Particle Transport in Viscous and Viscoelastic Fracturing Fluids

Abstract

Summary Particle settling velocity as related to fluid rheology in fracturing fluids is an important parameter in the determination of the final distribution of propping agent in a fracture. This paper describes theoretical and experimental analyses that account for viscous and elastic properties of the fluid to predict proppant settling characteristics and properties of the fluid to predict proppant settling characteristics and reviews existing theoretical models used to correlate proppant settling data. A closed-form expression for the terminal settling velocity of a single particle as derived from an approximate analysis is compared with experimental data and with data from the literature. The theoretical results are combined with the experimental data to obtain a correlation that is useful in the prediction of the settling velocity of a particle in viscous fluids at an intermediate Reynolds number. Introduction Hydraulic fracturing treatment has been used widely to stimulate oil and gas wells for the past 25 years. In a typical hydraulic fracturing treatment, propping material is pumped into a fracture created in a reservoir with a pumped into a fracture created in a reservoir with a carrier fluid. Propping materials are pumped into the fracture to hold it open so that fluids can flow easily to the wellbore. A highly conductive fracture can be maintained only if these propping materials can be placed in contact with a significant portion of the producing zone. To ensure the best placement of proppants, knowing the settling characteristics of these proppants in the carrying fluid is crucial. The settling velocity of a single particle is the rate at which it fats under a gravitational force and against a drag force exerted by the fluid. The fluids used in fracture jobs are essentially highly viscoelastic in nature. The rheology of these fluids plays a dominant role in the prediction of the settling velocity of the proppant. Also, for proppant transport in hydraulic fracturing, the propping agent consists of a cluster of particles rather than a single particle. In an actual particles rather than a single particle. In an actual multiparticle system, the settling rate of each particle is hindered by collisions with neighboring particles, which results in a much lower settling rate for a free settling single particle. Once the free settling velocity of a single particle is determined, however, it can be used to obtain particle is determined, however, it can be used to obtain the hindered settling rate by use of the following correlation ..........................................(1) Although the information pertaining to the settling velocity of a single particle is well documented for Newtonian fluids, only a few studies have been reported with non-Newtonian media, and they do not completely describe the rheology of the fluids because none of these studies consider the effects of fluid elasticity on the settling characteristics of the proppants. In this study, viscous and elastic properties of the fluid are used to predict the proppant settling characteristics. The solution of an approximate analysis for the terminal settling velocity of a single particle is obtained and compared with the available literature data both for NR, less than 2 and 2 less than NRe less than 500. Suitable correlations are provided to incorporate the influence of elasticity on the particle settling velocity in a fracture.