Integration of PCA with a Novel Machine Learning Method for Reparameterization and Assisted History Matching Geologically Complex Reservoirs
Authors: Honorio Jean , Chen Chaohui , Gao Guohua , Du Kuifu , Jaakkola Tommi 
Published: September 2015

Abstract
It is a common practice to reduce the number of parameters that are used to fully describe a static geological model for assisted-history-matching (AHM) of geologically complex reservoirs. However, a model reconstructed from the reduced parameters may often be distorted from prior geological information, especially when discrete facies indicator presents in the model; for example, a reconstructed “channel” does not look like a channel. This paper presents a novel machine learning (ML) method that learns prior geological information/data, and then reconstructs a model after pluri-principal-component-analysis (pluri-PCA) is applied. The main steps of the methods are: first, a dictionary of object-based channelized geological models is generated based on the prior geological data/information. A pluri-PCA approach is applied to reduce the dimensions of grid-based static model and to convert the facies models to Gaussian PCA-coefficients. Second, the PCA coefficients are tuned during history matching process and the pluri-Gaussian rock-type-rule is applied to reconstruct the complex geological facies model from the tuned coefficients. Finally, a ML technique called “Piecewise Reconstruction from a Dictionary” (PRaD), which is based on the Markov Random Field method, is introduced to minimize the feature distance between the reconstructed model and the training models. In order to enforce geological plausibility, the facies models are reconstructed or regenerated by putting together pieces from different patches in the training realizations.
An AHM workflow with the above described new method has been applied to a real turbidite channelized reservoir. The prior geological model indicates that there is clear sand deposition between a gas injector and oil producers. However, one of the production wells has been observed much less gas production than simulated result. Without adding the plausiable additonal fault, the AHM results convinced that the reasonable match on gas production can only be achieved by changing channel orientation and shales/facies distribution. In addition, the new method is observed to preserve both channel features and geostatistics of the model parameters (e.g. facies, permeability, porosity). The additional uncertainties in dynamic aspects (e.g. aquifer strength, relative permeability multipliers, etc.) will be included in AHM workflow and addressed by a derivative-free optimization approach.
The new method is able to leverage the prior information provided by geologists in order to produce a non-Gaussian geologically plausible facies model that matches the observation data. While the pluri-PCA reconstruction process helps to preserve the major features and facies fraction within the geological model description, the PRaD method recaptures the missing details of minor features and enables the final model to closely link to the training realizations. Unlike the conventional approach, e.g. adding artificial flow barrier, this method renders the whole history matching workflow applicable to practical problems. In summary, the proposed method can further enhance the quality of the model reconstructed from a training dictionary of geological models.