> restart;
> Digits:=14;

                             Digits := 14

> #read `c:/Maple V release 5/maple support files/newton.mpl`:read `c:/Maple V release 5/maple support files/Besirk`:read `c:/Maple V release 5/maple support files/fddiff_high.mpl`:
> read `c:/Users/ekim/Onedrive - Wetsus/PhD - Edward/MODELS/Maple V release 5/maple support files/newton.mpl`:read `c:/Users/ekim/Onedrive - Wetsus/PhD - Edward/MODELS/Maple V release 5/maple support files/Besirk`:read `c:/Users/ekim/Onedrive - Wetsus/PhD - Edward/MODELS/Maple V release 5/maple support files/fddiff_high.mpl`:
> cnst1:=[DC[f]=1.64e-9,area=5,H[ch]=711e-6,A=2.2,P=0.39,C=55,RT=298*8.3144,M=1e6,ConvPres=1e5,VT=3.6e6,L[ch]=2.236068,W[ch]=2.236068,alpha=0.662,k=7,eta=0.895e-3,epsilon[s]=1]; #,epsilon[s]=0.8,k=7,eta=1.4e-3],d[h]=3.55e-6,; PMB: changed D to DC ; unit P is LMH  PMB: area is 1 m2 

                           -8
  cnst1 := [DC[f] = .164 10  , area = 5, H[ch] = .000711, A = 2.2,

                                                  7
        P = .39, C = 55, RT = 2477.6912, M = .1 10 ,

                                       7
        ConvPres = 100000., VT = .36 10 , L[ch] = 2.236068,

        W[ch] = 2.236068, alpha = .662, k = 7, eta = .000895,

        epsilon[s] = 1]

> cnst2:=subs(cnst1,[c[f]=50,Q[f]=300]);EMK 

                   cnst2 := [c[f] = 50, Q[f] = 300]

> ae_check:=subs(cnst1,cnst2,initial_crossflow_velocity=Q[f]/VT/(W[ch]*H[ch])); # 

      ae_check := initial_crossflow_velocity = .052416032700414

> cnst3:=subs(cnst1,cnst2,[phi[f]=Q[f]/VT]); # pmb: Q[f] is feed flow rate in L/hr, and phi[f] in m3/s

               cnst3 := [phi[f] = .000083333333333334]

> np:=20;

                               np := 20

> ae_Delta:=Delta=1/np;

                       ae_Delta := Delta = 1/20

> ae_setpoints:=LMH*area=phi[f]*(1-f[np])*VT; # PMB: LMH is average, or you can call it total, flow through membrane

           ae_setpoints := LMH area = phi[f] (1 - f[20]) VT

50% water recovery
> #ae_setpoints:=LMH*area=phi[f]*f[0]/2*VT;EMK
> ae0:=f[0]=1,c[0]=c[f],DPh_bar[0]=20;  

            ae0 := f[0] = 1, c[0] = c[f], DPh_bar[0] = 20

> ae1:=(1-f[j])*cp[j]=c[f]*1-c[j]*f[j];#mass balance on the upstream side PMB: i would call it an overall balance

              ae1 := (1 - f[j]) cp[j] = c[f] - c[j] f[j]

> ae2:=phi[f]*(f[j-1]-f[j])*VT=+Delta*area*vw_LMH[j];# volume balance on the upstream side....vw in LMH

      ae2 := phi[f] (f[j - 1] - f[j]) VT = Delta area vw_LMH[j]

> ae3:=phi[f]*M*(c[j-1]*f[j-1]-c[j]*f[j])=+Delta*area*Jsalt_micron[j];# mass balance on the upstream side

  ae3 := phi[f] M (c[j - 1] f[j - 1] - c[j] f[j]) =

        Delta area Jsalt_micron[j]

> ae4:=vw_LMH[j]=A*(DPh_bar[j]-DPi_bar[j]);# I remove [j] in all cases where we do a substitution. just to show that more clearly to myself 

            ae4 := vw_LMH[j] = A (DPh_bar[j] - DPi_bar[j])

Axial change of DPh (z-direction) - Darcy law.
 
> ae_prefactor:=prefactor=1; # 1 means, that if phi[f] wouldn't go down from the initial value, pressure would go up by 1 bar to the end. so because phi[f] goes down, we will not reach a 1 bar decrease

                    ae_prefactor := prefactor = 1

> #ae5:=DPh_bar[j-1]-DPh_bar[j]=subs(ae_prefactor,prefactor)*Delta*f[np]; # PMB: pressure drop proportional to crossflowrate 
> ae5:=DPh_bar[j-1]-DPh_bar[j]=k*12*eta*phi[f]*(f[j-1]+f[j])/2*L[ch]*Delta/ConvPres/W[ch]/H[ch]^3;#EMK: (Bouchard et al. 1994; )

  ae5 := DPh_bar[j - 1] - DPh_bar[j] =

          k eta phi[f] (f[j - 1] + f[j]) L[ch] Delta
        6 ------------------------------------------
                                        3
                    ConvPres W[ch] H[ch]

> ae_gamma:=gamma=6*phi[f]*f[j]/(W[ch]*H[ch])/H[ch];# remove dependence on reduction of phi[f]

                                        phi[f] f[j]
                  ae_gamma := gamma = 6 ------------
                                                   2
                                        W[ch] H[ch]

Axial change of k_dbl. (z-direction) 
> ae_kdbl:=kdbl[j]=alpha*VT*(epsilon[s]^2*DC[f]^2*gamma/(L[ch]*j/np))^(1/3);#Biesheuvel CP 2024, kDBL in LMH  removed: epsilon[s]  PMB:  

  ae_kdbl :=

                                   /          2      2      \(1/3)
                             (1/3) |epsilon[s]  DC[f]  gamma|
        kdbl[j] = alpha VT 20      |------------------------|
                                   \        L[ch] j         /

> ae_kdbl_a:=evalf(seq(subs(ae_gamma,ae_kdbl),j=1..np)):
> #ae_kdbl_test:=evalf(subs(ae_gamma,cnst1,cnst3,f[j]=1,j=1,ae_kdbl));
> ae_Pe_dbl:=Pe_dbl=vw_LMH[j]/kdbl[j]; # removed [j]

                                         vw_LMH[j]
                   ae_Pe_dbl := Pe_dbl = ---------
                                          kdbl[j]

> #ae_Pe_dbl_tot:=seq(ae_Pe_dbl,j=1..np):
> #nops([ae_Pe_dbl_tot]);
> ae6:=ln(cstar[j]-Jsalt_micron[j]/M/(vw_LMH[j]/VT))-ln(c[j]-Jsalt_micron[j]/M/(vw_LMH[j]/VT))=Pe_dbl;#conc of salt at the mem-sol interface on the feed channel (dbl included).
PMB: i removed [j], also in ae_Pe_dbl. no reason.

                       Jsalt_micron[j] VT
  ae6 := ln(cstar[j] - ------------------)
                          M vw_LMH[j]

                     Jsalt_micron[j] VT
         - ln(c[j] - ------------------) = Pe_dbl
                        M vw_LMH[j]

> #ae6:=cstar[j]=Jsalt_micron[j]/M/(vw_LMH[j]/VT)+(c[j]-Jsalt_micron[j]/M/(vw_LMH[j]/VT))*exp(Pe_dbl);
> ae_DPi:=DPi_bar[j]=2*RT/ConvPres*(cstar[j]-cp[j]);

                                     RT (cstar[j] - cp[j])
            ae_DPi := DPi_bar[j] = 2 ---------------------
                                           ConvPres

> ae7:=Jsalt_micron[j]=M*P/VT*(sqrt(C^2+(cstar[j])^2)-sqrt(C^2+(cp[j])^2));

  ae7 := Jsalt_micron[j] =

                   2           2          2        2
        M P (sqrt(C  + cstar[j] ) - sqrt(C  + cp[j] ))
        ----------------------------------------------
                              VT

MODULE 1
> aes_1:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2,cnst3,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):  # ae3,ae_gamma,

> aes_M1:=subs(ae0,cnst1,cnst2,cnst3,[seq(op(aes_1),j=1..np),ae_setpoints]):
> ini:=[LMH=10,seq(c[j]=5.+5*j/np,j=1..np),seq(cp[j]=0.5+0.5*j/np,j=1..np),seq(f[j]=1.-0.2*j/np,j=1..np),seq(vw_LMH[j]=10-5*j/np,j=1..np),seq(DPh_bar[j]=9-1*j/np,j=1..np),seq(Jsalt_micron[j]=0.2+0.2*j/np,j=1..np),seq(cstar[j]=5+j/np*5,j=1..np)]:
> nops(aes_M1);nops(ini);

