Construction of prior models for ES-MDA by a deep neural network with a stacked autoencoder for predicting reservoir production

Abstract

The design of prior models has continued to receive research attention because of their importance for ensemble-based methods. There are two approaches to ensemble design: selection and regeneration. Both strategies try to utilize dynamic data in a qualified prior model. The regeneration approach has a higher degree of freedom than the selection approach because the latter is selected among given initial models. However, previous regeneration methods are still sensitive to prior models because these methods create new models based on the priors' statistics. In this study, a deep neural network (DNN) was implemented to build new prior models. If there is a data pair for a reservoir model and its production, the production data and model parameters become the input and output data, respectively, for training the DNN. The trained DNN can generate new prior models according to the observed production history. For the output layer of the DNN, the main information of the permeability field is extracted by a stacked autoencoder (SAE) to improve the DNN performance. New prior models from DNN with SAE become the qualified prior set for ensemble-based methods because they already reflect observed dynamic data. For validation, an ensemble smoother with multiple data assimilation (ES-MDA) was applied to an Egg model. The proposed method (i.e., prior models designed with DNN-SAE) gave reliable posterior permeability fields and future reservoir performances. Compared with the two control groups (i.e., prior models and prior models with DNN), the proposed method mitigated the overshooting problem and found channel connectivity in the reference field. In a comparison with reliable posterior models, the simulation results of the proposed method not only matched observed production data but also reliably predicted future production. This study is an example of the successful application of a machine learning algorithm to history matching.