This work aims to create an approximation of the reservoir numerical model using smart proxy modeling (SPM) to be used for production optimization. The constructed SPM in this work is further improved in different steps to increase its accuracy and efficiency compared to the existing literature. These steps include sequential sampling, average feature ranking, convolutional neural network (CNN) deep learning modeling, and feature engineering.
SPM is a novel methodology that generates results faster than numerical simulators. SPM decouples the mathematical equations of the problem into a numeric dataset and trains a statistical/AI-driven model on the dataset. Major SPM construction steps are: objective, input, and output selection, sampling, running numerical model, extracting new static and dynamic parameters, forming a new dataset, performing feature selection, training and validating the underlying model, and employing the SPM. Unlike traditional proxy modeling, SPM implements feature engineering techniques that generate new static/dynamic parameters. The extracted parameters help to capture hidden patterns within the dataset, eventually increasing SPMs’ accuracy.
SPM can either be constructed to predict the grids’ characteristics, called grid-based SPM, or to predict the wells' fluid rates, called well-based SPM. In this work, the well-based SPM is constructed to duplicate the Volve offshore field production results undergoing waterflooding. We used Latin hypercube sampling coupled with genetic algorithm (GA) in the sampling step. The designed parameters to perform sampling are the individual liquid rate of the producers, and the output is the individual well's cumulative oil production. In the formed dataset, various extracted parameters relating to the wells are prepared, such as well types, indexes, trajectories, and cumulative oil production. Furthermore, a grid-based SPM is constructed in parallel to the well-based SPM. At each timestep of the prediction, dynamic parameters relating to grids (in this case: grids’ pressure/saturations) are transferred to the existing well-based dataset. This technique helps the well-based SPM further increase in accuracy by finding new patterns within the dataset. We implement an average of 23 different models to rank, and perform the feature selection process. Finally, the CNN model is trained on the dataset, and is coupled with two derivative-free optimizers of GA and particle swarm optimizer to maximize the oil production over the selected time period.
Sequential sampling used in this work is a novel technique to construct the SPM with the lowest number of numerical model executions. It provides an efficient workflow to perform sampling, thereby saving time instead of repeating the whole SPM construction steps. The average feature ranking implemented in this paper provides the best prioritization of input parameters. It provides a confident ranking for the feature selection step. Finally, the underlying CNN model is compared to the prediction accuracy of the ANN model.