7/18/2019 A Deposition Velocity Correlation for Water Slurries http://slidepdf.com/reader/full/a-deposition-velocity-correlation-for-water-slurries 1/3 __-- NOTES A Deposition Velocity Correlation for Water Slurries R. G. GILLIES“’ and C. A. SHOOK ’) ‘)Saskatchewan Research Council, 1630 Quebec Avenue, Saskatoon, SK S7K I V7 ’’Department of Chemical Engineering, University of Saskatchewan, Saskatoon, SK S7N OW A correlation to predict the deposition velocity of aqueous slurries is presented. The correlation employs the viscosity and density of the mixture of fluid and (-74 pm) particles, as well as the mass median diameter dso) f the fraction coarser than 74 pm. The correlation is derived from isothermal flow experiments using pipelines of diameter between 0.053 and 0.495 m. On presente une correlation pour predire la vitesse de dep8t de suspensions aqueuses. La correlation utilise la visco- site et la densite du melange de fluide et de particles (-74 pm) ainsi que le diambre moyen de masse dso) e la frac- tion plus grosse que 74 p. La correlation est calculee a partir d’experiences d’ecoulement isotherme menees avec des conduites ayant entre 0,053 et 0,495 m de diamktre. Keywords: deposition velocity, aqueous slurries. o aspect of the flow of settling slurries is more impor- N ant than the limit-deposit velocity V,. Below this limit, a stationary deposit of particles forms on the bottom of the pipe. For flow with such a deposit, frictional head- losses begin to rise with decreasing velocity. This makes stable pipeline operation very difficult for flows driven by centrifugal pumps and thus V, is the normal lower limit for pipeline design. Because of its importance, innumerable correlations have been proposed to predict V, Carleton and Cheng (1974) identified 55 correlations and many more have been proposed since that time. Some of these have a theoretical basis but their validity is entirely dependent upon the scope of the data base which they incorporate. In the present communication we summarize our experience on the basis of tests conducted with a variety of slurries and pipelines over the past 10 years or so. The Data Source Determination of V, in experimental studies can be difficult when the particles are fine and dark in color because small quantities of ultra-fine material can make the liquid phase opaque. In those cases it is difficult to detect the first thin layer of particles to form on the bottom of the pipe. If the mixture contains very coarse particles, deposits are easier to see but a different problem arises. At velocities just above V,. slowly moving dunes form. These dunes are a few particles in depth and advance by simultaneous erosion of their upstream surfaces and deposition downstream of their crests Since they contain particles which are stationary for some time, a dune is easily mistaken for a stationary deposit unless the observation is prolonged. The electrical sensors described by Ercolani et al. (1979) help to resolve these difficulties with visual observations unless contaminants in the flow foul the electrode surfaces. The pipeline flow tests which provided the data used here were all isothermal. This restriction has been found to be essential for the generation of reproducible data. There are two reasons for this. First, deposition velocity is fairly strongly dependent upon fluid viscosity for fine particles. Secofidly temperature changes can produce physical and chemical changes in the solid particles which result in unexpected changes in the viscosity of the mixture formed by the fluid and the finest particles. Experience has shown that the viscosity must be measured continuously during testing if reproducible results are to be obtained. The data we have used were generated during research sponsored by a variety of Canadian government agencies. In addition, it incorporates experience gained in testing several industrial slurries. Three quarters of the data points were obtained with pipes 0.15 m in diameter and larger. Background Theory A layer force balance model for slurry pipeline flow can be used to interpret the deposition phenomenon and to justify use of an empirical correlation. Figure 1 shows an idealiza- tion of the flow of a “settling” slurry before a deposit is present. There are two constant composition regions and the upper layer contains only particles whose immersed weight is borne by fluid lift forces. The density of this mixture deter- mines the gradient of hydrostatic pressure. The total concentration in the lower layer, C2, is known to be a function of the mean in-situ concentration C, and the ratio of the mean flow velocity V to the terminal velocity v, of the mass median particle (Gillies et al, 1990). v is computed for settling in a hypothetical mixture consisting of the liquid and the finest (-74 pm) particles. The differ- ence C2 - C,) represents particles which are not supported by fluid lift forces. These particles experience a buoyant force which depends upon the density of the mixture of fluid and turbulently suspended particles. The particles which are not suspended generate an interparticle stress which increases with depth according to the relationship do, I dy = p, - p2) C2 - Ci . . . . . . . 1) where p2 is the density of the mixture of fluid and sus- pended solids in the lower layer. The interparticle stress a, is zero at the interface between layers 1 and 2. Stress u, contributes a velocity - ndependent frictional resistance to flow, which increases as p2 increases. From pressure drop measurements we know (Gillies et al, 1990) that p depends upon the factors which determine C2 f we now consider flow with a deposit (Figure 2), Equation I) THE CANADIAN JOURNAL OF CHEMICAL ENGINEERING. VOLUME 69, OCTOBER, 1991 1225