Document Type : Research Paper

**Authors**

Institute of Petroleum Engineering, College of Engineering, University of Tehran, Tehran, Iran

**Abstract**

In this paper, an inverse framework based on Bayes’ theorem is suggested for integrating well logs and seismic data into reservoir lithofacies modeling process. The proposed method is based on combination of the Sequential Indicator Simulation (SIS), and a stochastic optimization method (i.e. Probability Perturbation Method (PPM)). SIS is used to calculate the conditional probability of presence/absence of lithofacies indicators in each grid-block, and PPM is applied to update (perturb) the conditional probability used in SIS. A notable innovation presented in this study is using the Genetic algorithm’ crossover operator to increase the PPM exploitation capability. To demonstrate the efficiency of our proposed approach, the results of its application on a 3D test model is compared with outcomes of two commonly-used constraining approaches on SIS. Qualitative and quantitative analysis of the obtained results on 3D test model reveals a (23.8)% and (16.98)% (on average) improvement in consistency of lithofacies models generated using the proposed approach with the reference lithofacies model over the employed Vertical Probability Trend and Seismic Probability Trend constraining approaches on SIS, respectively. Besides, the obtained results show that implementing crossover operator leads to a 4.56% improvement in matching of the constructed lithofacies models with the reference model.

**Keywords**

**Article Title** [Persian]

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Besag, J., Green, P.J., 1993. Spatial statistics and Bayesian computation. Journal of the Royal Statistical Society: Series B (Methodological), 55(1), pp.25-37.##

Binitha, S., Sathya, S.S., 2012. A survey of bio inspired optimization algorithms. International journal of soft computing and engineering, 2(2):137-151.##

Blum, C. and Roli, A., 2003. Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM computing surveys (CSUR), 35(3), pp.268-308.##

Bornard, R., Allo, F., Coleou, T., Freudenreich, Y., Caldwell, D.H., Hamman, J.G., 2005, June.

Petrophysical Seismic Inversion to Determine More Accurate and Precise Reservoir Properties

(SPE94144). In 67th EAGE Conference & Exhibition (pp. cp-1). European Association of

Geoscientists & Engineers.##

Abdel-Fattah, M.I., Pigott, J.D., El-Sadek, M.S., 2020. Integrated seismic attributes and stochastic inversion for reservoir characterization: Insights from Wadi field (NE Abu-Gharadig Basin, Egypt). Journal of African Earth Sciences, 161: 103661.##

Abdelmaksoud, A., Amin, A.T., El-Habaak, G.H. and Ewida, H.F., 2019. Facies and petrophysical

modeling of the Upper Bahariya Member in Abu Gharadig oil and gas field, north Western Desert, Egypt. Journal of African Earth Sciences, 149: 503-516.##

Adelu, A.O., Aderemi, A.A., Akanji, A.O., Sanuade, O.A., Kaka, S.I., Afolabi, O., Olugbemiga, S., Oke, R., 2019. Application of 3D static modeling for optimal reservoir characterization. Journal of African Earth Sciences, 152: 184-196.##

Agarwal, M., Srivastava, G.M.S., 2018. Genetic Algorithm-Enabled Particle Swarm Optimization

(PSOGA)-Based Task Scheduling in Cloud Computing Environment. International Journal of

Information Technology & Decision Making, 17(04): 1237-1267.##

Angeleri, G.P., Carpi, R., 1982. Porosity prediction from seismic data. Geophysical prospecting, 30(5): 580-607.##

Besag, J., Green, P.J., 1993. Spatial statistics and Bayesian computation. Journal of the Royal Statistical Society: Series B (Methodological), 55(1), pp.25-37.##

Binitha, S., Sathya, S.S., 2012. A survey of bio inspired optimization algorithms. International journal of soft computing and engineering, 2(2):137-151.##

Blum, C. and Roli, A., 2003. Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM computing surveys (CSUR), 35(3), pp.268-308.##

Bornard, R., Allo, F., Coleou, T., Freudenreich, Y., Caldwell, D.H., Hamman, J.G., 2005, June.

