Abstract

This paper describes the implementation of a Genetic Algorithm (GA) to carry out hydrocarbon reservoir characterisation by conditioning the reservoir simulation model to production data (history matching) on a predefined geological and structural model. The proposed technique combines the advantages of the pilot point method for the description of petrophysical properties, with the advantages of GAs for global optimisation.

The modified GA uses a complex genome, which is divided into seven separate chromosomes for different types of reservoir parameters. Chromosomes containing the pilot point information are three-dimensional real number structures which include information for the wells, while the chromosomes for all other parameters are one-dimensional arrays. Specially designed crossover and mutation operators have been created to work with the non-standard genome structure. Results from tests on several GA design issues are presented, including crossover and mutation operators, encoding, selection, and other population strategies such as elitism. In addition, a comparison is made with a standard Simulated Annealing algorithm.

Introduction

Reservoir characterisation requires the incorporation into the reservoir models of all knowledge available, so that better predictions of reservoir performance can be achieved. The process makes use of measurements made in the field to restrict the range of values that the parameters might take. The measurements used are wide-ranging and include seismic data, data from geological analogues, core and log data from wells, well test data, and production data.

Many previous attempts have been made to automate this process, posing the inverse problem as an optimisation problem and using some optimisation technique to match the numerical results to the measurements. Papers describing this process include Tan and Kalogerakis,1 Oliver et al.,2 Deschamps et al.,3 Wu et al.,4 and Floris et al.5 Most of these attempts have used gradient-type methods.

Search methods such as simulated annealing (SA) and genetic algorithms (GA) have also been applied to address the optimisation problem. GAs have been used in reservoir engineering in several works, including those by Sen et al.,6 Bush and Carter,7 Guerreiro et al.,8 and Romero and Carter.9 Genetic Algorithms (GAs) were invented by John Holland10 as an abstraction of biological evolution, drawing on ideas from natural evolution and genetics for the design and implementation of robust adaptive systems. Over the last 20 years, GAs have received much attention because of their potential as optimisation techniques for complex functions.11 Their main drawback, however, is that they can be computationally intensive, and therefore very expensive.

This paper describes in detail the formulation of a modified GA using non-standard genome and genetic operators, as proposed by Romero et al.12 The method is computationally efficient, in that it requires only a modest number of forward simulations. The paper deals with some of the main GA design issues, and presents optimisation results on its application to a synthetic reservoir model constructed as part of the PUNQ project.13 Results with respect to the history matching at well level, and to the petrophysical property fields can be found in Ref. 12.

Genetic Algorithm

Genetic Algorithms (GAs) are heuristic type methods that can be applied to the optimisation of complex functions.14 They are randomised search algorithms based on an analogy to the mechanics of natural selection according to Darwinian evolutionary theory and the ‘survival of the fittest’ principle. GAs draw ideas from genetics to describe solutions to the problem under consideration as ‘individuals’, and mimic natural evolution by starting with an initial population of feasible solutions (individuals) to the problem being addressed.

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