                                 141


                                 141

> sol_module_1:=Newton(aes_M1,ini,tolerance=1e-6):
> listed_1a:=[[seq([c[i],cp[i],cstar[i],vw_LMH[i],DPh_bar[i],Jsalt_micron[i]], i=1..np)]]:
> #listed_1a:=[[seq([vw_LMH[i],Jsalt_micron[i],cp[i],DPh_bar[i]], i=1..np)]]:
> listed_data_1a:=op(subs(sol_module_1, listed_1a)):
> writedata(terminal, listed_data_1a):
51.414518374371  	.66199534363932	97.306370339063  	33.445077168278  	19.991406152876  	6.1501348209137 
52.824165457291  	.76694959215444	113.65032799156   	31.656340424825  	19.983048713377  	7.7191723150228 
54.242679750450  	.86173943689717	126.26324943206   	30.273741981041  	19.974916165199  	8.9608418559531 
55.676488320893  	.95050277318599	136.99889758363   	29.095618194455  	19.966999209399  	10.033689787735  
57.129476634528  	1.0352953509210 	146.54486198562   	28.047215471647  	19.959289760626  	10.997597229609  
58.604332589468  	1.1173113642937 	155.24438820619   	27.091227901610  	19.951780540189  	11.882848548017  
60.103081810803  	1.1973154610495 	163.29754912924   	26.205912506564  	19.944464861627  	12.707282765815  
61.627344129739  	1.2758312204828 	170.83290807666   	25.377296904363  	19.937336501015  	13.482466520725  
63.178471810710  	1.3532352688117 	177.93885863117   	24.595772762666  	19.930389611331  	14.216415979738  
64.757630374345  	1.4298089824269 	184.67928603950   	23.854393921970  	19.923618662346  	14.914966564815  
66.365848736430  	1.5057689963593 	191.10217249068   	23.147941490634  	19.917018396442  	15.582530143713  
68.004051706897  	1.5812862375413 	197.24467514340   	22.472372247372  	19.910583794981  	16.222544277957  
69.673081749268  	1.6564983420899 	203.13629481975   	21.824474491044  	19.904310051957  	16.837753932507  
71.373713889626  	1.7315180593986 	208.80094429438   	21.201643428791  	19.898192552880  	17.430396185427  
73.106666082674  	1.8064391175447 	214.25834935738   	20.601729035829  	19.892226857502  	18.002325875370  
74.872606463774  	1.8813404251425 	219.52502793871   	20.022929739372  	19.886408685473  	18.555103754913  
76.672158404399  	1.9562891497575 	224.61499278804   	19.463716122579  	19.880733904241  	19.090059989994  
78.505903978892  	2.0313430176702 	229.54026746508   	18.922774900121  	19.875198518733  	19.608340953710  
80.374386256482  	2.1065520616170 	234.31127290507   	18.398966946360  	19.869798662445  	20.110944401685  
82.278110707871  	2.1819599692144 	238.93712217633   	17.891295291290  	19.864530589689  	20.598746380791  
> post_sol1:=evalf(subs(sol_module_1,cnst1,cnst2,cnst3,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_1b:=[[seq([i,kdbl[i],vz[i],R[i],CP[i],WR[i],DPi_bar[i]], i=1..np)]]:
> #listed_1b:=[[seq([kdbl[i],DPi_bar[i]], i=1..np)]]:
> listed_data_1b:=op(subs(post_sol1, listed_1b)):
> writedata(terminal, listed_data_1b):
1               	51.927167350209  	5.0955150818313 	.98676009312721	1.8925854683795 	2.787089764023  	4.7890983491133 
2               	40.838387718834  	4.9572401005910 	.98466100815691	2.1514836440426 	5.425118132760  	5.5938030657298 
3               	35.355535449205  	4.8250043131209 	.98276521126206	2.3277472649388 	7.947929964511  	6.2141243556344 
4               	31.838087832412  	4.6979145735610 	.98098994453628	2.4606238955667 	10.372564814049  	6.7417182119191 
5               	29.296681149904  	4.5754042599512 	.97929409298158	2.5651357340993 	12.709832770019  	7.2105554553322 
6               	27.329477394446  	4.4570697026524 	.97765377271413	2.6490257860916 	14.967435095154  	7.6375860394580 
7               	25.736487321483  	4.3426022054116 	.97605369077901	2.7169580029736 	17.151261137369  	8.0326864495524 
8               	24.404809061338  	4.2317541033794 	.97448337559034	2.7720309951540 	19.266035879400  	8.4022015444856 
9               	23.264936576368  	4.1243197009277 	.97293529462377	2.8164476526798 	21.315683609622  	8.7504929010287 
10               	22.271274563327  	4.0201236432724 	.97140382035146	2.8518536730254 	23.303549769786  	9.0807123341781 
11               	21.392421904082  	3.9190133717624 	.96988462007281	2.8795257821479 	25.232544894006  	9.3952268097905 
12               	20.605903757062  	3.8208539885479 	.96837427524917	2.9004841651721 	27.105242581286  	9.6958691370845 
13               	19.895123092115  	3.7255246244987 	.9668700331582 	2.9155635106077 	28.923948788873  	9.9840943742098 
14               	19.247501711516  	3.6329157882264 	.96536963881203	2.9254599896157 	30.690752407940  	10.261081903429  
15               	18.653296735101  	3.5429273796576 	.96387121764911	2.9307635108826 	32.407563160924  	10.527804568489  
16               	18.104819438730  	3.4554671679929 	.96237319149715	2.9319805775017 	34.076140639205  	10.785076985758  
17               	17.595903596947  	3.3704496029302 	.96087421700485	2.9295509277740 	35.698116982752  	11.033590212159  
18               	17.121533949512  	3.2877948706011 	.9593731396466 	2.9238599370411 	37.275014891098  	11.273937200496  
19               	16.677580524230  	3.2074281328416 	.95786895876766	2.9152480512555 	38.808262136628  	11.506631868645  
20               	16.260604776513  	3.1292789062549 	.95636080061571	2.9040180932773 	40.299203410901  	11.732123639103  
MODULE 2
> cnst2a:=subs(sol_module_1,[c[f]=c[np]]);

                  cnst2a := [c[f] = 82.278110707871]

> cnst3a:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]]);

               cnst3a := [phi[f] = .000049750663824249]

> ae0a:=subs(sol_module_1,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0a := [f[0] = 1, c[0] = 82.278110707871,

        DPh_bar[0] = 19.864530589689]

> aes_2:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2a,cnst3a,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M2:=subs(ae0a,cnst1,cnst3a,[seq(op(aes_2),j=1..np),ae_setpoints]):
> ini2:=sol_module_1:
> nops(aes_M2);nops(ini2);

