How to find LMTD in multi stream Heat Exchanger??? 1

[devaxrayz]

just curious!!

Can anybody told me how to find Logarithmic Mean Temperature Difference (LMTD) of a multi stream Heat Exchanger (e.g. LNG heat exchanger) for case below?

case#1
my heat exchanger used in nitrogen plant consist of three stream. one hot stream and two cold stream.
Considered that the heat exchanger is in vertical arrangement, the hot stream entering from the top of HE and both of the cold stream entering from the bottom of HE.

Temperature data of those streams are :
Hot stream : in 285 K, out 105.7 K
Cold stream#1 : in 100.6 K, out 282 K
Cold stream#2 : in 100 K, out 282 K

Case#2
I want to add another cold stream into the system of case#1. The additional cold stream will enter at the bottom side but leave at the middle section of the HE (1/2 length of HE). Temperature data : in 100 K, out 120 K


I guessing for case#1, i can just mixed the two coldstream, find the temperature of mixing (it's not a problem since the inlet and outlet temperature are the same) and calculate the LMTD using the conventional method. Do you agree with my thougth???

Where can i find any good resources for this kind of HE (designing, evaluating, etc)???

Any comments will be very appreciated.... B-)

--devax--
borneo,ind

 

[davefitz]

I think that if the cold streams do not have direct contact with each other then it is not wise to try to find a single LMTD. If there is no contact between the 2 cold streams, the the problem should be approached as two separate heat exchangers, ie , an LMTD for cold stream 1 +hot stream and another LMTD for cold stream 2 + hot stream.

I would prefer to treat the problem using the e-NTU method.

 

[sshep]

My experience is dealing with this type equipment for rating, simulation, or specification; not rigorous design. My references are technical papers published by HTFS in the mid 80's, but my method is a shortcut. Since you are soliciting some general advice on an interesting topic I can give what I know.

A simplifying assumption which is usually good for rating (but maybe not rigorous enough for design) is to assume the exit temperature for all hot streams is the same, and all cold streams is the same (as per your data at 282K). With these assumptions an energy balance can be easily done. In your case set the cold streams out at 3K cold outlet approach (282K), you now have enough info to calculate the exit temp of the hot stream which you already give as 105.7K. If you had multiple hot streams you could find (by itteration if neccessary) the one common outlet temp that satisies the energy balance.

Once you know the energy balance (rating) or as a general way to do the energy balance (simulation), plot the hot and cold grand composite curves for use in an LMTD calculation. Even if rating, this plot must be done to insure that the exchanger is thermodynamically feasible (i.e. no pinch within the exchanger). If there is a pinch, then pull the curves apart until you get a min temp difference at the pinch and recalculate the outlet temps (this can be done as a graphical "simulation" if you calculate your composite curves out far enough. The LMTD can be calculated from an interval analysis based on your curves if they are not straight lines. If you are attempting a "simulation" based on existing area and some assumed U's, itterate on various approaches (by sliding the curves) until the heat transfer balance is satisfied.

In your case of an intermediate outlet cold stream you can treat the system as two zones using the hot and cold composite curves, since the cold curve will have an inflection at 120K. In this case the first zone (working from the cold inlet) will have all 3 cold streams exiting at 120K. In the next zone you have 2 cold streams entering at 120K. Use the methods above to find the hot stream intermediate temperature, at what temp the cold streams will exit at the hot end, and other related calculations.

In practice, some control is probably required to keep the intermediate stream temp at 120K in case 2. As always for these type cases, be aware of what kind of upsets to hot and cold flows can happen and insure safeguards exist for any carbon steel piping that might be downstream of the coldside out.