# Re: GFX vs home brew - Page 2

Posted by nicksanspam on April 15, 2006, 5:02 am

Here are some numbers for that. If 100' of 3 1" pipes (polyethylene, with
a 0.07" wall thickness) has 78.5 ft^2 of surface with U = 10 Btu/h-F-ft^2,
10' has 78.5 Btu/h-F...

20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F)
30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F)
40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3)
50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F)
60 FOR SHOWER = 1 TO 1000'simulate showers
70 FOR M=0 TO 359'simulate 10 min shower + 350 min rest
80 IF M>10 GOTO 170'rest vs shower
90 TF(0)=TF(1)'move fresh water up from below
100 TG(0)=(100*CFRESH+TG(0)*CGREY)/(CFRESH+CGREY)'move greywater in at the top
110 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out)
120 TF(S)=TF(S+1)'move fresh water up
130 TG(S)=(TG(S-1)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY)'move greywater down
140 NEXT S
150 TF(9)U'move cold water in at the bottom
160 TG(9)=(TG(8)*CFRESH+TG(9)*CGREY)/(CFRESH+CGREY)'move greywater down
170 FOR S=0 TO 9'rest
180 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)
190 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)
200 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)
210 NEXT S
220 NEXT M
230 NEXT SHOWER
240 FOR S=0 TO 9'results
250 PRINT S,TF(S),TG(S)
260 NEXT S
270 E=(TF(0)-55)/(100-55)'effectiveness
280 PRINT E

pipe          fresh water   greywater
section       temp (F)      temp (F)

0             93.32178      93.3218
1             90.556        90.55602
2             87.60851      87.60853
3             84.60492      84.60494
4             81.62819      81.62821
5             78.71178      78.71181
6             75.86447      75.8645
7             73.08838      73.0884
8             70.3852       70.38522
9             67.75679      67.75681

effectiveness

.8515951

The fresh and greywater temps are very close, about 6 hours after
a shower, since the pipe time constant is much shorter (less than
8 minutes.) These results wouldn't change much with only a half-hour
between showers. The effectiveness would be higher for shorter bursts.

Maybe it's worth adding 2 more \$0 100' pieces of 1" pipe (altho that
would be a tight squeeze), or a handheld showerhead that only runs
when a button is pushed. Who sells them?

Nick

Posted by nicksanspam on April 15, 2006, 6:14 am

Oops. Fixing lines 100, 130, and 160 improves the effectiveness to 88%.

20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F)
30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F)
40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3)
50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F)
60 FOR SHOWER = 1 TO 1000'simulate showers
70 FOR M=0 TO 359'simulate 10 min shower + 350 min rest
80 IF M>10 GOTO 170'rest vs shower
90 TF(0)=TF(1)'move fresh water up
100 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top
110 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out)
120 TF(S)=TF(S+1)'move fresh water up
130 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down
140 NEXT S
150 TF(9)U'move cold water in at the bottom
160 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down
170 FOR S=0 TO 9'rest
180 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)
190 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)
200 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)
210 NEXT S
220 NEXT M
230 NEXT SHOWER
240 FOR S=3 TO 9'results
250 PRINT 300+S;"'";S;TF(S),TG(S)
260 NEXT S
270 E=(TF(0)-55)/(100-55)
280 PRINT 410;"'";E

pipe      fresh water   greywater
section   temp (F)      temp (F)

0         94.53323      94.53326
1         92.54844      92.54847
2         90.32916      90.32919
3         87.93309      87.93311
4         85.42671      85.42674
5         82.85161      82.85163
6         80.22588      80.2259
7         77.55527      77.55529
8         74.8424       74.84241
9         72.08957      72.0896

effectiveness

.8785163

Nick

Posted by daestrom on April 15, 2006, 3:55 pm

Not bad, apparantly you've chosen a flow rate and section length so the time
step corresponds to exactly one section length.

Because the greywater drain cross-section is so much larger than the
freshwater, your Cmin/Cmax ratio ends up being about 0.24 (IIRC a 4-inch
pipe with three 1-inch pipes inside).  So a high efficiency of 87% doesn't
really tell us how much energy we're saving.  While your efficiency is 87%,
it looks like you're still putting (72-55)*1.25*8.337 BTU/minute down the
drain.  Out of a total of 468.6 BTU/minute needed to heat 1.25 gpm from 55
to 100, that's nearly 38% of the heating..  Print out the data *during* the
last shower, not 350 minutes later.  I'd like to see what the greywater
outlet temperature is while it's flowing.  I think it's going to be a lot
cooler than 72, but not sure.  Better yet, print out the freshwater and
greywater outlet temperatures *during* the ten time steps of the last
shower.

After all, it is the temperatures out *during* flow that matter.  The
temperatures at the end of the stagnation period only tell us the initial
startup point for the next shower.  How quickly they change *during* the
shower, and in what direction would be more telling.

