Evaluating the Performance of a Fracturing Treatment Design

This paper describes the combination of a Perkins-Kern-Nordgren (PKN) type model for hydraulic fracture propagation with a method for calculation of proppant transport and settling in order to simulate the dynamic growth, stress induced closure, and final geometry of vertically oriented two-dimensional fractures. A mathematical model is developed to describe the fracture growth, fluid flow, and proppant movement along with proppant settling and bank formation. A particle tracking method which uses the concept of pseudoparticles to represent the proppant phase is used for the computation of solids distribution within the fracture and the proppant bank growth. A technique for periodically combining the elements of the computational grid allows for reduced simulation time. Using the computational model, contraction of fracture dimensions after the end of pumping can be simulated in order to determine the final shape of the propped fracture. A sensitivity analysis was conducted to study the effects of pumping rate, inlet proppant concentration, and proppant particle size on the final fracture condition. To evaluate the efficacy of different treatment designs, the resulting geometry of the propped fracture dimensions and the achieved conductivities were compared. Based on the simulation results obtained, specific recommendations on how to avoid premature tip screen-out and achieve desired fracture conductivity are presented.