Abstract
This article is the first investigation on the dual permeability flow issue for horizontal well-production in a naturally fractured dual-porosity reservoir. Based on the inter-porosity flow from matrix system to fracture system and treating the media directly connected with horizontal wellbore as matrix and fracture systems, we established a model of horizontal well-production and then solved the model using some modern mathematical methods, such as Laplace integral transformation, separation of variables, eigenvalue, and eigenfunction. Later in the article, we obtained the standard log–log type curves using numerical simulation and analyzed the transient flow behavior thoroughly, which showed it is dual porosity and dual permeability flow behavior. The numerical simulation results showed that there are obvious differences between dual permeability and single permeability models. The dual permeability flow behavior accelerates energy supplement during production and reduces the classical matrix-fracture (V-shaped) response. We also showed that type curves characteristics are affected by external boundary conditions, the parameter κ, ω f and λ mf, etc. The research results show that our model would be a good semi-analytical model supplied to users. Because the single permeability modeling ignores the direct fluid supply from matrix to wellbore, we recommend using the dual permeability modeling to make well testing and rate decline interpretation in real case studies.
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Algharaib M., Gharbi R., Malallah A.: Scaling immiscible displacements in porous media with horizontal wells. Trans. Porous Med. 65(1), 89–105 (2006). doi:10.1007/s11242-005-6089-0
Al-Ghamdi A., Ershaghi I.: Pressure transient analysis of dually fractured reservoirs. SPE 26959-PA. SPE J. 1(1), 93–100 (1996). doi:10.2118/26959-PA
Al-Shaalan, T.M., Fung, L.S.K., Dogru, A.H.: A scalable massively parallel dual-porosity dual-permeability simulator for fractured reservoirs with super-k permeability. SPE 84371-MS, presented at the SPE annual technical conference and exhibition held in Denver, Colorado, 5–8 Oct 2003. doi:10.2118/84371-MS
Blasingame, T.A., McCray, T.L., Lee, W.J.: Decline curve analysis for variable pressure drop/variable flowrate systems. Paper SPE 21513 presented at the SPE gas technology symposium, Houston, 22–24 Jan 1991. doi:10.2118/21513-MS
Boughrara A.A., Reynolds A.C.: Analysis of injection/falloff data from horizontal wells. SPE-109799-PA. SPE J. 14(4), 721–736 (2009). doi:10.2118/109799-PA
Bourdet D.: Well test analysis: The use of advanced interpretation models, pp. 426. Elsevier Science B.V., Amsterdam (2002)
Braester C.: Influence of block size on the transition curve for a drawdown test in a naturally fractured reservoir. SPE 10543-PA. SPE J. 24(5), 498–504 (1984). doi:10.2118/10543-PA
Braester C., Zeitoun D.G.: Pressure transient response of stochastically heterogeneous fractured reservoirs. Trans. Porous Med. 11(3), 263–280 (1993). doi:10.1007/BF00614815
Bui, T.D., Mamora, D.D., Lee, W.J.: Transient pressure analysis for partially penetrating wells in naturally fractured reservoirs. SPE 60289-MS, presented at the 2000 SPE rocky mountain regional/low permeability reservoirs symposium and exbibition held in Denver, Colorado, 12–15 Mar 2000. doi:10.2118/60289-MS
Chastanet J., Royer P., Auriault J.-L.: Flow of low pressure gas through dual-porosity media. Trans. Porous Med. 66(3), 457–479 (2007). doi:10.1007/s11242-006-0023-y
Chen Z.X.: Transient flow of slightly compressible fluids through double-porosity, double-permeability systems—a state-of-the-art review. Trans. Porous Med. 4(2), 147–184 (1989). doi:10.1007/BF00134995
Corbett, P.W.M., Geiger, S., Borges, L., Garayev, M., Gonzalez, J., Camilo, V.: Limitations in the numerical well test modelling of fractured carbonate rocks, SPE 130252-MS. Presented at Europec/EAGE annual conference and exhibition, Barcelona, 14–17 June 2010. doi:10.2118/130252-MS
