The Study of Options for Identification Stress Contrasts via Pumping History

Abstract

AbstractA recorded pressure history is commonly the only quantitative information available as the result of a hydraulic treatment. It would be of value to use the history for decreasing uncertainty of in situ conditions, first of all, of in situ stresses. Yet the inversion of a pressure history in terms of in situ stresses is an ill-posed problem. This makes unclear the options for identification of the stresses. Of essence is to study when, to which extent and how the identification may be performed. The paper aims to meet this request. We start from formulation the inverse problem with employing truly and pseudo-three-dimensional models for generation experimental and theoretical histories. To simplify identification, we (1) reduce the number of input parameters present in these models by using specially normalized variables, and (2) distinguish three dimensionless key parameters $$R$$ R , $${k}_{\mathrm{asym}}$$ k asym and $${b}_{\mathrm{P}}$$ b P . They define, respectively, the strength of a stress contrast, asymmetry of stress contrasts, and the prevailing type of fracture growth. The analysis, based on these parameters, gives ranges within which the identification is possible in principle. It also yields a sound initial guess to facilitate rapid identification of stress contrasts within the ranges distinguished. Numerical examples illustrate the options for identification of stress contrasts. They demonstrate agreement with the theoretical conclusions. Specifically, on the one hand, they confirm impossibility of identification beyond the ranges distinguished, and, on the other hand, within these ranges, they demonstrate rapid identification of stress contrasts by the method suggested.