Deep Sequential Surrogate Model Enables New Work Flows
Authors: Carpenter Chris 
Published: August 2021

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 201775, “An End-to-End Deep Sequential Surrogate Model for High-Performance Reservoir Modeling: Enabling New Work Flows,” by Jiri Navratil, IBM; Giorgio De Paola, SPE, Repsol; and Georgos Kollias, IBM, et al., prepared for the 2020 SPE Annual Technical Conference and Exhibition, originally scheduled to be held in Denver, 5–7 October. The paper has not been peer reviewed.
Despite considerable progress in the development of rapid evaluation methods for physics-based reservoir simulators, a significant gap still exists in the acceleration and accuracy needed to enable complex optimization methods. The complete paper describes an end-to-end deep surrogate model capable of modeling field and individual-well production rates given arbitrary sequences of actions (schedules), including varying well locations, controls, and completions. Results provide concrete measures of the efficacy of the deep surrogate model as an enabling technology for the development of optimization techniques previously out of reach because of computational complexity.

Introduction
Recent advances in machine learning, particularly in deep learning, have enabled breakthroughs in technically challenging areas such as computer vision, natural language processing, and speech processing. The authors expand on these powerful algorithms to develop a deep neural network (DNN) surrogate model for reservoir dynamics. The objective of the DNN surrogate model is to predict field rates and individual well rates. The field rates typically include aggregate oil and water production and water-injection rates reported at equidistant timesteps over a desired production horizon. Economic metrics such as net present value are computed using the field rates. The individual well rates are optional, and, typically, the oil production per well is the desired output.
The contribution of this paper is twofold: It expands on the sequence-to-sequence approach by capturing additional varying inputs, namely well controls and completions, and it presents a thorough experimental analysis and validation on a publicly available synthetic reservoir model (SPE9) as well as a real large-scale reservoir model.

Methods and Procedures
Reservoir Models. SPE9 is a standard benchmark to validate and compare simulations of the black-oil model. The reservoir is described by a 24×25×15 grid, having a 10° dipping angle in the x direction and a heterogeneous geostatistically based permeability field. The grid has a uniform size of 300 ft in the x and y directions and is nonuniform along the z direction. The porosity values for each layer are constant and vary across layers. In this work, the original SPE9 benchmark has been modified to be suitable for field development plan (FDP) optimization. Different well-completion data and ranges have been used for the number of producer and injector wells. The areal well locations, the number of wells, and the well-drilling sequence are variables specified by a suitable FDP. A fixed well control has been used in all SPE9 simulations. In the original SPE9 benchmark, the field operating conditions led to free-gas formation and most of the wells switched from rate control to pressure control. The conditions that trigger the switch in well controls are provided as inputs to a reservoir model and are determined on the basis of operational logistics and geomechanical stability criteria. Neglecting such switches in well controls is disastrous in the real world. However, this is benign from the point of view of a numerical benchmark to test FDP optimization.