Degraff, J.M., Meurer, M.E., Landis, L.H., Lyons, S.: Fracture network modeling and dual-permeability simulation of carbonate reservoirs. SPE 10954-MS. Presented at the international petroleum technology conference held in Doha, Qatar, 21–23 Nov 2005. doi:10.2118/10954-MS
De Swaan O.A.: Analytical solutions for determining naturally fractured reservoir properties by well testing. SPE 5346-PA. SPE J. 16(3), 117–122 (1976). doi:10.2118/5346-PA
Doublet, L.E., Blasingame, T.A.: Decline curve analysis using type curves-analysis of oil well production data using material balance time: application to field cases. Paper SPE 28688 Presented at the petroleum conference and exhibition of Mexico, Veracruz, 10–13 Oct 1994. doi:10.2118/28688-MS
Du, K.F., Stewart, G.: Transient pressure response of horizontal wells in layered and naturally fractured reservoirs with dual-porosity behavior. Paper SPE 24682 presented at the SPE Annual Technical Conference and Exhibition, Washington, 4–7 Oct 1992. doi:10.2118/24682-MS
Duan, Y.G., Chen, W., Li, Q.S.: A comprehensive well test model for horizontal wells with complex boundaries. Paper PETSOC 98-21 presented at the Annual Technical Meeting, Calgary, 8–10 June 1998. doi:10.2118/98-21
Frick T.P., Brand C.W., Schlager B., Economides M.J.: Horizontal well testing of isolated segments. SPE 29959-PA. SPE J. 1(3), 261–274 (1996). doi:10.2118/29959-PA
Gill, H., Issaka, M.B.: Pressure transient behavior of horizontal and slant wells intersecting a high-permeability layer. Paper SPE 105616 presented at the SPE middle east oil and gas show and conference, Denver, 11–14 Mar 2007. doi:10.2118/105616-MS
Goode P.A., Thambynayagam R.K.M.: Pressure drawdown and buildup analysis of horizontal wells in anisotropic media. SPE 14250-PA. SPE Form. Eval. 2(4), 683–697 (1987). doi:10.2118/14250-PA
Hashemi A., Nicolas L.M., France G.D., Gringarten A.C.: Well test analysis of horizontal wells in gas-condensate reservoirs. SPE 89905-PA. SPE Reserv. Eval. Eng. 9(1), 86–99 (2006). doi:10.2118/89905-PA
Huang C.S., Chen Y.L., Yeh H.D.: A general analytical solution for flow to a single horizontal well by fourier and laplace transforms. Adv. Wat. Resour. 34(5), 640–648 (2011). doi:10.1016/j.advwatres.2011.02.015
Hu B.X., Huang H.: Stochastic analysis of reactive solute transport in heterogeneous, fractured porous media: a dual-permeability approach. Trans. Porous Med. 48(1), 1–39 (2002). doi:10.1023/A:1015671227317
Jia, Y.: The unity of well test analysis equations used for gas and oil wells respectively. Well Test. 2(4), 47–50 (1993) (in Chinese)
Jalali, Y., Ershaghi, I.: Pressure transient analysis of heterogeneous naturally fractured reservoirs. SPE 16341-MS, presented at the SPE California regional meeting held in Ventura, California, 8–10 Apr (1987). doi:10.2118/16341-MS
Kawecki M.W.: Transient flow to a horizontal water well. Gr. Wat. 38(6), 842–850 (2000)
Kompani-Zare M., Zhan H., Samani N.: Analytical study of capture zone of a horizontal well in a confined aquifer. J. Hydrol. 307(1-4), 48–59 (2005). doi:10.1016/j.hydrol.2004.09.021
Kuchuk E.J., Goode P.A., Wilkinson D.J., Thambynayagam R.K.M.: Pressure-transient behavior of horizontal wells with and without gas cap or aquifer. SPE 17413-PA. SPE Form. Eval. 6(1), 86–94 (1991). doi:10.2118/17413-PA
Kuchuk E.J., Hbashy T.: Pressure behavior of horizontal wells in multilayer reservoirs with cross flow. SPE 22731-PA. SPE Form. Eval. 11(1), 55–64 (1996). doi:10.2118/22731-PA
Langseth D.E., Smyth A.H., May J.: A method for evaluating horizontal well pumping tests. Gr. Wat. 42(5), 689–699 (2004)
Li K., Horne, Roland N.: Method to evaluate the potential of water injection in naturally fractured reservoirs. Trans. Porous Med. 83(3), 699–709 (2010). doi:10.1007/s11242-009-9473-3
Marhaendrajana, T., Blasingame, T.A.: Decline curve analysis using type curves-evaluation of well proformance behavior in a multiwell reservoir system. Paper SPE 71517 presented at the SPE annual technical conference and exhibition, New Orleans, 30 September–3 October 2001. doi:10.2118/71517-MS
