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Simulation of Transient Matrix-Fracture Transfers of Compressible Fluids

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Abstract

The dual-medium approach is convenient for simulating flows within two interacting continua such as fractured reservoirs, because it greatly simplifies the apparent complexity of the flow problem while offering a conceptual representation of flows within and between the two continua that helps the understanding of flow responses. Considerable work has been achieved during the last decades to model the coupling term of such models, that is, matrix-fracture transfers. Whereas pseudo-steady-state transfers taking place at late times can be fairly well predicted, the simulation of transient, i.e. early-time, transfers still encounters difficulties due to intrinsically complex transfer mechanisms that the resolution of diffusion equations entails. Those difficulties are emphasized for tight porous media where transient flow behaviour persists over a durable period of time, for compressible fluids that increase inaccuracy of linear approximations of transfers, and also because of the multi-directionality of transfers. Starting from analytical solutions of diffusivity equations, the present paper proposes a methodology to account for transient effects and for non-linearities in matrix-fracture transfer formulas of dual-porosity simulators in order that they can predict the production of unconventional low-permeability hydrocarbon reservoirs. Validation of these formulas for the production of very tight fractured media is shown at the matrix block scale and at the scale of a stimulated reservoir volume.

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References

  • Barenblatt, G.I., Zheltov, Iu P., Kochina, I.N.: Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. 24, 1286–1303 (1960)

    Google Scholar 

  • Bourbiaux, B., Granet, S., Landereau, P., Noetinger, B., Sarda S., Sabathier, J.C.: Scaling Up Matrix-Fracture Transfers in Dual-Porosity Models: Theory and Application. Paper SPE 56557, SPE Annual Technical Conference and Exhibition held in Houston, Texas, 3–6 Oct (1999)

  • Cai, L., Ding, D., Wang, C., Wu, Y.-S.: Accurate and efficient simulation of fracture-matrix interaction in shale gas reservoirs. Transp. Porous Media 107(2), 305–320 (2015)

    Article  Google Scholar 

  • Cipolla, C.L., Lolon, E.P., Erdle, J.C., Rubin, B.: Reservoir modeling in shale-gas reservoirs. SPE Reserv. Eval. Eng. 13(4), 638–653 (2010)

  • Coats, K.H.: Implicit compositional simulation of single-porosity and dual-porosity reservoirs. Paper SPE 18427, SPE Symposium on Reservoir Simulation, Houston, Texas, 6–8 Feb (1989)

  • Carlslaw, H.S., Jaeger, J.C.: Conduction of Heat in Solids. Oxford University Press, Oxford (1959)

    Google Scholar 

  • Crank, J.: The Mathematics of Diffusion, 2nd edn. Oxford University Press, Oxford (1975)

    Google Scholar 

  • Daviau, F.: Interprétation des essais de puits, les méthodes nouvelles. Publications de l’Institut Français du Pétrole, ed. Technip, Paris (1986)

  • de Swann, A.: Analytic solutions for determining naturally fractured reservoir properties by well testing. SPE J. 16(3), 117–122 (1976)

    Article  Google Scholar 

  • Dean, R.H., Lo, L.L.: Simulations of naturally fractured reservoirs. SPE Reserv. Eng. 3(2), 638–648 (1988)

  • Ding, D., Wu, Y.-S., Farah, N., Wang, C., Bourbiaux, B.: Numerical simulation of low permeability unconventional gas reservoirs. Paper SPE 167711, SPE/EAGE European Unconventional Conference & Exhibition, Vienna, Austria, 25–27 Feb (2014)

  • Hagoort, J.: Fundamentals of Gas Reservoir Engineering. Developments in Petroleum Science, vol. 23. Elsevier, Amsterdam (1988)

    Google Scholar 

  • Karimi-Fard, M., Gong, B., Durlofsky, L.J.: Generation of coarse-scale continuum flow models from detailed fracture characterizations. Water Resour. Res. 42, W10423 (2006)

    Article  Google Scholar 

  • Kazemi, H., Merrill, L.S., Porterfield, K.L., Zeman, P.R.: Numerical simulation of water-oil flow in naturally fractured reservoirs. SPE J. 16(6), 317–326 (1976)

