Skip to main content Accessibility help
×
Home

A Two-Phase Flow Simulation of Discrete-Fractured Media using Mimetic Finite Difference Method

  • Zhaoqin Huang (a1), Xia Yan (a1) and Jun Yao (a1)

Abstract

Various conceptual models exist for numerical simulation of fluid flow in fractured porous media, such as dual-porosity model and equivalent continuum model. As a promising model, the discrete-fracture model has been received more attention in the past decade. It can be used both as a stand-alone tool as well as for the evaluation of effective parameters for the continuum models. Various numerical methods have been applied to the discrete-fracture model, including control volume finite difference, Galerkin and mixed finite element methods. All these methods have inherent limitations in accuracy and applicabilities. In this work, we developed a new numerical scheme for the discrete-fracture model by using mimetic finite difference method. The proposed numerical model is applicable in arbitrary unstructured gridcells with full-tensor permeabilities. The matrix-fracture and fracture-fracture fluxes are calculated based on powerful features of the mimetic finite difference method, while the upstream finite volume scheme is used for the approximation of the saturation equation. Several numerical tests in 2D and 3D are carried out to demonstrate the efficiency and robustness of the proposed numerical model.

Copyright

Corresponding author

Corresponding author.Email:RCOGFRUPC@126.com

References

Hide All
[1]National-Research-Council-(US), Rock fractures and fluid flow: contemporary understanding and applications, National Academies Press, 1996.
[2]Barenblatt, G., Zheltov, I., Kochina, I., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech, 24 (5) (1960) 12861303.
[3]Warren, J., Root, P., The behavior of naturally fractured reservoirs, Old SPE Journal, 3 (3) (1963) 245255.
[4]Kazemi, H., A pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution, Old SPE Journal, 9 (4) (1969) 451462.
[5]Kazemi, H., Porterfield, K., Zeman, P., Numerical simulation of water-oil flow in naturally fractured reservoirs, Old SPE Journal, 16 (6) (1976) 317326.
[6]Arbogast, T., Douglas, J. Jr, Hornung, U., Derivation of the double porosity model of single phase flow via homogenization theory, SIAM Journal on Mathematical Analysis, 21 (4) (1990) 823836.
[7]Geiger, S., Dentz, M., Neuweiler, I., A novel multi-rate dual-porosity model for improved simulation of fractured and multiporosity reservoirs, in: SPE Reservoir Characterisation and Simulation Conference and Exhibition, SPE 148130, 2011, pp. 114.
[8]Lim, K., Aziz, K., Matrix-fracture transfer shape factors for dual-porosity simulators, Journal of Petroleum Science and Engineering, 13 (3) (1995) 169178.
[9]Lemonnier, P., Bourbiaux, B., Simulation of naturally fractured reservoirs. state of the art. Part 1 physical mechanisms and simulator formulation, Oil & Gas Science and TechnologyRevue de lInstitut Francais du Petrole, 65 (2) (2010) 239262.
[10]Lemonnier, P., Bourbiaux, B., Simulation of naturally fractured reservoirs. state of the art. Part 2 matrix-fracture transfers and typical features of numerical studies, Oil & Gas Science and Technology-Revue de lInstitut Français du Pétrole, 65 (2) (2010) 263286.
[11]Pruess, K., A practical method for modeling fluid and heat flow in fractured porous media, Old SPE Journal, 25 (1) (1985) 1426.
[12]Wu, Y., Pruess, K., A multiple-porosity method for simulation of naturally fractured petroleum reservoirs, SPE Reservoir Engineering, 3 (1) (1988) 327336.
[13]Narasimhan, T., Pruess, K., Minc: An approach for analyzing transport in strongly heterogeneous systems, in: Custodio, E., Gurgui, A., Ferreira, J. (Eds.), Groundwater Flow and Quality Modelling, Springer Netherlands, 1988, pp. 375391.
[14]Wu, Y., Qin, G., A generalized numerical approach for modeling multiphase flow and transport in fractured porous media, Communications in Computational Physics, 6 (1) (2009) 85.
[15]Wu, Y., Haukwa, C., Bodvarsson, G., A site-scale model for fluid and heat flow in the unsaturated zone of yucca mountain, nevada, Journal of Contaminant Hydrology, 38 (1) (1999) 185215.
[16]Huang, Z., Yao, J., Wang, Y., An efficient numerical model for immiscible two-phase flow in fractured karst reservoirs, Communications in Computational Physics, 13 (2) (2013) 540558.
[17]Ghorayeb, K., Firoozabadi, A., Numerical study of natural convection and diffusion in fractured porous media, SPE Journal, 5 (1) (2000) 1220.
[18]Gebauer, S., Neunhäuserer, L., Kornhuber, R., Ochs, S., Hinkelmann, R., Helmig, R., Equidimensional modelling of flow and transport processes in fractured porous systems i, Developments in Water Science, 47 (2002) 335342.
[19]Neunhäuserer, L., Gebauer, S., Ochs, S., Hinkelmann, R., Kornhuber, R., Helmig, R., Equidi-mensional modelling of flow and transport processes in fractured porous systems ii, Developments in Water Science, 47 (2002) 343350.
