1887
  1. Home
  2. Conferences
  3. Conference Proceedings
  4. ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
  5. Conference paper

Abstract

Summary

Simulation of coupled pressure-, buoyancy- and capillary driven multiphase fluid flow in geological media is challenging as they are aggregates of many rock types with sharp interfaces and extremely variable flow properties. Geological features have variable orientations, complex intersections, and aspect ratios up to >1000:1. Hence, realistic discretization is only possible with adaptively refined unstructured grids. Finite-element schemes for such meshes are not locally conservative and therefore ill suited for the simulation of transport processes. To overcome this restriction we developed a hybrid Finite-Element Node-Centered Finite Volume scheme (FEFVM). In this method, however, interface finite-volumes include multiple materials and smearing of transport variables occurs.

Here we present a new hybrid discretization technique that permits computation of conservative interelement fluxes. Finite elements are simultaneously used as finite volumes for a piecewise constant discretization of transport variables. This Finite Element-Centered Finite Volume Method (FECFVM) has the advantage that saturation discontinuities at material interfaces are honored without having to add extra degrees of freedom as in the embedded discontinuity method (DFEFVM), our earlier solution resolving the smearing problem. The FECFVM brings additional benefits regarding upwinding. The implementation presented here further allows representation of fractures or sand lenses by lower dimensional elements. This simplifies model construction, meshing, and fracture aperture modeling. It also speeds up computations. gradients allow accurate computation of interface fluxes and capillary effects on global pressure can be considered because it can be discontinuous.

© EAGE Publications BV
Loading

Article metrics loading...

