., Lusk E., Doss N., and Skjellum A. A high-performance, portable implementation of the MPI message passing interface standard. Parallel Computing 6 (1996) 789-828
21. Haar L., Gallagher J.S., and Kell G.S. NBS/NRC Steam Tables (1984), Hemisphere Publishing Corporation, New York, USA 320pp
22. Hayba D.O., and Ingebritsen S. Multiphase groundwater flow near cooling plutons. Journal of Geophysical Research 102 B6 (1994) 12235-12252
23. Huber R., and Helmig R. Multi-phase flow in heterogeneous porous media: a classical finite element method versus an implicit pressure-explicit saturation-based mixed finite element-finite volume approach. International Journal for Numerical Methods of Fluids 29 (1999) 899-920
24. Huyakorn P., and Pinder G. Computational Methods in Subsurface Flow (1983), Academic Press, New York, USA 473pp
25. Istok, J., 1989. Groundwater modeling by the finite element method. Water Resources Monograph 13.
26. Jupp T., and Schultz A. A thermodynamic explanation for black-smoker temperatures. Nature 403 6772 (2000) 880-883
27. Kaarstad, T., Froyen, J., Bjorstad, P., Espedal, M., 1995. A massively parallel reservoir simulator. In: Proceedings of 13th SPE Symposium on Reservoir Simulation, San Antonio, TX, SPE, pp. 467-478.
28. Karypsis, G., Kumar, V., 1998. METIS, A Software Package for Partitioning Unstructured Graphs, Partitioning Meshes, and Computing Fill-Reducing Orderings of Sparse Matrices. Version 4.0. Department of Computer Science/Army HPC Research Center, University of Minnesota, Minneapolis, USA, 44pp.
29. Killough, J., Commander, D., 1999. Scalable parallel reservoir simulation on a Windows NT-based workstation cluster. In: Proceedings of 15th SPE Symposium on Reservoir Simulation, Houston, TX, SPE, pp. 41-50.
30. Killough, J., Levesque, J., 1982. Reservoir simulation and the in-house vector processor experience for the first year. In: Proceedings of Sixth SPE Symposium on Reservoir Simulation, New Orleans, LA, SPE, pp. 481-487.
31. Krechel A., and Stuben K. Parallel algebraic multigrid based on subdomain blocking. Parallel Computing 27 (2001) 1009-1031
32. Krechel A., and Stuben K. User's Manual SAMGp (2005), Frauenhofer Institute SCAI, Schloss Birlinghoven St. Augustin, Germany
33. Laumbach D. High-accuracy finite-difference technique for treating convection-diffusion equation. Society of Petroleum Engineers Journal 15 6 (1975) 517-531
34. Ma Y., and Chen Z. Parallel computation for reservoir thermal simulation of multicomponent and multiphase fluid flow. Journal of Computational Physics 201 (2004) 224-237
35. Matthai S., Geiger S., and Roberts S. Complex systems platform: CSP50: user's guide (2004), Eidgenossische Technische Hochschule Zurich, Switzerland/Imperial College London, UK 151pp
36. Matthai S., Heinrich C., and Driesner T. Is the Mount Isa copper deposit the product of forced brine convection in the footwall of a major reverse fault?. Geology 32 4 (2005) 357-360
37. Mercer J., and Faust C. Geothermal reservoir simulation 3. Application of liquid-dominated and vapor-dominated hydrothermal modeling techniques of Wairakei, New-Zealand. Water Resources Research 15 3 (1979) 653-671
38. Narasimhan T., and Witherspoon P. Integrated finite-difference method for analyzing fluid-flow in porous-media. Water Resources Research 21 1 (1976) 57-64
39. Palliser C., and McKibbin R. A model for deep geothermal brines I: state-space description. Transport in Porous Media. 33 (1998) 65-80
40. Paluszny A., Matthai S., and Hohmeyer M. Hybrid finite-element finite-volume discretization of complex geologic structures and a new simulation workflow demonstrated on fractured rocks. Geofluids 7 (2007) 1-23
41. Peszynska M., Wheeler M., and Yotov I. Mortar upscaling for multiphase flow in porous media. Computational Geoscience 6 (2001) 73-100
42. Pini G., and Putti M. Parallel finite element laplace transform method for the non-equilibrium groundwater transport equation. International Journal for Numerical Methods in Engineering 40 (1997) 2653-2664
43. Pruess, K., 1987. TOUGH user's guide. U.S. Nuclear Regulatory Commission, Report NUREG/CR-4645, Washington DC, USA, 92pp.