Petrophysical Seismic Inversion to Determine More Accurate and Precise Reservoir Properties

(SPE94144). In 67th EAGE Conference & Exhibition (pp. cp-1). European Association of

Geoscientists & Engineers.##

Bosch, M., Mukerji, T., Gonzalez, E.F., 2010. Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review. Geophysics, 75(5): 75A165-75A176.##

Caers, J. and Hoffman, T., 2006. The probability perturbation method: a new look at Bayesian inverse modeling. Mathematical geology, 38(1), pp.81-100.##

Crawford, B., Soto, R., Astorga, G., García, J., Castro, C., Paredes, F., 2017. Putting continuous

metaheuristics to work in binary search spaces. Complexity, 2017.

Geopersia 2021, 11(1): 153-168 167##

Churanova, N.Y., Chorniy, A.V., Baranov, T.S., Solovyev, A.V., Sadreev, E.A., Kurelenkov, S.K.,

Yudin, E.V., Danko, D.A., 2018, October. Reservoir Properties Distribution Based on Petroelastic

Modeling PEM. In SPE Russian Petroleum Technology Conference. Society of Petroleum Engineers.##

Doyen, P., 2007. Seismic reservoir characterization: An earth modelling perspective (2: 255). Houten: EAGE publications.##

Elzain, H.E., Abdullatif, O., Senapathi, V., Chung, S.Y., Sabarathinam, C., Sekar, S., 2020. Lithofacies modeling of Late Jurassic in upper Ulayyah reservoir unit at central Saudi Arabia with inference of reservoir characterization. Journal of Petroleum Science and Engineering, 185, p.106664.##

El Khadragy, A.A., Eysa, E.A., Hashim, A., El Kader, A.A., 2017. Reservoir characteristics and 3D

static modelling of the Late Miocene Abu Madi Formation, onshore Nile Delta, Egypt. Journal of

African Earth Sciences, 132: 99-108.##

Emami Niri, M. and Lumley, D.E., 2015. Simultaneous optimization of multiple objective functions for reservoir modeling. Geophysics, 80(5): M53-M67.##

Emami Niri, M., 2018. 3D and 4D Seismic Data Integration in Static and Dynamic Reservoir Modeling: A Review. Journal of Petroleum Science and Technology, 8(2): 38-56.##

Emami Niri, M., Lumley, D.E., 2017. Initialising reservoir models for history matching using preproduction 3D seismic data: constraining methods and uncertainties. Exploration Geophysics, 48(1), pp.37-48.##

Emami Niri, M., Lumley, D.E., 2016. Estimation of subsurface geomodels by multi-objective stochastic optimization. Journal of Applied Geophysics, 129: 187-199.##

Niri, M.E. and Lumley, D., 2013, August. Uncertainty analysis in quantitative integration of inverted 3D seismic data for static reservoir modeling. In 13th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 26–29 August 2013 (pp. 993-997).##

Society of Exploration Geophysicists and Brazilian Geophysical Society.##

Galli, A., Beucher, H., 1997, January. Stochastic models for reservoir characterization: a user-friendly review. In Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers.##

Garg, H., 2016. A hybrid PSO-GA algorithm for constrained optimization problems. Applied

Mathematics and Computation, 274: 292-305.##

Gassmann, F., 1951. Über die elastizität poröser medien: Vierteljahrss-chrift der Naturforschenden Gesellschaft in Zurich 96, 1-23. Paper translation at http://sepwww. stanford.

edu/sep/berryman/PS/gassmann. pdf.##

Grana, D. and Della Rossa, E., 2010. Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion. Geophysics, 75(3): O21-O37.##

Grana, D., Mukerji, T. and Dvorkin, J., 2011. Single loop inversion of facies from seismic data using sequential simulations and probability perturbation method. In SEG Technical Program Expanded Abstracts 2011 (pp. 1769-1773). Society of Exploration Geophysicists.##

