This paper discusses and compares three different algorithms based on combinatorial optimization schemes for generating stochastic permeability fields. The algorithms are not restricted to generating Gaussian random fields and have the potential to accomplish geologic realism by combining data from many different sources. We have introduced a 'heat bath' algorithm for simulated annealing as an alternative to the commonly used 'Metropolis' algorithm and a new stochastic modeling technique based on the 'genetic' algorithm. We have applied these algorithms to a set of outcrop and tracer flow data and examined the associated uncertainties in predictions.
All three algorithms reproduce the major features of permeability distribution and fluid flow data. For relatively small problems, the Metropolis algorithm is the fastest. For larger problems, the heat bath algorithm is at least as fast and often faster than the Metropolis algorithm with significant potential for parallelization. The performance of the genetic algorithm is highly dependent on the choice of population size and probabilities of crossover, update and mutation.
Discrete or combinatorial optimization techniques, in particular simulated annealing (SA), have shown great promise in obtaining integrated reservoir description because they can combine data from many different sources such as cores, logs, seismic traces and interwell tracer data. One of the principal advantages of these techniques over traditional stochastic models is their ability to incorporate effective properties derived from integrated measures such as pressure transient analysis. The commonly used Metropolis method for SA, although simple and effective, can be computationally prohibitive for large-scale reservoir engineering problems because of the large number of rejection moves it makes as annealing progresses. In this paper we investigate an alternative algorithm for SA, the heat bath algorithm, for generating stochastic permeability fields with specified geostatistical attributes. Unlike the Metropolis algorithm, this method produces weighted selections that are always accepted. The heat bath algorithm also offers significant potential for parallelization.