Proppant Transport Simulation in Hydraulic Fractures and Fracture Productivity Optimization

Abstract

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.

Simulation and solution of a proppant migration and sedimentation model for hydraulically fractured inhomogeneously wide fractures

“…The proppant settling velocity is given by (Bai and Li, 2023; Kong et al, 2015; Li et al, 2024; Pan et al, 2018; Roostaei, 2017; Sahai and Moghanloo, 2019; Singh et al, 2022) (Table 1):…”

“…where ρ f g(1 + C(η − 1)) is the additional gravity component arising from the difference in density between proppant and fracturing fluid, which is only available in the longitudinal direction, η = ρ p ρ f . The proppant settling velocity is given by (Bai and Li, 2023;Kong et al, 2015;Li et al, 2024;Pan et al, 2018;Roostaei, 2017;Sahai and Moghanloo, 2019;Singh et al, 2022) (Table 1):…”

“…Meanwhile, numerical simulations of proppant migration and sedimentation in fractures have been conducted at home and abroad. Kong et al (2015) proposed a three-dimensional coupled model in combination with fracture morphology, and it is capable of calculating the proppant distribution under specific fracture morphology. Gadde et al (2004) introduced a pseudothree-dimensional solid-liquid coupled model based on the Euler method.…”

Numerical investigation of conjugate heat transfer and temperature-dependent viscosity in non-Brownian suspensions with application to hydraulic fracturing

“…A source term may be added to the right hand side to assist in modelling leak-off [26]. The use of Stokes drag correlations guide the estimation of proppant settling behaviour within the fluid [19,27] of this approach.…”

“…The effect of proppant choice was studied by Kong et al [26] using similar techniques to those already mentioned (e.g. corrected Stokes drag for settling velocity, proppant location treated with a volume fraction term).…”