/content/papers/10.3997/2214-4609.20141841
2014-09-08
2024-04-25

  • From This Site

    /content/papers/10.3997/2214-4609.20141841
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Aziz, K. and Settari, A.
    [1979] Petroleum Reservoir Simulation. Applied Science Publishers Ltd., USA.
     [Google Scholar]
  2. Belayneh, M.W., Matthäi, S.K., Blunt, M.J. and Rogers, S.F.
    [2009] Comparison of Deterministic with Stochastic Fracture Models in Water-Flooding Numerical Simulations. American Association of Petroleum Geologists Bulletin93(11), 1633–1648.
     [Google Scholar]
  3. Belayneh, M., Geiger, S. and Matthäi, S.K.
    [2006] Numerical Simulation of Water Injection into Layered Fractured Carbonate Reservoir Analogs. American Association of Petroleum Geologists Bulletin90(10), 1473–1493.
     [Google Scholar]
  4. Chavent, G. and Jaffré, J.
    [1986] Mathematical Models and Finite Elements for Reservoir Simulation. North–Holland, Amsterdam.
     [Google Scholar]
  5. Chavent, G., Cohen, G., Jaffre, J., Eyard, R., Guerillot, D.R. and Weill, L.
    [1990] Discontinuous and Mixed Finite Elements for Two-Phase Incompressible Flow. SPE Journal, SPE16018.
     [Google Scholar]
  6. Chen, Z., Huan, G. and Ma, Y.
    [2006] Computational Methods for Multiphase Flows in Porous Media. SIAM Journal, Dallas, Texas.
     [Google Scholar]
  7. Chen, Z. and Huan, G.
    [2003] Numerical Experiments with Various Formulations for Two Phase Flow in Petroleum Reservoirs. Transport in Porous Media51, 102–.
     [Google Scholar]
  8. Cordes, C. and Kinzelbach, W.
    [1992] Continuous Groundwater Velocity Fields and Path Lines in Linear, Bilinear, and Trilinear Finite Elements. Water Resources Research28(11), 2903–2911.
     [Google Scholar]
  9. Coumou, D., Matthäi, S.K., Geiger, S. and Driesner, T.
    [2008] A Parallel FE-FV Scheme to Solve Fluid Flow in Complex Geologic Media. Computers & Geosciences34(12), 1697–1707. doi: 10.1016/j.cageo.2007.11.010.
     https://doi.org/10.1016/j.cageo.2007.11.010 [Google Scholar]
  10. Dalen, V.
    [1979] Simplified Finite-Element Models for Reservoir Flow Problems. SPE Journal, SPE7196.
     [Google Scholar]
  11. Durlofsky, L. and Chien, M.
    [1993] Development of a Mixed Finite-Element-Based Compositional Reservoir Simulator. SPE Symposium on Reservoir Simulation. Society of Petroleum Engineers, New Orleans, Louisiana, SPE25253.
     [Google Scholar]
  12. Eymard, R. and Sonier, F.
    [1994] Mathematical and Numerical Properties of Control-Volume Finite-Element Scheme for Reservoir Simulation. SPE Reservoir Engineering, 9, SPE25267.
     [Google Scholar]
  13. Forsyth, P.A.
    [1990] A Control-Volume, Finite-Element Method for Local Mesh Refinement in Thermal Reservoir Simulation. SPE Reservoir Engineering, SPE18415.
     [Google Scholar]
  14. Fung, L.-K., Hiebert, A. and Nghiem, L.
    [1992] Reservoir Simulation With a Control-Volume Finite-Element Method. SPE Journal, SPE21224.
     [Google Scholar]
  15. Fu, Y., Yang, Y.-K. and Deo, M.
    [2005] Three-Dimensional, Three-Phase Discrete-Fracture Reservoir Simulator Based on Control Volume Finite Element (CVFE) Formulation. SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, The Woodlands, Texas.
     [Google Scholar]
  16. Geiger, S., Huangfu, Q., Reid, F., Matthäi, S.K., Coumou, D., Belayneh, M., Fricke, C. and Schmid, K.
    [2009] Massively Parallel Sector Scale Discrete Fracture and Matrix Simulations. SPE118924 presented at SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 2–4 February2009.
     [Google Scholar]
  17. Geiger, S., Matthäi, S.K., Niessner, J. and Helmig, R.
    June [2009] Black-Oil Simulations for Three-Component, Three-Phase Flow in Fractured Porous Media. SPE Journal6, 338–354. SPE107485.
     [Google Scholar]
  18. Geiger, S., Roberts, S., Matthäi, S., Zoppou, C. and Burri, A.
    [2004] Combining finite element and finite volume methods for efficient multiphase flow simulations in highly heterogeneous and structurally complex geologic media. Geofluids4, 299–.
     [Google Scholar]
  19. Gebauer, S., Neunhäuserer, L., Kornhuber, R., Ochs, S., Hinkelmann, R. Helmig, R.
    , [2002] Equidimensional modelling of flow and transport processes in fractured porous systems I, in: S.M.Hassanizadeh (Ed.), Computational Methods in Water Resources, Elsevier, 335–342.
     [Google Scholar]
  20. Hægland, H., Assteerawatt, A., Dahle, H., Eigestad, G. and Helmig, R.
    [2009] Comparison of cell- and vertex-centered discretization methods for flow in a two dimensional discrete-fracture-matrix system. Adv. in Water Resources32, 1755–.
     [Google Scholar]
  21. Helmig. R.
    [1997] Multiphase Flow and Transport Processes in the Subsurface. Springer, Berlin.
     [Google Scholar]
  22. Hoteit, H. and Firoozabadi, A.
    [2004] Compositional Modeling by the Combined Discontinuous Galerkin and Mixed Method. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Houston, Texas.
     [Google Scholar]
  23. Juanes, R., Samper, J. and Molinero, J.
    [2002] A general and efficient formulation for fractures and boundary conditions in the finite element method. Int. J. Numer. Meth. Eng. 54(12), 1751–1774.
