Optimal design of hydraulic fracturing in porous media using the phase field fracture model coupled with genetic algorithm. (English) Zbl 1405.76055
Comput. Geosci. 22, No. 3, 833-849 (2018); correction ibid. 22, No. 6, 1583 (2018).
Summary: We present a framework for the coupling of fluid-filled fracture propagation and a genetic inverse algorithm for optimizing hydraulic fracturing scenarios in porous media. Fracture propagations are described by employing a phase field approach, which treats fracture surfaces as diffusive zones rather than of interfaces. Performance of the coupled approach is provided with applications to numerical experiments related to maximizing production or reservoir history matching for emphasizing the capability of the framework.
Keywords:
hydraulic fracturing; phase field; genetic algorithm; production maximization; history matchingReferences:
| [1] | Abass, H.H., Soliman, M.Y., Al-Tahini, A.M., Surjaatmadja, J.B., Meadows, D.L., Sierra, L.: Oriented fracturing: a new technique to hydraulically fracture an openhole horizontal well. In: SPE Annual Technical Conference and Exhibition (2009) |
| [2] | Almani, T., Kumar, K., Dogru, A., Singh, G., Wheeler, M.F.: Convergence analysis of multirate fixed-stress split iterative schemes for coupling flow with geomechanics. Comput. Methods Appl. Mech. Eng. 311, 180-207 (2016) · Zbl 1439.74183 · doi:10.1016/j.cma.2016.07.036 |
| [3] | Almani, T., Lee, S., Wheeler, M.F., Wick, T.: Multirate coupling for flow and geomechanics applied to hydraulic fracturing using an adaptive phase-field technique. volume SPE-182610-MS Society of Petroleum Engineers (2017) |
| [4] | Ambrosio, L., Tortorelli, V.: Approximation of functionals depending on jumps by elliptic functionals via γ-convergence. Commun. Pure Appl. Math. 43, 999-1036 (1990) · Zbl 0722.49020 · doi:10.1002/cpa.3160430805 |
| [5] | Ambrosio, L., Tortorelli, V.: On the approximation of free discontinuity problems. Unione Matematica Italiana. Bollettino. B. 6, 105-123 (1992) · Zbl 0776.49029 |
| [6] | Amor, H., Marigo, J.-J., Maurini, C.: Regularized formulation of the variational brittle fracture with unilateral contact numerical experiments. J. Mech. Phys. Solids 57, 1209-1229 (2009) · Zbl 1426.74257 · doi:10.1016/j.jmps.2009.04.011 |
| [7] | Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kanschat, G., Kronbichler, M., Maier, M., Turcksin, B., Wells, D.: The deal.II library, version 8.4. J. Numer. Math. 24(3), 135-141 (2016) · Zbl 1348.65187 · doi:10.1515/jnma-2016-1045 |
| [8] | Bangerth, W., Klie, H., Wheeler, M.F., Stoffa, P.L., Sen, M.K.: On optimization algorithms for the reservoir oil well placement problem. Comput. Geosci. 10(3), 303-319 (2006) · Zbl 1197.76123 · doi:10.1007/s10596-006-9025-7 |
| [9] | Bourdin, B., Francfort, G., Marigo, J.-J.: Numerical experiments in revisited brittle fracture. J. Mech. Phys. Solids 48(4), 797-826 (2000) · Zbl 0995.74057 · doi:10.1016/S0022-5096(99)00028-9 |
| [10] | Britt, L.: Optimized oilwell fracturing of moderate-permeability reservoirs. In: SPE Annual Technical Conference and Exhibition (1985) |
| [11] | Castonguay, S.T., Mear, M.E., Dean, R.H., Schmidt, J.H.: Predictions of the growth of multiple interacting hydraulic fractures in three dimensions. In: SPE Annual Technical Conference and Exhibition, vol. 3, pp 2206-2217 (2013) |
| [12] | Cheng, C., Bunger, A.P., Peirce, A.P.: Optimal perforation location and limited entry design for promoting simultaneous growth of multiple hydraulic fractures. In: SPE Hydraulic Fracturing Technology Conference (2016) |
| [13] | Dean, R., Gai, X., Stone, C., Minkoff, S.: A comparison of techniques for coupling porous flow and geomechanics. SPE-79709-MS, 132-140 (2006) |
| [14] | Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Trans. Evol. Comput. 6(2), 182-197 (2002) · doi:10.1109/4235.996017 |
