Parameter Identification Within Rocks Using Genetic Algorithms

Transient ow analyses have numerous geophysical and geotechnical applications and they are necessary for the understanding and development of laboratory measurement techniques in rock and soil mechanics, particularly in the determination of the permeability of substances. In this paper, we formulate a Genetic Algorithm inversion technique for the retrieval of homogeneous or spacewise dependent material property coe cients. 1 PROBLEM DESCRIPTION The accurate determination of the hydraulic conductivity of rocks is a problem frequently encountered within petroleum, civil and mining engineering. In this paper we deal with low permeability rock testing and the `pump ow method' is employed. A cylindrical rock sample is placed in a sealed pressure cell and the permeability is measured by injecting uid at a constant rate into the in ow end of the rock sample, see Olsen et al. (1991). The transient pressure response can be used to obtain information about the permeability and storage properties of the sample. Here we make use of the numerical results of Lesnic et al. (1997) and the formulation models a heterogeneous single piece of material, as well as incorporating the presence of a fault within rocks. The Genetic Algorithm process optimises a tness evaluation function which measures the accuracy of predicted pressure and/or hydraulic ux values against some known (simulated or experimental) measurements. We employ k-Tournament Selection and TwoPoint Crossover. The governing equations of mass conservation equation and Darcy's law are combined with an equation of state for the pore uid and appropriate boundary conditions. The numerical method adopted for solving the initial boundary value direct problem is a time weighted average nite-di erence method. Both exact and simulated noisy data are incorporated at optimally selected instants in time through the test, the data measurements used being consistent with sensitivity analyses of each problem. 2 RESULTS AND CONCLUSIONS The present research has established that GAs are a feasible technique for retrieving highly accurate estimates to unknown material parameters in hydraulic pump ow experiments based upon both exact and noisy data. When a composite sample is investigated, the hydraulic conductivities and fault location can be retrieved from the steady state analysis based upon pressure measurements at the upstream face and one port combined with an interchange of the sample ordering. With these quantities speci ed, the material speci c storages and the compressive storage of the upstream reservoir can be readily determined from transient pressure values at the upstream face combined with a reversal of the order of the samples.