Mattar L., Santo M.: A practical and systematic approach to horizontal well test analysis. PETSOC 95-09-04. J. Can. Petroleum Technol. 34(9), 42–46 (1995). doi:10.2118/95-09-04
Ng M.G., Aguilera R.: Well test analysis of horizontal wells in bounded naturally fractured reservoirs. PETSOC 94-14. J. Can. Petroleum Technol. 38(7), 20–24 (1999). doi:10.2118/94-14
Nie R.S., Ding Y.: Research on the nonlinear spherical percolation model with quadratic pressure gradient and its percolation characteristics. Nat. Sci. 2(2), 98–105 (2010). doi:10.4236/ns.2010.22016
Nie R., Meng Y., Yang Z., Guo J., Jia Y.: New flow model for the triple media carbonate reservoir. Int. J. Comput. Fluid Dyn. 25(2), 95–103 (2011). doi:10.1080/10618562.2011.560573
Ozkan E.: Analysis of horizontal-well responses: contemporary vs. conventional. SPE 72494-PA. SPE Reserv. Eval. Eng. 4(4), 260–269 (2001). doi:10.2118/72494-PA
Ozkan E., Raghavan R., Joshi S.D.: Horizontal-well pressure analysis. SPE 16378-PA. SPE Form. Eval. 4(4), 567–575 (1989). doi:10.2118/16378-PA
Ozkan E., Raghavan R.: New solutions for well-test-analysis problems: Part 1—analytical considerations. SPE 18615-PA. SPE Form. Eval. 6(3), 359–368 (1991). doi:10.2118/18615-PA
Ozkan E., Raghavan R.: New solutions for well-test-analysis problems: part 2—conputational considerations and applications. SPE 18616-PA. SPE Form. Eval. 6(3), 369–378 (1991). doi:10.2118/18616-PA
Peres A.M.M., Reynolds A.C.: Theory and analysis of injectivity tests on horizontal well. SPE 84957-PA. SPE J. 8(2), 147–159 (2003). doi:10.2118/84957-PA
Sherrard D.W.: Prediction and evaluation of horizontal well performance. Petroleum Geosci. 1(1), 25–30 (1995). doi:10.1144/petgeo.1.1.25
Sheng J.J.: Analytical steady-state solution of single-probe tests in a horizontal well and its application to estimate horizontal and vertical permeabilities. SPE 102659-PA. SPE Reserv. Eval. Eng. 11(3), 590–597 (2008). doi:10.2118/102659-PA
Stehfest H.: Numerical inversion of Laplace transform-algorithm 368. Commun. ACM 13(1), 47–49 (1970)
Sun D., Zhan H.: Flow to a horizontal well in an aquitard-aquifer system. J. Hydrol. 321(1-4), 364–376 (2006). doi:10.1016/j.jhydrol.2005.08.008
Uba, H.M., Chiffoleau, Y., Pham, T., Divry, V., Kaabi, A., Thuwaini, J.: Application of a hybrid dual-porosity/ dual-permeability representation of large-scale fractures to the simulation of a giant carbonate reservoir. SPE 105560-MS, presented at the SPE middle east oil and gas show and conference held in kingdom of Bahrain, Bahrain, 11–14 Mar 2007. doi:10.2118/105560-MS
Van Everdingen A.F., Hurst W.: The application of the laplace transformation to flow problems in reservoir. Trans. AIME 186, 305 (1949)
Van Heel A.P.G., Boerrigter P.M., Van Dorp J.J.: Thermal and hydraulic matrix-fracture interaction in dual-permeability simulation. SPE 102471-PA. SPE Reserv. Eval. Eng. 11(4), 735–749 (2008). doi:10.2118/102471-PA
Warren J.E., Root P.J.: The behavior of naturally fractured reservoirs. SPE 426-PA. SPE J. 3(3), 245–255 (1963). doi:10.2118/426-PA
Zhan H., Zlotnik V.A.: Ground water flow to horizontal and slanted wells in unconfined aquifers. Wat. Resour. Res. 38(7), 1108 (2002). doi:10.1029/2001WR000401
Acknowledgments
The authors would like to thank the 4 anonymous reviewers. They thoroughly reviewed the manuscript and their critical comments were very helpful in preparing this article. The authors would like to also thank the editors of TIPM for their managing and editing the article. The authors would like to especially thank Mr Hong-Qiao Jia (an engineer of the company of SPT Group Inc. in Houston, Texas, U.S.A.) for his ardent help in English writing and usage.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Nie, RS., Meng, YF., Jia, YL. et al. Dual Porosity and Dual Permeability Modeling of Horizontal Well in Naturally Fractured Reservoir. Transp Porous Med 92, 213–235 (2012). https://doi.org/10.1007/s11242-011-9898-3
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DOI: https://doi.org/10.1007/s11242-011-9898-3