Variograms for permeability are typically calculated using well log and core measurements, if they are calculated at all. Such procedures are inadequate to estimate variograms for horizontal permeability as they yield almost no information about the short lag structure of the variogram. A well test samples a much larger region of the reservoir than log and core measurements and thus, well test responses are potential sources of data for estimating the horizontal permeability variogram In Ref. 1, we established the feasibility of calculating this variogram from a single set of well test data. Here we summarize further research on estimating horizontal permeability variograms from well test data. Our major focus in this paper is on improving horizontal variogram estimates by combining responses from tests on a number of different wells. We also address a few issues related to variogram estimation from single well test data. All work presented here is based on simulated well test data using permeability distributions generated with an imposed correlation structure and level of heterogeneity. Introduction In Ref. 1, we established the feasibility of calculating horizontal permeability variograms from single well test data. We also indicated some of the limitations for estimating variograms from single test data. If the region sampled is representative of the overall permeability distribution, then single well test data can be used to successfully estimate a normalized or scaled variogram. Even when the correlation length can be estimated successfully from the well test derived variogram, the shape of the variogram at short lags is often distorted or spurious. The nature of the sampled region governs the shape of the variogram. Selecting a region of the reservoir a priori, that reflects the nature of the overall permeability distribution is impossible. A logical approach for overcoming the difficulties outlined above is to estimate the permeability variogram by combining in some way data from multiple single well tests. It appears intuitive that by combining data influenced by different regions of the reservoir, variograms estimated from multiple single well tests are more likely to be representative of the true variogram than that derived from a single test. The major goal of this work is to test this idea for improving variogram estimates. We also address a number of issues raised by our earlier study. In particular, sensitivity of the well test derived variogram to time step grids and spatial grid sizes is examined. All results presented in this paper are based on simulated well test data. Every permeability realization is constrained to possess a log-normal histogram and an isotropic variogram All correlated realizations have a spherical variogram structure. Permeability realizations are generated using either simulated annealing or sequential gaussian algorithms. Drawdown well test responses are simulated for these realizations using a three dimensional, semi-implicit, multi- well, finite-difference simulator which was developed by Amoco for simulating pressure transient responses of complex, systems and for modeling full-field multi-well gas reservoirs. P. 597
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