# Modeling Consolidation of Slurries: A Water Balance Approach (May 2019)

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• Peter Serey

Hi Jason,

I have a question with entrained water volume estimation. Have you had any experiences where the volume of water entrained in the impounded tailing at each timestep is negative? I'm thinking in the condition that you have a high solids density (ρd = 4.266 t/m3).

Looking forward to hearing from you

• Rick Kossik

I don't understand what you mean by a negative volume of water entrained.  If the rate is negative doesn't it simply mean that water is being pushed out (by consolidation)? You simply need to represent this as a withdrawal from the entrained water stock.  Or are you trying to represent something else?

• Peter Serey

Hi Rick,

Thanks for yours response.

Please correct me if I am wrong.

I was referring to the equation used to calculate entrained water volume. The formula is Total Impounded Volume * (1-Density in Model/(Gs Specific Gravity Solids*Density Water)). Let's say the density in Model is 4.26 tonne/m3 (a constant) and the other variables remain the same. This would give a negative volume of water entrained.

• Rick Kossik

But the other variables most certainly cannot remain the same! The "Density in the Model" is the total bulk density.  If this is very high, it means that the specific gravity of the solids must also be high (you can't just keep this constant; it has to reflect whatever solid you are dealing with). That is, the equation is

Volume = Total Volume (1 - Bulk Density/Solid Density).  If the Bulk Density is high (due to the type of solid), then the Solid Density must also be high.  Since the Bulk Density consists of solid plus water (and water has a lower density than the solid), the fraction is always less than 1.

• Peter Serey

Hi Rick,

Thanks for clarifying this for me :)