**2. Horizontal slurry ducts**

Workers in the 1950s, following an influential study by Durand & Condiolis [1], identified *regimes* for the flow of slurries in horizontal ducts. Categories included a classification by size, but inter-relationships with pipe velocities, particularly those for deposition added a layer of complication in identifying the flow regime. Subsequently four regimes were proposed, based on increasing axial pipe velocity (other factors having been defined):


It is not always straightforward to identify visually the flow regime of a particular slurry against the list of velocity categories alone. An interesting, if rather controversial, approach to this problem was proposed by Turian and Yuen [2] who proposed coefficients based on friction factor, efflux concentration, pipe diameter, and relative density of solid particles in addition to pipe velocity. These coefficients were to be used to choose the regime (0…3). A critical evaluation of the Turian and Yuen method is given by Mediema [3]. The incorporation of slurry flow variables, in addition to pipe velocity, underlines the over-simplification implied by the list, but the convenient four-fold categorization by velocity remains in common use.

Homogeneity in flowing slurries is aided by turbulence. At a small scale, the flow might be extremely complex, but particles are spread by strong mixing actions. At high velocities, concentration profiles across the duct are sensibly uniform. Conversely, non-settling fines in high concentration can be in *laminar flow*. When the mixture is very well mixed prior to transmission, the medium is confined to streamlines and very little mixing takes place within the duct.

When a slurry can be treated as a homogeneous or pseudo-homogeneous liquid, continuum techniques (including rheological modeling) can be applied to the flow as a whole. Strictly, these methods are not really applicable to other regimes, but that does not always prevent them from being applied.

In the discussion above, particle concentration has only briefly been mentioned as an important factor. The transportation of slurry flows in turbulent flow has usually been constrained by a 40% *v/v* limit. The reasons for this limit are in the fear of pipe blockage if greater concentrations are used. Interestingly, much greater concentrations are possible at the cost of improved infrastructure as authors will explore in later pages.

## **3. Vertical slurry ducts**

The flow of slurry in a rising main brings a number of specific challenges. As already mentioned, the most obvious is the increased pressure that the pump must provide in addition to the frictional losses from the pipe wall. The weight in a rising main comes from the density of the slurry being pumped and this changes with elevation. The first task is therefore to establish the density of the slurry in the duct.

The *in situ* concentration, the concentration across a section of duct, yields the density of the slurry at that section. The *in situ* concentration (*Cr* ) should not be confused with the concentration supplied to, or delivered from, the duct ( ) *Cv* . *Holdup*, the ratio of the relative velocity of the solids to the pipe velocity governs the *in situ* concentration, and this determines the mean density. Holdup is defined here as

$$\mathcal{H} = \frac{U - U\_s}{U} = \mathbf{1} - \frac{C\_v}{C\_r} \tag{1}$$

where *Us* is the velocity of the solids component, and *U* is the pipe velocity.

Engineers usually have knowledge of the efflux or delivered concentration required ( ) *Cv* for an application, but holdup and *in situ* concentrations (*Cr* ) are not generally known at the outset. An *Artificial Neural Network (ANN)* developed by Lahiri and Ghanta [4] is claimed to predict holdup with an absolute average accuracy of 2.5%. The value can be used to determine the mean *in situ* concentration and the appropriate density. Their definition of holdup ( *<sup>r</sup> v C <sup>C</sup>* ) is algebraically linked to the

definition given above, but can exaggerate the accuracy obtained, particularly for high values of holdup.

Vertical rising mains are found in many situations. They assume great importance in the mining industry both historically and in present day operations. Interesting, examples of interest to researchers in coarse particle slurry technology are deep-ocean mining and the extraction of coal-water mixtures from depth.

### **4. Low pipe velocities and non-homogeneous mixtures**

At the low to medium pipe velocities found in industrial processes and pipelines, particle concentrations usually vary across a section. We recall the reluctance to pump a slurry of greater efflux concentration than 40% *v/v* for fear of blockages. For horizontal pipe runs, dense regions accumulate at the lower pipe wall as we have already discussed. Despite these difficulties, it is an economic proposition to reduce pipe velocity for at least two reasons:


#### **Figure 2.** *Swirl-inducing duct. Two-lobe, a low-loss design (illustrated). Four–lobe, for a greater swirl intensity.*

These factors have encouraged the development of *swirl-inducing* ducts (**Figure 2**). If sediment from a low to medium-concentration slurry can be swept into suspension at a low velocity, there will be savings in power consumption and pipe wear, not to mention the prevention of pipe blockages. The interested reader is encouraged to visit various contributions to the subject (*e.g.,* Jones [5]).

