I'd like to know why the energy that flows into the gwhx is less than
the energy that flows out during a shower, in that simulation...

0 94.38332 58.48365 71.9481 176.4721
1 92.75861 133.8847 72.28975 356.5016
2 91.17551 225.7697 72.71021 540.9092
3 89.71318 332.8812 73.10856 729.4646
4 88.41459 453.5143 73.48615 921.9516
5 87.28408 585.919 73.84426 1118.167
6 86.30738 728.4934 74.18405 1317.921
7 85.46612 879.8273 74.50663 1521.034
8 84.74309 1038.69 74.81306 1727.338
9 84.12328 *1204.006 75.10433 *1936.674

1204.006 4685.625 .7430426

Why 1204 Btu in and 1936 out?

20 UPIPE=78.5'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=10*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 CSERIES=CFRESH*CGREY/(CFRESH+CGREY)'caps in series (Btu/F)
70 RC=CSERIES/UPIPE'combined time constant (hours)
80 EXPF=EXP(-1/60/RC)'exponential factor
90 FOR SHOWER = 1 TO 100'simulate showers
100 FOR M=0 TO 59'simulate 10 min shower + 50 min rest
110 IF M9 GOTO 270'rest vs shower
120 IF SHOWER 100 GOTO 160
130 RHEAT=RHEAT+CFRESH*(100-TF(0))'reheat energy
140 GLOSS=GLOSS+CFRESH*(TG(9)-55)'greywater heat loss
150 PRINT 400+M;"'";M,TF(0),RHEAT,TG(9),GLOSS
160 TF(0)=TF(1)'move fresh water up
170 TGT=TG(0)'save original Tg(0) for later Tg(1) calc
180 TG(0)=(100*CFRESH+TG(0)*(CGREY-CFRESH))/CGREY'move greywater in at the top
190 FOR S=1 TO 8'pipe section (9-fresh water in and greywater out)
200 TF(S)=TF(S+1)'move fresh water up
210 TGP=TG(S)'save original Tg(s) for later Tg(s+1) calc
220 TG(S)=(TGT*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down
230 TGT=TGP'prepare for Tg(s+1) calc
240 NEXT S
250 TF(9)=55'move cold water in at the bottom
260 TG(9)=(TGT*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down
270 FOR S=0 TO 9'rest
280 TFINAL=(TF(S)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY)
290 TF(S)=TFINAL+(TF(S)-TFINAL)*EXPF'new fresh temp (F)
300 TG(S)=TFINAL+(TG(S)-TFINAL)*EXPF'new grey temp (F)
310 NEXT S
320 NEXT M
330 NEXT SHOWER
340 SHOWERGY=10*CFRESH*(100-55)'if no GWHX (Btu)
350 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY

0 93.72946 65.29199 67.76752 132.9418
1 91.50189 153.7785 68.01705 268.4818
2 89.30461 265.1443 68.32899 407.2698
3 87.3519 396.8427 68.61366 549.0221
4 85.71924 545.5411 68.89086 693.6606
5 84.37411 708.2456 69.15711 841.0716
6 83.2604 882.5468 69.41382 991.1554
7 82.33891 1066.443 69.66134 1143.817
8 81.58043 1258.237 69.90021 1298.965
9 80.95963 *1456.495 70.13091 *1456.516

1456.495 4685.625 .6891568

Ah. Much better with buffering in lines 170, 210, and 230.
The effectiveness dropped to 69%, but it still beats a GFX,
esp. for baths, with no large vertical space requirement.
And the pipe conductance might end up larger, with greywater
vs liquid manure, and warm greywater bouyancy (not simulated)
might also help.

Thanks, daestrom :-)

Nick