                                 141


                                 141

> sol_module_2:=Newton(aes_M2,ini,tolerance=1e-6):
> listed_data_2a:=op(subs(sol_module_2, listed_1a)):
> writedata(terminal, listed_data_2a):
85.412377247319  	1.6147295647666 	156.58866154388   	26.795722453163  	19.859424792228  	12.018845903705  
88.470214739369  	1.8485503906065 	178.54781666414   	24.416437371588  	19.854504965297  	14.277892442736  
91.505475545369  	2.0570807024964 	194.48207231309   	22.691596483170  	19.849756205277  	15.932703581969  
94.541455263912  	2.2506766499550 	207.43247838300   	21.290773395387  	19.845167161712  	17.285031740053  
97.591025765339  	2.4344555066072 	218.51812290896   	20.092504019708  	19.840728396325  	18.446958022299  
100.66219158289   	2.6113770506156 	228.29486913218   	19.036493688664  	19.836431722980  	19.474506320361  
103.76026850485   	2.7833290913050 	237.08553758720   	18.087738809820  	19.832269861626  	20.400370632397  
106.88891459169   	2.9515993388559 	245.09695516451   	17.223817346458  	19.828236229755  	21.245580385916  
110.05068061742   	3.1171103368522 	252.47096098058   	16.429353548582  	19.824324805150  	22.024605486302  
113.24732993856   	3.2805482144735 	259.30982674947   	15.693260489312  	19.820530029785  	22.747909549963  
116.48003652976   	3.4424385085863 	265.69019518118   	15.007228633857  	19.816846739393  	23.423354100526  
119.74951382518   	3.6031933902689 	271.67129174468   	14.364835637009  	19.813270109964  	24.057028024863  
123.05610200746   	3.7631424351476 	277.30004215790   	13.760991705076  	19.809795615947  	24.653765691679  
126.39982922144   	3.9225534279559 	282.61440911743   	13.191578025416  	19.806418996804  	25.217485489349  
129.78045584436   	4.0816468719401 	287.64565048965   	12.653202103802  	19.803136229735  	25.751419376369  
133.19750743774   	4.2406063784914 	292.41989605783   	12.143026952858  	19.799943507060  	26.258273442912  
136.65029997604   	4.3995862778296 	296.95927810293   	11.658648625769  	19.796837217181  	26.740343225497  
140.13795972222   	4.5587173058143 	301.28276083200   	11.198006377604  	19.793813928376  	27.199598432567  
143.65943935505   	4.7181109280015 	305.40676111023   	10.759315434781  	19.790870374829  	27.637746440768  
147.21353145148   	4.8778626794788 	309.34562123138   	10.341015791767  	19.788003444486  	28.056280718648  
> post_sol2:=evalf(subs(sol_module_2,cnst1,cnst2a,cnst3a,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_2b:=op(subs(post_sol2, listed_1b)):
> writedata(terminal, listed_data_2b):
1               	43.580769167917  	3.0122351175601 	.98037473696376	1.8333251759340 	3.740279860028  	7.6795509498808 
2               	34.176932788837  	2.9055840525854 	.9775329018289 	2.0181686818568 	7.148447305938  	8.7561243418476 
3               	29.512873879336  	2.8064670973116 	.97499844509313	2.1253599432601 	10.315852904579  	9.5353941674727 
4               	26.514710502874  	2.7134689411025 	.97264549914198	2.1940901777316 	13.287724667853  	10.167542891082  
5               	24.345791667387  	2.6257048287917 	.97041186913916	2.2391210789647 	16.092336047665  	10.707772023731  
6               	22.665825686180  	2.5425533724844 	.96826158223434	2.2679306454816 	18.749544267138  	11.183480046315  
7               	21.305226314548  	2.4635460800734 	.96617169418015	2.2849356598968 	21.274320574328  	11.610570402617  
8               	20.168130860994  	2.3883123989686 	.96412655427474	2.2930063056657 	23.678506438183  	11.999228345002  
9               	19.195448261894  	2.3165489378978 	.96211495001484	2.2941335715884 	25.971797104202  	12.356436828522  
10               	18.348366992045  	2.2480007333159 	.96012854225444	2.2897654795937 	28.162340249615  	12.687229807370  
11               	17.600124874678  	2.1824491177479 	.95816094367056	2.2809934053661 	30.257123665596  	12.995379178548  
12               	16.931543751844  	2.1197034765409 	.95620714477679	2.2686630038539 	32.262238680484  	13.283799365869  
13               	16.328443608399  	2.0595954272740 	.95426313994364	2.2534440603448 	34.183066163991  	13.554799386367  
14               	15.780064574502  	2.0019745785114 	.952325674542  	2.2358765107373 	36.024412061521  	13.810247167069  
15               	15.278061603100  	1.9467053572416 	.9503920685973 	2.2164019121231 	37.790608777296  	14.051680728007  
16               	14.815840471621  	1.8936645824213 	.94846009051487	2.1953856470964 	39.485592714788  	14.280385801215  
17               	14.388105564993  	1.8427395734537 	.94652786458053	2.1731330129169 	41.112964722626  	14.497451478195  
18               	13.990543650739  	1.7938266510814 	.9445938018436 	2.1499011504749 	42.676038000452  	14.703811029465  
19               	13.619597607815  	1.7468299319428 	.94265654756277	2.1259080675891 	44.177876620356  	14.900272449928  
20               	13.272301217586  	1.7016603467847 	.94071494061406	2.1013395859832 	45.621326901115  	15.087541720955  
MODULE 3
> cnst2b:=subs(sol_module_2,[c[f]=c[np]]);

                  cnst2b := [c[f] = 147.21353145148]

> cnst3b:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^2]);

               cnst3b := [phi[f] = .000029701542611442]

> ae0b:=subs(sol_module_2,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0b := [f[0] = 1, c[0] = 147.21353145148,

        DPh_bar[0] = 19.788003444486]

> aes_3:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2b,cnst3b,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M3:=subs(ae0b,cnst1,cnst3b,[seq(op(aes_3),j=1..np),ae_setpoints]):
> ini3:=sol_module_2:
> nops(aes_M3);nops(ini3);

                                 141


                                 141

> sol_module_3:=Newton(aes_M3,ini3,tolerance=1e-6):
> listed_data_3a:=op(subs(sol_module_3, listed_1a)):
> writedata(terminal, listed_data_3a):
153.27771412639   	4.3622670361539 	243.86204754012   	17.417026940069  	19.784960398436  	21.104922913577  
158.93539790184   	4.9186177699138 	265.29723465852   	15.134414689238  	19.782035558861  	23.369549096353  
164.37028689063   	5.4098055714384 	279.70667639880   	13.610863735536  	19.779215104155  	24.894721532445  
169.65665349592   	5.8629293738849 	290.82899082485   	12.441728642317  	19.776489256168  	26.072837682047  
174.83313581625   	6.2911750642408 	299.97859081696   	11.485134725584  	19.773850295582  	27.042199498893  
179.92234705197   	6.7020712359783 	307.78802691626   	10.672928953653  	19.771291799222  	27.869472571206  
184.93837718270   	7.1003634348331 	314.61577453881   	9.9665361253821 	19.768808252489  	28.592483930519  
189.89028352153   	7.4892519842129 	320.68696971447   	9.3417505274905 	19.766394821375  	29.235014017026  
194.78393358015   	7.8710035408535 	326.15343968309   	8.7822578413663 	19.764047205323  	29.813113211923  
199.62306928691   	8.2472840665872 	331.12308943065   	8.2764675466456 	19.761761535890  	30.338196764504  
204.40996454370   	8.6193538101245 	335.67576710868   	7.8158043938802 	19.759534303523  	30.818716999482  
209.14585370967   	8.9881881565145 	339.87248430204   	7.3937162795344 	19.757362302620  	31.261135786227  
213.83122310900   	9.3545560272797 	343.76109223423   	7.0050638887505 	19.755242589081  	31.670523573417  
218.46601654290   	9.7190726885539 	347.37994212997   	6.6457273315160 	19.753172446676  	32.050945893329  
223.04978455647   	10.082236458968  	350.76033760742   	6.3123427288045 	19.751149359876  	32.405722443332  
227.58179560033   	10.444454919842  	353.92823128384   	6.0021200595505 	19.749170991501  	32.737606405249  
232.06112056365   	10.806064068374  	356.90543100383   	5.7127137065772 	19.747235164075  	33.048911989912  
236.48669817608   	11.167342599208  	359.71047785754   	5.4421282587280 	19.745339844057  	33.341607314710  
240.85738631363   	11.528522745740  	362.35929854686   	5.1886485431852 	19.743483128371  	33.617383437659  
245.17200267705   	11.889798640962  	364.86569892659   	4.9507867063053 	19.741663232771  	33.877706603277  
> post_sol3:=evalf(subs(sol_module_3,cnst1,cnst2b,cnst3b,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_3b:=op(subs(post_sol3, listed_1b)):
> writedata(terminal, listed_data_3b):
1               	36.654011721493  	1.7921268133927 	.97036775768407	1.5909817609821 	4.072232124605  	11.868129971132  
2               	28.730102917402  	1.7260196487882 	.96658854847501	1.6692142729738 	7.610772306965  	12.902756154662  
3               	24.806517955369  	1.6665673589013 	.96325198153934	1.7016863673476 	10.793094797377  	13.592458860730  
4               	22.290520311359  	1.6122218542876 	.96017397778534	1.7142209564557 	13.702064694319  	14.121158055115  
5               	20.475790847496  	1.5620547545088 	.95726496741019	1.7157994073403 	16.387375726214  	14.553334511225  
6               	19.074829219950  	1.5154353717552 	.95447380977891	1.7106714755525 	18.882786929185  	14.919960456652  
7               	17.944258044061  	1.4719015148004 	.95176826909303	1.7011924692515 	21.213038166695  	15.238564559134  
8               	17.002975743569  	1.4310967230397 	.94912660602343	1.6888013634363 	23.397209824064  	15.520144581607  
9               	16.200957326790  	1.3927357968566 	.94653342350226	1.6744370733682 	25.450567876001  	15.772111822884  
10               	15.505324136198  	1.3565841640592 	.9439774048943 	1.6587416004247 	27.385668346230  	15.999730832869  
11               	14.893389512411  	1.3224447091684 	.94144998951428	1.6421692937426 	29.213062300544  	16.206895942668  
12               	14.348884375869  	1.2901489363113 	.93894455171414	1.6250500704348 	30.941768873563  	16.396582175559  
13               	13.859770752185  	1.2595507981562 	.93645586832238	1.6076281435242 	32.579605589373  	16.571122639649  
14               	13.416907102293  	1.2305222430623 	.9339797599261 	1.5900868593984 	34.133426710733  	16.732387295987  
15               	13.013197781799  	1.2029499128215 	.93151284151966	1.5725652383162 	35.609300000142  	16.881902664964  
16               	12.643031125852  	1.1767326360454 	.92905234446275	1.5551693418633 	37.012640892153  	17.020934600797  
17               	12.301896662022  	1.1517794870077 	.92659598637551	1.5379802964708 	38.348316398349  	17.150547115631  
18               	11.986117374448  	1.1280082559436 	.92414187412596	1.5210600876575 	39.620726988152  	17.271645180999  
19               	11.692658086963  	1.1053442249677 	.9216884301866 	1.5044558279604 	40.833872110655  	17.385006517832  
20               	11.418985527644  	1.0837191751435 	.91923433584038	1.4882029552420 	41.991403343562  	17.491305638996  
MODULE 4
> cnst2c:=subs(sol_module_3,[c[f]=c[np]]);

                  cnst2c := [c[f] = 245.17200267705]

