Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-10T12:59:20.217Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  03 June 2015

Zhaoqin Huang ,
Xia Yan  and
Jun Yao
Zhaoqin Huang*
Affiliation:
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, P.R. China
Xia Yan*
Affiliation:
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, P.R. China
Jun Yao*
Affiliation:
School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, P.R. China
*
Email:huangzhqin@upc.edu.cn
Email:jsyanxia@163.com
Corresponding author.Email:RCOGFRUPC@126.com
Get access

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.

Keywords

76S0565N0865N5535J25Fractured porous mediadiscrete-fracture modeltwo-phase flowmimetic finite dif-ference method
Type
Research Article
Information
Communications in Computational Physics , Volume 16 , Issue 3 , September 2014 , pp. 799 - 816
Copyright
Copyright © Global Science Press Limited 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]National-Research-Council-(US), Rock fractures and fluid flow: contemporary understanding and applications, National Academies Press, 1996.Google Scholar
[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) 1286–1303.Google Scholar
[3]Warren, J., Root, P., The behavior of naturally fractured reservoirs, Old SPE Journal, 3 (3) (1963) 245–255.Google Scholar
[4]Kazemi, H., A pressure transient analysis of naturally fractured reservoirs with uniform fracture distribution, Old SPE Journal, 9 (4) (1969) 451–462.Google Scholar
[5]Kazemi, H., Porterfield, K., Zeman, P., Numerical simulation of water-oil flow in naturally fractured reservoirs, Old SPE Journal, 16 (6) (1976) 317–326.Google Scholar
[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) 823–836.Google Scholar
[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. 1–14.Google Scholar
[8]Lim, K., Aziz, K., Matrix-fracture transfer shape factors for dual-porosity simulators, Journal of Petroleum Science and Engineering, 13 (3) (1995) 169–178.Google Scholar
[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) 239–262.Google Scholar
[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) 263–286.Google Scholar
[11]Pruess, K., A practical method for modeling fluid and heat flow in fractured porous media, Old SPE Journal, 25 (1) (1985) 14–26.Google Scholar
[12]Wu, Y., Pruess, K., A multiple-porosity method for simulation of naturally fractured petroleum reservoirs, SPE Reservoir Engineering, 3 (1) (1988) 327–336.Google Scholar
[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. 375–391.CrossRefGoogle Scholar
[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.CrossRefGoogle Scholar
[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) 185–215.CrossRefGoogle Scholar
[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) 540–558.CrossRefGoogle Scholar
[17]Ghorayeb, K., Firoozabadi, A., Numerical study of natural convection and diffusion in fractured porous media, SPE Journal, 5 (1) (2000) 12–20.Google Scholar
[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) 335–342.Google Scholar
[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) 343–350.Google Scholar
[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) 588–596.Google Scholar
[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) 117–126.Google Scholar
[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) 1667–1691.CrossRefGoogle Scholar
[23]Hoteit, H., Firoozabadi, A., An efficient numerical model for incompressible two-phase flow in fractured media, Advances in Water Resources, 31 (6) (2008) 891–905.Google Scholar
[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) 338–354.Google Scholar
[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) 443–455.Google Scholar
[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. 1–17.Google Scholar
[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) 465–489.Google Scholar
[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.Google Scholar
[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) 58–67.Google Scholar
[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) 261–269.Google Scholar
[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) 107–136.CrossRefGoogle Scholar
[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) 35–52.Google Scholar
[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.Google Scholar
[34]Karimi-Fard, M., Durlofsky, L., Aziz, K., An efficient discrete-fracture model applicable for general-purpose reservoir simulators, SPE Journal, 9 (2) (2004) 227–236.CrossRefGoogle Scholar
[35]Sandve, T., Berre, I., Nordbotten, J., An efficient multi-point flux approximation method for discrete fracture-matrix simulations, Journal of Computational Physics,.Google Scholar
[36]Kim, J., Deo, M., Finite element, discrete-fracture model for multiphase flow in porous media, AIChE Journal, 46 (6) (2000) 1120–1130.Google Scholar
[37]Brezzi, F., Fortin, M., Mixed and hybrid finite element methods, Springer-Verlag, Berlin, 1991.Google Scholar
[38]Wheeler, M., Yotov, I., A multipoint flux mixed finite element method, SIAM Journal on Numerical Analysis, 44 (5) (2006) 2082–2106.CrossRefGoogle Scholar
[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).Google Scholar
[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) 1533–1551.CrossRefGoogle Scholar
[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) 1872–1896.Google Scholar
[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) 297–322.Google Scholar
[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) 265–306.Google Scholar
[44]Niceno, B., Easymesh: a free two-dimensional quality mesh generator based on delaunay triangulation, http://web.mit.edu/easymesh v1.4.Google Scholar
[45]Si, H., Tetgen: A quality tetrahedral mesh generator and a 3d delaunay triangulator, http://tetgen.berlios.de.Google Scholar
[46]Notay, Y., An aggregation-based algebraic multigrid method, Electronic Transactions on Numerical Analysis, 37 (6) (2010) 123–146.Google Scholar