A pattern-matching method for flow model calibration under training image constraint

• Published in: Computational geosciences Vol. 23; no. 4; pp. 813 - 828
• Main Authors: Khaninezhad, Reza, Golmohammadi, Azarang, Jafarpour, Behnam
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.08.2019; Springer Nature B.V
• Subjects: Algorithms; Calibration; Computer simulation; Conditioning; Constraint modelling; Data; Data integration; Earth and Environmental Science; Earth Sciences; Geostatistics; Geotechnical Engineering & Applied Earth Sciences; Hydrogeology; Identification; Iterative methods; Mathematical Modeling and Industrial Mathematics; Original Paper; Parameterization; Pattern matching; Regularization; Regularization methods; Singular value decomposition; Soil Science & Conservation; Statistical analysis; Statistics; Training; Training image; Geologic feasibility; Flow model calibration; Multiple-point statistics; Pattern matching
• ISSN: 1420-0597; 1573-1499
• DOI: 10.1007/s10596-019-9822-4

Modern geostatistical modeling techniques are developed to simulate complex geologic connectivity patterns (e.g., curvilinear fluvial systems) at the grid-level using a training image (TI) that encodes multiple-point statistical (MPS) information. A challenging aspect of using MPS methods is conditioning the resulting models on nonlinear flow data. We develop a pattern-matching method for calibration of MPS-based facies models subject to the TI constraint. Since the exact statistical information in the TI can only be expressed empirically, flow data conditioning and pattern matching are carried out in two iterative steps, using an alternating-direction algorithm. Flow data integration is formulated through a regularized least-squares by taking advantage of learned k -SVD sparse parametrization and l 1 -norm sparsity-promoting regularization methods. The TI constraint is enforced through a MPS-based pattern-matching algorithm that uses the identified model calibration solution to generate a corresponding facies model that is consistent with the TI. The pattern-matching algorithm uses a local search template to scan the TI to find facies patterns with smallest distances from the corresponding local patterns in the parameterized approximate solution. The identified patterns for each location in the model are stored and used to estimate local conditional probabilities for assigning the facies types to each grid cell. The resulting solution is passed to the flow data conditioning step as a regularization term to perform the next iteration. The process is repeated until the MPS facies model provides an acceptable match to the data. Numerical experiments are presented to evaluate the performance of the pattern-matching method for calibration of complex facies models.