| [15] | Dohmen, T., Zhang, J.J., Blangy, J.-P.: Stress shadowing effect key to optimizing spacing of multistage fracture stages. American Oil & Gas Reporter (2015) |
| [16] | Fisher, M., Warpinski, N.: Hydraulic-fracture-height growth: real data. SPE Prod. Oper. 27(1), 8-19 (2012) |
| [17] | Fisher, M.K., Wright, C.A., Davidson, B.M., Goodwin, A., Fielder, E., Buckler, W., Steinsberger, N.: Integrating fracture mapping technologies to optimize stimulations in the Barnett Shale. In: SPE Annual Technical Conference and Exhibition (2002) |
| [18] | Francfort, G., Marigo, J.-J.: Revisiting brittle fracture as an energy minimization problem. J. Mech. Phys. Solids 46(8), 1319-1342 (1998) · Zbl 0966.74060 · doi:10.1016/S0022-5096(98)00034-9 |
| [19] | Girault, V., Kumar, K., Wheeler, M.F.: Convergence of iterative coupling of geomechanics with flow in a fractured poroelastic medium. Comput. Geosci. 20(5), 997-1011 (2016). https://doi.org/10.1007/s10596-016-9573-4 · Zbl 1391.76650 · doi:10.1007/s10596-016-9573-4 |
| [20] | Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Professional, Reading (1989) · Zbl 0721.68056 |
| [21] | Heider, Y., Markert, B.: A phase-field modeling approach of hydraulic fracture in saturated porous media. Mechanics Research Communications (2016) |
| [22] | Heister, T., Wheeler, M.F., Wick, T.: A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach. Comput. Methods Appl. Mech. Eng. 290, 466-495 (2015) · Zbl 1423.76239 · doi:10.1016/j.cma.2015.03.009 |
| [23] | Holditch, S.A., Jennings, J.W., Neuse, S.H., Wyman, R.E.: The optimization of well spacing and fracture length in low permeability gas reservoirs. In: SPE Annual Fall Technical Conference and Exhibition (1978) |
| [24] | Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. U Michigan Press, Ann Arbor (1975) · Zbl 0317.68006 |
| [25] | Karma, A., Kessler, D.A., Levine, H.: Phase-field model of mode iii dynamic fracture. Phys. Rev. Lett. 87, 045501 (2001) · doi:10.1103/PhysRevLett.87.045501 |
| [26] | Kim, J., Tchelepi, H., Juanes, R.: Stability, accuracy, and efficiency of sequentiel methods for flow and geomechanics. SPE J. 16(2), 249-262 (2011) · doi:10.2118/119084-PA |
| [27] | Kim, J., Tchelepi, H., Juanes, R.: Stability and convergence of sequentiel methods for coupled flow and geomechanics: fixed-stress and fixed-strain splits. Comput. Methods Appl. Mech. Eng. 200(13-16), 1591-1606 (2011) · Zbl 1228.74101 · doi:10.1016/j.cma.2010.12.022 |
| [28] | Lee, S., Lee, Y.-J., Wheeler, M.F.: A locally conservative enriched galerkin approximation and efficient solver for elliptic and parabolic problems. SIAM J. Sci. Comput. 38(3), A1404-A1429 (2016) · Zbl 1337.65128 · doi:10.1137/15M1041109 |
| [29] | Lee, S., Mikelić, A., Wheeler, M., Wick, T.: Phase-field modeling of two-phase fluid-filled fractures in a poroelastic medium. submitted (2017) · Zbl 1401.74084 |
| [30] | Lee, S., Mikelić, A., Wheeler, M.F., Wick, T.: Phase-field modeling of proppant-filled fractures in a poroelastic medium. Comput. Method Appl. Mech. Eng. 312, 509-541 (2016). Phase Field Approaches to Fracture · Zbl 1439.74359 · doi:10.1016/j.cma.2016.02.008 |
| [31] | Lee, S., Reber, J.E., Hayman, N.W., Wheeler, M.F.: Investigation of wing crack formation with a combined phase-field and experimental approach. Geophys. Res. Lett. 43(15), 7946-7952 (2016) · doi:10.1002/2016GL069979 |
| [32] | Lee, S., Wheeler, M.F., Wick, T.: Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model. Comput. Methods Appl. Mech. Eng. 305, 111-132 (2016) · Zbl 1425.74419 · doi:10.1016/j.cma.2016.02.037 |
| [33] | Lee, S., Wheeler, M.F., Wick, T.: Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches. J. Comput. Appl. Math. 314, 40-60 (2017) · Zbl 1388.76140 · doi:10.1016/j.cam.2016.10.022 |