> cnst3c:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^3]);

               cnst3c := [phi[f] = .000017732057538281]

> ae0c:=subs(sol_module_3,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0c := [f[0] = 1, c[0] = 245.17200267705,

        DPh_bar[0] = 19.741663232771]

> aes_4:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2c,cnst3c,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M4:=subs(ae0c,cnst1,cnst3c,[seq(op(aes_4),j=1..np),ae_setpoints]):
> ini4:=sol_module_3:
> nops(aes_M4);nops(ini4);

                                 141


                                 141

> sol_module_4:=Newton(aes_M4,ini4,tolerance=1e-6):
> listed_data_4a:=op(subs(sol_module_4, listed_1a)):
> writedata(terminal, listed_data_4a):
253.35477997922   	12.559521754486  	331.31808025596   	8.6770964586682 	19.739840260416  	30.272272704790  
260.55921857381   	14.016995389220  	345.74496396354   	7.2593087347158 	19.738075159116  	31.777871216416  
267.17903926928   	15.296975369153  	355.12118614790   	6.3728949450841 	19.736359561453  	32.745637945197  
273.37449105903   	16.473174822478  	362.23446239228   	5.7219665679301 	19.734687884761  	33.471983952175  
279.23216009653   	17.580940212896  	368.02794576868   	5.2075466576898 	19.733055897224  	34.057120430500  
284.80606978727   	18.640211632088  	372.94519202667   	4.7834458098375 	19.731460190723  	34.548157563058  
290.13310903179   	19.663421623890  	377.23345493676   	4.4240579276401 	19.729897920115  	34.971353282084  
295.24011293220   	20.658866774759  	381.04599792706   	4.1135736044885 	19.728366652844  	35.342985997100  
300.14755652547   	21.632361760207  	384.48502899949   	3.8414795386970 	19.726864273350  	35.673915333479  
304.87166206192   	22.588134690501  	387.62245744483   	3.6003931355828 	19.725388918083  	35.971786225979  
309.42568347990   	23.529348821079  	390.51098889508   	3.3849097163372 	19.723938929066  	36.242206726518  
313.82073023845   	24.458424518407  	393.19052077163   	3.1909403207871 	19.722512819423  	36.489426752085  
318.06631743362   	25.377247333128  	395.69205270550   	3.0153080253459 	19.721109246992  	36.716753005382  
322.17074532289   	26.287307663266  	398.04019372793   	2.8554897933898 	19.719726993626  	36.926814948110  
326.14136830072   	27.189797520498  	400.25483382834   	2.7094447575122 	19.718364948622  	37.121742089226  
329.98478987676   	28.085679407499  	402.35229551060   	2.5754961578896 	19.717022095217  	37.303286093032  
333.70700675560   	28.975736494430  	404.34614954987   	2.4522478553681 	19.715697499433  	37.472907257706  
337.31351708880   	29.860609916949  	406.24780692992   	2.3385238450222 	19.714390300735  	37.631837248019  
340.80940300384   	30.740826995806  	408.06695745914   	2.2333234979997 	19.713099704127  	37.781125563111  
344.19939434844   	31.616822924221  	409.81190081644   	2.1357878208932 	19.711824973398  	37.921674593807  
> post_sol4:=evalf(subs(sol_module_4,cnst1,cnst2c,cnst3c,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_4b:=op(subs(post_sol4, listed_1b)):
> writedata(terminal, listed_data_4b):
1               	30.935832263616  	1.0774313483497 	.94877261017837	1.3077238182881 	3.398230248589  	15.795705506476  
2               	24.310512288417  	1.0457226680146 	.94282791168581	1.3269342986827 	6.241209192487  	16.438389370609  
3               	21.047048831036  	1.0178858455281 	.93760716883607	1.3291506216922 	8.737039966827  	16.839589131869  
4               	18.964700246926  	.99289227996686	.93280972279622	1.3250485112529 	10.977946238316  	17.133793990247  
5               	17.469786134639  	.97014570197532	.92829140350069	1.3179998523145 	13.017389116172  	17.365989234638  
6               	16.320819583502  	.9492515976429 	.92397087991877	1.3094706594745 	14.890740452175  	17.557166640796  
7               	15.397454205202  	.92992730055925	.91979744257426	1.3002082257886 	16.623343926487  	17.718962498460  
8               	14.631664773662  	.91195919984522	.91573725160629	1.2906308500653 	18.234351746805  	17.858560468986  
9               	13.981523338850  	.89517960675202	.91176659029579	1.2809867035078 	19.738798773516  	17.980737210306  
10               	13.419494598628  	.87945307972462	.90786821315705	1.2714282948545 	21.148828605318  	18.088846583727  
11               	12.926594724767  	.86466778485964	.9040292180014 	1.2620509858887 	22.474468194736  	18.185343603458  
12               	12.489222220403  	.85072974884302	.90023973271277	1.2529144281605 	23.724143125883  	18.272085400883  
13               	12.097322708563  	.83755887517151	.89649206656538	1.2440551891763 	24.905034797348  	18.350514690017  
14               	11.743269057918  	.82508608797267	.89278014056975	1.2354945304826 	26.023336505374  	18.421777087540  
15               	11.421147956418  	.81325122588853	.88909909278543	1.2272433758213 	27.084442276840  	18.486799149752  
16               	11.126288728352  	.80200145165255	.8854449973862 	1.2193055796931 	28.093089465511  	18.546342023449  
17               	10.854942450407  	.79129002633785	.88181466000179	1.2116801306663 	29.053468652125  	18.601039383357  
18               	10.604057575265  	.78107534781023	.87820546558784	1.2043626666256 	29.969309856041  	18.651424916634  
19               	10.371119387902  	.77132018468507	.87461526332475	1.1973465340525 	30.843951218154  	18.697952659581  
20               	10.154032789873  	.76199105766332	.87104227815984	1.1906235384063 	31.680394469891  	18.741012327537  
MODULE 5
> cnst2d:=subs(sol_module_4,[c[f]=c[np]]);

                  cnst2d := [c[f] = 344.19939434844]

> cnst3d:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^4]);

               cnst3d := [phi[f] = .000010586179601992]

> ae0d:=subs(sol_module_4,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0d := [f[0] = 1, c[0] = 344.19939434844,

        DPh_bar[0] = 19.711824973398]

> aes_5:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2d,cnst3d,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M5:=subs(ae0d,cnst1,cnst3d,[seq(op(aes_5),j=1..np),ae_setpoints]):
> ini5:=sol_module_4:
> nops(aes_M5);nops(ini5);

