[Charles CL]

Hi All,

Good day to all.

Currently, i'm looking for the calculation of surface temperature of cooling pond with medium of palm oil mill effluent (POME).
This cooling pond is operated in plug flow system with retention time of 2 days for cooling.
On the upper layer of the POME, a layer of oil was found due to poor filtration after the palm oil extraction from the factory.

Generally the process is as below:
Factory  POME  Cooling Pond

Since there is a layer of oil on the top of the medium, evaporation is excluded from the heat transfer calculation. Conduction, convection and radiation are the main heat transfer involved.

Heat inputs:
1. qs = short-wave solar radiation,
2. qa = long-wave solar radiation,
Outputs:
1. qsr = reflected portion of qs,
2. qar = reflected portion of qa,
3. qbr = long-wave black radiation from water surface,
4. qc = conductive heat loss.

therefore,

qt = (qs + qa)-(qsr + qar + qbr) + qc

where,
qt = net heat flux across the air-water interface (pond surface).

Question:
May i know, is there any simplified equation for the above equation? As i found the following equation, but the equation included the evaporation, which is not fit to my current condition.
[The following equation aim to calculate the exit temperature of the medium]

dqt/dt = -K (Ts - E) 

where,
dqt/dt : net rate of surface heat exchange,
K : heat transfer coefficient,
Ts : pond surface temperature,
E : equilibrium temperature.

where it simplified from the equation below:
qt = (qs + qa)-(qsr + qar + qbr + qe) + qc

where,
qe : evaporation heat loss.

Appreciate if anyone can share some idea or information at here.

Advance Thanks,
Charles CL

[Enthalpy]

Hi Charles CL, welcome!

You could check how important the heat radiated by the pond is. For instance at 313K, a perfect black body radiates 544W/m². This already neglects any IR received from the surroundings, which I feel legitimate since ponds usually don't have much surroundings in direct sight.

Reflectance is not negligible, and the distinction between short and long waves is important. That's already a simplification; better accuracy would need to integrate over the full solar spectrum. Or you put an umbrella over your pond, which can then be smaller.

To my understanding, the difficult part is evaluating the heat exchange with the atmosphere, as it depends on the wind, the turbulence, and is an experimental value. Models exist in good books.

[Charles CL]

Hi Enthalpy,

Thank you for the reply, i'm very appreciate.

I had found a book related to the cooling pond design.
[Lawrence,K.W., Norman, C. P. & Yung, T. H. (2005). Advanced Air and Noise Pollution Control. Totowa: Humana Press.] ≡Referred to page 359 - 370≡

From the calculation, the solar radiation proven to have a significant effect on exit temperature of the medium from the cooling pond.
Meanwhile, other parameters such as humidity and wind speed also pay a significant role in determine the exit temperature.

All these were in the assumption of no oil layer on the top of the POME, while with the additional of oil layer, i believe that there should be another type of calculation involved. 

[Enthalpy]

I too suppose that the oil layer hampers evaporation.

If you book's data covers such cases, you could take 100% air humidity to compute cooling without evaporation.

Solar radiation: its importance is intuitive, since a natural shallow pond gets warmer on a sunny day. Have a sunshade? Or if the liquid is clear enough and doesn't favour algae nor fungi, have a white liner at the bottom.

[Charles CL]

Absolutely, with the oil layer on it, evaporation can be neglected.

The pond is an open field pond with no shelther.
While, for the liquid, it is opaque.

Please click on the below link for your reference. The cooling pond built exactly same like the picture shown.
http://i1.wp.com/www.bioenergyconsult.com/wp-content/uploads/2012/04/POME.jpg

I wish to have technically calculate out of the exit temperature with the current situation which is with the oil layer on it.

While other suggested to have agitation or air mix with blower, or mist/spray of water on the top. A very logical thinking where you can imagine a cup of hot tea, if you stir it, it will get cool faster or if you add cool water.