Adoucissement - Développements.rtf
5
Adoucissement de l'eau sur résines échangeuses d'ions. Une résine utilisée en adoucissement en c ycle sodium peut être assimilée à une formulation du type : (R - , Na + ) où R - est le "suelette" de la résine et Na + : l!ion moile susceptile d!être éc#an$é% &lle peut réa$ir a'ec le calcium ionisé de l!eau sui'ant une réaction d!éc#an$e symolisée à l!éuilire par : R - , Na + + a + → ← (R - ),a + + %Na + *n 'a s!intéresser à l!éuilire entre le calcium (resp% le sodium) ionisé de l!eau et le calcium (resp% le sodium) capté par la résine% *n supposera dans les uestions sui'antes : - ue la constante d!éuilire + Na a (appelée pour une résine coefficient de sélecti'ité) est é$al à , - ue les seules esp.ces cationiues en présence sont le calcium et le sodium, - ue les acti'ités s!e/priment en moles par l itre d!eau pour les esp.ces dissoutes et e n moles par litre de résine pour les esp.ces captées par la résine% *n notera : a (resp% Na ), la concentration en calcium (resp% sodium) capt é par la résine, et 0a1 (resp% 0Na1), la concentration en calcium (resp% sodium) dans l!eau en contact a'ec la résine% % 2crire la loi d!action de masse relati'e à l!éuilire des esp.ces ioniues en présence% 3a réaction résine 4 sodium 4 calcium : R - , Na + + a + → ← (R - ),a + + %Na + 2criture de la loi d!action de masse : ( ) ( ) ( ) ( ) + a Na a Na Na a ré e eau eau ré e = + + + + sin sin % % soit : + a Na aNa = % % Remarue : les unités utilisées dans cette e/pression sont la mole par litre pour les esp.ces dissoutes ou la mole par litre de résine pour les esp.ces captées% &lle reste 'alale si les unités utilisées sont l!éui'alent puisue pour le calcium il appara5t un facteur au numérateur et au dénominateur % % *n définit la fraction éui'alente 6i d !un ion i dans une solution de concentration totale 7 par : 6 i) 7 i = ( dans lauelle (i) est la concentration de l!ion i dans l!eau% et 6 i la fraction éui'alente d!un ion i dans la résine pour lauelle la concentration totale est 7 par : 6 i) 7 i = ( (toutes concentrations en éui'alent par litre) dans lauelle (i) est la concentration de l!ion i dans la résine% 3a concentration totale dans la résine 7 est dans des conditions données une caractéristiue de la résine appelée capacité totale d!éc#an$e% *n prendra par la suite : 7 éui'alents par litre de résine% 8ontrer apr.s a'oir introduit dans l!écriture de la loi d!action de masse les fractions éui'alentes, ue la fraction éui'alente en calcium dans la résine (pour une résine donnée), est fonction de : - la fraction éui'alente en calcium de l!eau, - de la concentration totale de l!eau% 5 10 15 20 25 30 35 40
-
Upload
abderrahim-nadifi -
Category
Documents
-
view
212 -
download
0
Transcript of Adoucissement - Développements.rtf
Adoucissement de l'eau sur rsines changeuses d'ions
Adoucissement de l'eau sur rsines changeuses d'ions.
Une rsine utilise en adoucissement en cycle sodium peut tre assimile une formulation du type : (R-, Na+) o R- est le "squelette" de la rsine et Na+ : l'ion mobile susceptible d'tre chang.Elle peut ragir avec le calcium ionis de l'eau suivant une raction d'change symbolise l'quilibre par : 2 R-, 2 Na+ + Ca2+ (R-)2,Ca2+ + 2.Na+On va s'intresser l'quilibre entre le calcium (resp. le sodium) ionis de l'eau et le calcium (resp. le sodium) capt par la rsine.
On supposera dans les questions suivantes : - que la constante d'quilibre K= (appele pour une rsine coefficient de slectivit) est gal 1,- que les seules espces cationiques en prsence sont le calcium et le sodium,- que les activits s'expriment en moles par litre d'eau pour les espces dissoutes et en moles par litre de rsine pour les espces captes par la rsine.
On notera : (resp. ), la concentration en calcium (resp. sodium) capt par la rsine, et [Ca] (resp. [Na]), la concentration en calcium (resp. sodium) dans l'eau en contact avec la rsine.
