Design Of A Large Vertical Prop Transport Model
Authors: Clark P.E. , Harkin M.W. , Wahl H.A. , Sievert J.A. 
Published: December 2007

A 4-ft by 12-ft transparent, vertical fracture model is being used to study the prop-carrying abilities of both non-Newtonian and Newtonian fluids. The design parameters and difficulties encountered in building and operating the model are discussed. Solutions to problems such as uniform distribution of prop in the sample area, uniform flow across the sample area, and reduction of end effects are described. A novel technique is used to record and reduce the prop trajectories. Observations of suspended prop flow in vertical fractures are presented.

Introduction

Prop transport mechanisms in hydraulically created fractures have been the subject of a number of papers. Good empirical methods have been developed to compute many of the necessary parameters for prop packs formed under equilibrium conditions. However, prop distribution under nonequilibrium (suspended) conditions is not well understood. With the increased use of high viscosity fluids, the non-equilibrium situation is more common. Methods for describing the actual settling velocities of particles under these conditions need to be developed. particles under these conditions need to be developed. It is not our purpose to present a comprehensive review of the literature on prop bank buildup in vertical fractures. However, a short discussion of the methods that can be used to calculate vertical settling velocities of particles falling in a liquid is necessary to provide the background for our study.

Most studies that have been conducted on particle transport by fluids have been carried out particle transport by fluids have been carried out in pipes or cylindrical vessels. In most cases the diameter of the vessel is large relative to the diameter of the particles. This experimental technique minimizes wall effects but does not correspond to the boundary conditions that exist in a vertical fracture.

The falling velocity of a single spherical particle in an infinite walled vessel filled with a particle in an infinite walled vessel filled with a quiescent Newtonian fluid can be adequately described by Stoke's law type calculation. This type calculation is also good for Newtonian fluids in laminar flow.

2g(p - p) dU = p fo —--------------18 (1)

The falling velocity is primarily dependent on the density of the fluid (pf), the density of the particle (pp), the diameter of the particle (d), particle (pp), the diameter of the particle (d), and the viscosity of the fluid (uapp). A problem arises in attempts to extend this type of calculation to non-Newtonian fluids. Govier and Aziz suggest in their book on the flow of complex fluid in pipes that a Stoke's law type calculation using an apparent viscosity (uapp) in place of the Newtonian viscosity (u) is adequate.

Daneshy has used a method that treats a spherical particle falling through a power law fluid by calculating the shear effects of the particle falling through the fluid while ignoring particle falling through the fluid while ignoring the shear of the fluid by the walls. This method should be adequate as long as the particle is traveling in the center of the vessel or parallel plates; but as the concentration of particles plates; but as the concentration of particles increases, more of the particles will be forced toward the walls and the calculated settling velocities will be too low.

Another complication arises from particle-particle interaction and hydrodynamic particle-particle interaction and hydrodynamic interference within flowing slurries. These effects can results in an increase or a decrease in the particle settling rate depending on the nature of the particle-particle interaction. The effect of hindered settling, resulting in a decrease in falling rate, is well recognized and has been applied to prop transport in vertical fractures.