×

Uncertainties consideration in elastically heterogeneous fluid-saturated media using first-order second moment stochastic method and Green’s function approach. (English) Zbl 1510.86016

MSC:

86A32 Geostatistics
62P12 Applications of statistics to environmental and related topics
65M80 Fundamental solutions, Green’s function methods, etc. for initial value and initial-boundary value problems involving PDEs
Full Text: DOI

References:

[1] Morgan, K.; Lewis, R. W.; White, I. R., The mechanisms of ground surface subsidence above compacting multiphase reservoirs and their analysis by the finite element method, Appl. Math. Model., 4, 217-224 (1980) · Zbl 0431.76076
[2] Minkoff, S. E.; Kridler, N. M., A comparison of adaptive time stepping methods for coupled flow and deformation modeling, Appl. Math. Model., 30, 993-1009 (2006) · Zbl 1197.76112
[3] Teatini, P.; Ferronato, M.; Gambolati, G.; Gonella, M., Groundwater pumping and land subsidence in the Emilia-Romagna coastland, Italy: modeling the past occurrence and the future trend, Water Resour. Res., 42, 1-19 (2006)
[4] Ferronato, M.; Gambolati, G.; Janna, C.; Teatini, P., Geomechanical issues of anthropogenic CO_2 sequestration in exploited gas fields, Energy Convers. Manag., 51, 1918-1928 (2010)
[5] Teatini, P.; Castelletto, N.; Ferronato, M.; Gambolati, G.; Janna, C.; Cairo, E.; Marzorati, D.; Colombo, D.; Ferretti, A.; Bagliani, A.; Bottazzi, F., Geomechanical response to seasonal gas storage in depleted reservoirs: a case study in the Po River basin, Italy, J. Geophys. Res. Earth Surf., 116, 1-21 (2011)
[6] Nagelhout, A. C.G.; Roest, J. P.A., Investigating fault slip in a model of an underground gas storage facility, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 34, 645 (1997)
[7] Baù, D.; Ferronato, M.; Gambolati, G.; Teatini, P.; Alzraiee, A., Ensemble smoothing of land subsidence measurements for reservoir geomechanical characterization, Int. J. Numer. Anal. Methods Geomech., 39, 207-228 (2015)
[8] Ferronato, M.; Gambolati, G.; Teatini, P.; Baù, D., Stochastic poromechanical modeling of anthropogenic land subsidence, Int. J. Solids Struct., 43, 3324-3336 (2006) · Zbl 1121.74351
[9] Bourne, S. J.; Oates, S. J.; Van Elk, J.; Doornhof, D., A seismological model for earthquakes induced by fluid extraction from a subsurface reservoir, J. Geophys. Res. Solid Earth., 119, 8991-9015 (2014)
[10] Verdon, J. P.; Kendall, J. M.; Horleston, A. C.; Stork, A. L., Subsurface fluid injection and induced seismicity in southeast Saskatchewan, Int. J. Greenh. Gas Control, 54, 429-440 (2016)
[11] Paullo Muñoz, L. F.; Roehl, D., An analytical solution for displacements due to reservoir compaction under arbitrary pressure changes, Appl. Math. Model., 52, 145-159 (2017) · Zbl 1480.76124
[12] Colazas, X. C.; Strehle, R. W., Chapter 6 Subsidence in the wilmington oil field, long beach, california, USA, Dev. Pet. Sci., 41, 285-335 (1995)
[13] Finol, A. S.; Sancevic, Z. A., Chapter 7 Subsidence in venezuela, Dev. Pet. Sci., 41, 337-372 (1995)
[14] Hermansen, H.; Landa, G. H.; Sylte, J. E.; Thomas, L. K., Experiences after 10 years of waterflooding the Ekofisk Field, Norway, J. Pet. Sci. Eng., 26, 11-18 (2000)
[15] T.G. Kristiansen, B. Plischke. History Matched Full Field Geomechanics Model of the Valhall Field Including Water Weakening and Re-Pressurisation. Paper presented at the SPE EUROPEC/EAGE Annual Conference and Exhibition, Barcelona, Spain, June 2010. doi:10.2118/131505-MS.
