Surrogate-based Bayesian comparison of computationally expensive models: application to microbially induced calcite precipitation. (English) Zbl 1477.86031

Scheurer, Stefania; Schäfer Rodrigues Silva, Aline; Mohammadi, Farid; Hommel, Johannes; Oladyshkin, Sergey; Flemisch, Bernd; Nowak, Wolfgang

Comput. Geosci. 25, No. 6, 1899-1917 (2021).

Summary: Geochemical processes in subsurface reservoirs affected by microbial activity change the material properties of porous media. This is a complex biogeochemical process in subsurface reservoirs that currently contains strong conceptual uncertainty. This means, several modeling approaches describing the biogeochemical process are plausible and modelers face the uncertainty of choosing the most appropriate one. The considered models differ in the underlying hypotheses about the process structure. Once observation data become available, a rigorous Bayesian model selection accompanied by a Bayesian model justifiability analysis could be employed to choose the most appropriate model, i.e. the one that describes the underlying physical processes best in the light of the available data. However, biogeochemical modeling is computationally very demanding because it conceptualizes different phases, biomass dynamics, geochemistry, precipitation and dissolution in porous media. Therefore, the Bayesian framework cannot be based directly on the full computational models as this would require too many expensive model evaluations. To circumvent this problem, we suggest to perform both Bayesian model selection and justifiability analysis after constructing surrogates for the competing biogeochemical models. Here, we will use the arbitrary polynomial chaos expansion. Considering that surrogate representations are only approximations of the analyzed original models, we account for the approximation error in the Bayesian analysis by introducing novel correction factors for the resulting model weights. Thereby, we extend the Bayesian model justifiability analysis and assess model similarities for computationally expensive models. We demonstrate the method on a representative scenario for microbially induced calcite precipitation in a porous medium. Our extension of the justifiability analysis provides a suitable approach for the comparison of computationally demanding models and gives an insight on the necessary amount of data for a reliable model performance.

MSC:

86A32

Geostatistics

Keywords:

microbially induced calcite precipitation; Bayesian model selection; Bayesian model justifiability analysis; arbitrary polynomial chaos expansion; surrogate-based model selection and comparison; surrogate-based Bayesian model justifiability analysis

Software:

TOUGHREACT; BaPC; aPC

References:

