Displacement Discontinuity Analysis of the Effects of Various Hydraulic Fracturing Parameters on the Crack Opening Displacement (COD)

The combination of horizontal drilling along with hydraulic fracturing has significantly improved the production of hydrocarbon reservoirs and made it possible to extract the relatively impermeable and uneconomical reservoirs. The production rate of oil and gas wells increases proportional to hydraulic fracture aperture or crack opening displacement (COD). This is an important parameter in fracture mechanics literature and hydraulic fracturing of hydrocarbon reservoirs. Despite the significance of COD there are a few analytical solutions for the estimation of COD under certain conditions. In this paper the effect of various parameters on COD is investigated semi-analytically. A higher order displacement discontinuity method is used to consider the effects of different parameters (Young’s modulus, Poisson’s ratio, internal pressure, maximum and minimum horizontal stresses, crack half-length and its inclination with maximum horizontal stress) on the COD in a hydraulic fracturing process under arbitrarily conditions. The coefficient of determination and standard error of the estimate were 94.35% and 4.37×10-4 respectively, showing a good agreement between the fitted equation and the numerical results. The effect of propagation and well radius on the maximum COD was also investigated. The results showed that COD increases almost linearly with the crack propagation and increase of well radius of hydraulic fractures (HFs). These effects are more significant when HFs are propagating in the direction of maximum horizontal stress. The proposed equation and the results from propagation of hydraulic fractures can be used in early stages of a hydraulic fracturing design.