Conditioning Permeability Fields by Simulated Annealing

A new approach for conditioning stochastic fields is proposed. In this paper, the Simulated An nealing Method (SAM) is applied to laboratory and field permeability data. A generated field of a desired rock property preserves the spatial distribution and honors the actual measured data from field and/or laboratory. In this approach, in contrast to the traditional conditional simula tion, no interpolation technique is used to smooth data at unknown locations. The least-squares objective function is the difference between the spatial variability of the generated field and that of the actual spatial structure of the known data. Hence, theoretical models for fitting experimental variograms are no longer required in this approach. The simulated annealing algorithm is tested on an exhaustive permeability data measured by minipermeameter on a slabbed carbonate core. Comparison of the generated permeability field with the actual data indicates that this approach is efficient and the conditioning is sensitive to the spatial distribution of the known points. A field application is also presented in this study. The anisotropic permeability field generated by SAM on a North Sea Oil Reservoir indicates the capability of SAM to preserve the spatial variability and to represent the uncertainty that exists more realistically than the smoothed representation used in most geostatistical approaches.