Homogeneous and pseudo-homogeneous flow

Classification of slurries is necessary to properly design slurry transport systems. Different slurries can form different flow types, with different flow patterns exhibiting different flow behaviors. Slurries of smaller particles (smaller than say 40 µm) tend to behave as homogenous slurries. The distribution of particles is virtually uniform throughout the flow. The distribution of particle velocity is axisymmetric across the pipe cross-section and there is no local slip between the velocity of particles and the velocity of the carrying fluid. Some homogenous slurries behave as Newtonian slurries, and they flow in the turbulent regime in a pipe. The fraction of total mass of solids which is less than 40 µm is known as carrier-fluid fraction, denoted by Xf. Others behave as non-Newtonian slurries, exhibiting either a laminar or turbulent flow regime in a pipe.

Slurry of somewhat larger particles (say between 40 µm and 200 µm which is the fine sand range) exhibits slightly different behavior, called pseudo-homogenous flow. The flow is Newtonian at all concentrations of solids and is usually turbulent. The particles tend to separate from the carrying liquid at very low velocities, but if the mean velocity of flow is sufficiently high, all particles will be supported by turbulent diffusion. There will be a weak concentration gradient with a measurable decrease in concentration with the increasing height of the pipe cross-section. The corresponding velocity distribution would be slightly asymmetrical, and the local slip would be negligible.

Water forms the carrier liquid in majority of slurry flows. Pressure drop due to friction for water is expressed using hydraulic gradient i. For water of density ρw flowing in a horizontal pipe, i is related to the pressure gradient as follows:

\dpi{100} \bg_white \LARGE i_{w} = \frac{1}{p_{w}g}\left ( -\frac{\Delta p}{\Delta x} \right )

where ‘i’ represents the slope of the hydraulic grade line, i.e. drop in level per unit length of pipe.

For a mixture with a density ρm flowing in a horizontal pipe, the mixture-height hydraulic gradient is given by

\dpi{100} \bg_white \LARGE j=\frac{1}{p_{m}g}\left ( -\frac{\Delta p}{\Delta x} \right )

The ratio of i and j equals to the relative density of the mixture (Sm = ρmw).

The equivalent fluid model of slurry flow assumes that solids have little effect on the friction factor, and that the mixture acts as a liquid as far as relative density effect is concerned. The resulting hydraulic gradient for homogenous mixture flow, imh, is equivalent to the product of Sm and iw. The equivalent fluid model, though used extensively in the past, doesn’t support the experimental value. An appropriate general equation for hydraulic gradient, capable of representing both types of flow, is:

\dpi{100} \bg_white \LARGE i_{mh}=\left [ 1+A{}' \left ( S_{m_{}}-1 \right )\right ]i_{w}

The above equation is referred to as “homogenous flow equation”, with the specific case of A’ = 1 is called the ‘equivalent fluid model’ as observed by Carstens and Addie.

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