Numerical investigation of the perforation friction loss, coefficient of discharge and erosional processes during limited entry hydraulic fracturing treatments

Abstract

Hydraulic fracturing is behind the successful and feasible exploitation of unconventional hydrocarbon resources around the world. Pioneered by North American operators, the multi-stage massive treatments have enabled producing shale resources very efficiently and at a competitive cost. Recently, limited entry perforating has been found to be useful to increase the stage length and reduce the total stage count with no compromise on productivity. Limited entry hydraulic fracturing treatments rely on the concept of limiting the number of perforations, creating a high perforation frictional loss, and elevating the pressure inside the wellbore. The elevated pressure helps to overcome the closure stress variations along the stage and divert the fracturing fluid more evenly among the clusters. The slurry flow at such a high flow rate through limited perforations is very abrasive, causing a rapid and significant change to the perforation shape and size. This dissertation addresses two critical aspects of the limited entry hydraulic fracturing treatments; the high perforation frictional loss and the dynamic perforation erosion process. Utilizing Computational Fluid Dynamics (CFD), this work modeled the flow through perforations and developed a quantitative understanding of the kinetic energy correction factor used in the perforation friction equation, the coefficient of discharge (Cd). The Cd sensitivity to the perforation design parameters was investigated using an experimentally calibrated model. Using the discrete phase model (DPM), the proppant distribution among the clusters for actual field completion designs was modeled, and the steady-state erosion distribution and rate were predicted. The erosion rate sensitivity analysis was carried out on a field-scale completion design case and showed reasonable agreement to the erosion field data analysis. The results identified a Cd value of 0.72 for a 0.35 in. sharp-edge drilled perforation. Real jet perforations of the same size display higher Cd values, ranging from 0.75 to 0.83 due to the semi-round perforation entry and inlet burr effect. The erosion process increases the perforation discharge efficiency, and the Cd value increases significantly, reaching the 0.9 range as estimated by the transient erosion model. The model indicated that the smaller the perforation size, the longer the tunnel, the higher the viscosity and proppant concentration, and the smaller the proppant size, the lower the Cd. The two-phase DPM modeling results revealed the importance of the particle inertia and gravity force on the proppant transport and distribution. CFD is a useful tool in capturing the impact of those two major forces, predicting the proppant and erosion distribution for various completion designs. The DPM modeling indicated that the perforation erosion process is governed by the mass of particles flowing out and their impact velocity. Supported by field data, the erosion rate is highly sensitive to the flow rate; a 20% rise in the flow rate showed more than 60% increase in the erosion rate. The gravity force also has an impact on the erosion rate; bottom perforations suffer from 20% more erosion than top perforations.