Browse > Article
http://dx.doi.org/10.12989/csm.2019.8.2.129

Numerical simulation of single-phase two-components flow in naturally fractured oil reservoirs  

Debossam, Joao Gabriel Souza (Polytechnic Institute, Rio de Janeiro State University)
dos Santos Heringer, Juan Diego (Polytechnic Institute, Rio de Janeiro State University)
de Souza, Grazione (Polytechnic Institute, Rio de Janeiro State University)
Souto, Helio Pedro Amaral (Polytechnic Institute, Rio de Janeiro State University)
Publication Information
Coupled systems mechanics / v.8, no.2, 2019 , pp. 129-146 More about this Journal
Abstract
The main goal of this work is to develop a numerical simulator to study an isothermal single-phase two-component flow in a naturally fractured oil reservoir, taking into account advection and diffusion effects. We use the Peng-Robinson equation of state with a volume translation to evaluate the properties of the components, and the discretization of the governing partial differential equations is carried out using the Finite Difference Method, along with implicit and first-order upwind schemes. This process leads to a coupled non-linear algebraic system for the unknowns pressure and molar fractions. After a linearization and the use of an operator splitting, the Conjugate Gradient and Bi-conjugated Gradient Stabilized methods are then used to solve two algebraic subsystems, one for the pressure and another for the molar fraction. We studied the effects of fractures in both the flow field and mass transport, as well as in computing time, and the results show that the fractures affect, as expected, the flow creating a thin preferential path for the mass transport.
Keywords
compositional simulation; equation of state; operator splitting; finite difference method; fractured oil reservoir;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 Anca-Couce, A., Zobel, N. and Jakobsen, H.A. (2013), "Multi-scale modeling of fixed-bed thermo-chemical processes of biomass with the representative particle model: Application to pyrolysis", Fuel, 103, 773-782.   DOI
2 Biryukov, D. and Kuchuk, F.J. (2012), "Transient pressure behavior of reservoirs with discrete conductive faults and fractures", Transp. Por. Med., 95(1), 239-268.   DOI
3 Cavalcante Filho, J.S.A. and Sepehrnoori, K. (2017), "Simulation of planar hydraulic fractures with variable conductivity using the embedded discrete fracture model", J. Petrol. Sci. Eng., 153, 212-222.   DOI
4 Chen, Z. (2007) Reservoir Simulation-Mathematical Techniques in Oil Recovery, Society of Industrial and Applied Mathematics, Philadelphia, Pennsylvania, U.S.A.
5 Das, S. and Dutta, P. (2017), "Preliminary understanding of $CO_2$ sequestration and enhanced methane recovery in Ranigang coalfield of India by reservoir simulation", Energy Proc., 114, 4643-4657.   DOI
6 De Borst, R., Rethore, J. and Abellan, M.A. (2000), "A numerical approach for arbitrary cracks in a fluidsaturated medium", Arch. Appl. Mech., 75(10-12), 595-606.   DOI
7 Douglas Jr., J., Pereira, F. and Yeh, L.M. (2000), "A locally conservative Eulerian-Lagrangian method for flow in a porous medium of a mixture of two components having different densities", Numer. Treat. Multiph. Flow. Por. Med., 138-155.
8 Ezekwe, N. (2010), Petroleum Reservoir Engineering Practice, Prentice-Hall, Bergen County, New Jersey, U.S.A.
9 Geiger, S., Schmid, K.S. and Zaretskiy, Y. (2012), "Mathematical analysis and numerical simulation of multiphase multi-component flow in heterogeneous porous media", Curr. Opin. Colloid & Interf. Sci., 17(3), 147-155.   DOI
10 Hadzalic, E., Ibrahimbegovic, A. and Dolarevic, S. (2018), "Failure mechanisms in coupled soil-foundation systems", Coupled Syst. Mech., 7(1), 27-42.   DOI
11 Hadzalic, E., Ibrahimbegovic, A. and Nikolic, M. (2018), "Failure mechanisms in coupled poro-plastic medium", Coupled Syst. Mech., 7(1), 43-59.   DOI
12 Hanspal, N.S., Waghode, A.N., Nassehi, V. and Wakeman, R.J. (2009), "Development of a predictive mathematical model for coupled Stokes/Darcy flows in cross-flow membrane filtration", Chem. Eng. J., 149(1-3), 132-142.   DOI
13 Jmili, A., Wilhite, G.P. and Green, D. (2011), "Modeling gas-phase mass transfer between fracture and matrix in naturally fractured reservoirs", Soc. Petrol. Eng. J., 16(4), 795-811.
