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.

Changing the heatflow from linear to a more accurate exponential (two caps
equalizing voltage through a resistor) made little difference...

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
100 FOR SHOWER = 1 TO 100'simulate showers
110 FOR M=0 TO 59'simulate 10 min shower + 50 min rest
120 IF M9 GOTO 250'rest vs shower
130 IF SHOWER 100 GOTO 170
140 RHEAT=RHEAT+CFRESH*(100-TF(0))'reheat energy
150 GLOSS=GLOSS+CFRESH*(TG(9)-55)'greywater heat loss
160 PRINT 400+M;"'";M,TF(0),RHEAT,TG(9),GLOSS
170 TF(0)=TF(1)'move fresh water up
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 TG(S)=(TG(S-1)*CFRESH+TG(S)*(CGREY-CFRESH))/CGREY'move greywater down
220 NEXT S
230 TF(9)=55'move cold water in at the bottom
240 TG(9)=(TG(8)*CFRESH+TG(9)*(CGREY-CFRESH))/CGREY'move greywater down
250 FOR S=0 TO 9'rest
260 TFINAL=(TF(S)*CFRESH+TG(S)*CGREY)/(CFRESH+CGREY)
270 TF(S)=TFINAL+(TF(S)-TFINAL)*EXPF'new fresh temp (F)
280 TG(S)=TFINAL+(TG(S)-TFINAL)*EXPF'new grey temp (F)
290 NEXT S
295 NEXT M
310 NEXT SHOWER
320 SHOWERGY=10*CFRESH*(100-55)
330 PRINT RHEAT,SHOWERGY,1-RHEAT/SHOWERGY

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?

Nick