9 replies to this topic

[ankur2061]

Dear All,

An open concrete Blowdown tank 12 m L X 8 m W X 2.75 m D receives hot blowdown water at 80 deg C. The tank is allowed 80% filling.

I would like to calculate the time taken for the tank to cool down to 40 deg C without any external cooling aid, essentially by natural convective and radiant cooling also accounting for any heat gain due to solar radiation.

I could not find any firm calculation methodology and steps for the same.

Maybe some of the forum members are probably familiar with such calculation.

Any help would be appreciated.

Regards,
Ankur.

[Art Montemayor]

Ankur:

I may be wrong in my old age, but I seem to remember Milton Beychok covering this very subject and application some years back in our Forums. I don't remember the exact date or thread, but if you search through Milton you may hit upon the application.

Good Luck.

[delphitt]

Hi,

I have been working on a similar problem for some weeks now. Please find attached an excel spreadsheet of my calculations - well, it's an attempt bearing in mind that, like you, I have not found any solid calculations on this.

My problem involves the design of a metal trough to collect and cool hot blowdown water from a Saturator. The dimensions I chose were: 56ft x 11ft x 4ft. My cooling requirement is from 100/125 degC to atmospheric temperature (32 degC), or 35 degC which is our environmental compliance.
I added an air sparger to my trough to help increase the rate of cooling...
I'm hoping that this may offer some guidence. Your comments are most welcomed so that it could be improved...

thanks,
Sophia
delphitt@yahoo.com

Attached Files

•  Calculations__BD_re_route.xls   233KB   517 downloads

[ankur2061]

Hi,

I have been working on a similar problem for some weeks now. Please find attached an excel spreadsheet of my calculations - well, it's an attempt bearing in mind that, like you, I have not found any solid calculations on this.

My problem involves the design of a metal trough to collect and cool hot blowdown water from a Saturator. The dimensions I chose were: 56ft x 11ft x 4ft. My cooling requirement is from 100/125 degC to atmospheric temperature (32 degC), or 35 degC which is our environmental compliance.
I added an air sparger to my trough to help increase the rate of cooling...
I'm hoping that this may offer some guidence. Your comments are most welcomed so that it could be improved...

thanks,
Sophia
delphitt@yahoo.com

Sophia,

Thanks for the spreadsheet. Can you provide the book reference for the equations. You have given the page number and the name without the author.

A new information which I recently found out was to assume a heat dissipation of 3.5 Btu/h.ft2 of water surface per degree difference between the wet-bulb temperature of the ambient air and the entering warm water. Essentially it means that if the warm water temperature is 80 deg C and the WBT is 25 deg C, the heat dissipation will be 3.5*(80-25) Btu/h.ft2. Considering a 1 sq. ft area the heat dissipation will be 192.5 Btu/h for the given WBT and warm water temperature. This guideline is provided in the last paragraph of Section 19.14 , 'Cooling-Pond Size for a Known Heat Load' in the book "Handbook of Chemical Engineering Calculations" by Nicholas P.Chopey, 3rd Edition.

Based on the heat load per hour the temperature drop can be calculated per hour.

You can probably cross-check your results with this assumption and find out whether there is a large deviation between your earlier calculated result and the result obtained with the above mentioned assumption.

Regards,
Ankur.

[delphitt]

Hi,

Thanks for the update.
The references were in the comments attached to the respective cell - all the formulae were taken from the 'Fundamentals of momentum heat & mass transfer 2; 2nd Edition'.

I'll try the calculations with the recent data and get back to you - hopefully it won't make a large difference.

Thanks again,
Sophia

[delphitt]

Hi again,

This morning, I measured my wet bulb temperature as 27 degC. For the water temperature of 125 degC and area 616 ft2, the heat dissipation worked out to be 211,288 BTU/hr. The heat load was estimated to be 1,122,595 BTU/hr.

I can't figure out how to factor in a continuous flowing stream of hot water - won't there be an accumulation parameter somewhere. I'm thinking that the heat dissipation of 3.5 BTU/hr/ft2 is for standing water. Am i getting too complicated and missing something?

thanks
sophia.

[ankur2061]

Hi again,

This morning, I measured my wet bulb temperature as 27 degC. For the water temperature of 125 degC and area 616 ft2, the heat dissipation worked out to be 211,288 BTU/hr. The heat load was estimated to be 1,122,595 BTU/hr.

I can't figure out how to factor in a continuous flowing stream of hot water - won't there be an accumulation parameter somewhere. I'm thinking that the heat dissipation of 3.5 BTU/hr/ft2 is for standing water. Am i getting too complicated and missing something?

thanks
sophia.

Sophia,

As you must have noted the heat dissipation is for one hour. After calculating the heat loss in Btu/hr, you calculate temperature T2 by the equation:

Q = m*C_p*(T1-T2)

where Q = calculated heat loss in Btu/h
m = mass flow rate of the incoming warm stream, lb/hr
C_p = Specific heat of the warm stream, Btu/lb.degF (water =1)
T1 = Initial temperature of warm water, deg F
T2 = Temperature after one hour of heat loss, deg F

Now if this is not the temperature you are looking for, then you have to go for iterative calcualtions for the 2nd hour. Assume that the temperature drop after one hour is 20 deg C, and considering an initial temperature of 80 deg C , the temperature after one hour would be 60 deg C. Using the earlier method described by me, the heat loss per square feet for the 2nd hour will be 3.5*(60-25) Btu/hr. This clearly shows that the heat dissipation rate decreases with time. Iterative calculations can be continued till you are close to your desired temperature and the time calculated to reach the desired temperature.

Hope this makes things clearer.

Regards,
Ankur.

[delphitt]

Hi ...
The iteration is what had slipped me... it's funny to know how the simplest things elude me...

The iteration gave me a time frame of 12 hours to reach the desired 35 degC, compared to the one hour using the calculations from the Heat and mass transfer text....
This is a large difference!

For operations purposes, this large time frame is not feasible...
how did your calculations turn out?

sophie

[ankur2061]

Hi ...
The iteration is what had slipped me... it's funny to know how the simplest things elude me...

The iteration gave me a time frame of 12 hours to reach the desired 35 degC, compared to the one hour using the calculations from the Heat and mass transfer text....
This is a large difference!

For operations purposes, this large time frame is not feasible...
how did your calculations turn out?

sophie

Sophie,

The time frame of 12 hours seems more realistic for natural evaporative cooling then the one hour you calculated. Forced cooling using sparged air seems a better option if you cannot tolerate the 12 hour time period for cooling. The equation I have mentioned is for natural evaporative cooling and does not consider forced cooling by any external means. In all probability if you are using sparged air for cooling, the calculations would be different. I saw a different heat dissipation rate equation in the same text I have mentioned, for a water spray cooled pond (tank/trough in your case).

I am still to conclude with my calculations.

I am still a little lost on the name and author of the text book mentioned in your spreadsheet. Could you please clarify?

Regards,
Ankur.

[delphitt]

Hi...

The text i mentioned is:
Fundamentals of momentum heat & mass transfer 2; 2nd Edition
by James Welty, Charles E. Wicks, Robert E. Wilson, Gregory L. Rorrer.

It's a common book used here for mass and heat transfer operations and has worked well in almost all instances applied. I believe the most recent edition is a fourth edition, however, the one i used is the 2nd edition - though there isn't much difference.

regards,
Sophia