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An enhanced ensemble Kalman filter scheme incorporating model error in sequential coupling between flow and geomechanics
Author(s) -
Caballero Edison,
Rochinha Fernando A.,
Borges Marcio,
Murad Marcio A.
Publication year - 2018
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2872
Subject(s) - geomechanics , data assimilation , discretization , ensemble kalman filter , kalman filter , computer science , algorithm , mathematical optimization , mathematics , context (archaeology) , extended kalman filter , engineering , geology , artificial intelligence , geotechnical engineering , mathematical analysis , paleontology , physics , meteorology
Summary In this work, we construct a new methodology for enhancing the predictive accuracy of sequential methods for coupling flow and geomechanics while preserving low computational cost. The new computational approach is developed within the framework of the fixed‐stress split algorithm procedure in conjunction with data assimilation based on the ensemble Kalman filter (EnKF). In this context, we identify the high‐fidelity model with the two‐way formulation where additional source term appears in the flow equation containing the time derivative of total mean stress. The iterative scheme is then interlaced with data assimilation steps, which also incorporate the modeling error inherent to the EnKF framework. Such a procedure gives rise to an “enhanced one‐way formulation,” exhibiting substantial improvement in accuracy compared with the classical one‐way method. The governing equations are discretized by mixed finite elements, and numerical simulation of a 2D slab problem between injection and production wells illustrate the tremendous achievement of the method proposed herein.