[1]	Alpaydin, E., Introduction to Machine Learning. Adaptive computation and machine learning (2004), Massachusetts: MIT Press, Massachusetts
[2]	Baartman, JE; Melsen, LA; Moore, D.; van der Ploeg, MJ, On the complexity of model complexity: Viewpoints across the geosciences, CATENA, 186, 10426 (2020)
[3]	Babu, GJ, Resampling methods for model fitting and model selection, J. Biopharm. Stat., 21, 6, 1177-1186 (2011)
[4]	Bachmann, RT; Johnson, AC; Edyvean, RG, Biotechnology in the petroleum industry: an overview, Int. Biodeteriorat. Biodegrad., 86, 225-237 (2014)
[5]	Barkouki, T.; Martinez, B.; Mortensen, B.; Weathers, T.; De Jong, J.; Ginn, T.; Spycher, N.; Smith, R.; Fujita, Y., Forward and Inverse bio-Geochemical Modeling of Microbially Induced Calcite Precipitation in half-Meter Column Experiments, Transp. Porous Media, 90, 1, 23 (2011)
[6]	Beckers, F.; Heredia, A.; Noack, M.; Nowak, W.; Wieprecht, S.; Oladyshkin, S., Bayesian Calibration and Validation of a Large-Scale and Time-Demanding Sediment Transport Model, Water Resourc. Res., 56, 7, e2019WR026966 (2020)
[7]	Blatman, G.; Sudret, B., An adaptive algorithm to build up sparse polynomial chaos expansions for stochastic finite element analysis, Probab. Eng. Mechan., 25, 2, 183-197 (2010)
[8]	Bottero, S.; Storck, T.; Heimovaara, TJ; van Loosdrecht, MC; Enzien, MV; Picioreanu, C., Biofilm development and the dynamics of preferential flow paths in porous media, Biofouling, 29, 9, 1069-1086 (2013)
[9]	Brunetti, G.; Šimůringnek J.; glöckler, D.; Stumpp, C., Handling model complexity with parsimony: Numerical analysis of the nitrogen turnover in a controlled aquifer model setup, J. Hydrol., 584, 124681 (2020)
[10]	Burnham, KP; Anderson, DR, A Practical Information-Theoretic Approach. Model Selection and Multimodel Inference (2002), New York: Springer, New York · Zbl 1005.62007
[11]	Cremers, KJM, Stock return predictability: a bayesian model selection perspective, Rev. Financ. Stud., 15, 4, 27 (2002)
[12]	Cunningham, AB; Class, H.; Ebigbo, A.; Gerlach, R.; Phillips, AJ; Hommel, J., Field-scale modeling of microbially induced calcite precipitation, Comput. Geosci., 23, 2, 399-414 (2019)
[13]	Cuthbert, MO; McMillan, LA; Handley-Sidhu, S.; Riley, MS; Tobler, DJ; Phoenix, VR, A field and modeling study of fractured rock permeability reduction using microbially induced calcite precipitation, Environ. Sci. Technol., 47, 23, 13637-13643 (2013)
[14]	Dupraz, S.; Parmentier, M.; Ménez, B.; Guyot, F., Experimental and numerical modeling of bacterially induced pH increase and calcite precipitation in saline aquifers, Chem. Geol., 265, 1-2, 44-53 (2009)
[15]	Ebigbo, A.; Phillips, AJ; Gerlach, R.; Helmig, R.; Cunningham, AB; Class, H.; Spangler, LH, Darcy-scale modeling of microbially induced carbonate mineral precipitation in sand columns, Water Resour. Res., 48, 7, W07519 (2012)
[16]	Enemark, T.; Peeters, LJ; Mallants, D.; Batelaan, O., Hydrogeological conceptual model building and testing: a review, J. Hydrol., 569, 310-329 (2019)
[17]	Gomez, MG; Anderson, CM; Graddy, CMR; DeJong, JT; Nelson, DC; Ginn, TR, Large-Scale comparison of bioaugmentation and biostimulation approaches for biocementation of sands, J. Geotechnical Geoenviron. Eng., 143, 5, 04016124 (2017)
[18]	Gupta, H.V., Clark, M.P., Vrugt, J.A., Abramowitz, G., Ye, M.: Towards a comprehensive assessment of model structural adequacy. Water Resour. Res. 48(8). doi:10.1029/2011WR011044 (2012)
[19]	Hamdan, N., Kavazanjian, E. Jr, Rittmann, B.E.: Sequestration of radionuclides and metal contaminants through microbially-induced carbonate precipitation. In: Proc. 14Th Pan American Conf. Soil Mech. Geotech., Engng., Toronto (2011)
[20]	Head, IM, Bioremediation: towards a credible technology, Microbiology, 144, 3, 599-608 (1998)
[21]	Helmig, R., Multiphase Flow and Transport Processes in the Subsurface - A Contribution to the Modeling of Hydrosystems (1997), Berlin: Springer, Berlin
[22]	Højberg, A.; Refsgaard, J., Model uncertainty – parameter uncertainty versus conceptual models, Water Sci. Technol., 52, 6, 177-186 (2005)
