A novel localization scheme for scalar uncertainties in ensemble-based data assimilation methods

Abstract

History matching, also known as data assimilation, is an inverse problem with multiple solutions responsible for generating more reliable models for use in decision-making processes. An iterative ensemble-based method (Ensemble Smoother with Multiple Data Assimilation-ES-MDA) has been used to improve the solution of history-matching processes with a technique called distance-dependent localization. In conjunction, ES-MDA and localization can obtain consistent petrophysical images (permeability and porosity). However, the distance-dependent localization technique is not used to update scalar uncertainties, such as relative permeability; therefore, the variability for these properties is excessively reduced, potentially excluding plausible answers. This work presents three approaches to update scalar parameters while increasing the final variability of these uncertainties to better scan the search space. The three approaches that were developed and compared using a benchmark case are: binary correlation coefficient (BCC), based on correlation calculated by ES-MDA through cross-covariance matrix C f MD (BCC-C MD); BCC, based on a correlation coefficient between the objective functions and scalar uncertainties (R) (BCC-R); and full correlation coefficient (FCC). We used the work of Soares et al. (J Pet Sci Eng 169:110-125, 2018) as a base case to compare the approaches because although it showed good matches with geologically consistent petrophysical images, it generated an excessive reduction in the scalar parameters. BCC-C MD presented similar results to the base case, excessively reducing the variability of the scalar uncertainties. BCC-R increased the variability in the scalar parameters, especially for BCC with a higher threshold value. Finally, FCC found many more potential answers in the search space without impairing data matches and production forecast quality.

Data assimilation with multiple types of observation boreholes via the ensemble Kalman filter embedded within stochastic moment equations

“…Iterative forms of the EnKF and ES, usually denoted by IEnKF (Gu and Oliver, 2007;Sakov et al, 2012) and IES (Chen and Oliver, 2013;Emerick and Reynolds, 2013;Luo et al, 2015;Chang et al, 2017;Li et al, 2018), have been developed to improve assimilation performance in scenarios characterized by strongly nonlinear behaviors. A variety of studies investigate challenges linked to such (ensemble) data assimilation algorithms, including, e.g., the possibility of coping with non-Gaussian model parameter distributions (Zhou et al, 2011;Li et al, 2018), physical unphysical results stemming from the estimation workflow (Wen and Chen, 2006;Song et al, 2014), or spurious correlations (Panzeri et al, 2013;Bauser et al, 2018;Luo et al, 2019;Soares et al, 2019). All of these works contribute to improve the robustness of these algorithms for parameter estimation in complex environmental systems.…”

Data assimilation with multiple types of observation boreholes via ensemble Kalman filter embedded within stochastic moment equations

“…Iterative forms of EnKF and ES, usually denoted by IEnKF (Gu and Oliver, 2007;Sakov et al, 2012;Gharamti et al, 2015;Luo, 2014) and IES (Chen and Oliver., 2013;Emerick and Reynolds, 2013;Luo et al 2015;Chang et al, 2017;Li et al, 2018), have been developed to improve assimilation performance in scenarios characterized by strongly nonlinear behaviors. A variety of studies investigate challenges linked to such (ensemble) data assimilation algorithms, including, e.g., the possibility of coping with non-Gaussian model parameter distributions (Zhou et al, 2011;Li et al, 2018), physical inconsistency/unphysical results stemming from the estimation workflow (Wen and Chen, 2006;Song et al, 2015), or spurious correlations (Panzeri et al, 2013;Bauser et al, 2018;Luo et al, 2018;Soares et al, 2019). All of these works contribute to improve the robustness of these algorithms for parameter estimation in complex environmental systems.…”

Integração da geoestatística no processo de assimilação de dados de produção em reservatórios de petróleo

“…Comparação com outros trabalhos de assimilação de dados para o mesmo caso de estudo Este subcapítulo tem o objetivo de mostrar que a metodologia proposta apresenta resultados tão consistentes quanto trabalhos da literatura que apresentaram outras metodologias de assimilação de dados aplicadas ao mesmo caso de estudo UNISIM-I-H. Destacam-se os recentes trabalhosde Cavalcante et al (2019) eSoares et al (2018Soares et al ( , 2019.No trabalho de Cavalvante et al (2019) é proposta uma metodologia de assimilação de dados através de um processo iterativo, usando machine learning para calibrar os modelos. Este trabalho permite perturbações locais e considera incerteza tanto nas propriedades petrofísicas como nos atributos escalares.Os trabalhosde Soares et.al (2018de Soares et.al ( , 2019 usa o Conjunto Suavizado com Múltiplas Assimilações de Dados (Ensemble Smoother with Multiple Data Assimilation, ES-MDA) (Emerick e Reynolds, 2013) para ajustar o caso de estudo, considerando também incerteza nas propriedades petrofísicas e atributos escalares.Um ponto importante de lembrar é um dos objetivos deste trabalho: desenvolvimento de uma metodologia de assimilação de dados que permita um ajuste local integrando técnicas geoestatísticas no processo para garantir a consistência geológica dos modelos.…”