[16] Hatchell, P. J.; Jorgensen, O.; Gommesen, L.; Stammeijer, J., Monitoring reservoir compaction from subsidence and time-lapse time shifts in the Dan field, Soc. Explor. Geophys., 2867-2871 (2007), SEG Tech. Progr. Expand. Abstr. 2007
[17] Van Thienen-Visser, K.; Fokker, P. A., The future of subsidence modelling: compaction and subsidence due to gas depletion of the Groningen gas field in the Netherlands, Geol. Mijnb.Neth. J. Geosci., 96, s105-s116 (2017)
[18] Sun, H.; Zhang, Q.; Zhao, C.; Yang, C.; Sun, Q.; Chen, W., Monitoring land subsidence in the southern part of the lower Liaohe plain, China with a multi-track PS-InSAR technique, Remote Sens. Environ., 188, 73-84 (2017)
[19] Bonazzi, A.; Jha, B.; de Barros, F. P.J., Transport analysis in deformable porous media through integral transforms, Int. J. Numer. Anal. Methods Geomech., 45, 307-324 (2021)
[20] Geertsma, J., A remark on the analogy between thermoelasticity and the elasticity of saturated porous media, J. Mech. Phys. Solids, 6, 13-16 (1957) · Zbl 0090.16003
[21] Geertsma, J., A basic theory of subsidence due to reservoir compaction: the homogeneous case, Verh. van Het Ned. Geol. Mijnb. Kundig Genoot., 28, 43-62 (1973)
[22] Geertsma, J., Land subsidence above compacting oil and gas reservoirs, Pet. Technol., 25, 734-744 (1973), J. JPT
[23] Mindlin, R. D.; Cheng, D. H., Thermoelastic stress in the semi-infinite solid, J. Appl. Phys., 21, 931-933 (1950) · Zbl 0038.37205
[24] Lewis, R. W.; Morgan, K.; White, I. R., The influence of integration rule accuracy on the calculation of surface subsidence by the nucleus of strain method in conjunction with a finite element reservoir simulator, Appl. Math. Model., 7, 419-422 (1983) · Zbl 0524.76085
[25] Van Opstal, G. H.C., The effect of base-rock rigidity on subsidence due to reservoir compaction, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 12, 173 (1975)
[26] Segall, P., Induced stresses due to fluid extraction from axisymmetric reservoirs, Pure Appl. Geophys., 139, 535-560 (1992), PAGEOPH
[27] Du, J.; Olson, J. E., A poroelastic reservoir model for predicting subsidence and mapping subsurface pressure fronts, J. Pet. Sci. Eng., 30, 181-197 (2001)
[28] Fokker, P. A.; Orlic, B., Semi-analytic modelling of subsidence, Math. Geol., 38, 565-589 (2006) · Zbl 1112.74040
[29] Tempone, P.; Fjær, E.; Landrø, M., Improved solution of displacements due to a compacting reservoir over a rigid basement, Appl. Math. Model., 34, 3352-3362 (2010) · Zbl 1201.86010
[30] Mehrabian, A.; Abousleiman, Y. N., Geertsma’s subsidence solution extended to layered stratigraphy, J. Pet. Sci. Eng., 130, 68-76 (2015)
[31] Settari, A.; Walters, D. A., Advances in coupled geomechanical and reservoir modeling with applications to reservoir compaction, SPE J., 6, 334-342 (2001)
[32] Belayneh, M.; Geiger, S.; Matthäi, S. K., Numerical simulation of water injection into layered fractured carbonate reservoir analogs, Am. Assoc. Pet. Geol. Bull., 90, 1473-1493 (2006)
[33] Watanabe, N.; Wang, W.; McDermott, C. I.; Taniguchi, T.; Kolditz, O., Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media, Comput. Mech., 45, 263-280 (2010) · Zbl 1362.74024
[34] S.P. Lele, S.-Y. Hsu, J.L. Garzon, N. DeDontney, K.H. Searles, G.A. Gist, P.F. Sanz, E.A. Biediger, B.A. Dale. Geomechanical Modeling to Evaluate Production-Induced Seismicity at Groningen Field. Paper presented at the Abu Dhabi International Petroleum Exhibition & Conference, Abu Dhabi, UAE, November 2016. doi:10.2118/183554-MS.
