Multiple Fluids, Proppant Transport, and Thermal Effects in Three-Dimensional Simulation of Hydraulic Fracturing

Abstract

ABSTRACT Realistic simulation of hydraulic fracturing requires the modeling of the flow of the fluid and proppant when multiple fluids, proppants and proppant concentrations are injected in a single fracturing treatment. Furthermore, the temperature of the fracturing fluid is required throughout the fracture for realistic modeling of the rheological properties of temperature-sensitive fluids. Such a detailed model for two-dimensional flow of fluid and proppant in a vertical fracture is presented in this paper. This flow is coupled to a fully three-dimensional elasticity model for the propagation and opening of the fracture. Fluid and proppant particles are tracked during their flow in order to allow the determination of which of the fluids and proppants being injected are at a given position in the fracture at any time. Each fluid is modeled as a non-Newtonian, power-law fluid. Modeling of proppant transport includes the effects of proppant diameter and crack opening; empirical relations are used to account for the effects of proppant concentration, including bridging. Temperature distributions within the fracture are calculated by solving a two-dimensional heat equation obtained by averaging across the width of the fracture. This equation includes the primary effects of convection within the fracture and heat exchange between the fluid and the reservoir. Secondary effects of heat conduction and heat dissipation in the fluid are included for completeness. The numerical method used for fluid tracking, proppant transport, and heat transfer involves integration along backward-drawn streamlines through the nodes at which the respective quantities are being evaluated. Numerical results are presented for representative types of fracture treatments in order to illustrate the nature of the above effects on the fracture geometry, proppant distribution, and injection pressure in the various types of hydraulic fractures.