## Friday, September 20, 2013

### A large streamwater heat exchanger

Drew asks about a 2 million Btu/h heat exchanger (big enough to heat 40 houses):

>a heat pump loop cooled by gravity flow stream thru a shell and tube htx...
>200 gpm 90 degrees on tube side  heat pump loop
>600 gpm 70 degrees gravity flow on shell side. 8 inch pipe stream water

So the heat capacity rate ratio Z = Cmin/Cmax = 1/3.

>It is now able to get the leaving loop water temp down to 75

So the heat exchanger effectiveness E = (90-75)/(90-70) = 0.75
= (1-e(-NTU(1-Z)))/(1-Ze(-NTU(1-Z))), ie
0.75-0.75x0.33e^(-NTU(1-1/3)) = 1-e^(-NTU(1-1/3)), ie
0.75-0.25e(-NTU2/3) = 1-e^(-NTU2/3), ie
0.75e^(-NTU2/3) = 0.25, ie
e^(-NTU2/3) = 1/3, ie
-NTU2/3 = -1.099, ie
NTU = 1.648 = AU/Cmin, ie
AU = 1.648x200x500 = 165K Btu/h-F.

>1) if we parallel another identical htx my guess is flow would be 100 gpm on each tube side still 600 gpm on shell sides and the leaving loop water would drop to 72.5? what you think?

If the 600 gpm is divided into 2 300 gpm streams for the 2 heat exchangers,
Z = 1/3 and NTU = 165K/(100x500) = 3.3 and
E = (1-e(-3.3x2/3)))/(1-e(-3.3x2/3))/3)
= 0.8889/0.9630 = 0.9231, so
Tho = Thi-E(Thi-Tci)
= 90-0.9231(90-70)
= 71.54 F. Or a bit more, with less water velocity in the tubes.

http://www.gewater.com/handbook/cooling_water_systems/ch_23_heat.jsp and
http://www.gewater.com/handbook/cooling_water_systems/fig23-3.jsp say
a single moving water film has conductance
U = 100+200V Btu/h-F-ft^2, with V in fps, eg
U = 1500 at V = 7 fps.

>2) as an alternate we are thinking of laying some poly pipe directly in the stream.  my suggestion is 20 100 foot 1 inch pipes in parallel so the loop water flow in each would be 10 gpm. Stream flows at about 7 fps.  what's your guess as to the leaving loop temp?

1" 100 psi NSF HDPE pipe with a 0.07" wall thickness would have a 0.38x6.93/0.07 = 37.6 Btu/h-F-ft^2 conductance. The water velocity inside the pipe would be about 10gpm/60s/m/7.48g/ft ^3/(Pi(1.049"/24)^2) = 3.7 fps with a 100+200x3.7 = 843 Btu/h-F-ft^2 film conductance. With 7 fps water on the outside, U = 1/(1/843+1/37.6+1/1500) = 35.15 Btu/h-F-ft^2. A = 100'xPi1.12"/12 = 29.3 ft^2 makes NTU = AU/Cmin = 29.3x35.15/(10x500) = 0.206. With an infinite stream heat capacity and Z = 0, E = 1-e^-NTU = 0.186, and Tho = Thi-E(Thi-Tci) = 90-0.186(90-70) = 86.3 F.

>3) as another alternate, we are thinking of diverting some drainage water from the exterior of the parking garage to an isolated  section of the stream bed and laying the pipes in it. its advantage is it is 50 degrees. There is less flow perhaps 200 gpm.  if this were in a 2 inch by 24 inch crossection with the tubes it would flow at about 3 fps. What do you think the exiting loop temp would be?

U = 1/(1/843+1/37.6+1/700) = 34.23 Btu/h-F-ft^2. NTU = 29.3x34.23/(10x500) = 0.201. With Z = 1, E = NTU/(NTU+1) = 0.167, and Tho = 90-0.167(90-50) = 81.6 F.

Nick