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### Topic: Dynamic Material Balance with composition dependent solution density  (Read 3277 times)

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#### nanopico

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##### Dynamic Material Balance with composition dependent solution density
« on: June 29, 2009, 02:43:07 AM »
Hi,
I am working on a dynamic model of a dissolution (mineral leaching) process. So there are solid and solution feed and exit streams, and a dissolution reaction in the tank. The temperature is constant. The total reactor volume is constant, so the volume of solution in the reactor changes according to how much solid is present.
So far, the model is working OK for a constant density assumption. However the solution density changes as the solute concentration changes.
My question is, how do I account for the density change in my mass balance equations? I know it should be straight forward, but I just can't quite get my head around it.

Any help much appreciated, thanks!!

#### clustro

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##### Re: Dynamic Material Balance with composition dependent solution density
« Reply #1 on: June 29, 2009, 06:07:45 PM »
This actually could be kind of complicated.

From how the problem is stated, I am assuming there is a liquid input, a solids input, a solids output, a liquids output, and a 2-phase solid-liquid mix inside the reactor.

For a given chemical component i:

dN_i/dt = x_i*L_in + y_i*S_in - r_i*V_mixture - z_i*L_out - w_i*S_out

where N_i is the total moles of i
x_i, y_i, z_i, and w_i are mole fractions
L_in is the molar flow rate of liquid into reactor (mol/s)
S_in is molar flow rate of solid into reactor (mol/s)
r_i is the reaction rate of component i (mol L^-1 s^-1)
L_out and S_out are analogous to their aforementioned counterparts.
V_mixture is the volume of the reacting medium. Presumably, it can be determined from simple level measurements in the tank. It is a function of L_in, S_in, L_out, and S_out.

N_i = rho_mixture*V_mixture*MW_i

where rho_mixture is the density of the mixture, which is a function of L_in, S_in, L_out, and S_out. I assume the reaction does little to change the density.
MW_i is the molecular weight of component i.

rho_mixture and V_mixture however, are function of the amount of liquid and solid in their content.

The best thing I can think of is to do some simple experiments in the lab with different amounts of liquid and solid to make a chart of the density as a function of liquid or solid mass %. Then you can take the density change into account and get the greater precision you seek.

Hope this works pal!