1.1 crire la loi d'action de masse relative l'quilibre des espces ioniques en prsence.La raction rsine / sodium / calcium :2 R-, 2 Na+ + Ca2+ (R-)2,Ca2+ + 2.Na+criture de la loi d'action de masse :
soit :
Remarque : les units utilises dans cette expression sont la mole par litre pour les espces dissoutes ou la mole par litre de rsine pour les espces captes. Elle reste valable si les units utilises sont l'quivalent puisque pour le calcium il apparat un facteur 2 au numrateur et au dnominateur. 1.2 On dfinit la fraction quivalente Xi d'un ion i dans une solution de concentration totale T par : dans laquelle (i) est la concentration de l'ion i dans l'eau.et la fraction quivalente d'un ion i dans la rsine pour laquelle la concentration totale est par : (toutes concentrations en quivalent par litre) dans laquelle est la concentration de l'ion i dans la rsine.La concentration totale dans la rsine est dans des conditions donnes une caractristique de la rsine appele capacit totale d'change. On prendra par la suite : = 2 quivalents par litre de rsine.Montrer aprs avoir introduit dans l'criture de la loi d'action de masse les fractions quivalentes, que la fraction quivalente en calcium dans la rsine (pour une rsine donne), est fonction de :- la fraction quivalente en calcium de l'eau,- de la concentration totale de l'eau.
Par dfinition des fractions quivalentes : et avec toutes concentrations en quivalents par litre.On a bien sr : .Dans la rsine : et de mme : .T=Ca+Na et on en tire : et
Reports dans l'expression dtermine en 1.1, on obtient :
1.3) Tracer la courbe d'quilibre XCa=f() pour une eau de concentration totale : T=2 eq.l-1.Pour une eau T=5 meq.l-1 dterminer la fraction quivalente pour XCa=2.10-2.Pour une valeur de XCa donne le terme de droite de l'quation prcdente est une constante : =p.L'quation se rduit soit : ou encore : quation du second degr dont le discriminant est : et dont la racine infrieure 1 est :
Exemple : XCa=0,02 ; T=5.10-3 meq.l-1 et =2 eq.l-1 et
Pour ce qui concerne la courbe d'quilibre pour une eau 2 quivalents par litre, le jeu des valeurs numriques rsume la courbe un segment de droite de pente 1.
1.4) Une eau initialement THCa=25F est mise en contact avec la rsine dont la fraction quivalente en sodium est gale 1.Quelle en est la consquence pour l'eau (la dcrire qualitativement) ?Si l'on note : - Ca : le nombre de moles de calcium par litre d'eau initialement dissous dans l'eau (identifiable T),- Na : le nombre de moles de sodium par litre de rsine initialement capt par la rsine (identifiable ),- Vr : le volume de rsine,- Ve : le volume d'eau mis en contact avec la rsine,- a : le nombre de moles de calcium capts par la rsine l'quilibre,montrer que a est solution de l'quation suivante :
Application numrique : avec : Ca=2,5 mmol.l-1 ; Na=2 mol.l-1 (=) ; Ve=2 litres ; Vr=10-2 litre, dterminer la position du point d'quilibre sur les courbes traces en 1.3, ainsi que la concentration en calcium dissous au sein de l'eau en F.Si l'on accepte une eau adoucie 0,5F de calcium quel sera le volume d'eau que l'on pourra mettre en contact avec la rsine ?
Si une eau initialement THCa=25F est mise en contact avec la rsine dont la fraction quivalente en sodium est gale 1, celle-ci va absorber du calcium, relarguer du sodium jusqu' arriver un tat d'quilibre que l'on va quantifier.
