How Can I Calculate Evaporation Rates for My Sugared Liquid Evaporation Tank?

[David S]

Hello Physics Forum Members,

I have chosen this particular forum topic area because I was not to sure in which it would belong or if this is the appropriate forum site for such topics at all other than a having a pool of expert on such matters. If a member(s) believes or knows of a more appropriate forum, I would appreciate the direction. I am a budding entrepreneur, and as such I am finding that equipment vendors are either unable to provide full solutions or quite vague - knowledge being proprietary perhaps.

I am building a proto evaporation tank to evaporate a sugared liquid from 3% to 6%.
The evaporation tank will send vapour to a shotgun condenser then to a catch tank – I want to save the water for reconstitution- I am formulating a pop/cola.
A venturi will be installed between the evaporation tank and the condenser to pull a vacuum at 1”HG/25.4 mmHG/0.03 atm – that should allow me to evaporate somewhere around 25 deg C. As well a venturi will be placed between the catch tank and the condenser to pump the condensate into it – 10”HG/254 mmHG/0.33 atm.

Some specs:

225 liter round evaporation tank/flat bottom – 45 deg down pumping pitch blade impeller at center bottom – turbulent flow with baffles – top surface area (liquid level full) – 0.292 sq meters
- turbulent flows should actually help with evaporation.

Liquid – 3% sugar reduced to 6% sugar - approx. 1 to 150 cP, p ≈ 1 - 1.3 g/cm3 ≈ 1.3 kg/L , μ ≈ 1.14 - 1.19 mPa/s - approximately half/112.5 liters of water to be removed.

In-tank heaters will be used: not to boiling but rather to 80-90 C to apply a slow pasteurization method. This will take place during evaporation by applying heat to batch contents from the beginning starting at 25 C – with any luck, arriving at this temp by the time the evaporation stage is complete. And of course this will raise pressures.

I realize that there are a number of variables here. I’ve tried to cover as many specifications as possible – I am not a calculus guy – but can punch numbers in a calculator as good as any. This is where my questions come in;

Is there a formulation I could use to calculate the evaporation flow rate and the time to spec – 3% to 6% sugar of evaporation tank?

Is there a formulation I could use to calculate the dew point or points temperature required of the condenser – the required temp of the circulating fluid to allow condensing? It is a shotgun type condenser (tube in shell with cold fluid pumped through it).

Could you provide an example using the above specs ?

Do you foresee any problems with this setup or have any recommendations?

Empirical formulations are fine as from what I’ve been reading it is not an exact science – but close would be nice. My efforts to use equilibrium equations (Clausius–Clapeyron, PV=nRT, etc...) have gotten me no where.

Well, that’s a mouth full.

Appreciate any help.

Regards,

David S.

 

[AndyW]

Dear David S.,

Thank you for reaching out to the Physics Forum for help with your evaporation tank project. It is great to see budding entrepreneurs like yourself utilizing the expertise of forums like this to solve technical problems.

To address your questions, there are several key factors to consider when calculating the evaporation flow rate and time for your specific setup. These include the heat transfer rate, the vapor pressure of the liquid, and the temperature difference between the liquid and the surrounding environment.

To calculate the heat transfer rate, you can use the following formula:

Q = U x A x ΔT

Where Q is the heat transfer rate (in watts), U is the overall heat transfer coefficient (in watts/m^2K), A is the surface area of the evaporation tank (in m^2), and ΔT is the temperature difference between the liquid and the surrounding environment (in K).

To calculate the vapor pressure of the liquid, you can use the Antoine equation:

ln(P) = A - (B / (T + C))

Where P is the vapor pressure (in mmHg), T is the temperature (in K), and A, B, and C are constants specific to the liquid being evaporated.

Using these equations, you can then calculate the evaporation flow rate by dividing the heat transfer rate by the heat of vaporization of the liquid (specific to the liquid being evaporated). The time it takes to reach 6% sugar concentration can then be calculated by dividing the amount of liquid to be evaporated (112.5 liters) by the evaporation flow rate.

As for the dew point temperature of the condenser, this can be determined by considering the temperature difference between the hot vapor entering the condenser and the cold fluid circulating through it. The temperature of the circulating fluid should be lower than the dew point temperature of the hot vapor to ensure effective condensation. You can use the same equations mentioned above to calculate the dew point temperature, taking into account the specific heat of the hot vapor and the heat transfer rate in the condenser.

In terms of recommendations, it is important to ensure that the evaporation tank is properly sealed and insulated to minimize heat loss and maintain a consistent temperature. Additionally, it may be beneficial to periodically monitor the liquid concentration during the evaporation process to ensure it is reaching the desired 6% sugar concentration.

I hope this information helps you with your project. Best of luck with your entrepreneurial endeavors![Your