Uncertainty analysis of hydraulic fracture height containment in a layered formation

Abstract

The prediction of hydraulic fracture height growth is of extreme interest in various engineering practices. To fully understand the dependence of the fracturing height in complex underground geological structures, it is crucial to develop theoretical and numerical hydraulic fracturing models to identify the key variables and their interactions to hydraulic fracture height containment. In this work, we adopt a three-dimensional hydro-mechanical coupling cohesive zone finite element model supported by logging data from a practical engineering project. A novel response surface method with Box–Behnken design is introduced to evaluate the statistical significance of tested variables and to forecast the optimal variable combinations for hydraulic fracture height. The key controlling variables are sorted according to their statistical significance from the analysis of variance, and only the minimum lateral stress ratios in mudstone layer and conglomerate layer are highly statistically significant. The minimum lateral in situ stress contrast is the predominant influence of fracture height containment regarding to their significant negative correlation, while the Young’s modulus contrast is probably not an important parameter in terms of direct control of fracture height. Upon optimization, 41 optimized variable combinations were achieved and could be served as references in regulating this engineering practice or even similar events.