Slurry yield stress models

You must determine the horsepower required to pump a coal slurry through an 18 in. diameter pipeline, 300 mi long, at a rate of 5 million tons/yr. The slurry can be described by the Bingham plastic model, with a yield stress of 75 dyn/cm2, a limiting viscosity of 40 cP, and a density of 1.4 g/cm3. For non-Newtonian fluids, the flow is not sensitive to the wall roughness. 

The Bingham plastic model usually provides a good representation for the viscosity of concentrated slurries, suspensions, emulsions, foams, etc. Such materials often exhibit a yield stress that must be exceeded before the material will flow at a significant rate. Other examples include paint, shaving cream, and mayonnaise. There are also many fluids, such as blood, that may have a yield stress that is not as pronounced. 

A pipeline is installed to transport a red mud slurry from an open tank in an alumina plant to a disposal pond. The line is 5 in. sch 80 commercial steel, 12,000 ft long, and is designed to transport the slurry at a rate of 300 gpm. The slurry properties can be described by the Bingham plastic model, with a yield stress of 15 dyn/cm2, a limiting viscosity of 20 cP, and an SG of 1.3. You may neglect any fittings in this pipeline. 

The Bingham Fluid. The Bingham fluid is an empirical model that represents the rheological behavior of materials that exhibit a no flow region below certain yield stresses, tv, such as polymer emulsions and slurries. Since the material flows like a Newtonian liquid above the yield stress, the Bingham model can be represented by... 

Experimental rheologic data were fit to the power law, Herschel-Bulkley, and Casson models. The power law model does not predict yield stress. Yield stress for 21% grain slurries predicted by the Herschel-Bulkley model was a negative value, as shown in Table 6. Yield stress values predicted by the Herschel Bulkley model for 23 and 25% solids were 8.31 and 56.3 dyn/cm2, respectively. Predicted yield stress values from the Casson model were 9.47 dyn/cm2 for 21% solids, 28.5 dyn/cm2 for 23% solids, and 44.0 dyn/cm2 for 25% solids. 

The Bingham plastic model usually provides a good representation for the viscosity of concentrated slurries, suspensions, sediments, emulsions, foams, etc. Such materials often exhibit a yield stress,... 

Four models (Herschel-Bulkley, Casson, Bingham, and power law) were used to fit the experimental data and to determine the yield stress of the slurries. Table 1 list the results obtained for the different parameters used to fit the experimental data of fermentation suspensions at the various concentrations. The Herschel-Bulkley model fits the data satisfactorily over the whole experimental range at 10 to 20% solids concentration. On the other hand, the Bingham and Casson equations are in excellent agreement with results of the enzymatic suspension and fermentation broth testing at 10 and 20%, respectively (Table 1). The results of the power law model (n and K) were compared to those power law parameters obtained with the impeller method. The Herschel-Bulkley, Bingham, and the... 

The behaviour of slurries which exhibit a yield stress can be represented by a model in which the relationship between the effective stress t — ty and the shear rate is either linear, as in Newtonian fluids (Bingham plastic model), or follows a power-law, as in pseudoplastic or dilatant fluids (Herschel-Bulkley model or yield power-law model). The shear stress-shear rate relationship for these models is shown in Figure 4.4. 

In the Bingham plastic model, the yield stress Ty and the plastic viscosity Hp (the slope of the line on the shear stress-shear rate plot in Figure 4.4) characterize the slurry. 

In the Herschel-Bulkley model, the yield stress, consistency index k, and the flow behaviour index n characterize the slurry. 

As with slurries following a power-law flow model, it is necessary to reliably predict the pressure drop in a horizontal pipe of diameter D under laminar, fully developed flow conditions. A fundamental analysis of the Bingham plastic model yields the following expression for the mean velocity in terms of the yield stress Ty and the wall shear stress tq. 

The shear stress at zero shear rate is 6.00 Pa. Hence there is a yield stress equal to 6.00 Pa. In order to determine whether the slurry behaves as a Bingham fluid or if it follows the Herschel-Bulkley model, we need to plot r — Ty versus shear rate. 

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