                                 141


                                 141

> sol_module_5:=Newton(aes_M5,ini5,tolerance=1e-6):
> listed_data_5a:=op(subs(sol_module_5, listed_1a)):
> writedata(terminal, listed_data_5a):
351.84156314682   	35.753061043703  	399.70989286152   	3.6856125440848 	19.710731216627  	36.603313818067  
358.34075307031   	39.401063502174  	408.95184611129   	3.0734166406835 	19.709662004421  	37.372502051061  
364.17003508069   	42.537493437129  	415.43498765969   	2.7062573595867 	19.708613780376  	37.865729351609  
369.52219035133   	45.368397183028  	420.65663750185   	2.4433570622585 	19.707584256510  	38.235141191836  
374.50301592646   	47.991660184353  	425.12983818796   	2.2394522506533 	19.706571737677  	38.531815291109  
379.17981796880   	50.462261672685  	429.09902179546   	2.0738861245022 	19.705574882192  	38.779802898350  
383.59944084191   	52.814458977046  	432.70189971468   	1.9353778569890 	19.704592585845  	38.992565610243  
387.79652476799   	55.071173691474  	436.02454173950   	1.8170410796485 	19.703623915936  	39.178490428382  
391.79782659370   	57.248564370580  	439.12470469096   	1.7143390496232 	19.702668069792  	39.343200943641  
395.62470207506   	59.358487495154  	442.04321073835   	1.6241124322112 	19.701724346814  	39.490675322859  
399.29463483600   	61.409924323236  	444.81007899113   	1.5440663539288 	19.700792128681  	39.623844910605  
402.82223053619   	63.409857513800  	447.44808578184   	1.4724778021397 	19.699870864748  	39.744940083763  
406.21989200914   	65.363835295250  	449.97495570207   	1.4080182421655 	19.698960060976  	39.855702299609  
409.49829441825   	67.276348629048  	452.40477439264   	1.3496406959408 	19.698059271295  	39.957520458133  
412.66672982995   	69.151091491775  	454.74893508575   	1.2965049119564 	19.697168090761  	40.051522100856  
415.73336354259   	70.991145396114  	457.01679340438   	1.2479260840641 	19.696286150008  	40.138636440976  
418.70542900950   	72.799113258353  	459.21613281689   	1.2033386923950 	19.695413110715  	40.219639158664  
421.58937893581   	74.577218479940  	461.35350331190   	1.1622703749755 	19.694548661835  	40.295185011093  
424.39100439493   	76.327379579646  	463.43447287321   	1.1243226416605 	19.693692516430  	40.365832073296  
427.11553014733   	78.051267284718  	465.46381755194   	1.0891563708591 	19.692844408997  	40.432060091246  
> post_sol5:=evalf(subs(sol_module_5,cnst1,cnst2d,cnst3d,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_5b:=op(subs(post_sol5, listed_1b)):
> writedata(terminal, listed_data_5b):
1               	26.136682155700  	.64976387779256	.89612689147411	1.1360508101617 	2.417730712913  	18.035452787498  
2               	20.600835102704  	.63633918553089	.88552837643204	1.1412373351547 	4.433866081694  	18.312654440475  
3               	17.884352753223  	.62451824600956	.87641612932629	1.1407720230679 	6.209148061842  	18.478496798746  
4               	16.155918993288  	.61384565570338	.86819152523813	1.1383799092063 	7.811969666495  	18.596967410029  
5               	14.917733757025  	.60406372216995	.8605701782968 	1.1351840175072 	9.281031436211  	18.688638896472  
6               	13.967597739467  	.59500498192672	.85339235774017	1.1316504767951 	10.641483224975  	18.762899371054  
7               	13.204883553739  	.58655124617343	.84655853599911	1.1280045110728 	11.911074759615  	18.824875378123  
8               	12.572790728329  	.57861440578602	.84000211913295	1.1243642319909 	13.103038367384  	18.877696152459  
9               	12.036358606726  	.57112616814562	.83367616181037	1.1207941312710 	14.227630310527  	18.923423047235  
10               	11.572659992229  	.56403204061596	.82754621748386	1.1173296521168 	15.293034354390  	18.963491423082  
11               	11.165910820621  	.55728755457436	.82158619296968	1.1139896211574 	16.305928846695  	18.998943785985  
12               	10.804818768915  	.55085576752207	.81577580159944	1.1107830001990 	17.271861853415  	19.030562772866  
13               	10.481048931260  	.54470554000341	.81009892414546	1.1077127549725 	18.195509932994  	19.058951769082  
14               	10.188288192912  	.53881030576572	.80454251305003	1.1047781652799 	19.080862835108  	19.084586227686  
15               	9.9216495874725 	.53314716877726	.79909583622982	1.1019762491470 	19.931359111532  	19.107847676236  
16               	9.6772791723897 	.52769622424143	.79374994098843	1.0993026624325 	20.749988086986  	19.129047020888  
17               	9.4520884874465 	.5224400375539 	.78849726509206	1.0967522773784 	21.539368109938  	19.148440977808  
18               	9.2435676069734 	.51736323738879	.78333134890864	1.0943195591797 	22.301807663383  	19.166243945937  
19               	9.0496514703237 	.51245219302618	.77824661857953	1.0919988125902 	23.039353824152  	19.182636770221  
20               	8.8686223569588 	.50769475503029	.77323822015298	1.0897843433400 	23.753831208167  	19.197773331333  
MODULE 6
> cnst2e:=subs(sol_module_5,[c[f]=c[np]]);

                  cnst2e := [c[f] = 427.11553014733]

> cnst3e:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^5]);

                                                    -5
              cnst3e := [phi[f] = .63200335507416 10  ]

> ae0e:=subs(sol_module_5,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0e := [f[0] = 1, c[0] = 427.11553014733,

        DPh_bar[0] = 19.692844408997]

> aes_6:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2e,cnst3e,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M6:=subs(ae0e,cnst1,cnst3e,[seq(op(aes_6),j=1..np),ae_setpoints]):
> ini6:=sol_module_5:
> nops(aes_M6);nops(ini6);

                                 141


                                 141

> sol_module_6:=Newton(aes_M6,ini6,tolerance=1e-6):
> listed_data_6a:=op(subs(sol_module_6, listed_1a)):
> writedata(terminal, listed_data_6a):
433.90274742138   	81.768343430712  	463.06791293589   	1.7541437070309 	19.692189807186  	39.842618072692  
439.78451489432   	87.909930916009  	471.32088859874   	1.5225495727048 	19.691547104275  	40.172348553683  
445.14296849904   	93.025880592748  	477.70694491834   	1.3826938260687 	19.690914951390  	40.386030190307  
450.12824081160   	97.544537307993  	483.14928199445   	1.2806262001729 	19.690292470018  	40.547850276538  
454.82203807036   	101.66240717840   	487.99530323293   	1.1998946516700 	19.689678996346  	40.678994575383  
459.27635836915   	105.48752392360   	492.42063412322   	1.1331292547382 	19.689073994758  	40.789439126449  
463.52749432147   	109.08634944116   	496.52849088219   	1.0763221245986 	19.688477016515  	40.884796895343  
467.60236415215   	112.50305172236   	500.38553222031   	1.0270205110375 	19.687887676296  	40.968588624377  
471.52180861403   	115.76868807456   	504.03771508557   	.98359933811985	19.687305637391  	41.043191166651  
475.30248506217   	118.90606057354   	507.51828999692   	.9449188772422 	19.686730601658  	41.110296539361  
478.95803739497   	121.93249177367   	510.85222574247   	.91014496130809	19.686162302357  	41.171158450819  
482.49986015371   	124.86151098622   	514.05883541848   	.87864652180714	19.685600498827  	41.226735346953  
485.93762014994   	127.70392993007   	517.15342263738   	.84993337860397	19.685044972418  	41.277778550502  
489.27962561707   	130.46855691224   	520.14836003473   	.82361651461996	19.684495523296  	41.324889239158  
492.53309537164   	133.16268715899   	523.05382201186   	.79938164290097	19.683951967887  	41.368556754707  
495.70436006577   	135.79244917431   	525.87829799604   	.77697100668496	19.683414136805  	41.409185216888  
498.79901592887   	138.36305545966   	528.62896143450   	.75617048156475	19.682881873134  	41.447112531470  
501.82204441094   	140.87898790869   	531.31194109332   	.73680020719427	19.682355030999  	41.482624291995  
504.77790680570   	143.34413748379   	533.93252446870   	.71870763637955	19.681833474358  	41.515964157997  
507.67062015480   	145.76191120630   	536.49531294845   	.70176228127124	19.681317075975  	41.547341743196  
> post_sol6:=evalf(subs(sol_module_6,cnst1,cnst2e,cnst3e,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_6b:=op(subs(post_sol6, listed_1b)):
> writedata(terminal, listed_data_6b):
1               	22.044623305336  	.38986319782364	.8085568478334 	1.0672159042270 	1.927450767981  	18.894851758535  
2               	17.396767794620  	.38321269714106	.79417762944446	1.0717086951367 	3.600426209753  	18.999479116681  
3               	15.117213579315  	.37717308674091	.7821997234316 	1.0731539723723 	5.119728343470  	19.062417757723  
4               	13.666661734231  	.37157930800881	.77162025161121	1.0733591856474 	6.526878705853  	19.108189651758  
5               	12.627071963383  	.36633816490056	.76197913678453	1.0729368024982 	7.845321350312  	19.144272336496  
6               	11.828772773599  	.36138865322804	.75302344101791	1.0721663006382 	9.090402265585  	19.174015242605  
7               	11.187381819472  	.35668727525478	.74459755794051	1.0711953378494 	10.273063581951  	19.199239687152  
8               	10.655297238001  	.35220124686391	.73659807761251	1.0701090725399 	11.401552351028  	19.221060171279  
9               	10.203236184558  	.34790488227465	.72895228596669	1.0689594964168 	12.482329993160  	19.240215029155  
10               	9.8120045420153 	.34377747404393	.7216067968015 	1.0677795844693 	13.520605596419  	19.257222021094  
11               	9.4683942411908 	.33980195837276	.71452105304715	1.0665907780167 	14.520671667185  	19.272460047217  
12               	9.1629597668865 	.33596402797115	.70766337870423	1.0654072215787 	15.486127294599  	19.286215716187  
13               	8.8887319229629 	.33225151665732	.70100846043688	1.0642382914865 	16.420032958516  	19.298711618507  
14               	8.6404337642494 	.32865395747708	.69453567547114	1.0630901693050 	17.325021687353  	19.310124380287  
15               	8.4139816066091 	.32516225628254	.68822794358927	1.0619668544653 	18.203381171441  	19.320596675659  
16               	8.2061557996934 	.32176844480806	.68207091620511	1.0608708342333 	19.057115878315  	19.330245497403  
17               	8.0143767407853 	.318465490084  	.6760523893572 	1.0598035372024 	19.887994995899  	19.339168017878  
18               	7.8365484092344 	.31524714477118	.67016186964662	1.0587656461306 	20.697590081816  	19.347445845911  
19               	7.6709465249472 	.31210782785697	.66439024721404	1.0577573171684 	21.487305075029  	19.355148185094  
20               	7.5161369725187 	.30904252830004	.658729545245  	1.0567783354980 	22.258400534631  	19.362334220852  
MODULE 7
> cnst2f:=subs(sol_module_6,[c[f]=c[np]]);

