Calculation method of proppant embedment depth in hydraulic fracturing

For the issue of proppant embedment in hydraulic fracturing, a new calculation method of embedment depth considering elastic-plastic deformation was proposed based on the mechanism of proppant embedment into rocks by combining proppant embedment constitutive equations and contact stresses on the rock-proppant system. And factors affecting embedment depth of proppant were analyzed using the new method. Compared with the elastic embedment model, the results calculated by the new method match well with the experimental data, proving the new method is more reliable and more convenient to make theoretical calculation and analysis. The simulation results show the process of proppant embedment into rocks is mainly elastic-plastic. The embedment depth of monolayer proppants decreases with higher proppant concentration. Under multi-layer distribution conditions, increasing the proppant concentration will not change its embedment depth. The larger the proppant embedment ratio, the more the stress-bearing proppants, and the smaller the embedment depth will be. The embedment depth under higher closure stress is more remarkable. The embedment depth increased with the drawdown of fluid pressure in the fracture. Increasing proppant radius or the ratio of proppant Young's modulus to rock Young's modulus can reduce the proppant embedment depth.