Reliability analysis models for hydraulic fracturing

For many decades, hydraulic fracturing has been the technique most commonly used in the oil and gas industry to increase the productivity of low permeability reservoirs. However, much uncertainty remains when applying this technique, which can influence performance. It has proved difficult, for example, to evaluate the uncertainties inherent in traditional deterministic hydraulic fracturing models using classic analytical and numerical methods. Thus, in this study, we adapted reliability analysis to evaluate the performance of hydraulic fracturing including the length, width, and nature of a fracture when considering uncertainty. Random variables are assumed to follow a normal distribution, and the first-order reliability method (FORM) was used to calculate a reliability index for hydraulic fracturing based on Khristianovic-Geertsma-de Klerk (KGD) and Perkins-Kern-Nordgren (PKN) models. Reliability indexes obtained under different conditions show excellent agreement with Monte Carlo simulations, and indicate that use of this method provides an efficient and effective scientific approach for the uncertainty analysis of hydraulic fracturing. We also investigate and discuss the influence of elastic mechanical parameters of rock formations as well as in situ stress as random variables affecting the performance of hydraulic fracturing alongside various other factors that can influence this process, including rock tensile strength, injection rate and time. This analysis provides quantitative insights into the uncertainties that underlie hydraulic fracturing models and enables the identification of potentially influencing factors to reduce performance uncertainties. The results also show reliability analysis provides an appropriate solution for evaluation of uncertainty and can further improve the performance of hydraulic fracturing.