The success of hydraulic fracturing stimulation is highly reliant on the flow area and permeability of the induced fractures. The flow area can be significantly affected by proppant distribution while fracture permeability is mainly governed by proppant sizes. To create a fracture with a large flow area, small proppants are essential to maintain a minimum proppant settling velocity; on the other hand, large proppant sizes provide higher proppant pack permeability (i.e., fracture permeability). Therefore, it is critical to study the effect of proppant on the efficiency of hydraulic fracturing stimulation.

In this paper, a 3-D numerical simulator is developed to simulate proppant distribution profile, calculate fracture geometry based on the proppant distribution and forecast productivity through each fracture. More specifically, finite difference method is applied to calculate proppant distribution profile during the hydraulic fracturing and flow back processes for different settings such as proppant size and relative density. Both single-proppant and multi-proppant size combination are investigated and their after-stimulation productivities are compared. Proppant slippage velocity is considered over a wide range of fracturing fluid viscosity and density. Fracture geometry is firstly determined through the hydraulic fracturing operating parameters and then recalculated based on simulated proppant concentration profile. The adjusted fracture geometry is then used to simulate fluid flow from reservoir matrix to the fracture with non-uniform proppant distribution and non-Darcy flow of compressible fluid.

Results show that, among all parameters, reservoir permeability mostly affects proppant size selection and pumping scheduling in order to achieve an optimum fracturing performance. Multi-proppant size combination simulation results indicate that properly designed multi-proppant combination treatment can increase after-stimulation productivity and improve fracture performance. There exists an optimum combination of proppants size and their volume portion exists for a specific reservoir. The approach presented here can help further understand proppant transport and settling, fracture geometry variation and fracture production performance.

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