S lurry fl ows are often separated into two categories for convenience in predicting pipeline friction losses. The fi rst category is denoted as non-settling or homogeneous or occasionally, pseudohomogeneous. The diameters of the particles in these slurries are very fi ne and settling in the quiescent state is very slow. A non-Newtonian fl uid model is usually applicable for these slurries and stationary deposits do not form at low velocities. Pipeline fl ows of these slurries may be either laminar or turbulent and the solid particles are distributed uniformly within the slurry at all velocities. The particles are usually fl occulated and the suspension mechanism for these particles may be fl uid turbulence or interaction between the fl ocs.For the second category, the so-called settling or heterogeneous fl ows, the particles are larger and not fl occulated. The fl ows are usually turbulent and stationary deposits form at low velocities. The concentration distribution is less uniform for these slurries and the velocity distribution is asymmetric. Homogeneous fl uid models are not appropriate for predicting pressure gradients for these slurries.When the particles settle so rapidly that turbulence does not contribute signifi cantly to particle suspension, the immersed weight of the particles is transmitted by particle-particle interaction to the pipe wall. These slurries are highly stratifi ed and the frictional resistance to fl ow at the pipe wall depends upon the normal force that arises from the immersed weight of the particles. This Coulombic friction is quite different from the velocity dependent friction which arises in both laminar and turbulent fl uid fl ow. A layer model for these slurries was fi rst proposed by Wilson (1976) and numerous subsequent investigations, principally by Wilson and associates, have established a thorough understanding of this important limiting case.A model for the turbulent fl ow of slurries of particles that are only partially supported by turbulence has been used (the SRC model) to generalize experimental pipeline friction measurements. The layered feature of Wilson's original model has been retained because it provides a method for taking the asymmetry of the fl ows into account. As the particle size decreases and the fl ows become more nearly axisymmetrical, the difference in concentration between the layers diminishes and the layer simplifi cation becomes merely a computational convenience.The most recent version of the SRC model (Gillies and Shook, 2000) was produced in response to experiments conducted with slurries of high solids concentration. Since the optimum pipeline velocity is usually close to the deposition velocity, most of the data that were incorporated in the year 2000 model were obtained at velocities that were fairly close to deposition.Since any useful model must respect the physics of the fl ow, it is important that any theoretical or experimental advances should be Experiments have been conducted with sand slurries of median diameter 0.09 mm and 0.27 mm in...

Experimental investigations of the flow of water‐heavy oil mixtures at velocities typical of oil‐field gathering systems show that continuous water assisted flow at very low pressure gradients can be achieved. The principal criterion to be satisfied in establishing this desirable flow regime appears to be use of sufficient water, with the velocity also playing a role. It also appears that oil viscosity and water fraction effects on pressure gradient are small provided the beneficial flow regime is established. The flows resemble core‐annular flow, which has been observed previously in Bitumen froth and water‐heavy oil flows, with an oil layer on the pipe wall. However, the correlation for pressure gradient is somewhat different from that reported previously for Bitumen froth flows.

Despite substantial theoretical progress in recent years, predicting pipeline friction for slurry flows continues to provide challenges for research. The parameter of dominant importance has long been recognized to be the particle diameter and the limiting cases in the spectrum of flow phenomena are understood fairly well, at least at low and moderate solids concentrations.Slurries of very fine particles can be tested in viscometers and are often assumed to behave as continuous media. This assumption is often justified because the particles are flocculated and the interaction between the flocs provides a structure which prevents deposits from forming at low velocities. Although discrepancies between flow parameters observed in viscometers and in pipe flow do arise, these can be attributed to phenomena which are influenced by the finite size of the flocs (Bartosik et al., 1997).Slurries of very large particles are highly stratified when the particle density is different from that of the fluid and pipeline friction for these slurries has been recognized as a combination of fluid friction and Coulomb friction between the particles and the pipe wall. Velocities near the deposition condition are appropriate for pipeline transport and at low velocities, all the immersed weight of the particles will contribute to particle-wall friction. Although a mechanistic description of this type of friction was given by Newitt et al. (1 955), the derivation of Wilson (1 970, 1976) is more rigorous because it considers the stress transmission mechanism and facilitates further mechanistic modelling.The vast majority of "settling" slurries fall between these two limiting cases, displaying deposition velocities and frictional energy losses which may be regarded as combinations of kinetic "fluid-like" friction and Coulombic friction. An indication of the nature of the kinetic friction is the fact that the lower limit to total friction, e.g., when Coulomb friction is unimportant, has long been calculated using a fluid model which employs the density of the slurry and the viscosity of the carrier fluid (e.g., Spells, 1955). This method of calculating kinetic friction was found to be appropriate by Cillies et al. (1 985) for slurries of solids concentration less than 30% to 35% by volume. The model which they employed was based upon Wilson's two-layer model (1 976) and incorporated a number of features which allowed it to be extended to slurries containing particles that do not contribute Coulomb friction.In this model the total solids content is separated into two fractions: a) solids which contribute Coulomb friction; these solids are assumed to be concentrated in a lower layer; and b) solids which are suspended by lift forces derived from the fluid. These solids are assumed to be uniformly distributed within the pipe and combine with the liquid in the two layers to produce pseudofluids whose densities determine kinetic friction and provide buoyancy for the particles contributing Coulomb friction.'Author to whom correspondence may be add...

lurry flows are encountered frequently in the chemical process industries and one of the simplest methods of classification is based S upon the tendency of the slurry to segregate or "settle" in the quiescent state. Non-settling slurries are composed of fine particles and are usually flocculated. The floc interaction which generates the internal structure that prevents settling is also responsible for the non-Newtonian behaviour which is commonly observed with these slurries. Satisfactory prediction of pipeline friction can usually be achieved for these slurries in both laminar and turbulent flow, using models which assume the slurry is a continuum.Slurries of particles which are too coarse to flocculate usually approximate Newtonian behaviour, so that the ratio of slurry viscosity to that of the carrier fluid can be considered as a function of particle shape and solids concentration. The effect of particle shape is sometimes taken into account by including the maximum settled concentration, C , , , , , as a parameter in correlations for relative viscosity. One equation describing this effect for sand grains with C, , , , , near 0.63 is (Cillies et al., 1999):where C is the solids volume fraction. At high solids concentrations, where the last two terms become important, particle-particle interactions are considered to play a major role in energy dissipation when the slurry is sheared in laminar flow. Recent experimental studies of sand transported by liquids of high viscosity have indicated that these interactions provide the mechanism for particle suspension in laminar flow (Cillies et al., 1999). For slurries of coarse particles, i.e., "settling" slurries, the frictional processes are fairly complex, especially when the flows are turbulent. Energy losses for flows of these settling slurries have been considered by many researchers to be a combination of kinetic (fluid-like) and Coulombic (velocity independent) friction. However a paradox is introduced by the fact that slurry viscosity does not appear to be an important parameter in kinetic slurry friction, at least at low and moderate solids concentrations. Spells (1 955) has given an equation for estimating the velocity above which pressure gradients can be calculated from a "homogenous" rule of thumb using the slurry density and the carrier fluid viscosity. Although predictions from Spells' equation are not particularly useful, the asymptotic high velocity behaviour which he described was confirmed at concentrations below about 30% to 35% solids by volume in horizontal flow by Cillies et al. (1 991).

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