| [34] | Lee, S., Wheeler, M.F., Wick, T., Srinivasan, S.: Initialization of phase-field fracture propagation in porous media using probability maps of fracture networks. Mech. Res. Commun. 80, 16-23 (2017). Multi-Physics of Solids at Fracture · doi:10.1016/j.mechrescom.2016.04.002 |
| [35] | Liu, C.H.: Optimizing Hydraulic Fracture Spacing and Lateral Well Spacing in Tight/Unconventional Resource Development through Fully Coupling Stress Shadowing Effects and Fluid Flow - an Integrated Approach. PhD thesis, Colorado School of Mines (2016) |
| [36] | Ma, X., Gildin, E., Plaksina, T.: Efficient optimization framework for integrated placement of horizontal wells and hydraulic fracture stages in unconventional gas reservoirs. J Unconventional Oil Gas Res. 9, 1-17 (2015) · doi:10.1016/j.juogr.2014.09.001 |
| [37] | Mauthe, S., Miehe, C.: Hydraulic fracture in poro-hydro-elastic media. Mechanics Research Communications (2016) · Zbl 1425.74423 |
| [38] | Meyer, B.R., Bazan, L.W.: A discrete fracture network model for hydraulically induced fractures-theory, parametric and case studies. In: SPE Hydraulic Fracturing Technology Conference (2011) |
| [39] | Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: robust algorithmic implementation based on operator splits. Comput. Methods Appl. Mech. Eng. 199, 2765-2778 (2010) · Zbl 1231.74022 · doi:10.1016/j.cma.2010.04.011 |
| [40] | Miehe, C., Kienle, D., Aldakheel, F., Teichtmeister, S.: Phase field modeling of fracture in porous plasticity: a variational gradient-extended eulerian framework for the macroscopic analysis of ductile failure. Computer Methods in Applied Mechanics and Engineering (2016) · Zbl 1353.74065 |
| [41] | Miehe, C., Welschinger, F., Hofacker, M.: Thermodynamically consistent phase-field models of fracture: variational principles and multi-field fe implementations. Int. J. Numer. Methods Eng. 83, 1273-1311 (2010) · Zbl 1202.74014 · doi:10.1002/nme.2861 |
| [42] | Mikelić, A., Wang, B., Wheeler, M.F.: Numerical convergence study of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 18(3-4), 325-341 (2014) · Zbl 1386.76115 · doi:10.1007/s10596-013-9393-8 |
| [43] | Mikelić, A., Wheeler, M., Wick, T.: A phase-field approach to the fluid filled fracture surrounded by a poroelastic medium. ICES Report, 13-15 (2013) |
| [44] | Mikelić, A., Wheeler, M., Wick, T.: Phase-field modeling of a fluid-driven fracture in a poroelastic medium. In: Press in Computational Geosciences. https://doi.org/10.1007/s10596-015-9532-5 (2013) · Zbl 1390.86010 |
| [45] | Mikelić, A., Wheeler, M.F.: Convergence of iterative coupling for coupled flow and geomechanics. Comput. Geosci. 17(3), 455-462 (2012) · Zbl 1392.35235 · doi:10.1007/s10596-012-9318-y |
| [46] | Mikelić, A., Wheeler, M.F., Wick, T.: A phase-field method for propagating fluid-filled fractures coupled to a surrounding porous medium. SIAM Multiscale Model Simul. 13(1), 367-398 (2015) · Zbl 1317.74028 · doi:10.1137/140967118 |
| [47] | Mikelić, A., Wheeler, M.F., Wick, T.: A quasi-static phase-field approach to pressurized fractures. Nonlinearity 28(5), 1371-1399 (2015) · Zbl 1316.35287 · doi:10.1088/0951-7715/28/5/1371 |
| [48] | Min, B., Kang, J.M., Chung, S., Park, C., Jang, I.: Pareto-based multi-objective history matching with respect to individual production performance in a heterogeneous reservoir. J. Pet. Sci. Eng. 122, 551-566 (2014) · doi:10.1016/j.petrol.2014.08.023 |
| [49] | Min, B., Kang, J.M., Lee, H., Jo, S., Park, C., Jang, I.: Development of a robust multi-objective history matching for reliable well-based production forecasts. Energy Explor. Exploit. 34(6), 795-809 (2016) · doi:10.1177/0144598716665008 |
| [50] | Min, B., Park, C., Jang, I., Kang, J.M., Chung, S.: Development of pareto-based evolutionary model integrated with dynamic goal programming and successive linear objective reduction. Appl. Soft Comput. 35, 75-112 (2015) · doi:10.1016/j.asoc.2015.06.007 |
