Computation of permeability variograms from pressure transient data

Geostatistical methods in reservoir characterization have received a tremendous boost in the last ten years, with a major effort geared toward conditioning geostatistical descriptions to conventional data such as production data, tracer and well test data, core measurements, log and seismic signatures, etc., in addition to the histogram and variogram. In typical field applications variograms can be estimated in the vertical direction from log and core data, but almost always impossible to estimate in the horizontal direction. A well test offers a potential source of data for computing horizontal variograms as it samples a relatively large areal region. If successful, this concept has the potential to overcome shortcomings in existing geostatistical reservoir characterization methods.;The central theme of this work is to estimate geostatistical parameters for heterogeneous systems from well test data. Specifically our goals are to: (1) examine the significance of the single "average" value of permeability estimated from a well test in heterogeneous systems, and (2) investigate the feasibility of estimating horizontal permeability variograms from well test data. Using synthetic well test data we demonstrate that for a really uncorrelated permeability distributions, the well test derived permeability is a good estimate for the true average at low levels of heterogeneity. As the degree of heteogeneity increases, the well test underestimates the true average. A correlation is presented to illustrate this effect and we show that it is completely general. In correlated systems, the well test derived permeability is strongly dependent on the features of the region sampled by the test and no general statements can be made whether the well test underestimates or overestimates the true average. We show that permeability variograms can be computed either by using a single test under somewhat restrictive conditions, or by combining responses from multiple tests to overcome the limitations of using a single well test.;The major contribution of this work is that it makes a significant inter-disciplinary effort linking well testing and geostatistics by establishing the feasibility of computing geostatistical parameters from well test data, and offers avenues to overcome the limitations of existing geostatical reservoir characterization methods.