High-concentration conveying offers an alternative way to exploit the benefits of low pipe velocity as explained in later pages of this volume. An example can be found in the pumping of liquid concrete. This material is a mixture of several particulate elements of widely differing sizes. Utilizing specialized pumping equipment, liquid concrete can be pumped at high concentrations and low velocity. Coarse particles cannot pack at the pipe wall, so a particle-depleted layer exists there. This is sometimes given the rather misleading term: the "lubricating layer" [6].

Broad size distribution in the material to be pumped is an important pre-requisite for pumping at high concentrations in a Newtonian fluid, such as water. There is a very inventive way around this stipulation. Some of the particulate materials can be ground to make a non-settling *visco-plastic* carrier, and the rest of the material can be carried within it. Essentially, at low velocity, the carrier is in *laminar* flow. Machines to create this carrier and to separate coarse particles add to plant costs. Dense-phase horizontal coarse particle transportation for coal slurries became available when a Rotary Ram Slurry Pump (RRSP) was invented [7]. To the incredulity of plant engineers, high-concentration slurries were not required to exceed a minimum velocity and could be stopped and restarted at will.

There are empirical methods to determine headloss in non-homogeneous slurries, but an alternative is a *two-layer model* invented by Wilson [8, 9]. Shook and Roco [10] presented the model "… in a form which should be easier to follow or modify." Over the years, modifications were needed to improve stability and usability of the model, and a completely new interpretation (*2LM*) is now available. The essence of the model is the simplification of the non-homogeneous flow of slurry into two layers. The upper layer represents a component completely supported by hydrodynamic forces, and the lower layer is a component gaining support from pipe walls and hindered settling. This is a severe oversimplification in some eyes, but very good estimates can be obtained.

Designers rely on an estimate of the *critical deposit velocity,* which is the velocity at which a single particle, or perhaps a raft of several particles, will rest immobile at the base of a horizontal pipe. The roughness of the particle surface is greater than that of the pipe alone and this encourages greater accumulations of particles. These particles accumulate into dune-like *saltation heaps*. The curvature of streamlines around the tops of the heaps has an erosive action on the upper particles, which causes a downstream rolling action. This low-velocity downstream motion of dunes characterizes *heterogeneous* flow, but it can be overwhelmed, ultimately causing a pipe blockage. Hence, a

fundamental design requirement is to apply a pipe velocity greater than the deposition velocity. The *2LM* model estimates the pipe velocity for a stationary bed. This velocity is not identical to the critical deposit velocity because the stationary bed is not necessarily a single layer of particles but the differences in estimates are relatively unimportant.

### **5. Instrumentation and measurement of slurry flows**

Slurries are fundamental *mixtures,* and this lies at the heart of problems in making useful measurements. Designers have little choice but to use historical empirical evidence often based on examples of differing flow regimes and differing circumstances. It is encouraging to note how successful these designs have been in the hands of experienced practitioners.

Size distributions of industrial slurries can often be broad, non-symmetrical, or perhaps multimodal. Similarly, distracting is the spread of property values in a particle population. This is particularly true of coal slurries in which constituents can have hydrophilic (easily wetted) or hydrophobic (resisting wetting) tendencies and a broad spread of density. The particles themselves can differ markedly in solid geometry from spherical models from which many theoretical predictions have been built.

Setting aside difficulties in accurate prediction, the situation is not entirely bleak. Great progress has been made in online measurements of slurry flows. Radiometric methods have been used to measure the physical properties of a slurry flow. The same methods, at a higher energy level, can indicate the concentration of a flow by interrogating the transmission of the radiometric beam across it. Most interesting of all is visualization technologies which can give us concentration and distribution mapping. These include *Particle Image Velocimetry* (PIV), *Laser Doppler Anemometry* (LDA), and *Tomographic* techniques [11]. Electrical Resistance Tomography stems from early work in the 1930s and 1940s [12], before computational methods opened it up to widespread use. Electrical Capacitance Tomography used to form computed images of pipe contents was investigated from the 1980s [13]. The techniques involve the measurement of electrical properties of the slurry from the pipe periphery. The difficult job has been to reconstruct the interior structure from the measurements obtained—"The Reconstruction Problem."
