Sand Movement in Horizontal Fractures
Authors: Wahl Harry A. , Campbell John M. 
Published: December 2007

Abstract
This study extends our information on solid-liquid slurries to the flow of sand in horizontal fractures. Inasmuch as this is basically an unsteady-state process. a comprehensive photographic study was undertaken in a 10- ft windowed cell to determine if the basic flow regimes described for steady-state flow in pipes applied to the subject process. Since the number of potential variables far exceeds the capacity of a single study, emphasis has been placed on the effects of sand concentration, oil viscosity and oil flow rate. The extensive photographic evidence obtained has proven very valuable in gaining an insight into the basic flow mechanisms. Being able to follow visually the flow characteristics that accompany the quantitative data is valuable in the application of the results. Although the use of dimensionless parameters was carefully investigated, it was found that the data obtained could be more easily, and as accurately, correlated by judicious use of the dimensional variables investigated. However, a study into the feasibility of scaling slurry flow was made in the event this technique is justified in future investigations. The data presented show that the pressure behavior observed in solids transport in pipes basically applies to slurry flow in horizontal fractures. The roles of the parameters are altered but a basic equivalence exists. The most significant correlating parameter was the oil viscosity (mu) and the bulk velocity of the slurry (vB), expressed as "muv" product. The most significant correlation expresses the rate of advance of the sand as a function of the variables investigated. There are many practical ramifications of this phase of the investigation that should aid in better treatment design. Evaluation of sand advance rates provides a means of estimating sand placement efficiencies during a treatment and the resulting sand distribution in the fracture. The results show that sand placement efficiencies are low under typical treatment conditions. A brief description of the effects of overflushing is also included.

Introduction
The flow of sand-oil slurries in fractures is an area in which little basic knowledge is available. This stems to some degree from the fact that it is impossible to duplicate fractures at the surface. They occur in various shapes and sizes with an infinite combination of irregularities. Unfortunately, we can never "see" these fractures except in cores and by indirect means of measurement. In spite of this inherent difficulty, it is desirable to develop some basic concepts that will provide a better understanding of the sand transport mechanism. An insight into the problem is provided by investigations of fluid flow in rectangular conduits. Several studies on the flow of liquids in non-circular conduits show that a Reynolds number-Fanning friction factor relationship can be written if the hydraulic diameter is substituted for the regular diameter in a circular pipe. This hydraulic, or equivalent, diameter is taken as four times the cross-sectional area occupied by the flowing fluid divided by the wetted perimeter. Eq. expresses an extension of this same work when applied to infinite parallel planes b distance apart.(1)