Abstract

Realistic simulation of hydraulic fracturing requires the modeling of the flow of the fluid and proppant when multiple fluids, proppants and proppant when multiple fluids, proppants and proppant, concentrations are injected in a single 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 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 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 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 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 proppant distribution, and injection pressure in the various types of hydraulic fractures.

Introduction

Fully three-dimensional models have been developed for predicting the fracture geometry that, is to be expected for a given hydraulic fracturing treatment. So far, however, these models have been limited to a single frac fluid, without proppant, and with uniform temperature. Realistic fracture designs require the consideration of multiple fluids, the transport of proppants, the variation in temperature throughout the fracture, and the effects of temperature variations on the viscosity of the fluid. Extensions of fully three-dimensional modeling of hydraulic fracturing to include such considerations are presented in this paper.

The overall plan of the paper is to first review briefly the principal features of the formulation of a three-dimensional model and then show how such a model can be extended to include the effects of multiple fluids, proppant transport, heat, transfer, and temperature-sensitive rheological properties. Finally, the extended model is applied to a series of example problems to show the nature and significance of the newly considered effects. These examples suggest that the fracture geometry depends relatively weakly on the effects of fluid temperature and corresponding change in rheological properties. However, proppant distribution is affected significantly.

2. THREE-DIMENSIONAL MODELING

The overall approach in the three-dimensional modeling is to subdivide the fracture into discrete elements and convert the governing partial differential equations into a system of algebraic equations for the nodal pressures and crack openings.

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