[20]Noorishad, J., Mehran, M., An upstream finite element method for solution of transient transport equation in fractured porous media, Water Resources Research, 18 (3) (1982) 588596.
[21]Karimi-Fard, M., Firoozabadi, A., Numerical simulation of water injection in fractured media using the discrete-fracture model and the galerkin method, SPE Reservoir Evaluation & Engineering, 6 (2) (2003) 117126.
[22]Martin, V., Jaffré, J., Roberts, J., Modeling fractures and barriers as interfaces for flow in porous media, SIAM Journal on Scientific Computing, 26 (5) (2005) 16671691.
[23]Hoteit, H., Firoozabadi, A., An efficient numerical model for incompressible two-phase flow in fractured media, Advances in Water Resources, 31 (6) (2008) 891905.
[24]Geiger-Boschung, S., Matthäi, S., Niessner, J., Helmig, R., Black-oil simulations for three- component, three-phase flow in fractured porous media, SPE Journal, 14 (2) (2009) 338354.
[25]Lee, S., Lough, M., Jensen, C., Hierarchical modeling of flow in naturally fractured formations with multiple length scales, Water Resources Research, 37 (3) (2001) 443455.
[26]Moinfar, A., Narr, W., Hui, M., Mallison, B., Lee, S., Comparison of discrete-fracture and dual-permeability models for multiphase flow in naturally fractured reservoirs, in: SPE Reservoir Simulation Symposium, SPE 142295, 2011, pp. 117.
[27]Carlo, D., Scotti, A., A mixed finite element method for darcy flow in fractured porous media with non-matching grids, ESAIM: Mathematical Modelling and Numerical Analysis, 46 (02) (2012) 465489.
[28]Karimi-Fard, M., Gong, B., Durlofsky, L., Generation of coarse-scale continuum flow models from detailed fracture characterizations, Water resources research, 42 (10) (2006) W10423.
[29]Gong, B., Karimi-Fard, M., Durlofsky, L., Upscaling discrete fracture characterizations to dual-porosity, dual-permeability models for efficient simulation of flow with strong gravitational effects, SPE Journal, 13 (1) (2008) 5867.
[30]Slough, K., Sudicky, E., Forsyth, P., Grid refinement for modeling multiphase flow in discretely fractured porous media, Advances in water resources, 23 (3) (1999) 261269.
[31]Slough, K., Sudicky, E., Forsyth, P., Numerical simulation of multiphase flow and phase partitioning in discretely fractured geologic media, Journal of contaminant hydrology, 40 (2) (1999) 107136.
[32]Granet, S., Fabrie, P., Lemonnier, P., Quintard, M., A two-phase flow simulation of a fractured reservoir using a new fissure element method, Journal of Petroleum Science and Engineering, 32 (1) (2001) 3552.
[33]Monteagudo, J., Firoozabadi, A., Control-volume method for numerical simulation of two-phase immiscible flow in two-and three-dimensional discrete-fractured media, Water resources research, 40 (7) (2004) W07405.
[34]Karimi-Fard, M., Durlofsky, L., Aziz, K., An efficient discrete-fracture model applicable for general-purpose reservoir simulators, SPE Journal, 9 (2) (2004) 227236.
[35]Sandve, T., Berre, I., Nordbotten, J., An efficient multi-point flux approximation method for discrete fracture-matrix simulations, Journal of Computational Physics,.
[36]Kim, J., Deo, M., Finite element, discrete-fracture model for multiphase flow in porous media, AIChE Journal, 46 (6) (2000) 11201130.
[37]Brezzi, F., Fortin, M., Mixed and hybrid finite element methods, Springer-Verlag, Berlin, 1991.
[38]Wheeler, M., Yotov, I., A multipoint flux mixed finite element method, SIAM Journal on Numerical Analysis, 44 (5) (2006) 20822106.
[39]Singh, G., Mimetic finite difference method on gpu: application in reservoir simulation and well modeling, Ph.D. thesis, Norwegian University of Science and Technology (2010).
[40]Brezzi, F., Lipnikov, K., Simoncini, V., A family of mimetic finite difference methods on polygonal and polyhedral meshes, Mathematical Models and Methods in Applied Sciences, 15 (10) (2005) 15331551.
[41]Brezzi, F., Lipnikov, K., Shashkov, M., Convergence of the mimetic finite difference method for diffusion problems on polyhedral meshes, SIAM Journal on Numerical Analysis, 43 (5) (2005) 18721896.
[42]Lie, K., Krogstad, S., Ligaarden, I., Natvig, J., Nilsen, H., Skaflestad, B., Open-source matlab implementation of consistent discretisations on complex grids, Computational Geosciences, 16 (2) (2012) 297322.
[43]Aarnes, J., Gimse, T., Lie, K., An introduction to the numerics of flow in porous media using matlab, Geometric Modelling, Numerical Simulation, and Optimization, (2007) 265306.
[44]Niceno, B., Easymesh: a free two-dimensional quality mesh generator based on delaunay triangulation, http://web.mit.edu/easymesh v1.4.
[45]Si, H., Tetgen: A quality tetrahedral mesh generator and a 3d delaunay triangulator, http://tetgen.berlios.de.
[46]Notay, Y., An aggregation-based algebraic multigrid method, Electronic Transactions on Numerical Analysis, 37 (6) (2010) 123146.

Keywords

Related content

Powered by UNSILO

A Two-Phase Flow Simulation of Discrete-Fractured Media using Mimetic Finite Difference Method

  • Zhaoqin Huang (a1), Xia Yan (a1) and Jun Yao (a1)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed.