Uncertainty Quantification for a Hydraulic Fracture Geometry: Application to Woodford Shale Data

Abstract

Hydraulic fracturing enhances hydrocarbon production from low permeability reservoirs. Laboratory tests and direct field measurements do a decent job of predicting the response of the system but are expensive and not easily accessible, thus increasing the need for robust deterministic and numerical solutions. The reliability of these mathematical models hinges on the uncertainties in the input parameters because uncertainty propagates to the output solution resulting in incorrect interpretations. Here, I build a framework for uncertainty quantification for a 1D fracture geometry using Woodford shale data. The proposed framework uses Monte-Carlo-based statistical methods and is comprised of two parts: sensitivity analysis and the probability density functions. Results reveal the transient nature of the sensitivity analysis, showing that Young’s modulus controls the initial pore pressure, which after 1 hour depends on the hydraulic conductivity. Results also show that the leak-off is most sensitive to permeability and thermal expansion coefficient of the rock and that temperature evolution primarily depends on thermal conductivity and the overall heat capacity. Furthermore, the model shows that Young’s modulus controls the initial fracture width, which after 1 hour of injection depends on the thermal expansion coefficient. Finally, the probability density curve of the transient fracture width displays the range of possible fracture aperture and adequate proppant size. The good agreement between the statistical model and field observations shows that the probability density curve can provide a reliable insight into the optimal proppant size.