| [51] | Min, B., Park, C., Kang, J., Park, H., Jang, I.: Optimal well placement based on artificial neural network incorporating the productivity potential. Energy Sources, Part A 33(18), 1726-1738 (2011) · doi:10.1080/15567030903468569 |
| [52] | Min, B., Wheeler, M.F., Sun, A.Y.: Parallel multiobjective optimization for the coupled compositional/geomechanical modeling of pulse testing. In: SPE Reservoir Simulation Conference. Society of Petroleum Engineers (2017) |
| [53] | Nagel, N., Zhang, F., Sanchez-Nagel, M., Lee, B., Agharazi, A., et al: Stress shadow evaluations for completion design in unconventional plays. In: SPE Unconventional Resources Conference Canada. Society of Petroleum Engineers (2013) |
| [54] | Peirce, A., Bunger, A.: Interference fracturing: non-uniform distributions of perforation clusters that promote simultaneous growth of multiple hydraulic fractures. SPE J. 20(2), 384-395 (2015) · doi:10.2118/172500-PA |
| [55] | Peirce, A., Detournay, E.: An implicit level set method for modeling hydraulically driven fractures. Comput. Methods Appl. Mech. Eng. 197(33), 2858-2885 (2008) · Zbl 1194.74534 · doi:10.1016/j.cma.2008.01.013 |
| [56] | Rice, J.R.: Mathematical analysis in the mechanics of fracture. Fracture: An Advan. Treatise 2, 191-311 (1968) · Zbl 0214.51802 |
| [57] | Saputelli, L., Lopez, C., Chacon, A., Soliman, M.: Design optimization of horizontal wells with multiple hydraulic fractures in the bakken shale. In: SPE/EAGE European Unconventional Resources Conference and Exhibition (2014) |
| [58] | Settari, A., Mourits, F.: A coupled reservoir and geomechanical simulation system. SPE J. 3(3), 219-226 (1998) · doi:10.2118/50939-PA |
| [59] | Singh, G., Pencheva, G., Kumar, K., Wick, T., Ganis, B., Wheeler, M.: Impact of Accurate Fractured Reservoir Flow Modeling on Recovery Predictions. SPE 188630-MS, SPE Hydraulic Fracturing Technology Conference, Woodlands, TX (2014) |
| [60] | Veatch, R.: Overview of current hydraulic fracturing design and treatment technology-part 1. J. Petrol. Tech. 35(4), 677-687 (1983) · doi:10.2118/10039-PA |
| [61] | Vincent, M.: The next opportunity to improve hydraulic-fracture stimulation. J. Petrol. Tech. 64(3), 118-127 (2012) · doi:10.2118/144702-JPT |
| [62] | Wheeler, J., Wheeler, M.: Ipars technical manual. Center for Subsurface Modeling, The University of Texas at Austin (1990) |
| [63] | Wick, T., Lee, S., Wheeler, M.F.: 3D phase-field for pressurized fracture propagation in heterogeneous media. VI International Conference on Computational Methods for Coupled Problems in Science and Engineering 2015 Proceedings (2015) |
| [64] | Wick, T., Singh, G., Wheeler, M.: Fluid-filled fracture propagation using a phase-field approach and coupling to a reservoir simulator. SPE J. 21, 981-999 (2015) · doi:10.2118/168597-PA |
| [65] | Wu, K., Olson, J., Balhoff, M.T., Yu, W., et al.: Numerical analysis for promoting uniform development of simultaneous multiple-fracture propagation in horizontal wells. SPE Production & Operations (2016) |
| [66] | Wu, K., Olson, J.E., et al.: Investigation of the impact of fracture spacing and fluid properties for interfering simultaneously or sequentially generated hydraulic fractures. SPE Prod. Oper. 28(04), 427-436 (2013) |
| [67] | Wu, K., Olson, J.E., et al.: Mechanisms of simultaneous hydraulic-fracture propagation from multiple perforation clusters in horizontal wells. SPE Journal (2016) |
| [68] | Xiong, H.: Optimizing cluster or fracture spacing: an overview (2017) |
| [69] | Zangeneh, N., Eberhardt, E., Bustin, R.: Investigation of the influence of stress shadows on horizontal hydraulic fractures from adjacent lateral wells. J Unconventional Oil Gas Res. 9, 54-64 (2015) · doi:10.1016/j.juogr.2014.11.001 |
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