Calculating Physical Properties Of Slurries

 A slurry consists of solid particles suspended in a liquid. A slurry pipeline is used to transport slurries from the source such as a coal mine to its destination such as a coal power plant. In this case the coal slurry will be a mixture of coal and water, which is a transportation medium used to propel the combined solid-liquid mass through the pipeline using centrifugal pumps to provide the required pressure.

Slurries may be newtonian or non-newtonian in nature. When the particle concentration of solid within the liquid is less than 10 percent by volume, the slurry may be considered newtonian. When the slurry concentration is higher than 10 percent, it is generally regarded as non-newtonian.

Physical Properties of a Slurry:

Since the slurry consists of solid particles suspended in a liquid, the properties of a slurry mixture will depend upon those of the constituents. The density of slurry can be calculated from the following equation:

ρ_m = 100 / (C_w/ρ_s) + [(100 - C_w) / ρ_L] 

where:

ρ_m =density of slurry mixture, kg/m³
C_w = solids concentration by weight, %
ρ_s = density of solid in mixture, kg/m³
ρ_L = density of liquid in mixture, kg/m³

The variable C_w represents the amount of solid in the mixture by weight. The term C_v is a corresponding value in terms of volume. Thus C_w may be 50 percent solids by weight, whereas C_v may be 15 percent solids by volume. The term volume fraction represented by the symbol Φ is equal to C_v/100. The term volume ratio represents the ratio of the volume of solid to the volume of liquid. Thus we get the following equations for the volume fraction and volume ratio:

Φ = C_v / 100

Volume Ratio = Φ / 1 - Φ

where:
C_v = Concentration of solids by volume, %
Φ = Volume fraction

The concentration of solids by volume C_v and the concentration of solids by weight C_w are related to the solid density and the mixture density by the following equation:

C_v = C_w*(ρ_m / ρ_s)

where:
C_v = solid concentration by volume, %

The viscosity of a dilute suspension consisting of solids in a liquid can be calculated approximately from the volume fraction Φ and the viscosity of the liquid using the following equation:

µ_m = µ_L*(1 + 2.5Φ)

where:

µ_m = viscosity of slurry mixture, cP
µ_L = viscosity of liquid in slurry mixture, cP

The preceding equation of the mixture viscosity applies only to laminar flow and to spherical particles. Also the equation does not apply for solid concentrations exceeding 1 percent by volume.

For higher-concentration suspensions the viscosity of the mixture can be calculated using a modified form of the above equation attributed to D. G. Thomas.

µ_m = µ_L*[1 + 2.5*Φ + 10.05*Φ² + 0.00273*exp(16.6*Φ)]

where the terms are as defined above

Some example calculations:

Example 1:
A slurry mixture consisting of magnetite in water has a concentration of 65 percent solids by weight, and the specific gravity of the solids is 5.2. Calculate the specific gravity, volume fraction, and volume ratio of the slurry mixture.

Calculations:

Inputs:
C_w = 65%
ρ_s = 5.2

Results:

SG_m = 100 / (65/5.2) + (35/1.0) = 2.10
C_v = 65*(2.1 / 5.2) = 26.25%
Φ = 26.25 / 100 = 0.2625
Volume Ratio = 0.2625 / (1 - 0.2625) = 0.3559

Example 2:

A slurry consists of raw salt in a brine solution. Experiments indicate that this slurry weighs 1522 kg/m³). Calculate the concentration of solids by weight and by volume and the volume ratio. Use 2082 kg/m³ for the density of salt and 1281 kg/m³ for the density of brine.

Calculations:

Input:
Slurry Density, ρ_m = 1522 kg/m³
Liquid Density, ρ_L = 1281 kg/m³
Solid Density, ρ_s = 2082 kg/m³

Results:
1522 = 100 / (C_w / 2082) + [(100 - C_w) / 1281]

C_w / 2082 + 100 / 1281 - C_w / 1281 = 100 / 1522

C_w*((1/2082) - (1/1281)) = 100*((1/1522) - (1/1281))

C_w*(-0.0003) = -0.0124

C_w = 41.2%

C_v = 41.2*(1522 / 2082) = 30%

Volume Fraction Φ = 30 / 100 = 0.3
Volume Ratio = 0.3 / (1 - 0.3) = 0.4286

Example 3:

Calculate the viscosity of a slurry mixture consisting of salt (50 percent by weight) in saturated brine assuming a newtonian fluid. The viscosity of brine is 2.0 cP, and the density of brine is 1200 kg/m³ and that of salt is 2082 kg/m³.

Calculations:

Inputs:
Liquid Density, ρ_L = 1200 kg/m³
Solid Density, ρ_s = 2082 kg/m³
C_w = 50%

Results:
ρ_m = 100 / (50/2082) + (50/1200) = 1522 kg/m³
C_v  = 50*(1522 / 2082) = 36.55%
Φ = 36.55 / 100 = 0.3655
µ_m = 2.0*[1 + 2.5*0.3655 +10.05*(0.3655)² + 0.00273*exp(16.6*0.3655)] = 8.9 cP

To conclude, the above methods can be used to calculate the density, viscosity, volume fraction and volume ratio of slurries.

Hoping to have quite a few comments and from the members of Cheresources.

Reference: Chapter 10, Slurry & Sludge Systems Piping, "Piping Calculations Manual" by E. Shashi Menon