# Calculating Physical Properties Of Slurries

Today's blog entry addresses how to calculate the physical properties of slurries. Before we go into the details let us understand the basic concept of a slurry.

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:

ρm = 100 / (Cws) + [(100 - Cw) / ρL]

where:

ρm =density of slurry mixture, kg/m3
Cw = solids concentration by weight, %
ρs = density of solid in mixture, kg/m3
ρL = density of liquid in mixture, kg/m3

The variable Cw represents the amount of solid in the mixture by weight. The term Cv is a corresponding value in terms of volume. Thus Cw may be 50 percent solids by weight, whereas Cv may be 15 percent solids by volume. The term volume fraction represented by the symbol Φ is equal to Cv/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 = Cv / 100

Volume Ratio = Φ / 1 - Φ

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

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

Cv = Cw*(ρm / ρs)

where:
Cv = 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:

µm = µL*(1 + 2.5Φ)

where:

µm = viscosity of slurry mixture, cP
µL = 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.

µm = µL*[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:
Cw = 65%
ρs = 5.2

Results:

SGm = 100 / (65/5.2) + (35/1.0) = 2.10
Cv = 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, ρm = 1522 kg/m3
Liquid Density, ρL = 1281 kg/m3
Solid Density, ρs = 2082 kg/m3

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

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

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

Cw*(-0.0003) = -0.0124

Cw = 41.2%

Cv = 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, ρL = 1200 kg/m3
Solid Density, ρs = 2082 kg/m3
Cw = 50%

Results:
ρm = 100 / (50/2082) + (50/1200) = 1522 kg/m3
Cv  = 50*(1522 / 2082) = 36.55%
Φ = 36.55 / 100 = 0.3655
µm = 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

Regards,
Ankur

S.R.Shah

Ankur;

Blog is very helpful .for deciding slurry physical properties for heat exchanger

SRShah

ericdayo26

Hi Ankur,

Is paper stock (white water) considered a slurry?

If so, would that mean that its consistency(%) is equal to Cw in your equation..?

ankur2061

Hi Ankur,

Is paper stock (white water) considered a slurry?

If so, would that mean that its consistency(%) is equal to Cw in your equation..?

ericdayo26,

I don't know much about the pulp and paper industry, hence cannot provide you a definitive answer. You may look at the links below to find an answer:

http://www.pumpfunda....com/help9.html

Regards,

Ankur

Technical Bard

Ankur - the Einstein correlation for suspension viscosity is generally ok for suspensions / emulsions up to about 2% dispersed phase.  The Guth-Simha equation can handle up to about 6%, and the Thomas equation is only moderately better than 10%.   Concentrated slurried often begin to exhibit dramatically different rheology (non-newtonian) and I know of no generic viscosity function that would apply.

Ankur;

Thank's, this blog is very helpful.

Please give information/reference if any another equations for determination another properties of slurry. (specific heat capacity, thermal conductivity, etc.)

Regards

How can I get the viscosity of corn mash with 36% solids by weight

I know that we had some problems handling density measurement of coal slurries with a tuning fork sensor but much later we were able to provide a reliable online tuning fork viscosity sensor for chalk slurries at a cement manufacturing plant.

By reducing the viscosity using ligno-sulphonate as a viscosity modifier (controlled by the viscometer) they were able to increase the %solids of the slurry in the pipeline which meant less energy used in the kilns. The trouble was that instead of being a nice fine particle slurry there were often bits of flint included and bits of broken machinery, one suspected.

ralancannon

There is a typo in the equation for slurry density, I think. The answer is only correct if everything after the "/" is enclosed in an additional set of ().

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