Application of Neural Network and Global Optimization in History Matching
Authors: Silva P.C. , Maschio C. , Schiozer D.J. 
Published: March 2010

Abstract
This article presents the application of global optimizers combined with Artificial Neural Networks (ANN) to the history matching problem. An evolutionary algorithm is executed on the proxy generated through the ANN technique. The results obtained from evolutionary algorithms are fine-tuned by using a local optimizer based on the Hooke and Jeeves optimization method. The methodology is applied in two reservoir models and promising results were obtained.

Introduction
The history matching process consists of adjusting or alternating the key parameters in a reservoir model. The process uses comparisons among production data obtained from reservoir well tests, to develop the model. Some important steps in history matching include the choice of the parameters, the objective function definition, sensitivity analysis and the stopping criteria.
Some problems related to history matching are:history matching is generally realized manually;because of the manual element, history matching is not efficient with very large amounts of data;the number of parameters for the reservoir model that can be used to find a solution for a problem can be large, which makes it difficult to determine which parameter will resolve the problem;the algorithms used are local optimizers which do not work satisfactorily in multi-dimensional solution space with several different minimums; andconventional history matching works with only one reservoir model, and does not have the ability to work with multiple models.
To solve the problems mentioned above, reservoir engineers have proposed automatic history matching. Some advantages of automatic history matching are:the reduction in the number of tasks related to manipulating the reservoir models;optimization algorithms in automatic history matching can work with objective functions, parameterization, stopping criteria and, possibly, sensitivity and uncertainty analysis together;automatic history matching has the capacity to work simultaneously with multiple reservoir models with uncertainty associated with each model, thereby, satisfying the problem regarding which parameter to use to resolve the matter investigated;automatic history matching has the capacity to work with large amount of data, allowing the use of new technologies that have been recently introduced for reservoir management, such as 4D seismic downhole gauge; andautomatic history matching offers the possibility to combine the experience of reservoir engineers with rules transformed in mathematical algorithms. One of the most important topics of research on automatic history matching is the development of optimization algorithms. These algorithms are divided into two groups in accordance with the type of objective function with which they work: global optimizers, which are able to work with noisy multi-modal objective functions; and local optimizers, which are able to work with uni-modal objective functions.
The algorithms that have been used more in practical cases are based on the following methods: the Gauss-Newton Method(1), the Levenberg-Marquardt Method(2) and the Fletcher-Powell Method(3). The difficulty with the algorithms generated with these methods is that they do not work efficiently with non-linearity. Moreover, they are local optimizers. The research about global optimizers in automatic history matching is fundamental(4).