Pattern-Based History Matching Maintains Consistency for Complex-Facies Reservoirs
Authors: Carpenter Chris 
Published: March 2019

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 190128, “Pattern-Based History Matching for Reservoirs With Complex Geologic Facies,” by A. Golmohammadi, M.R. Khaninezhad, and B. Jafarpour, SPE, University of Southern California, prepared for the 2018 SPE Western Regional Meeting, Garden Grove, California, USA, 22–27 April. The paper has not been peer reviewed.
A challenging problem of automated history-matching work flows is ensuring that, after applying updates to previous models, the resulting history-matched models remain consistent geologically. This is particularly challenging in formations with complex connectivity patterns. In this work, the authors introduce a novel machine-learning approach with the aim of preserving the main connectivity patterns of previous reservoir models during history matching of complex geologic formations.
Introduction
The authors introduce a machine-learning algorithm to incorporate discrete connectivity patterns in history matching of complex-geologic-facies models. This is achieved by splitting the introduced history-matching optimization problem into two iterative subproblems: a continuous approximation of the solution that is obtained by solving a regularized least-squares inversion (while maintaining the expected connectivity of the patterns) followed by a machine-learning-based mapping of the continuous solution to the discrete feasible set defined by previous models. The second step involves a machine-learning approach that uses offline training to implement the mapping. The offline learning process uses the k-nearest neighbor (k-NN) algorithm to construct local pattern (feature) vectors and compare them with the feature vectors in the training data set. For each spatial template, the feature vectors with the smallest distance in the learning data set are selected and their corresponding label vectors (i.e., multivariate discrete patterns) are identified and stored. Once all local patterns are scanned and processed using a defined template size, an aggregation step is applied on the overlapping templates to incorporate the multipoint statistics patterns collectively in assigning discrete labels to each gridblock.
Methodology
History Matching With Facies-Feasibility Constraint. An indirect method is developed for solving the constrained minimization problem by defining a two-step alternating-directions method. In this approach, the first step uses a standard gradient-based method to find an approximate continuous solution to the problem and the second step maps the resulting continuous solution onto the feasible set while ensuring that the updated solution remains close to the continuous solution from the first step. These two steps are repeated until no further improvement in the data match is obtained. A machine-learning algorithm is used to implement the mapping in the second step.
Mapping Onto the Feasible Set. The authors use a supervised-learning approach to implement the mapping in Step 2 of the solution approach. The k-NN method is implemented in this paper as a simple classification technique in which the decision about the label of a feature vector is based on a distance measure defined between the feature vector and the learning data set. Using a predefined distance measure, the algorithm selects feature vectors with minimum distances from the training data set and assigns the most-frequent label corresponding to these feature vectors as the output label.