44. Pruess K. Numerical simulation of multiphase tracer transport in fractured geothermal reservoirs. Geothermics 31 4 (2002) 475-499
45. Ruge J., and Stuben K. Algebraic multigrid. In: McCormick S.F. (Ed). Multigrid Methods vol. 4 (1987), SIAM, Philadelphia, USA 73-130
46. Schamberger S., and Wierum J. Partitioning finite element meshes using space-filling curves. Parallel Computing Technology 5 (2005) 759-766
47. Scott, A., Sutton, B., Dunn, J., Minto, P., Thomas, C., 1982. An implementation of a fully implicit reservoir simulator on an ICL distributed array processor. In: Proceedings of Sixth SPE Symposium on Reservoir Simulation, New Orleans, LA, SPE, pp. 523-533.
48. Snir M., Otto S., Huss-Lederman S., Walker D., and Dongarra J. MPI-The Complete Reference: Volume 1, The MPI Core (1996), The MIT Press, Cambridge, MA, USA, London, UK 426pp
49. Stein J., and Fisher A. Observations and models of lateral hydrothermal circulation on a young ridge flank: numerical evaluation of thermal and chemical constraints. G-Cubed. 4 1026 (2003)
50. Straus J., and Schubert G. Thermal convection of water in a porous medium: effects of temperature and pressure-dependent thermodynamic and transport properties. Journal of Geophysical Research 82 2 (1977) 325-332
51. Stuben K., and Clees T. SAMG user's manual (2005), Fraunhofer Institute SCAI, Schloss Birlinghoven, St. Augustin, Germany 88pp
52. Tsai W., Shen C., Fu H., and Kou C. Study of parallel computation for groundwater solute transport. Journal of Hydrologic Engineering 4 1 (1999) 49-56
53. Wang, P., Balay, S., Spernhoori, K., Wheeler, M., Abate, J., Smith, B., Pope, G., 1999. A fully implicit parallel EOS compositional simulator for large scale reservoir simulation. In: Proceedings of 15th SPE Symposium on Reservoir Simulation, Houston, TX, SPE, pp. 63-71.
54. Wu Y., Zhang K., Ding C., Pruess K., Elmroth E., and Bodvarsson G. An efficient parallel-computing method for modeling isothermal multiphase flow and multicomponent transport in porous media. Advances in Water Research 25 (2002) 243-261
55. Yang, U., 2004. Parallel algebraic multigrid methods-high performance preconditioners. Technical Report UCRL-BOOK-208032, Lawrence Livermore National Laboratory, Livermore, CA, USA, 97pp.
56. Young, L., Hemanth-Kumar, K., 1991. High-performance block oil computations. In: Proceedings of 11th SPE Symposium on Reservoir Simulation, Anaheim, CA, SPE, pp. 135-144.
57. Zhang, K., Wu, Y.S., W., Ding, C., Pruess, K., 2001. Application of parallel computing techniques to large scale reservoir simulation. In: Proceedings of 26th Annual Workshop, Geothermal Reservoir Engineering, Stanford, CA, Stanford University, pp. 1-8.
58. 2 geologic sequestration in saline acquifers. In: Proceedings of 2007 SPE Reservoir Simulation Symposium, Houston, USA, SPE, pp. 26-28.