re: greywater heat exchange SOLAR.KnowledgePublications.com

re: greywater heat exchange
2 feb 2003
>>> ...4 10 min showers per day and 20 minutes of dishwashing at 1.25 gpm
>>> might involve heating 75 gallons of 55 f water to 110 with 8x75(110-55)
>>> = 33k btu, about 10 kwh worth about $1...

>is there an easy way to figure that a coil with more volume will be more
>efficient, since we use hot water in bursts? adjust the flow rate? with no
>volume, c = 600 btu/h-f at 1.25 gpm. with infinite volume, c = 75gx8/24h
>= 25 btu/h-f... what's an effective flow rate formula for a coil with
>volume v...

if the cold volume v in gallons is less than a 12.5 gallon hot water burst
and the first v gallons that leaves the coil has had 4 hours to warm, and
the next 12.5-v gallons passes through once in real-time and the coil has
a ft^2 of surface with u = 14 btu/h-f-ft^2 (for a 0.070" hdpe pipe wall with
slow-moving water on both sides), ntu1 = 14a/(8v/4) = 7a/v for the first v
gallons. the rest takes t = (12.5-v)/(1.25x60) hours to pass, so ntu2
= 14a/(8(12.5-v)/t) = 7a/300.

if greywater enters at 105 f, and e1 = ntu1/(ntu1+1) = 1/(1+v/7a), and
e2 = 1/(1+300/7a), the first v gallons warms to 55+e1(105-55), and the
rest warms to 55+e2(105-55), which makes the average burst temperature
55+50e2+50v(e1-e2)/12.5 = 55+e(105-55) with average e = e2+v(e1-e2)/12.5.
  
>for more of a counterflow ambiance, the box might contain a rectangular
>spiral instead of a tank, with 5 turns (60') of 4" thick-walled pvc pipe
>with cold water entering the coil at the bottom and warm water leaving at
>the top, surrounded by stratified greywater...

this is easier inside a 55 gallon plastic drum, with a long black plastic
pipe, eg 1"x300' of 100 psi/73 f silo-flex pipe from silverline plastics
in ashville nc or pt industries (800) 44 endot. lowes sells 100' lengths
of this 0.070" wall stuff for $16.37 and 300' lengths of 160 psi thicker-
walled pipe for $81. they sell 90 degree elbow combo insert/fipt fittings
(with a 1" barb and a 3/4" female pipe thread) for $0.74 each (2 required)
and pipe-to-hose thread adapters for $1.83 each. 

longer and smaller diameter pipes seem better than shorter and larger ones 
in this application, since they can coil more easily into a 55 gallon drum,
and they have less hoop stress and thinner walls for the same pressure spec,
so they use less material and cost less. with more area and less volume and
a higher flow velocity and thermal conductance, they can come closer to
heating water in real time for long usage bursts.

a = 300pi/12 = 78.5 ft^2 for 300' of 1" pipe, with v = 8x300pi(1/2/12)^2
= 13 gal, so e1 = 1/(1+12.5/(7x78.5)) = 0.98 for the first 12.5 gal and
e2 = 0.65 after that, and e = 0.65+12.5(0.98-0.65)/12.5 = 0.98.

nick