                  cnst2f := [c[f] = 507.67062015480]

> cnst3f:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^6]);

                                                    -5
              cnst3f := [phi[f] = .37731103744911 10  ]

> ae0f:=subs(sol_module_6,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0f := [f[0] = 1, c[0] = 507.67062015480,

        DPh_bar[0] = 19.681317075975]

> aes_7:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2f,cnst3f,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M7:=subs(ae0f,cnst1,cnst3f,[seq(op(aes_7),j=1..np),ae_setpoints]):
> ini7:=sol_module_6:
> nops(aes_M7);nops(ini7);

                                 141


                                 141

> sol_module_7:=Newton(aes_M7,ini7,tolerance=1e-6):
> listed_data_7a:=op(subs(sol_module_7, listed_1a)):
> writedata(terminal, listed_data_7a):
514.49588631609   	147.11859393594   	535.02209118974   	1.0094139093003 	19.680926136127  	41.250987509836  
520.61145524857   	154.79238806311   	543.57612947644   	.91260637555084	19.680542175854  	41.391820767122  
526.30158550761   	161.18240805784   	550.52892101287   	.85042328759141	19.680164617801  	41.487505948440  
531.67652767760   	166.84655370580   	556.62361515806   	.80266815266082	19.679793062743  	41.562760898621  
536.79772928427   	172.02828347872   	562.15814482757   	.76340155813998	19.679427194671  	41.625534033089  
541.70544288265   	176.85795924071   	567.28762176363   	.72992473044607	19.679066749425  	41.679614075975  
546.42852959254   	181.41469484083   	572.10500505306   	.70072778303453	19.678711499415  	41.727180238925  
550.98890546445   	185.75074204270   	576.67128507672   	.67485760579055	19.678361244670  	41.769632294037  
555.40388556848   	189.90278072855   	581.02910546387   	.6516636485031 	19.678015807020  	41.807937058395  
559.68755241510   	193.89777111636   	585.20972418258   	.63067702431825	19.677675026030  	41.842797464750  
563.85161585258   	197.75625321120   	589.23690480334   	.6115459847507 	19.677338756016  	41.874744459153  
567.90598435757   	201.49433210737   	593.12924539858   	.59399845625611	19.677006863786  	41.904191069440  
571.85916149403   	205.12493621625   	596.90164946055   	.57781884920457	19.676679226864  	41.931466207967  
575.71853085869   	208.65864923406   	600.56629632653   	.56283296036101	19.676355732075  	41.956836844557  
579.49056686283   	212.10428001687   	604.13330492039   	.54889773715879	19.676036274396  	41.980523128615  
583.18099445309   	215.46926475378   	607.61120172191   	.53589410262385	19.675720756003  	42.002709040319  
586.79491263866   	218.75995813739   	611.00725936269   	.52372178337391	19.675409085473  	42.023550098694  
590.33689171871   	221.98184888901   	614.32774715439   	.5122954921577 	19.675101177108  	42.043179070065  
593.81105098298   	225.13972241585   	617.57812011052   	.50154205236097	19.674796950368  	42.061710280540  
597.22112164229   	228.23778568311   	620.76316403012   	.49139819349427	19.674496329365  	42.079242930846  
> post_sol7:=evalf(subs(sol_module_7,cnst1,cnst2f,cnst3f,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_7b:=op(subs(post_sol7, listed_1b)):
> writedata(terminal, listed_data_7b):
1               	18.566588548033  	.23291664941939	.71020857206375	1.0398957609178 	1.857835610108  	19.222101631899  
2               	14.651758366817  	.22893038228411	.69509287731499	1.0441109660503 	3.537496061466  	19.265721096058  
3               	12.729883358668  	.22521573104647	.68250593660769	1.0460331797821 	5.102707965916  	19.293608577987  
4               	11.505535040614  	.22170967436835	.67134880948019	1.0469215513226 	6.580026104063  	19.314943902442  
5               	10.626975077518  	.21837513428211	.66114193603272	1.0472438949716 	7.985073712832  	19.332426486425  
6               	9.9514586240391 	.21518682107045	.65162853192728	1.0472252572262 	9.328506911467  	19.347282781040  
7               	9.4079987310767 	.21212604020464	.64265276019811	1.0469896318914 	10.618202859107  	19.360198870762  
8               	8.9565506958938 	.20917826034354	.634111696308  	1.0466114278483 	11.860284506917  	19.371607787492  
9               	8.5724800257673 	.20633179175107	.62593308891768	1.0461379917592 	13.059677462420  	19.381805057701  
10               	8.2396386623255 	.20357699279023	.6180638322989 	1.0456007493062 	14.220444342544  	19.391003651340  
11               	7.9469137879289 	.20090575826236	.6104634671376 	1.0450212223164 	15.346000367893  	19.399363308402  
12               	7.6863574947479 	.19831117138677	.60310026992318	1.0444145012304 	16.439260005204  	19.407007565488  
13               	7.4521048791973 	.19578725707886	.59594877451504	1.0437913557266 	17.502740926517  	19.414034295407  
14               	7.2397145425723 	.19332880117426	.58898813334827	1.0431595721451 	18.538640181188  	19.420522568274  
15               	7.0457488820110 	.19093121436259	.58220099490453	1.0425248303712 	19.548891529027  	19.426537302961  
16               	6.8674971718657 	.188590427462  	.57557271151897	1.0418912953289 	20.535209567571  	19.432132527538  
17               	6.7027871636640 	.18630280928507	.56909076583811	1.0412620256286 	21.499124340264  	19.437353729394  
18               	6.5498534771967 	.1840651011793 	.56274434628238	1.0406392617033 	22.442008918590  	19.442239589765  
19               	6.4072435244357 	.18187436412787	.55652402664703	1.0400246325632 	23.365101691789  	19.446823290204  
20               	6.2737488895701 	.17972793547961	.55042152013146	1.0394193064088 	24.269524599182  	19.451133514141  
MODULE 8
> cnst2g:=subs(sol_module_7,[c[f]=c[np]]);

                  cnst2g := [c[f] = 597.22112164229]

> cnst3g:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^7]);

                                                    -5
              cnst3g := [phi[f] = .22525769497571 10  ]

> ae0g:=subs(sol_module_7,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0g := [f[0] = 1, c[0] = 597.22112164229,

        DPh_bar[0] = 19.674496329365]

> aes_8:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2g,cnst3g,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M8:=subs(ae0g,cnst1,cnst3g,[seq(op(aes_8),j=1..np),ae_setpoints]):
> ini8:=sol_module_7:
> nops(aes_M8);nops(ini8);