[23]	Höge, M.; Wöhling, T.; Nowak, W., A primer for model selection: The decisive role of model complexity, Water Resour. Res., 54, 3, 1688-1715 (2018)
[24]	Höge, M.; Guthke, A.; Nowak, W., The hydrologist’s guide to Bayesian model selection, averaging and combination, J. Hydrol., 572, 96-107 (2019)
[25]	Hommel, J.; Lauchnor, E.; Phillips, A.; Gerlach, R.; Cunningham, AB; Helmig, R.; Ebigbo, A.; Class, H., A revised model for microbially induced calcite precipitation: Improvements and new insights based on recent experiments, Water Resour. Res., 51, 5, 3695-3715 (2015)
[26]	Hommel, J.; Ebigbo, A.; Gerlach, R.; Cunningham, AB; Helmig, R.; Class, H., Finding a balance between accuracy and effort for modeling biomineralization, Energy Procedia, 97, 379-386 (2016)
[27]	Hommel, J.; Lauchnor, EG; Gerlach, R.; Cunningham, AB; Ebigbo, A.; Helmig, R.; Class, H., Investigating the influence of the initial biomass distribution and injection strategies on Biofilm-Mediated calcite precipitation in porous media, Transp. Porous Media, 114, 2, 557-579 (2016)
[28]	Hooten, MB; Hobbs, NT, A guide to Bayesian model selection for ecologists, Ecol. Monogr., 85, 1, 3-28 (2015)
[29]	Huang, S.; Cao, M.; Cheng, L., Experimental study on the mechanism of enhanced oil recovery by multi-thermal fluid in offshore heavy oil, Int. J. Heat Mass Transf., 122, 1074-1084 (2018)
[30]	Hunter, KS; Wang, Y.; Van Cappellen, P., Kinetic modeling of microbially-driven redox chemistry of subsurface environments: coupling transport, microbial metabolism and geochemistry, J. Hydrol., 209, 1-4, 53-80 (1998)
[31]	Jefferys, WH; Berger, JO, Ockham’s razor and bayesian analysis, Am. Sci., 80, 1, 64-72 (1992)
[32]	Kass, RE; Raftery, AE, Bayes factors, J. Amer. Stat. Assoc., 90, 430, 773-795 (1995) · Zbl 0846.62028
[33]	Kirkland, CM; Thane, A.; Hiebert, R.; Hyatt, R.; Kirksey, J.; Cunningham, AB; Gerlach, R.; Spangler, L.; Phillips, AJ, Addressing wellbore integrity and thief zone permeability using microbially-induced calcium carbonate precipitation (MICP): a field demonstration, J. Pet. Sci. Eng., 190, 107060 (2020)
[34]	Köpel, M.; Franzelin, F.; Kröker, I.; Oladyshkin, S.; Santin, G.; Wittwar, D.; Barth, A.; Haasdonk, B.; Nowak, W.; Pflüger, D.; Rohde, C., Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario, Comput. Geosci., 23, 2, 339-354 (2019) · Zbl 1414.76058
[35]	Landa-Marbán, D., Tveit, S., Kumar, K., Gasda, S.E.: Practical approaches to study microbially induced calcite precipitation at the field scale. arXiv:201104744 (2020)
[36]	Lever, J.; Krzywinski, M.; Altman, N., Model selection and overfitting, Nat. Methods, 13, 9, 703-704 (2016)
[37]	Lovley, DR; Chapelle, FH, Deep subsurface microbial processes, Rev. Geophys., 33, 3, 365-381 (1995)
[38]	MacQuarrie, KTB; Mayer, KU, Reactive transport modeling in fractured rock: a state-of-the-science review, Earth Sci. Rev., 72, 3-4, 189-227 (2005)
[39]	McInerney, M.J., Nagle, D.P., Knapp, R.M.: Microbially enhanced oil recovery: past, Present, and Future. Petroleum Microbiology 215-237 (2005)
[40]	Megharaj, M.; Ramakrishnan, B.; Venkateswarlu, K.; Sethunathan, N.; Naidu, R., Bioremediation approaches for organic pollutants: a critical perspective, Environ. Int., 37, 8, 1362-1375 (2011)
[41]	Minto, JM; Lunn, RJ; El Mountassir, G., Development of a reactive transport model for Field-Scale simulation of microbially induced carbonate precipitation, Water Resour. Res., 55, 8, 7229-7245 (2019)
[42]	Mitchell, AC; Phillips, AJ; Schultz, L.; Parks, S.; Spangler, LH; Cunningham, AB; Gerlach, R., Microbial CaCO3 mineral formation and stability in an experimentally simulated high pressure saline aquifer with supercritical CO2, International Journal of Greenhouse Gas Control, 15, 86-96 (2013)
[43]	Mohammadi, F.; Kopmann, R.; Guthke, A.; Oladyshkin, S.; Nowak, W., Bayesian selection of hydro-morphodynamic models under computational time constraints, Adv. Water Resour., 117, 53-64 (2018)
[44]	Mujah, D.; Shahin, MA; Cheng, L., State-of-the-art Review of Biocementation by Microbially Induced Calcite Precipitation (MICP) for Soil Stabilization, Geomicrobiol. J., 34, 6, 524-537 (2017)
[45]	Mulligan, CN; Galvez-Cloutier, R., Bioremediation of metal contamination, Environ. Monit. Assess., 84, 1-2, 45-60 (2003)