[35] Haddad, M.; Eichhubl, P., Poroelastic models for fault reactivation in response to concurrent injection and production in stacked reservoirs, Geomech. Energy Environ., 24, Article 100181 pp. (2020)
[36] Peres, M. L.; Mesquita, L. C.; Leroy, Y. M.; Sotelino, E. D., Stress evolution in elastically heterogeneous and non-linear fluid-saturated media with a Green’s function approach, Int. J. Numer. Anal. Methods Geomech., 45, 1323-1346 (2021)
[37] Baù, D.; Alzraiee, A.; Zoccarato, C.; Gambolati, G.; Ferronato, M.; Bottazzi, F.; Mantica, S.; Teatini, P., Testing a data assimilation approach to reduce geomechanical uncertainties in modelling land subsidence, Environ. Geotech., 3, 386-396 (2016)
[38] Muller, A. L.; do A. Vargas, E.; Vaz, L. E.; Gonçalves, C. J., Three-dimensional analysis of boreholes considering spatial variability of properties and poroelastoplasticity, J. Pet. Sci. Eng., 68, 268-276 (2009)
[39] Muller, A. L.; do Amaral Vargas, E.; Vaz, L. E.; Gonçalves, C. J., Borehole stability analysis considering spatial variability and poroelastoplasticity, Int. J. Rock Mech. Min. Sci., 46, 90-96 (2009)
[40] Geddes, J. D., Principles of engineering geology, Endeavour, 1, 39-40 (1977)
[41] Deng, Z. P.; Li, D. Q.; Qi, X. H.; Cao, Z. J.; Phoon, K. K., Reliability evaluation of slope considering geological uncertainty and inherent variability of soil parameters, Comput. Geotech., 92, 121-131 (2017)
[42] Suchomel, R.; Mašín, D., Comparison of different probabilistic methods for predicting stability of a slope in spatially variable c-φ soil, Comput. Geotech., 37, 132-140 (2010)
[43] Yang, Z.; Ching, J., A novel simplified geotechnical reliability analysis method, Appl. Math. Model., 74, 337-349 (2019) · Zbl 1481.62128
[44] El-Ramly, H.; Morgenstern, N. R.; Cruden, D. M., Probabilistic slope stability analysis for practice, Can. Geotech. J., 39, 665-683 (2002)
[45] Brza̧kała, W.; Puła, W., A probabilistic analysis of foundation settlements, Comput. Geotech., 18, 291-309 (1996)
[46] Bungenstab, F. C.; Bicalho, K. V., Settlement predictions of footings on sands using probabilistic analysis, J. Rock Mech. Geotech. Eng., 8, 198-203 (2016)
[47] Fiori, A.; Bellin, A.; Cvetkovic, V.; de Barros, F. P.J.; Dagan, G., Stochastic modeling of solute transport in aquifers: from heterogeneity characterization to risk analysis, Water Resour. Res., 51, 6622-6648 (2015)
[48] Sohn, M. D.; Small, M. J.; Pantazidou, M., Reducing uncertainty in site characterization using bayes Monte Carlo methods, J. Environ. Eng., 126, 893-902 (2000)
[49] Batalha, N. A.; Duran, O. Y.; Devloo, P. R.B.; Vieira, L. C.M., Stability analysis and uncertainty modeling of vertical and inclined wellbore drilling through heterogeneous field, Oil Gas Sci. Technol., 75 (2020)
[50] Udegbunam, J. E.; Aadnøy, B. S.; Fjelde, K. K., Uncertainty evaluation of wellbore stability model predictions, J. Pet. Sci. Eng., 124, 254-263 (2014)
[51] Aichi, M., Land subsidence modelling for decision making on groundwater abstraction under emergency situation, Proc. Int. Assoc. Hydrol. Sci., 382, 403-408 (2020)
[52] Bottazzi, F.; Rossa, E. Della, A functional data analysis approach to surrogate modeling in reservoir and geomechanics uncertainty quantification, Math. Geosci., 49, 517-540 (2017) · Zbl 1369.86025