                                 141


                                 141

> sol_module_8:=Newton(aes_M8,ini8,tolerance=1e-6):
> listed_data_8a:=op(subs(sol_module_8, listed_1a)):
> writedata(terminal, listed_data_8a):
604.80859563593   	229.88910123718   	620.89579721016   	.65644949818847	19.674263130607  	41.919606984957  
611.77151435813   	238.74242634853   	630.18164082674   	.6087940880355 	19.674034526422  	41.987982930741  
618.33961886594   	246.26673538846   	638.00356297097   	.57585531476143	19.673810224143  	42.037247826806  
624.60338502454   	253.04063380913   	645.01615260114   	.54934910222186	19.673590007902  	42.077517207110  
630.61527104202   	259.30963033612   	651.48715233435   	.52685115535837	19.673373699747  	42.112024602364  
636.41087423662   	265.20435656480   	657.55770046836   	.50721571355024	19.673161146676  	42.142360227531  
642.01646195968   	270.80435162522   	663.31347134388   	.48977362965188	19.672952214047  	42.169471274874  
647.45245203255   	276.16255666896   	668.81143006081   	.47408595453088	19.672746781554  	42.193986021316  
652.73528948623   	281.31650047804   	674.09194376409   	.45984301524998	19.672544740505  	42.216350883160  
657.87856684057   	286.29406052394   	679.18499399390   	.44681521171569	19.672345991873  	42.236898568458  
662.89374283751   	291.11670488175   	684.11366583961   	.43482605973293	19.672150444810  	42.255885889128  
667.79062908564   	295.80144477827   	688.89624772744   	.42373613667032	19.671958015508  	42.273516468395  
672.57773363885   	300.36207554539   	693.54756572563   	.41343290237674	19.671768626280  	42.289955220486  
677.26251181908   	304.81000048685   	698.07986955028   	.40382392324166	19.671582204818  	42.305338028481  
681.85155440485   	309.15479795208   	702.50344264304   	.39483218262407	19.671398683575  	42.319778462435  
686.35073208298   	313.40462370146   	706.82703525886   	.38639273041904	19.671217999252  	42.333372590311  
690.76530849019   	317.56650389597   	711.05817999224   	.37845022516714	19.671040092361  	42.346202514068  
695.10003014928   	321.64655327516   	715.20342686049   	.37095709026282	19.670864906848  	42.358339026619  
699.35919905772   	325.65014081979   	719.26852189210   	.36387210409585	19.670692389775  	42.369843646508  
703.54673201303   	329.58201772207   	723.25854514430   	.3571593040946 	19.670522491037  	42.380770201783  
> post_sol8:=evalf(subs(sol_module_8,cnst1,cnst2g,cnst3g,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_8b:=op(subs(post_sol8, listed_1b)):
> writedata(terminal, listed_data_8b):
1               	15.624778386944  	.13881800327346	.61506870251841	1.0265988309199 	2.023760862529  	19.375876995067  
2               	12.321696198243  	.13615878903794	.60024450292044	1.0300931410445 	3.900605390714  	19.397309940951  
3               	10.697297596941  	.13364345145383	.58764563665925	1.0318012035863 	5.675903340838  	19.412057808342  
4               	9.6606194070968 	.13124389307834	.5763032742156 	1.0326811670670 	7.369485582899  	19.423885870528  
5               	8.9153982517049 	.12894260579604	.56580633045421	1.0330976464586 	8.993709154605  	19.433895901856  
6               	8.3413818265515 	.12672708617707	.55593607299836	1.0332282603705 	10.557398840979  	19.442608549608  
7               	7.8787570175000 	.1245877536281 	.54655931980347	1.0331720612260 	12.067316520745  	19.450327836933  
8               	7.4937751680036 	.12251694488681	.537587425057  	1.0329892611592 	13.528870841225  	19.457253165858  
9               	7.1656701239277 	.12050834934311	.52895754975235	1.0327187063759 	14.946515762485  	19.463525188119  
10               	6.8808261667029 	.11855665928075	.52062301524658	1.0323865652831 	16.323997413013  	19.469248168366  
11               	6.6298707310724 	.11665733786692	.51254787492912	1.0320110473683 	17.664517840135  	19.474502235841  
12               	6.4060986906218 	.11480645726725	.50470364483285	1.0316051434724 	18.970849266693  	19.479350680658  
13               	6.2045607831436 	.11300058122305	.4970672257548 	1.0311783025782 	20.245416966753  	19.483844579745  
14               	6.0215078810408 	.1112366772259 	.48961952375587	1.0307375018813 	21.490361251827  	19.488025876072  
15               	5.8540372823854 	.10951204917626	.48234450064001	1.0302879535946 	22.707584999681  	19.491929509654  
16               	5.6998593110205 	.10782428467686	.47522850022513	1.0298335853941 	23.898790854123  	19.495584939971  
17               	5.5571385049210 	.10617121306204	.46825975775489	1.0293773749964 	25.065510847394  	19.499017262740  
18               	5.4243826625730 	.1045508714809 	.46142803457677	1.0289215880294 	26.209130338341  	19.502248047638  
19               	5.3003635212414 	.10296147713864	.45472434075291	1.0284679501767 	27.330907604175  	19.505295978822  
20               	5.1840588911507 	.10140140432509	.44814072078403	1.0280177737090 	28.431990053486  	19.508177352812  
MODULE 9
> cnst2h:=subs(sol_module_8,[c[f]=c[np]]);

                  cnst2h := [c[f] = 703.54673201303]

> cnst3h:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^8]);

                                                    -5
              cnst3h := [phi[f] = .13448063827874 10  ]

> ae0h:=subs(sol_module_8,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0h := [f[0] = 1, c[0] = 703.54673201303,

        DPh_bar[0] = 19.670522491037]

> aes_9:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2h,cnst3h,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M9:=subs(ae0h,cnst1,cnst3h,[seq(op(aes_9),j=1..np),ae_setpoints]):
> ini9:=sol_module_8:
> nops(aes_M9);nops(ini9);

                                 141


                                 141

> sol_module_9:=Newton(aes_M9,ini9,tolerance=1e-6):
> listed_data_9a:=op(subs(sol_module_9, listed_1a)):
> writedata(terminal, listed_data_9a):
712.49722035699   	333.15999657053   	725.91860571068   	.45692353038256	19.670383505625  	42.285733837568  
720.83574776437   	343.38726874076   	736.38918957431   	.43009939429099	19.670247741326  	42.323260444131  
728.76808408702   	352.29869014777   	745.47919583894   	.41033838938393	19.670115028971  	42.351753382454  
736.37748153981   	360.45385265739   	753.78278490087   	.39387161990432	19.669985237004  	42.375759776854  
743.71409145318   	368.08805924483   	761.54556699288   	.37957515922782	19.669858253711  	42.396751473072  
750.81298927526   	375.32739908906   	768.89874276614   	.36689154722243	19.669733981119  	42.415481584834  
757.70067037532   	382.24962695459   	775.92318426418   	.35548075058638	19.669612331731  	42.432415744418  
764.39811707595   	388.90725173888   	782.67351945704   	.3451115773905 	19.669493226456  	42.447872806780  
770.92248825732   	395.33804782647   	789.18906213601   	.33561604525166	19.669376593158  	42.462085516973  
777.28814787208   	401.57047878943   	795.49944538382   	.32686651021527	19.669262365582  	42.475231353926  
783.50733652260   	407.62676324429   	801.62780543807   	.31876280004927	19.669150482528  	42.487450025526  
789.59063342387   	413.52473252946   	807.59271139412   	.31122436069647	19.669040887193  	42.498854199805  
795.54728723835   	419.27901954588   	813.40940075415   	.3041851630267 	19.668933526641  	42.509536485771  
801.38546073153   	424.90185389397   	819.09060630554   	.29759024147228	19.668828351361  	42.519574187130  
807.11241649624   	430.40361339175   	824.64713002597   	.29139325262614	19.668725314900  	42.529032660026  
812.73466104427   	435.79321846275   	830.08825374477   	.28555470045098	19.668624373553  	42.537967756718  
818.25805867192   	441.07842157211   	835.42204070776   	.28004061343153	19.668525486095  	42.546427648745  
823.68792286761   	446.26602443430   	840.65556201682   	.27482153763589	19.668428613549  	42.554454215987  
829.02909069697   	451.36204421123   	845.79506998159   	.26987175638784	19.668333718988  	42.562084124115  
834.28598406072   	456.37184286381   	850.84613310085   	.26516867614005	19.668240767359  	42.569349673374  
> post_sol9:=evalf(subs(sol_module_9,cnst1,cnst2h,cnst3h,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_9b:=op(subs(post_sol9, listed_1b)):
> writedata(terminal, listed_data_9b):
1               	13.141460716600  	.08259145517725	.52645647913498	1.0188371055637 	2.359506998713  	19.462690991816  
2               	10.350691665743  	.08071277985095	.51191974446639	1.0215769568285 	4.580496865709  	19.474748016648  
3               	8.9747283907538 	.07892042064793	.49925332018849	1.0229306306311 	6.699442897624  	19.483597579251  
4               	8.0943941769171 	.07719998833888	.48766181938471	1.0236363873114 	8.733356193751  	19.490952682501  
5               	7.4599874879508 	.07554200300901	.47681078953827	1.0239762507456 	10.693444009727  	19.497324090426  
6               	6.9701190781515 	.07393941973096	.466521011312  	1.0240882266946 	12.588034933322  	19.502965096018  
7               	6.5743396751404 	.07238667884370	.45668196644042	1.0240497528923 	14.423701654654  	19.508030172373  
8               	6.2441731512401 	.07087923053321	.44721902036826	1.0239082252727 	16.205823012046  	19.512624327643  
9               	5.9620906723822 	.06941325873299	.43807848173027	1.0236944364147 	17.938910399752  	19.516823845316  
10               	5.7165943748932 	.06798550492565	.42921989326789	1.0234292746668 	19.626816071522  	19.520686679120  
11               	5.4997661315369 	.06659314814639	.42061167411302	1.0231273761850 	21.272875001811  	19.524258300687  
12               	5.3059387619782 	.06523371929077	.41222847934173	1.0227992547128 	22.880006192054  	19.527575268695  
13               	5.1309271613947 	.06390503766976	.40404951019215	1.0224526106774 	24.450787675917  	19.530667543448  
14               	4.9715594767036 	.06260516268406	.39605738388094	1.0220931704424 	25.987513650425  	19.533560059783  
15               	4.8253786516216 	.06133235616253	.38823734969211	1.0217252431896 	27.492238999923  	19.536273836433  
16               	4.6904454466202 	.06008505245282	.38057672840605	1.0213521011620 	28.966814655210  	19.538826782439  
17               	4.5652043801600 	.05886183429023	.37306450090378	1.0209762456403 	30.412916121603  	19.541234298171  
18               	4.4483900483353 	.05766141306494	.36569099943452	1.0205995968596 	31.832066807289  	19.543509732806  
19               	4.3389601369022 	.05648261249762	.35844767138672	1.0202236320447 	33.225657322138  	19.545664738812  
20               	4.2360465415960 	.05532435499765	.35132689543166	1.0198494872939 	34.594961605216  	19.547709550931  
MODULE 10
> cnst2i:=subs(sol_module_9,[c[f]=c[np]]);