  • Khvoenkova, N., Delorme M.: An optimal method to model transient flows in 3D discrete fracture network. In: Proceedings of the IAMG2011 Conference, pp. 1238–1249, Salzburg, Austria, 5–9 Sept (2011)

  • Landereau, P., Noetinger, B., Quintard, M.: Quasi-steady two-equation models for diffusive transport in fractured porous media: large-scale properties for densely fractured systems. Adv. Water Resour. 24(8), 863–876 (2001)

    Article  Google Scholar 

  • Lim, K.T., Aziz, K.: Matrix-fracture transfer shape factors for dual-porosity simulators. J. Pet. Sci. Eng. 13, 169–178 (1995)

    Article  Google Scholar 

  • Moinfar, A., Varavei, A., Sepehrnoori, K., Johns, R.T.: Development of a coupled dual continuum and discrete fracture model for the simulation of unconventional reservoirs. Paper SPE 163647, Reservoir Simulation Symposium held in The Woodlands, Texas, USA, 18–20 Feb (2013)

  • Noetinger, B., Estebenet, T., Landereau, P.: A direct determination of the transient exchange term of fractured media using a continuous time random walk method. Transp. Porous Media 44, 539–557 (2001)

    Article  Google Scholar 

  • Noetinger, B.: A quasi-steady state method for solving transient Darcy flow in complex 3D fractured networks accounting for matrix to fracture flow. J. Comput. Phys. 283, 205–223 (2015)

    Article  Google Scholar 

  • Pruess, K., Narasimhan, T.N.: A practical method for modeling fluid and heat flow in fractured porous media. SPE J. 25, 14–26 (1985)

    Article  Google Scholar 

  • Quintard, M., Whitaker, S.: Transport in chemically and mechanically heterogeneous porous media. Adv. Water Resour. 19(1), 29–60 (1996)

    Article  Google Scholar 

  • Ranjbar, E., Hassanzadeh, H.: Matrix-fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media. Adv. Water Resour. 34, 627–639 (2011)

    Article  Google Scholar 

  • Ranjbar, E., Hassanzadeh, H., Chen, Z.: Effect of fracture pressure depletion regimes on the dual-porosity shape factor for flow of compressible fluids in fractured porous media. Adv. Water Resour. 34, 1681–1693 (2011)

    Article  Google Scholar 

  • Rossen, R.H., Shen, E.I.C.: Simulation of Gas/Oil Drainage and water/oil imbibition in naturally fractured reservoirs. Paper SPE 16982, SPE Annual Technical Conference and Exhibition held in Dallas, Texas, 27–30 Sept (1987)

  • Stoll, W.M., Hofman, J.P., Ligthelm, D.J., Faber, M.J., van den Hoek, P.J.: Toward field-scale wettability modification—the limitations of diffusive transport. Paper SPE 107095, SPE/Europec/EAGE Annual Conference and Exhibition, London, 11–14 June (2007)

  • Thomas, L.K., Dixon, T.N., Pierson, R.G.: Fractured reservoir simulation. SPE J. 23, 42–54 (1983)

    Article  Google Scholar 

  • van Heel, A.P.G., Boerrigter, P.M., Van Dorp, J.J.: Thermal and hydraulic matrix-fracture interaction in dual-permeability simulation. SPE Reserv. Eval. Eng. 11(4), 735–749 (2008)

  • Warren, J.E., Root, P.J.: The behavior of naturally fractured reservoirs. SPE J. 3(3), 245–255 (1963)

  • Wu, Y.S., Li, J., Ding, D., Wang, C., Di, Y.: A generalized framework model for simulation of gas production in unconventional gas reservoirs. SPE J. 19(5), 845–857 (2014)

    Article  Google Scholar 

  • Zimmerman, R.W., Chen, G., Hadgu, T., Bodvarsson, G.S.: A numerical dual-porosity model with semianalytical treatment of matrix-fracture flow. Water Resour. Res. 29(7), 2127–2137 (1993)

    Article  Google Scholar 

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Bourbiaux, B., Ding, D. Simulation of Transient Matrix-Fracture Transfers of Compressible Fluids. Transp Porous Med 114, 695–717 (2016). https://doi.org/10.1007/s11242-016-0740-9

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  • DOI: https://doi.org/10.1007/s11242-016-0740-9

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