Production by Weight or Volume?

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We have previously talked about “slurry specific gravity” with a view to helping everyone understand its numerical value, but how does it really help pump owners? Today, we will look at how the knowledge of specific gravity can help us determine production rates when the game’s name is moving solids.

Dealing with plain liquids is all about how much liquid you can move in a certain period of time. It is always measured in units of volume per time (e.g. USGPM or litres per second); however, when using a liquid to move a solid, we need to be able to quantify the number of solids moved or, in other words, the amount of production.

When dealing with a slurry, the production rate becomes a function of both volume (flow rate) and concentration of solids (density of the slurry). You will need both values to determine the rate of production. Flow rate is easily established with flow meters, and the density of the slurry can be established by weighing a known volume of slurry and using it to determine the specific gravity (Sg) of the slurry.

Production can be measured in terms of volume of product/solid moved or in terms of weight of product/solid moved. To use a sample to determine concentration by volume directly requires the drying /complete removal of the carrier liquid from a known volume of slurry. This can be a time-consuming process and, as such, is normally avoided. Instead, we usually solve for the concentration of solids by weight first, and if required, use a formula and the solids by weight to establish the concentration by volume.

To determine a concentration by weight, we must first establish the Sg of the slurry. To do this, we simply obtain a sample of the slurry and use the measured weight in relation to that of water, thereby giving you the Sg of the slurry (You can refer to last month’s lesson for more detail). With the slurry Sg, the known Sg of the dry solid, and the Sg of the carrier liquid, we can use the following formula to calculate the concentration of solids by weight.

Sgm =   1 / {(Cw / Sgs ) + [(1 – Cw) / Sgl]}

Sgm = specific gravity of slurry   |   Cw  = concentration of solids by weight

Sgs =  specific gravity of the solids    |   Sgl =  specific gravity of liquid without solids

Example: Given that the slurry Sg is 1.23, the Sg of the solids is 2.7, and the Sg of the liquid is 1.0, the concentration of solids by weight would be as follows:

Sgm =   1 / {(Cw / Sgs ) + [(1 – Cw) / Sgl]} 

1.23 = 1 /  {(Cw / 2.7)  + [(1 – Cw) / 1.0]}

Solving for Cw, we obtain 0.30 or 30%  

If you are like me and have trouble with the mathematics of solving the equation above, first solve for the concentration of solid by volume, then use it to convert to solids by weight. This is done as follows.

If we know the slurry Sg, the Sg of the dry solid, and the Sg of the carrier liquid, we can use the following formula to calculate the concentration of solids by volume.

Cv=(Sgm –  Sgl)/(Sgs-Sgl)

Sgm = specific gravity of slurry   |   Cv  = concentration of solids by Volume

Sgs =  specific gravity of the solids   |   Sgl =  specific gravity of liquid without solids

Example: Given that the slurry Sg is 1.23, the Sg of the solids is 2.7, and the Sg of the liquid is 1.0, the concentration of solids by volume would be as follows:

Cv =  (1.23 – 1.0) / (2.7 – 1.0) = 0 .23/1.7 = .135

Or 13.5% by volume

It is important to note that the mathematical concentration of solids by volume does not take into account another important factor, the bulk density ratio.  As such, volumetric concentration on its own can not be directly used for real-world volumetric calculations.

Please see a previous lesson titled “Bulk Density” for more info on that subject.

We can now apply the formula below to convert from a concentration by volume to a concentration by weight.

Cw=Cv x Sgs / Sgm

Sgm = specific gravity of slurry    |    Cv  = concentration of solids by Volume

Sgs =  specific gravity of the solids    |    Cw  = concentration of solids by weight

Example:  Given that the slurry Sg is 1.23, the Sg of the solids is 2.7, and the concentration of solids by Volume  is 13.5%, then the concentration of solids by weight would be as follows:

Cw =   13.5 x  2.7 / 1.23   =   30% by weight 

As you can see from the examples used above, a slurry with an Sg of 1.23 may have a concentration by weight of 30% while also having a concentration by volume of 13.5 %. This difference illustrates the need to clearly identify whether the percentage of solid is being stated by weight or volume when discussing production figures.

In closing, remember to factor in “bulk density” if any real-world calculations of solids by volume are required.

 

Cheers

RJ

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