Grana, D., Mukerji, T., Dvorkin, J. and Mavko, G., 2012. Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method. Geophysics, 77(4): M53-M72.##

Hoffman, B.T., 2005. Geologically consistent history matching while perturbing facies.##

Hoffman, B.T. and Caers, J., 2003, January. Geostatistical history matching using a regional probability perturbation method. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.##

Journel, A.G., Gomez-Hernandez, J.J., 1993. Stochastic imaging of the Wilmington clastic

sequence. SPE formation Evaluation, 8(01): 33-40.##

Journel, A.G., 2002. Combining knowledge from diverse sources: An alternative to traditional data independence hypotheses. Mathematical geology, 34(5): 573-596.##

Kar, A.K., 2016. Bio inspired computing–a review of algorithms and scope of applications. Expert Systems with Applications, 59: 20-32.##

Khajehzadeh, M., Taha, M.R., El-Shafie, A. and Eslami, M., 2011. A survey on meta-heuristic global optimization algorithms. Research Journal of Applied Sciences, Engineering and Technology, 3(6):569-578.##

Khormouji, H.B., Hajipour, H., Rostami, H., 2014, September. BODMA: a novel metaheuristic

algorithm for binary optimization problems based on open source development model algorithm. 168 Shad salanghouch & Emami Niri In 7'th International Symposium on Telecommunications (IST'2014) (pp. 49-54). IEEE.##

Kim, K.H., Lee, K., Lee, H.S., Rhee, C.W., Shin, H.D., 2018. Lithofacies modeling by multipoint

statistics and economic evaluation by NPV volume for the early Cretaceous Wabiskaw Member in Athabasca oilsands area, Canada. Geoscience Frontiers, 9(2): 441-451.##

Koneshloo, M., Aryana, S.A., Grana, D., Pierre, J.W., 2017. A workflow for static reservoir modeling guided by seismic data in a fluvial system. Mathematical Geosciences, 49(8), pp.995-1020.##

Mavko, G., Mukerji, T., 1998. A rock physics strategy for quantifying uncertainty in common

hydrocarbon indicators. Geophysics, 63(6): 1997-2008.##

Mavko, G., Mukerji, T. and Dvorkin, J., 1998. The rock physics handbook: Tools for seismic analysis in porous media: University of Cambridge.##

Mondol, N.H., 2010. Seismic exploration. In Petroleum Geoscience (pp. 375-402). Springer, Berlin, Heidelberg.##

Nur, A., Mavko, G., Dvorkin, J., Galmudi, D., 1998. Critical porosity: A key to relating physical

properties to porosity in rocks. The Leading Edge, 17(3): 357-362.##

Ravalec-Dupin, L., Enchery, G., Baroni, A. and Da Veiga, S., 2011. Preselection of reservoir models from a geostatistics-based petrophysical seismic inversion. SPE Reservoir Evaluation &

Engineering, 14(05): 612-620.##

Strebelle, S., 2002. Conditional simulation of complex geological structures using multiple-point statistics. Mathematical geology, 34(1): 1-21.##

Tang, M., Lu, S., Zhang, K., Yin, X., Ma, H., Shi, X., Liu, X., Chu, C., 2019. A three dimensional highresolution reservoir model of Napo Formation in Oriente Basin, Ecuador, integrating sediment dynamic simulation and geostatistics. Marine and Petroleum Geology, 110: 240-253.##

Tewari, S., Dwivedi, U.D., 2019. Ensemble-based big data analytics of lithofacies for automatic

development of petroleum reservoirs. Computers & Industrial Engineering, 128: 937-947.