[46]	Nassar, MK; Gurung, D.; Bastani, M.; Ginn, TR; Shafei, B.; Gomez, MG; Graddy, CM; Nelson, DC; DeJong, JT, Large-Scale Experiments in Microbially Induced Calcite Precipitation (MICP): Reactive Transport Model Development and Prediction, Water Resour. Res., 54, 1, 480-500 (2018)
[47]	Nearing, GS; Gupta, HV, Ensembles vs. information theory: supporting science under uncertainty, Frontiers of Earth Science, 12, 4, 653-660 (2018)
[48]	Neuman, SP, Maximum likelihood bayesian averaging of uncertain model predictions, Stoch. Env. Res. Risk A., 17, 5, 291-305 (2003) · Zbl 1036.62113
[49]	Oladyshkin, S: aPC Matlab Toolbox: Data-driven Arbitrary Polynomial Chaos, Matlab Central File Exchange. https://www.mathworks.com/matlabcentral/fieexchange/72014-apc-matlab-toolbox-data-driven-arbitrary-polynomial-chaos (2020a)
[50]	Oladyshkin, S: BaPC Matlab Toolbox: Bayesian Arbitrary Polynomial Chaos, Matlab Central File Exchange. https://www.mathworks.com/matlabcentral/fieexchange/74006-bapc-matlab-toolbox-bayesian-arbitrary-polynomial-chaos (2020b)
[51]	Oladyshkin, S.; Nowak, W., Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion, Reliab. Eng. Syst. Safe., 106, 179-190 (2012)
[52]	Oladyshkin, S.; de Barros, F.; Nowak, W., Global sensitivity analysis: a flexible and efficient framework with an example from stochastic hydrogeology, Adv. Water Resour., 37, 10-22 (2012)
[53]	Oladyshkin, S.; Class, H.; Nowak, W., Bayesian updating via bootstrap filtering combined with data-driven polynomial chaos expansions: methodology and application to history matching for carbon dioxide storage in geological formations, Comput. Geosci., 17, 4, 671-687 (2013) · Zbl 1382.86022
[54]	Oladyshkin, S.; Schröder, P.; Class, H.; Nowak, W., Chaos Expansion based Bootstrap Filter to Calibrate CO2 Injection Models, Energy Procedia, 40, 398-407 (2013)
[55]	Oladyshkin, S.; Mohammadi, F.; Kroeker, I.; Nowak, W., Bayesian3 active learning for the gaussian process emulator using information theory, Entropy, 22, 8, 890 (2020)
[56]	van Paassen, LA; Ghose, R.; van der Linden, TJM; van der Star, WRL; van Loosdrecht, MCM, Quantifying Biomediated Ground Improvement by Ureolysis: Large-Scale Biogrout Experiment, J. Geotechnical Geoenviron. Eng., 136, 12, 1721-1728 (2010)
[57]	Parkinson, D.; Mukherjee, P.; Liddle, AR, Bayesian model selection analysis of wMAP3, Phys Rev D, 73, 123523 (2006)
[58]	Phillips, AJ; Lauchnor, E.; Eldring, J.; Esposito, R.; Mitchell, AC; Gerlach, R.; Cunningham, AB; Spangler, LH, Potential CO2 Leakage Reduction Through Biofilm-induced calcium carbonate precipitation, Environ. Sci. Technol., 47, 1, 142-149 (2013)
[59]	Phillips, AJ; Cunningham, AB; Gerlach, R.; Hiebert, R.; Hwang, C.; Lomans, BP; Westrich, J.; Mantilla, C.; Kirksey, J.; Esposito, R.; Spangler, LH, Fracture sealing with Microbially-Induced calcium carbonate precipitation: a field study, Environ. Sci. Technol., 50, 4111-4117 (2016)
[60]	Raftery, A.E.: Bayesian model selection in social research. Sociol. Methodol. 111-163 (1995)
[61]	Refsgaard, JC; Christensen, S.; Sonnenborg, TO; Seifert, D.; Højberg, AL; Troldborg, L., Review of strategies for handling geological uncertainty in groundwater flow and transport modeling, Adv. Water Resour., 36, 36-50 (2012)
[62]	Renard, B., Kavetski, D., Kuczera, G., Thyer, M., Franks, S.W.: Understanding predictive uncertainty in hydrologic modeling: The challenge of identifying input and structural errors. Water Resour. Res. 46(5). doi:10.1029/2009WR008328 (2010)
[63]	Rojas, R., Feyen, L., Dassargues, A.: Conceptual model uncertainty in groundwater modeling: Combining generalized likelihood uncertainty estimation and Bayesian model averaging. Water Resour. Res. 44(12). doi:10.1029/2008WR006908 (2008)
[64]	Rojas, R.; Kahunde, S.; Peeters, L.; Batelaan, O.; Feyen, L.; Dassargues, A., Application of a multimodel approach to account for conceptual model and scenario uncertainties in groundwater modelling, J. Hydrol., 394, 3-4, 416-435 (2010)
[65]	Schäfer Rodrigues Silva, A., Guthke, A., Höge, M., Cirpka, O.A., Nowak, W.: Strategies for simplifying reactive transport models - a Bayesian model comparison. Water Res. Res. p e2020WR028100. doi:10.1029/2020WR028100 (2020)