14 Hoteit, H. and Firoozabadi, A. (2006), "Compositional modeling of discrete-fractured media without transfer functions by the discontinuous Galerkin and mixed methods", SPE J., 11(3), 341-352.   DOI
15 Hoyos, B. (2004), "Generalized liquid volume shifts for the Peng-Robinson equation of state for $C_1$ to $C_8$ hydrocarbons", Lat. Am. Appl. Res., 34(2), 83-89.
16 Jiang, J. andYounis, R.M. (2015), "Amultimechanistic multicontinuum model for simulating shale gas reservoir with complex fractured system", Fuel, 161, 333-344.   DOI
17 Lake, W.L. (1989), Enhanced Oil Recovery, Prentice-Hall, Bergen County, New Jersey, U.S.A.
18 Lee, S.H., Jensen, C.L. and Lough, M.F. (2000) "Efficient finite-difference model for flow in a reservoir with multiple length-scale fractures", SPE J., 5(3), 268-275.   DOI
19 Lee, S.H., Lough, M.F. and Jensen, C.L. (2001) "Hierarchical modeling of flowin naturally fractured formations with multiple length scales", Wat. Res. Res., 37(3), 443-455.   DOI
20 Lewis, R.W. and Schrefler, B.A. (1998) The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media, 2nd Edition, John Wiley & Sons, Chichester, England.
21 Li, L. and Yin, Z. (2017), "Numerical simulation of groundwater pollution problems based on convection diffusion equation", Am. J. Comput. Math., 7(3), 350-370.   DOI
22 Nair, N., Bryant, S.L. and Jennings, J.W. (2008), "Finding the continuum scale in highly heterogeneous rocks: Example of a large touching vug carbonate", Proceedings of the Society of Petroleum Engineers Annual Technical Conference and Exhibition, Denver, Colorado, U.S.A., September.
23 Maes, J., Muggeridge, A.H., Jackson, M.D., Quintard, M. and Lapene, A. (2016), "Modelling in-situ upgrading of heavy oil using operator splitting method", Comput. Geosci., 20(3), 581-594.   DOI
24 Mendes, M.A., Murad, M.A. and Pereira, F. (2012), "A new computational strategy for solving two-phase flow in strongly heterogeneous poroelastic media of evolving scales", Int. J. Numer. Analy. Meth. Geomech., 36(15), 1683-1716.   DOI
25 Moinfar, A. (2013), "Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs", Ph.D. Dissertation, The University of Texas at Austin, Austin, Texas, U.S.A.
26 Nelson, R. (2001), Geologic Analysis of Naturally Fractured Reservoirs, 2nd Edition, Gulf Professional Publishing, Houston, Texas, U.S.A.
27 Nikolic, M., Ibrahimbegovic, A. and Miscevic, P. (2016), "Discrete element model for the analysis of fluidsaturated fractured poro-plastic medium based on sharp crack representation with embedded strong discontinuities", Comput. Meth. Appl. Mech. Eng., 298, 407-427.   DOI
28 Saad, Y. (2003), Iterative Methods for Sparse Linear Systems, 2nd Edition, Society of Industrial and Applied Mathematics, Philadelphia, Pennsylvania, U.S.A.
29 Secchi, S. and Schrefler, B.A. (2012), "A method for 3-D hydraulic fracturing simulation", Int. J. Fract., 178(1-2), 245-258.   DOI
30 Souza, G. and Amaral Souto, H.P. (2016), "A comparative study of non-Darcy flows in naturally fractured gas reservoirs", J. Brazil. Soc. Mech. Sci. Eng., 38(6), 1701-1715.   DOI
31 Tiab, D. and Donaldson, E.C. (2004), Petrophysics, Gulf Professional Publishing, U.S.A.
32 Vennemo, S. (2016), "Multiscale simulation of thermal flow in porous media", M.Sc. Dissertation, Norwegian University of Science and Technology, Trondheim, Norway.
33 Wang, C. (2013), "Pressure transient analysis of fractured wells in shale reservoirs", M.Sc. Dissertation, Colorado School of Mines, Golden, Colorado, U.S.A.
34 Wu, Y. and Sun, S. (2016), "Equivalence of two models in single-phase multicomponent flow simulations", Comput. Math. Appl., 71(6), 1303-1316.   DOI
35 Zaydullin, R., Voskov, D.V., James, S.C., Henley, H. and Lucia, A. (2014), "Fully compositional and thermal reservoir simulation", Comput. Chem. Eng., 63, 51-65.   DOI
36 Zidane, A. and Firoozabadi, A. (2017), "Fracture-cross-flow equilibrium in compositional two-phase reservoir simulation", SPE J., 22(3), 1-21.   DOI