Wood, A.B., 1941. A textbook of sound: Bell.##

Zhang, Z., Li, H., Zhang, D., 2017. Reservoir characterization and production optimization using the ensemble-based optimization method and multi-layer capacitance-resistive models. Journal of Petroleum Science and Engineering, 156: 633-653.##

Caers, J. and Hoffman, T., 2006. The probability perturbation method: a new look at Bayesian inverse modeling. Mathematical geology, 38(1), pp.81-100.##

Crawford, B., Soto, R., Astorga, G., García, J., Castro, C., Paredes, F., 2017. Putting continuous

metaheuristics to work in binary search spaces. Complexity, 2017.

Geopersia 2021, 11(1): 153-168 167##

Churanova, N.Y., Chorniy, A.V., Baranov, T.S., Solovyev, A.V., Sadreev, E.A., Kurelenkov, S.K.,

Yudin, E.V., Danko, D.A., 2018, October. Reservoir Properties Distribution Based on Petroelastic

Modeling PEM. In SPE Russian Petroleum Technology Conference. Society of Petroleum Engineers.##

Doyen, P., 2007. Seismic reservoir characterization: An earth modelling perspective (2: 255). Houten: EAGE publications.##

Elzain, H.E., Abdullatif, O., Senapathi, V., Chung, S.Y., Sabarathinam, C., Sekar, S., 2020. Lithofacies modeling of Late Jurassic in upper Ulayyah reservoir unit at central Saudi Arabia with inference of reservoir characterization. Journal of Petroleum Science and Engineering, 185, p.106664.##

El Khadragy, A.A., Eysa, E.A., Hashim, A., El Kader, A.A., 2017. Reservoir characteristics and 3D

static modelling of the Late Miocene Abu Madi Formation, onshore Nile Delta, Egypt. Journal of

African Earth Sciences, 132: 99-108.##

Emami Niri, M. and Lumley, D.E., 2015. Simultaneous optimization of multiple objective functions for reservoir modeling. Geophysics, 80(5): M53-M67.##

Emami Niri, M., 2018. 3D and 4D Seismic Data Integration in Static and Dynamic Reservoir Modeling: A Review. Journal of Petroleum Science and Technology, 8(2): 38-56.##

Emami Niri, M., Lumley, D.E., 2017. Initialising reservoir models for history matching using preproduction 3D seismic data: constraining methods and uncertainties. Exploration Geophysics, 48(1), pp.37-48.##

Emami Niri, M., Lumley, D.E., 2016. Estimation of subsurface geomodels by multi-objective stochastic optimization. Journal of Applied Geophysics, 129: 187-199.##

Niri, M.E. and Lumley, D., 2013, August. Uncertainty analysis in quantitative integration of inverted 3D seismic data for static reservoir modeling. In 13th International Congress of the Brazilian Geophysical Society & EXPOGEF, Rio de Janeiro, Brazil, 26–29 August 2013 (pp. 993-997).##

Society of Exploration Geophysicists and Brazilian Geophysical Society.##

Galli, A., Beucher, H., 1997, January. Stochastic models for reservoir characterization: a user-friendly review. In Latin American and Caribbean Petroleum Engineering Conference. Society of Petroleum Engineers.##

Garg, H., 2016. A hybrid PSO-GA algorithm for constrained optimization problems. Applied

Mathematics and Computation, 274: 292-305.##

Gassmann, F., 1951. Über die elastizität poröser medien: Vierteljahrss-chrift der Naturforschenden Gesellschaft in Zurich 96, 1-23. Paper translation at http://sepwww. stanford.

edu/sep/berryman/PS/gassmann. pdf.##

Grana, D. and Della Rossa, E., 2010. Probabilistic petrophysical-properties estimation integrating statistical rock physics with seismic inversion. Geophysics, 75(3): O21-O37.##

Grana, D., Mukerji, T. and Dvorkin, J., 2011. Single loop inversion of facies from seismic data using sequential simulations and probability perturbation method. In SEG Technical Program Expanded Abstracts 2011 (pp. 1769-1773). Society of Exploration Geophysicists.##

Grana, D., Mukerji, T., Dvorkin, J. and Mavko, G., 2012. Stochastic inversion of facies from seismic data based on sequential simulations and probability perturbation method. Geophysics, 77(4): M53-M72.##