Raction2R-, 2.Na+Ca2+
(R-)2, Ca2+2.Na+1 A la mise en contact en molVr.NaVe.Ca
002 A l'quilibre en mol.,Vr.Na-2.a,Ve.Ca-a
a2a3 A l'quilibre exprim en activit,
Graph1
0
0.1460068354
0.2347265809
0.2972258839
0.3828212828
0.4408260661
0.4838620502
0.5176126671
0.5450975229
0.5681006639
0.5877577905
0.6048331709
0.6198637588
0.6332400237
0.6452540335
0.656129455
0.6660410234
0.6751276058
0.6835012181
0.6912534026
0.6984598382
0.7051837349
0.7114783767
0.7173890548
0.722954557
0.72820833
0.7331793966
0.7378930855
0.7423716195
0.7466345917
0.7506993557
0.7545813467
0.7582943472
0.7618507101
0.7652615446
0.7685368741
0.7831710614
0.7954845072
0.8060503449
0.8152596715
0.823390037
0.8306447778
0.8371768395
0.8431038474
0.8485179952
0.8534927383
0.858087446
0.8623507117
0.8663227565
0.870037207
0.8735224299
0.8768025508
0.8798982404
0.8828273289
0.8856052922
0.8882456388
0.8907602225
0.8931594953
0.8954527151
0.8976481165
0.8997530528
0.9017741143
0.9037172278
0.9055877408
0.9073904926
0.9091298753
0.910809886
0.9124341713
0.9140060665
0.9155286291
0.9170046679
0.9184367688
0.919827317
0.9211785171
0.92249241
0.9237708886
0.9250157115
0.9262285147
0.927410823
0.9285640591
0.9296895526
0.9307885479
0.9318622105
0.9329116343
0.9339378464
0.9349418126
0.9359244423
0.9368865923
0.9378290709
0.9387526414
0.9396580253
0.9405459051
0.9414169272
0.9422717041
0.9431108169
0.9439348173
0.9447442294
0.9455395514
0.9463212578
0.9470897999
0.9478456081
0.9485890927
0.9493206453
0.9500406398
0.9507494332
0.9514473671
0.9521347682
0.9528119492
0.9534792094
0.9541368358
0.9547851036
0.9554242766
0.9560546081
0.9566763413
0.9572897099
0.9578949384
0.9584922428
0.9590818309
0.9596639026
0.9602386505
0.96080626
0.96136691
0.9619207727
0.9624680144
0.9630087955
0.9635432708
0.9640715898
0.9645938968
0.9651103315
0.9656210287
0.9661261188
0.9666257281
0.9671199785
0.9676089883
0.9680928718
0.96857174
0.9690457001
0.9695148563
0.9699793094
0.9704391573
0.9708944947
0.9713454139
0.9717920042
0.9722343522
0.9726725424
0.9731066563
0.9735367737
0.9739629717
0.9743853254
0.9748039078
0.9752187899
0.9756300408
0.9760377278
0.9764419162
0.9768426696
0.9772400501
0.977634118
0.9780249321
0.9784125497
0.9787970266
0.9791784173
0.9795567747
0.9799321505
0.9803045953
0.9806741581
0.9810408871
0.9814048289
0.9817660294
0.9821245331
0.9824803835
0.9828336233
0.9831842939
0.983532436
0.9838780891
0.984221292
0.9845620826
0.9849004979
0.9852365741
0.9855703464
0.9859018496
0.9862311174
0.9865581829
0.9868830786
0.9872058361
0.9875264865
0.98784506
0.9881615863
0.9884760947
0.9887886135
0.9890991707
0.9894077936
0.989714509
0.990019343
0.9903223214
0.9906234693
0.9909228115
0.9912203722
0.9915161749
0.9918102431
0.9921025996
0.9923932665
0.992682266
0.9929696196
0.9932553482
0.9935394728
0.9938220134
0.9941029903
0.9943824228
0.9946603302
0.9949367313
0.9952116448
0.9954850888
0.9957570811
0.9960276392
0.9962967805
0.9965645218
0.9968308797
0.9970958706
0.9973595106
0.9976218153
0.9978828004
0.9981424809
0.998400872
0.9986579883
0.9989138444
0.9991684543
0.9994218322
0.9996739917
0.9999249465
Feuil1
320
111
0.1250.251
1.5-440-2
-1.756-613
0.25-120.50.0
RESINE1
T10.005T224.88E-031.97E+004.98E-01
xay
0.0000.000.000.000.0000
0.0010.200.150.000.0010.0000007498a0.00000.00050.00100.00150.00200.00250.00300.00350.00400.00410.00420.00430.00440.00450.00460.00470.00480.00490.00500.00510.00520.00530.00540.00550.00560.00570.00580.00590.00600.00610.00620.00630.00640.00650.00660.00710.00760.00810.00860.00910.00960.01010.01060.01110.01160.01210.01260.01310.01360.01410.01460.01510.01560.01610.01660.01710.01760.01810.01860.01910.01960.02010.02060.0211
