Pipeline Flow of Gas, Liquid And Sand Mixtures At Low Velocities
Authors: Gillies R.G. , McKibben M.J. , Shook C.A. 
Published: March 2010

Abstract
Experiments have been conducted to investigate the ability of gas-liquid mixtures to transport sand in a horizontal pipe or well at low velocities. Both laminar and turbulent liquid flow regimes! were investigated. The gas-containing flows were predominant1y in the slug regime.
Sand transport rates in laminar oil flows were very low until the axial pressure gradient exceeded 1.5 kPaim. Gas addition did not improve this performance.
With turbulent liquid flows, sand transport rates at low velocities could be estimated by the Meyer-Peter equation as long as the sand particle diameter exceeded 0.1 mm. As the gas flowrate increased, sand transport rates eventually exceeded these predictions because of mixing caused by passage of the slugs.
Axial pressure gradients for turbulent gas-liquid-sand mixtures could be estimated from the Lockhart-Martinelli correlation.

Introduction
Horizontal wells are of growing importance in petroleum production in Western Canada and the flow within these wells have been under investigation at the Saskatchewan Research Council since 1990. Experimental studies have been conducted with the goal of defining the approaches to be taken in mechanistic modelling of wellbore flows of allldnds. Since as many as four phases (oil, water, gas and sand) may be present, a systematic investigation of gradually increasing complexity has been undertaken.
In the first investigation, the effects of radial influx at a slotted section of wellbore were examined(1). Axial pressure gradients for single phase flows were shown to be predictable from the known laws of laminar and turbulent flow. No additional complications such as turbulence generation were detected in the experiments.
When a stationary sand layer was present, the ability of the influx to mobilize the sand could be explained in terms of concepts defmed by previous studies of liquid-solid fluidization. Thus over a wide range of experimental conditions, a horizontal well with fluid influx resembles a horizontal pipe whose flowrate increases with distance downstream.
A second investigation(2) studied the ability of a turbulent (water) flow to transport sand at low velocities above a stationary deposit. A threshold velocity for sand transport was observed and at at velocities just above the threshold, the flow resembled that which occurs in channels with stationary bottom deposits. Very fine particles, 0.01 mm in diameter, were uniformly distributed in the flow by the turbulence. In this case pressure gradients and sand transport rates could be predicted rather easily by treating the sand-liquid mixture as a pseudo-liquid. The transport rates for sands of diameter 0.2 and 0.1 mm could be predicted from the empirical Meyer-Peter equation(3) which is known to describe channel sediment transport. However this equation was completely unsatisfactory for very fine (0.01 mm) particles.
At higher velocities, but with a stationary deposit still present, pressure gradients and solids throughputs could be predicted from a three layer model which was derived from the two layer model which is known to describe well the flow of slurries in deposit-free pipelines(4). The transition from the mechanistic layer model regime to the Meyer-Peter regime seemed to occur where dune formation in the stationary layers became predominant.