[66]	Schmidt, E.: Zur theorie der linearen und nichtlinearen integralgleichungen. In: Integralgleichungen und Gleichungen mit unendlich vielen Unbekannten, pp 190-233. Springer (1989)
[67]	Schöniger, A.; Wöhling, T.; Samaniego, L.; Nowak, W., Model selection on solid ground: Rigorous comparison of nine ways to evaluate Bayesian model evidence, Water Resour. Res., 50, 12, 9484-9513 (2014)
[68]	Schöniger, A.; Illman, W.; Wöhling, T.; Nowak, W., Finding the right balance between groundwater model complexity and experimental effort via Bayesian model selection, J. Hydrol., 531, 96-110 (2015)
[69]	Schöniger, A.; Wöhling, T.; Nowak, W., A statistical concept to assess the uncertainty in Bayesian model weights and its impact on model ranking, Water Resour. Res., 51, 9, 7524-7546 (2015)
[70]	Steefel, C., MacQuarrie, K.: Reactive transport in porous media. Reviews in mineralogy, mineralogical society of america. Washington, chap Approaches to modelling of reactive transport in porous media 82-129 (1996)
[71]	Steefel, C.; Depaolo, D.; Lichtner, P., Reactive transport modeling: An essential tool and a new research approach for the Earth sciences, Earth Planet. Sci. Lett., 240, 3-4, 539-558 (2005)
[72]	Stocks-Fischer, S.; Galinat, JK; Bang, SS, Microbiological precipitation of CaCO3, Soil Biol. Biochem., 31, 1563-1571 (1999)
[73]	Suliman, F.; French, H.; Haugen, L.; Søvik, A., Change in flow and transport patterns in horizontal subsurface flow constructed wetlands as a result of biological growth, Ecologic. Eng., 27, 2, 124-133 (2006)
[74]	Terzis, D.; Laloui, L., A decade of progress and turning points in the understanding of bio-improved soils: a review, Geomechan. Energ. Environ., 19, 100116 (2019)
[75]	Troldborg, L.; Refsgaard, JC; Jensen, KH; Engesgaard, P., The importance of alternative conceptual models for simulation of concentrations in a multi-aquifer system, Hydrogeol. J., 15, 5, 843-860 (2007)
[76]	Umar, M.; Kassim, KA; Chiet, KTP, Biological process of soil improvement in civil engineering: A review, J. Rock Mechan. Geotechnic. Eng., 8, 5, 767-774 (2016)
[77]	Villadsen, J.; Michelsen, M., Solution of Differential Equation Models by Polynomial Approximation, vol. 7 (1978), Englewood Cliffs: Prentice-Hall, Englewood Cliffs · Zbl 0464.34001
[78]	van der Vorst, HA, BI-CGSTAB: A fast and smoothly converging variant of BI-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput., 13, 2, 631-644 (1992) · Zbl 0761.65023
[79]	Wasserman, L., Bayesian model selection and model averaging, J. Math. Psychol., 44, 1, 92-107 (2000) · Zbl 0946.62032
[80]	Whiffin, VS; La, vanPaassen; Harkes, MP, Microbial carbonate precipitation as a soil improvement technique, Geomicrobiol J., 24, 5, 417-423 (2007)
[81]	Wöhling, T.; Schöniger, A.; Gayler, S.; Nowak, W., Bayesian model averaging to explore the worth of data for soil-plant model selection and prediction, Water Resour. Res., 51, 4, 2825-2846 (2015)
[82]	Wiener, N., The homogeneous chaos, Am. J. Math., 60, 4, 897-936 (1938) · JFM 64.0887.02
[83]	van Wijngaarden, WK; van Paassen, LA; Vermolen, FJ; van Meurs, GAM; Vuik, C., A reactive transport model for biogrout compared to experimental data, Transp. Porous Media, 111, 3, 627-648 (2016)
[84]	Xiu, D.; Karniadakis, GE, Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos, Comput. Methods Appl. Mechan. Eng., 191, 43, 4927-4948 (2002) · Zbl 1016.65001
[85]	Xiu, D.; Karniadakis, GE, The wiener-askey polynomial chaos for stochastic differential equations, SIAM J. Scientif. Comput., 24, 2, 619-644 (2002) · Zbl 1014.65004
[86]	Xu, T.; Sonnenthal, E.; Spycher, N.; Pruess, K., TOUGHREACT - A simulation program for non-isothermal multiphase reactive geochemical transport in variably saturated geologic media: Applications to geothermal injectivity and CO2 geological sequestration, Comput. Geosci., 32, 2, 145-165 (2006)
[87]	Yang, Y.; Chu, J.; Cao, B.; Liu, H.; Cheng, L., Biocementation of soil using non-sterile enriched urease-producing bacteria from activated sludge, J. Clean. Prod., 262, 121315 (2020)