                  cnst2i := [c[f] = 834.28598406072]

> cnst3i:=subs(sol_module_1,cnst1,cnst2,[phi[f]=Q[f]/VT*f[np]^9]);

                                                    -6
              cnst3i := [phi[f] = .80286012310512 10  ]

> ae0i:=subs(sol_module_9,[f[0]=1,c[0]=c[np],DPh_bar[0]=DPh_bar[np]]);

  ae0i := [f[0] = 1, c[0] = 834.28598406072,

        DPh_bar[0] = 19.668240767359]

> aes_10:=subs(ae_DPi,ae_Pe_dbl,ae_kdbl,ae_gamma,ae_Delta,cnst1,cnst2i,cnst3i,[ae1,ae2,ae3,ae4,ae5,ae6,ae7]):
> aes_M10:=subs(ae0i,cnst1,cnst3i,[seq(op(aes_10),j=1..np),ae_setpoints]):
> ini10:=sol_module_9:
> nops(aes_M10);nops(ini10);

                                 141


                                 141

> sol_module_10:=Newton(aes_M10,ini10,tolerance=1e-6):
> listed_data_10a:=op(subs(sol_module_10, listed_1a)):
> writedata(terminal, listed_data_10a):
845.21529979386   	462.95370927805   	856.82661920510   	.33054811860405	19.668158001713  	42.507910445168  
855.49647415014   	475.01038006534   	869.03401778453   	.31393907834337	19.668077576442  	42.530452990730  
865.32976139890   	485.76036371298   	879.90050956490   	.30106552432459	19.667999384483  	42.548312618230  
874.79870812747   	495.73708503029   	889.97660461981   	.29006465742084	19.667923339138  	42.563701036448  
883.95533677210   	505.16568156396   	899.49272528899   	.28036017246589	19.667849365220  	42.577354261340  
892.83693278809   	514.16861461360   	908.57409077728   	.27165125990546	19.667777395862  	42.589665655936  
901.47218886914   	522.82275532690   	917.29932454588   	.26374675257354	19.667707370735  	42.600887545357  
909.88416327492   	531.18095130502   	925.72250430958   	.25651242449954	19.667639234864  	42.611197959114  
918.09193938147   	539.28187278626   	933.88321719645   	.24984820676301	19.667572937778  	42.620730065273  
926.11165243171   	547.15512355669   	941.81177833829   	.24367644705236	19.667508432864  	42.629587489429  
933.95716977526   	554.82415193812   	949.53220400712   	.23793513315464	19.667445676863  	42.637853202200  
941.64056495105   	562.30802950573   	957.06402916561   	.23257365859867	19.667384629455  	42.645595087799  
949.17246124106   	569.62259948828   	964.42348159294   	.22755001734801	19.667325252928  	42.652869638811  
956.56228847400   	576.78125181028   	971.62427475078   	.2228288600477 	19.667267511896  	42.659724518545  
963.81847988847   	583.79546555853   	978.67816304317   	.21838009876737	19.667211373059  	42.666200401608  
970.94862623971   	590.67520039864   	985.59534268271   	.21417787645049	19.667156805002  	42.672332334148  
977.95959858481   	597.42918638584   	992.38474864490   	.21019978762992	19.667103778019  	42.678150763088  
984.85764760255   	604.06514334936   	999.05427956328   	.20642627743079	19.667052263961  	42.683682330465  
991.64848498926   	610.58995018404   	1005.6109713411    	.20284017024997	19.667002236104  	42.688950496865  
998.33735093451   	617.00977769882   	1012.0611334371    	.19942629477669	19.666953669026  	42.693976037826  
> post_sol10:=evalf(subs(sol_module_10,cnst1,cnst2i,cnst3i,[ae_kdbl_a,seq(vz[i]=100*phi[f]/(W[ch]*H[ch])*f[i],i=1..np),seq(R[i]=1-cp[i]/c[f],i=1..np),seq(CP[i]=cstar[i]/c[i],i=1..np),seq(WR[i]=(1-f[i])/1*100,i=1..np),seq(ae_DPi,j=1..np)])):
> listed_data_10b:=op(subs(post_sol10, listed_1b)):
> writedata(terminal, listed_data_10b):
1               	11.046576568135  	.04905545587703	.44508991146573	1.0137377061372 	2.859119515094  	19.517908856893  
2               	8.6852037225627 	.04768416912733	.4306384271814 	1.0158241957079 	5.574576947534  	19.525377995377  
3               	7.5168251778769 	.04636911409666	.41775317697581	1.0168383763231 	8.178682877873  	19.531151418880  
4               	6.7667099447437 	.04510211088261	.40579478200344	1.0173501587866 	10.687635360113  	19.536075767584  
5               	6.2242813452401 	.04387749688529	.39449338570313	1.0175771194206 	13.112647620773  	19.540412923190  
6               	5.8039906133826 	.04269092344176	.383702202318  	1.0176260159177 	15.462330994484  	19.544299550451  
7               	5.4632470333390 	.04153887690780	.37332909180357	1.0175569871951 	17.743643290288  	19.547822483201  
8               	5.1779965005239 	.04041842993858	.36331070945291	1.0174069861571 	19.962381311997  	19.551042678275  
9               	4.9334232681688 	.03932709229060	.35360070396797	1.0172001050631 	22.123476304111  	19.554005571066  
10               	4.7198028142144 	.03826271290585	.34416359137007	1.0169527355210 	24.231187847225  	19.556746411476  
11               	4.5304335517609 	.03722341159585	.33497126580312	1.0166763902413 	26.289239139125  	19.559293343610  
12               	4.3605153177623 	.03620752922132	.32600086750974	1.0163793540642 	28.300915650265  	19.561669330090  
13               	4.2065002528545 	.03521359012546	.31723340632461	1.0160677021033 	30.269139514335  	19.563893426859  
14               	4.0656968793922 	.03424027305755	.30865283268587	1.0157459545063 	32.196527106131  	19.565981666421  
15               	3.9360179775012 	.03328638819105	.30024538741859	1.0154175121818 	34.085434550923  	19.567947691799  
16               	3.8158141278063 	.03235085864307	.29199913257127	1.0150849551121 	35.937994319975  	19.569803224800  
17               	3.7037603839443 	.03143270539790	.28390360404001	1.0147502515247 	37.756145085496  	19.571558420007  
18               	3.5987770463988 	.03053103485556	.27594954860781	1.0144149075709 	39.541656377237  	19.573222137857  
19               	3.4999729829590 	.02964502843916	.2681287210267 	1.0140800763206 	41.296149162298  	19.574802158717  
20               	3.4066042469521 	.02877393384013	.26043372478149	1.0137466383380 	43.021113181538  	19.576305353216  
> 