Hoffman, B.T., 2005. Geologically consistent history matching while perturbing facies.##

Hoffman, B.T. and Caers, J., 2003, January. Geostatistical history matching using a regional probability perturbation method. In SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers.##

Journel, A.G., Gomez-Hernandez, J.J., 1993. Stochastic imaging of the Wilmington clastic

sequence. SPE formation Evaluation, 8(01): 33-40.##

Journel, A.G., 2002. Combining knowledge from diverse sources: An alternative to traditional data independence hypotheses. Mathematical geology, 34(5): 573-596.##

Kar, A.K., 2016. Bio inspired computing–a review of algorithms and scope of applications. Expert Systems with Applications, 59: 20-32.##

Khajehzadeh, M., Taha, M.R., El-Shafie, A. and Eslami, M., 2011. A survey on meta-heuristic global optimization algorithms. Research Journal of Applied Sciences, Engineering and Technology, 3(6):569-578.##

Khormouji, H.B., Hajipour, H., Rostami, H., 2014, September. BODMA: a novel metaheuristic

algorithm for binary optimization problems based on open source development model algorithm. 168 Shad salanghouch & Emami Niri In 7'th International Symposium on Telecommunications (IST'2014) (pp. 49-54). IEEE.##

Kim, K.H., Lee, K., Lee, H.S., Rhee, C.W., Shin, H.D., 2018. Lithofacies modeling by multipoint

statistics and economic evaluation by NPV volume for the early Cretaceous Wabiskaw Member in Athabasca oilsands area, Canada. Geoscience Frontiers, 9(2): 441-451.##

Koneshloo, M., Aryana, S.A., Grana, D., Pierre, J.W., 2017. A workflow for static reservoir modeling guided by seismic data in a fluvial system. Mathematical Geosciences, 49(8), pp.995-1020.##

Mavko, G., Mukerji, T., 1998. A rock physics strategy for quantifying uncertainty in common

hydrocarbon indicators. Geophysics, 63(6): 1997-2008.##

Mavko, G., Mukerji, T. and Dvorkin, J., 1998. The rock physics handbook: Tools for seismic analysis in porous media: University of Cambridge.##

Mondol, N.H., 2010. Seismic exploration. In Petroleum Geoscience (pp. 375-402). Springer, Berlin, Heidelberg.##

Nur, A., Mavko, G., Dvorkin, J., Galmudi, D., 1998. Critical porosity: A key to relating physical

properties to porosity in rocks. The Leading Edge, 17(3): 357-362.##

Ravalec-Dupin, L., Enchery, G., Baroni, A. and Da Veiga, S., 2011. Preselection of reservoir models from a geostatistics-based petrophysical seismic inversion. SPE Reservoir Evaluation &

Engineering, 14(05): 612-620.##

Strebelle, S., 2002. Conditional simulation of complex geological structures using multiple-point statistics. Mathematical geology, 34(1): 1-21.##

Tang, M., Lu, S., Zhang, K., Yin, X., Ma, H., Shi, X., Liu, X., Chu, C., 2019. A three dimensional highresolution reservoir model of Napo Formation in Oriente Basin, Ecuador, integrating sediment dynamic simulation and geostatistics. Marine and Petroleum Geology, 110: 240-253.##

Tewari, S., Dwivedi, U.D., 2019. Ensemble-based big data analytics of lithofacies for automatic

development of petroleum reservoirs. Computers & Industrial Engineering, 128: 937-947.

Wood, A.B., 1941. A textbook of sound: Bell.##

Zhang, Z., Li, H., Zhang, D., 2017. Reservoir characterization and production optimization using the ensemble-based optimization method and multi-layer capacitance-resistive models. Journal of Petroleum Science and Engineering, 156: 633-653.##

January 2021

Pages 153-168

**Receive Date:**25 April 2020**Revise Date:**01 September 2020**Accept Date:**14 September 2020