Complex geology and pressure tests

The focus of this work is on the evaluation of well-test (single well and interference) responses in systems with complex geology where the assumption of statistical homogeneity does not hold. A 3D array (ordered set) of values for the properties of the porous medium (porosity cube) as a function of the coordinates is used to understand well-test responses. This array of values contains all relevant information available from prior geological and geophysical interpretations, core and outcrop measurements and rock physics. As this model is constrained by geological considerations, the underlying permeability field is nonGaussian. Characteristics of interference-test responses in the context of the reciprocity principle are discussed. Evaluations of transmissivity and storativity by various measures are given. Quantitative evaluations of tests along classical lines by the methods suggested by Theis or Jacob are compared with estimates obtained by the flow-based, upscaling technique. In the specific examples considered here, it is shown that estimates of transmissivity from pressure tests are much different from the upscaled estimate. For systems with complex geology, we show that measures of point values of permeability such as the median must account for connectivity within the reservoir before such measures may be used to reflect permeability. Both well-test and upscaled estimates of transmissivity are significantly higher than the median value corresponding to point values of permeability within the porosity cube. Estimates of the storativity product are also different from the upscaled estimate. Such differences are problematic in that the conservation of mass principle is violated. The results emphasize that it is essential to use geological models to obtain a realistic estimate of reservoir properties.