Treating Uncertainties in Reservoir-Performance Prediction With Neural Networks
Authors: Denney Dennis 
Published: February 2015

This article, written by Technology Editor Dennis Denney, contains highlights of paper SPE 94357, "Treating Uncertainties in Reservoir-Performance Prediction With Neural Networks," by J.P. Lechner, SPE, OMV A.G., and G. Zangl, SPE, Schlumberger Information Solutions, prepared for the 2005 SPE Europec/EAGE Annual Conference, Madrid, Spain, 13–16 June.
In development projects, reservoir parameters are known only within certain ranges, which results in various realizations of the subsurface. Because of the computational time involved, simulation models to obtain a probability distribution of possible outcomes cannot cover all possible parameter combinations. Creating a response surface based on a reduced number of simulation runs becomes necessary. Such a response surface can be used to approximate results for several variations of input parameters. An approach in which reservoir response is captured by an artificial neural network (ANN) has been investigated. The trained ANN model was used in Monte Carlo simulations to generate the probability distribution of possible outcomes.

Introduction
Often, simulation models are built to design field-development plans. Because of the low level of information during the early development stage, a range of uncertainty in the prediction scenarios must be considered. Such uncertainties can be handled with ANNs.
Numerical models (simulation models) are detailed and powerful predictive tools that can answer many questions regarding subsurface engineering. However, especially in the early development phase, uncertainties are large, and prediction results will span a broad range. To take into account the whole range of possible outcomes of reservoir simulation, optimization routines would have to run the numerical models perhaps thousands of times. Although the most likely solution that respects subsurface uncertainties is of interest, the most profitable solution for reservoir management must be found. Because of the computational time involved, these methodologies often are not used. Building a response surface that can predict many possible outcomes of a numerical simulation by processing a large variety of input parameters could provide a solution to this problem. The response surface must cover the non-linear dependencies between input and output parameters.
Experimental design and response-surface modeling has been used to delineate subsurface uncertainty. Common applications include determining the probability distribution of original oil in place from geological models, quantifying uncertainty in predevelopment or preredevelopment projects, predicting production performance from different realizations of a geological model, and optimizing the location of new wells to maximize net profit.

Methodology
Fig. 1 shows the proposed workflow. As a first step, a limited number of simulation runs is carried out to define the most sensitive input parameters. In these runs, parameters are altered one at a time, either to the minimum or to the maximum. After selecting the most influential input parameters, three values (minimum, best-estimate, and maximum) are defined, and an experimental design is set up. The experimental design aims at obtaining the maximum information with a minimum number of simulation runs. However, practice showed that a minimum number of training data sets are required by the ANN to be able to make sufficiently accurate predictions. With these data sets containing varying input parameters and the corresponding output, an ANN is trained and tested with several additional simulation runs. After defining the probability distribution of the input parameters, the trained ANN is used as a proxy function for a Monte Carlo simulation. Thereby, a probability distribution of the desired output parameter (e.g., cumulative production after a certain number of years) is gained. The quality of the ANN is measured by the root-mean-square error of the deviation between the predicted and the actual output.