[53] Gazzola, L.; Ferronato, M.; Frigo, M.; Teatini, P.; Zoccarato, C.; Corradi, A. A.I.; Dacome, M. C.; Della Rossa, E.; De Simoni, M.; Mantica, S., Blending measurements and numerical models: a novel methodological approach for land subsidence prediction with uncertainty quantification, Proc. Int. Assoc. Hydrol. Sci., 382, 457-462 (2020)
[54] Zoccarato, C.; Gazzola, L.; Ferronato, M.; Teatini, P., Generalized polynomial chaos expansion for fast and accurate uncertainty quantification in geomechanical modelling, Algorithms, 13, 1-23 (2020)
[55] Frias, D. G.; Murad, M. A.; Pereira, F., Stochastic computational modelling of highly heterogeneous poroelastic media with long-range correlations, Int. J. Numer. Anal. Methods Geomech., 28, 1-32 (2004) · Zbl 1075.74525
[56] Mallor, C.; Calvo, S.; Núñez, J. L.; Rodríguez-Barrachina, R.; Landaberea, A., Full second-order approach for expected value and variance prediction of probabilistic fatigue crack growth life, Int. J. Fatigue, 133, Article 105454 pp. (2020)
[57] Hwang, H.; Lansey, K.; Jung, D., Accuracy of first-order second-moment approximation for uncertainty analysis of water distribution systems, J. Water Resour. Plan. Manag., 144, Article 04017087 pp. (2018)
[58] Wu, F.; Zeng, W.; Yao, L. Y.; Liu, G. R., A generalized probabilistic edge-based smoothed finite element method for elastostatic analysis of Reissner-Mindlin plates, Appl. Math. Model., 53, 333-352 (2018) · Zbl 1480.74210
[59] Yang, Z.; Ching, J., A novel reliability-based design method based on quantile-based first-order second-moment, Appl. Math. Model., 88, 461-473 (2020) · Zbl 1481.62104
[60] WenXin, Z.; Zhenzhou, L., An inequality unscented transformation for estimating the statistical moments, Appl. Math. Model., 62, 21-37 (2018) · Zbl 1462.62163
[61] M. Lloret-Cabot, G.A. Fenton & M.A. Hicks (2014) On the estimation of scale of fluctuation in geostatistics, Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 8:2, 129-140, doi:10.1080/17499518.2013.871189.
[62] Criel, P.; Reybrouck, N.; Caspeele, R.; Matthys, S., Uncertainty quantification of creep in concrete by Taylor expansion, Eng. Struct., 153, 334-341 (2017)
[63] Wang, J. P.; Yun, X.; Wu, Y. M., A first-order second-moment calculation for seismic hazard assessment with the consideration of uncertain magnitude conversion, Nat. Hazards Earth Syst. Sci., 13, 2649-2657 (2013)
[64] Cheng, H.; Chen, J.; Chen, R.; Chen, G., Comparison of modeling soil parameters using random variables and random fields in reliability analysis of tunnel face, Int. J. Geomech., 19, Article 04018184 pp. (2019)
[65] Duncan, J. M., Factors of safety and reliability in geotechnical engineering, J. Geotech. Geoenviron. Eng., 126, 307-316 (2000)
[66] Mishra, S., Alternatives to Monte-Carlo simulation for probabilistic reserves estimation and production forecasting, (Proceedings of the SPE Annual Technical Conference and Exhibition (1998), SPE), 785-792
[67] Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Phys., 12, 155-164 (1941) · JFM 67.0837.01
[68] Lehner, F. K.; Knoglinger, J. K., Use of a Maysel integral representation for solving poroelastic inclusion problems, (Proceedings of the 6th International Congress on Thermal Stresses (2005)), 77-80, 26-29 May 2005, Vienna, Austria
[69] Melan, E., Der spannungszustand der durch eine einzelkraft im innern beanspruchten halbscheibe, ZAMM Z. Fur Angew. Math. Mech., 12, 343-346 (1932) · JFM 58.0852.01
[70] H.G. Poulos and E. Davis, Elastic Solutions for Soil and Rock Mechanics, Wiley [New York], (1973), http://www.usucger.org/PandD/complete_book.pdf.
