Determination of the Geomechanical Parameters and Associated Uncertainties in Hydraulic Fracturing by Hybrid Probabilistic Inverse Analysis

Abstract

Determination of the geomechanical parameters and in situ stress of petroleum reservoir rocks by hydraulic fracturing is critical in performing fracturing operations and reservoir simulation in petroleum engineering. Many uncertainties are associated with the determination of petroleum geomechanical parameters and in situ stress because of the complexity and nonlinearity of hydraulic fracturing and the variation of rock properties. Inverse analysis is commonly used to determine petroleum geomechanical parameters, but conventional analysis does not allow the uncertainty to be considered. This study proposes a probabilistic inverse analysis method that integrates numerical simulation, Bayesian theory and a multi-output support vector machine (MSVM) to determine in situ stress, geomechanical parameters, and related uncertainties. Furthermore, this study tried to establish the relationships between those parameters and numerically simulated borehole pressure. The proposed method was verified by a numerical example in which the uncertainties in the values of the Young’s modulus, Poisson’s ratio, and in situ stress were modeled as random variables. Compared with the traditional inverse analysis methodology, the proposed method was found to improve the accuracy of maximum in situ stress to 45% and 5% with and without considering the poroelastic effects, respectively. Using the parameters determined by probabilistic inverse analysis, the simulated borehole pressure agreed closely with the measured pressure, indicating that the MSVM model reproduced the relationship between the geomechanical parameters and borehole pressure reasonably well. An analysis of the effect of the uncertainty of borehole pressure showed that estimates of the geomechanical parameters are greatly improved by decreasing the error in monitoring borehole pressures.