C. A. Shook

A conductivity probe for measuring local concentrations in slurry systems

Abstract A simple, economical and accurate technique has been developed to measure local in situ solids concentration in slurry systems. The instrument relies on measuring slurry resistivity, as it changes with the solids concentration, for a small region in space. The device was tested in comparison with isokinetic sampling and γ-ray absorption for a variety of slurry pipeline flows. The effects of fluid properties, temperature, velocity, particle size and pipe wall material were examined experimentally. In contrast with previous techniques the effect of fluid velocity upon the measurements was eliminated by a dual electrode-pair system.

Solids transport by laminar Newtonian flows

Abstract An experimental investigation of the horizontal transport of solid particles by viscous Newtonian fluids has been conducted. The independent variables were: fluid density, fluid viscosity, particle diameter, pipe diameter, in situ solids concentration and bulk velocity. The measured variables included pressure gradients, delivered solids concentrations, concentration distributions and fluid velocity distributions. The pressure gradient, velocity distribution and delivered solids concentrations could be explained in terms of the slurry viscosity and the local solids concentration, which varied considerably in the vertical direction. This variation of solids concentration is interpreted in terms of particle–particle interactions which oppose the effect of gravity. The experimental results show that pressure gradients of the order of 2 kPa/m are required to transport significant quantities of sand in laminar flow. The experimental results should find application in horizontal oil well technology.

The lateral variation of solids concentration in horizontal slurry pipeline flow

Abstract Measurements of the solids concentration in the horizontal plane through the pipe axis have been made for slurries of sand in water and solid polystyrene in water. The experiments were conducted in a pipeline of 51 mm dia. At low concentrations, and especially with fine particles, no variation of concentration could be detected in the central 80% of the pipe. As the concentration or the particle diameter increased, a region of reduced concentration near the wall was detected. Experiments at mean velocities of 2 and 3.4 m/s indicated that the migration tendency is insensitive to velocity, for fully suspended flow. The migration tendency seems to result from the dispersive stress effect discovered by Bagnold. Modifications to include this effect in the Schmidt-Rouse model appear to be justified.

Computational method for coal slurry pipelines with heterogeneous size distribution

Abstract Design of industrial slurry pipelines is usually performed by applying semi-empirical procedures, requiring a significant experimental study for each project. This paper presents a new computational technique for coal slurry pipelines based on a two-phase flow analysis. The calculation model gives numerical solutions for the concentration, velocity and particle size distributions in the pipeline cross-section, which can be integrated to provide mean velocities and flowrates, delivered concentration, etc. Design calculations for headlosses can be performed using this approach for any set of given conditions: the properties of the transported material, carrier liquid and pipeline. The computational technique was developed using data for uniform sand—water mixtures flowing in pipelines of 51.5 mm, 263 mm and 495 mm diameter. The approach is extended to coal—water mixtures with heterogeneous size distribution of particles, and tested with experimental measurements in pipelines of 158 mm and 495 mm diameter. The model is shown to be a useful vehicle for generalizing experimental measurements and scale-up to headloss predictions.

Particle—wall stresses in vertical slurry flows

Abstract Pressure gradients have been measured for vertical flows of slurries of particles with diameters between 1.37 and 3.4 mm in pipes of diameter 26 and 40 mm. By expressing the wall shear stress as the sum of fluid and particle components, the wall stresses for the particles have been evaluated. The stresses increase with particle diameter and density, mean flow velocity and particle concentration. Measurements of the velocity of the particles closest to the pipe wall suggest that considerable distortion of the velocity distribution occurs, compared to that of the clear carrier fluid. The measurements confirm that a region of reduced particle concentration forms at the pipe wall, with coarse particles giving a pronounced change of this type. The wall stresses resemble those discovered by Bagnold for particles sheared in Couette flow. In Bagnolds experiments, wall stresses were found to be strongly dependent on solids concentration. Since the particle concentration at the wall was unknown in the present investigation, a correlation for wall stresses has been obtained in terms of the mean concentration. The correlation can be used to estimate pressure gradients for vertical flows of nearly isometric angular particles.

Particle segregation in slurry flow through vertical tees

Abstract An experimental study has been conducted of particle segregation in slurry flow through vertical tees. Water-sand slurries with solids concentrations to 25% by volume were used with tees of various sizes and angles. The experiments showed that the branch concentration is less than the upstream value for all the branches studied at velocity ratios less than unity. The separation ratio was found to be a function of upstream conditions. velocity ratio. branch size and angle. For lateral branches. the inertia effect is dominant at low velocity ratios. whereas the gravity effect becomes important at high velocity ratios. A two-dimensional model explains the results qualitatively.

Pipeline transport of large ablating particles in a non-Newtonian carrier

Substantial environmental advantages can be achieved by transporting overburden in a clay slurry if the rate of ablation of the overburden particles is not excessive. An experimental investigation of this form of hydrotransport has been undertaken and changes in pipeline pressure drop have been used to infer the rate of overburden particle ablation. The experiments suggest that the fine particles disperse quickly and the larger ones remain for longer periods of time. A reasonable model of the experimental results is obtained by assuming the particle diameter decreases at a rate which is independent of particle size.

The pseudohomogeneous flow approximation for dispersed two-phase systems

ABSTRACT The unsuitabllity of a continuum model for turbulent flow of solid-liquid mixtures has been demonstrated by a number of experimental studies which employed industrial slurries and a wide range of pipe diameters. However effective particle sizes and slurry viscosities are difficult to define for such mixtures. Using spherical glass particles of median diameter 125 μm and 240 μm, vertical flow experiments have been conducted in a test pipeline 26.17 mm in diameter. These experiments confirm earlier sand flow measurements by showing that wall friction decreases as particle size increases, in the absence of Bagnold stress or Coulombic friction effects. Using a turbulent flow simulation, and assuming a linear increase of solids concentration in a thin layer near the pipe wall, dimensionless excess wall frictional resistances have been calculated. These predictions are likely to be valid for fine particles which do not display Bagnold stress or Coulombic friction effects. The turbulent flow simulations...

Flow of sand-water mixtures at velocities below the deposition condition

ABSTRACT An experimental study of sand-water flow in a horizontal pipeline has been conducted for the regime in which a stationary deposit was present. The particle diameter ranged between 0.2 mm and 0.01 mm and the particles were not flocculated. Axial pressure gradients and delivered concentrations were measured as functions of mean velocity and in-situ concentration. A three layer model was found to be useful to predict the pipeline behavior at all but the lowest velocities. The Meyer-Peter sediment transport equation was satisfactory for very low velocities with the larger particles.

Elastic gravity stresses in a flat-bottomed bin

Abstract The theory of linear elasticity is used to determine stresses within a flat-bottomed bin in plane strain. Photoelastic studies are used to verify the displacement boundary conditions employed in the finite element method of solution. For a bin with smooth walls, the stress distribution far from the opening is linear. An interesting dependence upon Poissons ratio of the material is observed in all cases except a fully open bin. This effect is probably due to the mixed boundary conditions of the stress calculations. Increasing wall friction produces a more uniform shear stress distribution within the bin. Increasing the height to width ratio of the bin appears to produce a better design for failure of a bulk material.