[71] Telles, J. C.F.; Brebbia, C. A., Boundary element solution for half-plane problems, Int. J. Solids Struct., 17, 1149-1158 (1981) · Zbl 0472.73095
[72] Bartholomew, G. E., Numerical integration over the triangle, Math. Tables Other Aids Comput., 13, 295 (1959) · Zbl 0093.13504
[73] Mousavi, S. E.; Sukumar, N., Generalized duffy transformation for integrating vertex singularities, Comput. Mech., 45, 127-140 (2010)
[74] Bonnet, M., Boundary integral equation methods for elastic and plastic problems, Encyclopedia of Computational Mechanics, 1-33 (2017), John Wiley & Sons: John Wiley & Sons Ltd, Chichester, UK
[75] Ang, A. H.; Tang, W. H., Probability Concepts in Engineering: Emphasis on Applications in Civil & Environmental Engineering, 27, 1-419 (2015), John Wiley Sons, Inc
[76] Vanmarcke, E., Random Fields (2010), World Scientific · Zbl 1220.60030
[77] Cho, S. E., Probabilistic analysis of seepage that considers the spatial variability of permeability for an embankment on soil foundation, Eng. Geol., 133, 134, 30-39 (2012)
[78] Li, D. Q.; Jiang, S. H.; Cao, Z. J.; Zhou, W.; Zhou, C. B.; Zhang, L. M., A multiple response-surface method for slope reliability analysis considering spatial variability of soil properties, Eng. Geol., 187, 60-72 (2015)
[79] Uzielli, M.; Vannucchi, G.; Phoon, K. K., Random field characterisation of stress-nomalised cone penetration testing parameters, Géotechnique, 55, 3-20 (2005)
[80] Lloret-Cabot, M.; Fenton, G. A.; Hicks, M. A., On the estimation of scale of fluctuation in geostatistics, Georisk, 8, 129-140 (2014)
[81] Plúa, C.; Vu, M. N.; Seyedi, D. M.; Armand, G., Effects of inherent spatial variability of rock properties on the thermo-hydro-mechanical responses of a high-level radioactive waste repository, Int. J. Rock Mech. Min. Sci., 145, Article 104682 pp. (2021)
[82] Plúa, C.; Vu, M. N.; Armand, G.; Rutqvist, J.; Birkholzer, J.; Xu, H.; Guo, R.; Thatcher, K. E.; Bond, A. E.; Wang, W.; Nagel, T.; Shao, H.; Kolditz, O., A reliable numerical analysis for large-scale modelling of a high-level radioactive waste repository in the Callovo-Oxfordian claystone, Int. J. Rock Mech. Min. Sci., 140 (2021)
[83] Jha, B.; Bottazzi, F.; Wojcik, R.; Coccia, M.; Bechor, N.; McLaughlin, D.; Herring, T.; Hager, B. H.; Mantica, S.; Juanes, R., Reservoir characterization in an underground gas storage field using joint inversion of flow and geodetic data, Int. J. Numer. Anal. Methods Geomech., 39, 1619-1638 (2015)
[84] Kolmogorov-Smirnov Test, in: The Concise Encyclopedia of Statistics, Springer New York, New York, NY, n.d.: pp. 283-287. 10.1007/978-0-387-32833-1_214. · Zbl 1267.62001
[85] Wang, B.; Liu, L.; Li, Y.; Jiang, Q., Reliability analysis of slopes considering spatial variability of soil properties based on efficiently identified representative slip surfaces, J. Rock Mech. Geotech. Eng., 12, 642-655 (2020)
[86] Wu, Z.; Li, J.; Bian, K.; Chen, J., Reliability analysis of slope with cross-correlated spatially variable soil properties using AFOSM, Environ. Earth Sci., 80, 1-12 (2021)
[87] Yang, Y.; Wang, P.; Brandenberg, S. J., An algorithm for generating spatially correlated random fields using Cholesky decomposition and ordinary kriging, Comput. Geotech., 147, Article 104783 pp. (2022)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.