     [Google Scholar]
  24. Karimi-Fard, M. and Firoozabadi, A.
    [2001] Numerical Simulation of Water Injection in 2D Fractured Media Using Discrete-Fracture Model. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers Inc., New Orleans, Louisiana.
     [Google Scholar]
  25. Kim, J.G. and Deo, M.D.
    [1999] Comparison of the Performance of the Discrete-Fracture Multiphase Model With Those Using Conventional Methods. SPE 51928 presented at SPE Reservoir Simulation Symposium, Houston, Texas.
     [Google Scholar]
  26. Kiraly, L. and Morel, G.
    [1976] Etude de régularisation de l’Areuse par modèle mathématique. Bulletin d’Hydrogéologie, Neuchâtel1, 36–.
     [Google Scholar]
  27. Langsrud, O.
    [1976] Simulation of Two-Phase Flow by Finite Element Methods. SPE Symposium on Numerical Simulation of Reservoir Performance, SPE, Los Angeles, California, USA.
     [Google Scholar]
  28. Lemonnier, P.A.
    [1979] Improvement of Reservoir Simulation by a Triangular Discontinuous Finite Element Method. SPE Annual Technical Conference and Exhibition. American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc., Las Vegas, Nevada.
     [Google Scholar]
  29. Matringe, S.F., Juanes, R. and Tchelepi, H.A.
    [2007] Mixed-Finite-Element and Related-Control-Volume Discretizations for Reservoir Simulation on Three-Dimensional Unstructured Grids. SPE Reservoir Simulation Symposium, Society of Petroleum Engineers, Houston, Texas, U.S.A..
     [Google Scholar]
  30. Matthäi, S.K., Nick, H.M., Pain, C.C. and Neuweiler, I.
    [2009] Simulation of Solute Transport Through Fractured Rock: a Higher-Order Accurate Finite-Element Finite-Volume Method Permitting Large Time Steps. Transport in Porous Media. doi: 10.1007/s11242‑009‑9440‑z.
     https://doi.org/10.1007/s11242-009-9440-z [Google Scholar]
  31. Matthäi, S.K., Geiger, S., Roberts, S.G., Paluszny, A., Belayneh, M., Burri, A., Mezentsev, A., Lu, H., Coumou, D., Driesner, T. and Heinrich, C.A.
    [2007] Numerical Simulation of Multiphase Fluid Flow in Structurally Complex Reservoirs. In: Jolley, S.J., Barr, D., Walsh, J.J. and Knipe, R.J. (Eds) Structurally Complex Reservoirs. Geological Society, London, Special Publications292, 405–429. doi: 10.1144/SP292.22.
     https://doi.org/10.1144/SP292.22 [Google Scholar]
  32. Matthäi, S.K., Mezentsev, A.A., Pain, C.C. and Eaton, M.D.
    [2005] A High-order TVD Transport Method for Hybrid Meshes on Complex Geological Geometry, International Journal for Numerical Methods in Fluids, 47, 1181–1187. doi: 10.1002/fld.901.
     https://doi.org/10.1002/fld.901 [Google Scholar]
  33. Neunhäuserer, L., Gebauer, S., Ochs, S., Hinkelmann, R., Kornhuber, R. and Helmig, R.
    [2002] Equidimensional modelling of flow and transport processes in fractured porous systems II. In: S.M.Hassanizadeh (Ed.) Computational Methods in Water Resources. Elsevier, 343–350.
     [Google Scholar]
  34. Nick, H.M., Matthäi, S.K.
    [2011] A Hybrid FE-FV Method with Embedded Discontinuities for Solute Transport in Heterogeneous Media. Vadose Zone Journal, 10(1), 299–312; DOI: 10.2136/vzj2010.0015
     https://doi.org/10.2136/vzj2010.0015 [Google Scholar]
  35. Noorishad, J. and Mehran, M.
    [1982] An Upstream Finite Element Method for Solution of Transient Transport Equation in Fractured Porous Media. Water Resources Research, 18(3), 588.
     [Google Scholar]
  36. Paluszny, A., Matthäi, S.K. and Hohmeyer, M.
    [2007] Hybrid Finite Element-Finite Volume Discretisation of Complex Geologic Structures and a New Simulation Workflow Demonstrated on Fractured Rocks. Geofluids, 7, 186–208. doi: 10.1111/j.1468‑8123.2007.00180.x
     https://doi.org/10.1111/j.1468-8123.2007.00180.x [Google Scholar]
  37. Sandve, T., Berre, I. and Nordbotten, J.
    [2012] An efficient multi-point flux approximation method for Discrete Fracture-Matrix simulations. Journal of Computational Physics, 231(9), 3784–3800.
     [Google Scholar]
  38. Sonier, F., Lehuen, P. and Nabil, R.
    [1993] Full-Field Gas Storage Simulation Using a Control-Volume Finite-Element Model. SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, Inc., Houston, Texas.
     [Google Scholar]
  39. Stone, H.L. and Garder, A.O.
    [1961] Analysis of gas-cap or dissolved-gas reservoirs. Trans. SPE AIME, 222, 104–.
     [Google Scholar]
  40. Unsal, E., Matthäi, S.K. and Blunt, M.J.
    [2009] Simulation of Multiphase Flow in Fractured Reservoirs Using a Fracture-Only Model with transfer functions. Computational Geosciences. doi: 10.1007/s10596‑009‑9168‑4.
     https://doi.org/10.1007/s10596-009-9168-4 [Google Scholar]
http://instance.metastore.ingenta.com/content/papers/10.3997/2214-4609.20141841
Loading
The Finite-element-centered Finite-volume Discretization Method (FECFVM) for Multiphase Transport in Porous Media with Sharp Material Discontinuities
Conference Proceedings 2014, 1 (2014); https://doi.org/10.3997/2214-4609.20141841
/content/papers/10.3997/2214-4609.20141841
/content/papers/10.3997/2214-4609.20141841
Loading

Data & Media loading...

Most Cited This Month Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error