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)

where Re equals

Eq. 1 is a theoretical equation expressing the friction factor as a function of the Reynolds number for laminar single-phase fluid flow. This expression has been verified experimentally. The equivalent expression for a smooth circular conduit differs only in that the value of the constant is 16 instead of 24. Numerous studies have related friction losses to Reynolds number in both circular and non-circular conduits. These results are widely used and are not reviewed here.Huitt investigated the effect of surface roughness on fluid flow in simulated fractures. He concluded that fluid flow in fractures may be treated similarly to fluid flow in circular conduits. This work, together with that of Nikuradse, shows that surface roughness has no appreciative effect upon the resistance to flow in the viscous flow region. In the region of turbulent flow, surface roughness is a prominent factor.Hydraulic conveyance literature is another important source of inform ation. Durand has attempted to organize systematically the variables involved in hydraulic-solid transport in pipes. He has classified the modes of flow into three types according to the size of the particles in the mixture-homogeneous mixtures, intermediary mixtures and heterogeneous mixtures. With the usual concentrations and flow rates used in hydraulic transportation, particles with diameters of less than 20 or 30 microns form essentially homogeneous mixtures with water. The data show, however, that even small materials will tend to settle out under laminar flow conditions.Mixtures containing solids over 50 microns in diameter do not achieve total homogeneity even under turbulent flow conditions. Particles from 50 microns to 0.2 mm in diameter may be transported in fully suspended flow at normal transport velocities although the concentration in the vertical plane is not uniform. Above 2 mm in diameter solid materials are transported along the bottom of the conduit at a velocity substantially less than that of the liquid itself. Between 0.2 and 2 mm in diameter, the particles tend to be in a transition zone between heterogeneous suspended flow and deposit flow at normal hydraulic transport velocities. The sand sizes used in fracturing usually fall in this size range.It is interesting to note that the grain size range designated by Durand for this transition zone corresponds closely to the transition zone between

JPT

P. 1239^

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