After all, if the freshwater outlet during the shower really is at 94F, and
the greywater really leaves at 72F, then you don't have conservation of
energy (freshwater side picks up (94-55)*1.25*8.33 = 406 btu/min, while the
greywater side gives off (100-72)*1.25*8.33)1 btu/min).  That's a clue
that something is wrong with these results.

daestrom

Posted by nicksanspam on April 15, 2006, 7:27 pm

How about the fresh water outlet temp? Line 100 below accumulates
the heat energy that needs to be added during the last shower...

20 UPIPEx.5'U-value of 10' section of pipe (Btu/h-F)
30 CFRESH=1.25*8.33'thermal capacitance of 10' of fresh water (Btu/F)
40 VGREY*3.14159*(2/12)^2'volume of 10' of greywater (ft^3)
50 CGREY=VGREY*62.33-CFRESH'thermal capacitance of 10' of greywater (Btu/F)
60 FOR SHOWER = 1 TO 1000'simulate showers
70 FOR M=0 TO 359'simulate 10 min shower + 350 min rest
80 IF M>9 GOTO 200'rest vs shower
90 IF SHOWER <1000 GOTO 120
100 RHEAT=RHEAT+1.25*8.33*(100-TF(0))'reheat energy required
110 PRINT 300+M;"'";M,TF(0),RHEAT
120 TF(0)=TF(1)'move fresh water up
130 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top
140 FOR S=1 TO 8'pipe section (9<->fresh water in and greywater out)
150 TF(S)=TF(S+1)'move fresh water up
160 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down
170 NEXT S
180 TF(9)U'move cold water in at the bottom
190 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down
200 FOR S=0 TO 9'rest
210 HEATFLOW=(TG(S)-TF(S))*UPIPE/60'heatflow into fresh water (Btu)
220 TF(S)=TF(S)+HEATFLOW/CFRESH'new fresh temp (F)
230 TG(S)=TG(S)-HEATFLOW/CGREY'new grey temp (F)
240 NEXT S
250 NEXT M
260 NEXT SHOWER
280 SHOWERGY=1.25*10*8.33*(100-55)'total heat energy with no gwhx
290 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY

time    fresh         cum reheat
(min)   temp (F)      (Btu)

0       94.56091      56.6345
1       92.93514      130.1973
2       91.38136      219.9389
3       89.96538      324.4244
4       88.72086      441.8685
5       87.6472       570.492
6       86.72784      708.6885
7       85.94302      855.0568
8       85.27464      1008.385
9       84.70704      1167.623

cum reheat    shower        effectiveness
(Btu)         heat (Btu)    (fraction)

1167.623      4685.625      .7508075

Nick

Posted by daestrom on April 18, 2006, 8:28 pm

More like I expect.  Your system's outlet temperature drops from the high of
94F the longer you run the shower.  The fact that it's a 'batch' process
allows you to get better performance than the steady-state parameters would
allow.

But show the greywater too.  As I said before, if the greywater is giving
off less energy than the freshwater is picking up, then something's broke.
I notice you chose to show the more optimistic of the two numbers.  I'll bet
the greywater shows more energy going down the drain than physics would
allow if these numbers were accurate.

So then it's just a matter of adjusting gwhx versus shower time to keep
performance high.  Too long a shower, or too short a gwhx and performance
drops.

How would two showers spaced fairly close together look?  Looks like this
would support four, 10-minute showers a day, spaced 6 hours apart right now.

daestrom

•
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 Re: GFX vs home brew AstickfortheMUL... 04-14-2006
 Re: GFX vs home brew Robert Gammon 04-14-2006
 Re: GFX vs home brew nicksanspam 04-14-2006
 Re: GFX vs home brew daestrom 04-14-2006
 Re: GFX vs home brew nicksanspam 04-15-2006
 Re: GFX vs home brew nicksanspam 04-15-2006
 Re: GFX vs home brew daestrom 04-15-2006
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 Re: GFX vs home brew Derek Broughton 04-14-2006
 Re: GFX vs home brew Robert Gammon 04-15-2006
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 Re: GFX vs home brew daestrom 04-14-2006
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 Re: GFX vs home brew Robert Gammon 04-19-2006
 Re: GFX vs home brew nicksanspam 04-19-2006
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 Re: GFX vs home brew Robert Gammon 04-22-2006
 Re: GFX vs home brew nicksanspam 04-22-2006
 Re: GFX vs home brew Robert Gammon 04-22-2006
 Re: GFX vs home brew nicksanspam 04-22-2006
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 Re: GFX vs home brew Robert Gammon 04-16-2006
 Re: GFX vs home brew nicksanspam 04-16-2006
 Re: GFX vs home brew Robert Gammon 04-16-2006
 Re: GFX vs home brew daestrom 04-18-2006
 Re: GFX vs home brew Robert Gammon 04-16-2006
 Re: GFX vs home brew nicksanspam 04-16-2006
 Re: GFX vs home brew Robert Gammon 04-16-2006
 Re: GFX vs home brew nicksanspam 04-16-2006
 Re: GFX vs home brew Robert Gammon 04-16-2006
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