0.0010.400.230.000.0010.000002998Equation 3.2-0.01-0.0081224875-0.0064799-0.0050571625-0.0038392-0.0028109375-0.0019573-0.0012632125-0.0007136-0.0006196879-0.0005308312-0.0004469093-0.0003678016-0.0002933875-0.0002235464-0.0001581577-0.0000971008-0.00004025511.25E-056.13E-051.06E-041.47E-041.85E-042.19E-042.50E-042.77E-040.00030175120.00032311790.00034160.00035731810.00037039280.00038094470.00038909440.00039496250.00039866960.00038901110.00034341760.00027696410.00020472560.00014177710.00010319360.00010405010.00015942160.00028438310.00049400960.00080337610.00122755760.00178162910.00248066560.00333974210.00437393360.00559831510.00702796160.00867794810.01056334960.01269924110.01510069760.01778279410.02076060560.02404920710.02766367360.03161908010.03593050160.0406130131
0.0020.600.300.000.0020.0000067433
0.0031.010.380.000.0030.0000187188
0.0041.410.440.000.0040.0000366643
0.0051.820.480.000.0050.0000605678
0.0062.220.520.010.0060.0000904173
0.0072.630.550.010.0070.0001262008
0.0083.050.570.010.0080.0001679063
0.0093.460.590.010.0090.0002155218
0.00953.870.600.010.0100.0002690353
0.0114.290.620.010.0110.0003284348
0.0124.710.630.010.0120.0003937083
0.0135.130.650.010.0130.0004648438
0.0145.550.660.010.0140.0005418293
0.0155.970.670.010.0150.0006246528
0.0166.400.680.020.0160.0007133023
0.0176.820.680.020.0170.0008077658Txy
0.0187.250.690.020.0180.00090803130.54.7500003.6
0.0197.680.700.020.0190.00101408680.252.3750006.7
0.0208.110.710.020.0200.00112592030.10.95000014.2
0.0218.550.710.020.0210.00124351980.050.47500023.0
0.0228.980.720.020.0220.00136687330.010.09500049.5
0.0239.420.720.020.0230.00149596880.0050.04750060.5
0.0249.860.730.020.0240.00163079430.0010.009579.7
0.02510.300.730.030.0250.0017713378
0.02610.740.740.030.0260.001917587310.10000.250.170.1
0.02711.180.740.030.0270.00206953080.90.10000.270.180.09
0.02811.630.750.030.0280.00222715630.80.10000.310.200.08
0.02912.080.750.030.0290.00239045180.70.10000.350.220.07
0.03012.530.750.030.0300.00255940530.60.10000.410.240.06
0.03112.980.760.030.0310.00273400480.50.10000.490.270.05
0.03213.430.760.030.0320.00291423830.40.10000.620.300.04
0.03313.890.770.030.0330.00310009380.30.10000.820.350.03
0.03414.350.770.040.0340.00329155930.20.10001.230.420.02
0.03916.660.780.040.0390.00433261680.150.10001.650.470.015
0.04419.020.800.050.0440.00551212430.10.10002.470.530.01
0.04921.430.810.050.0490.00682858180.050.10004.940.640.005
0.05423.890.820.060.0540.00828048930.040.10006.170.670.004
0.05926.400.820.070.0590.00986634680.030.10008.230.710.003
0.06428.960.830.070.0640.01158465430.020.100012.350.750.002
0.06931.580.840.080.0690.01343391180.010.100024.690.820.001
0.07434.250.840.090.0740.01541261930.0090.100027.430.830.0009
0.07936.980.850.090.0790.01751927680.0080.100030.860.840.0008
0.08439.760.850.100.0840.01975238430.0070.100035.270.850.0007
0.08942.610.860.110.0890.02211044180.0060.100041.150.860.0006
0.09445.510.860.110.0940.02459194930.0050.100049.380.870.0005
0.09948.480.870.120.0990.02719540680.0040.100061.730.880.0004
0.10451.510.870.130.1040.02991931430.0030.100082.300.900.0003
0.10954.610.870.140.1090.03276217180.0020.1000123.460.910.0002
0.11457.770.880.140.1140.03572247930.0010.1000246.910.940.0001
0.11961.000.880.150.1190.03879873680.00050.1000493.830.960.00005
0.12464.300.880.160.1240.04198944430.00040.1000617.280.960.00004
0.12967.680.890.170.1290.04529310180.00030.1000823.050.970.00003
0.13471.120.890.180.1340.04870820930.00020.10001234.570.970.00002
0.13974.640.890.190.1390.05223326680.00010.10002469.140.980.00001
0.14478.250.890.200.1440.0558667743
0.14981.930.900.200.1490.0596072318
0.15485.690.900.210.1540.0634531393
0.15989.530.900.220.1590.0674029968
0.16493.460.900.230.1640.0714553043
0.16997.480.900.240.1690.0756085618
0.174101.600.910.250.1740.0798612693
0.179105.800.910.260.1790.0842119268
0.184110.100.910.280.1840.0886590343
0.189114.500.910.290.1890.0932010918
0.194119.000.910.300.1940.0978365993
0.199123.600.910.310.1990.1025640568
0.204128.310.920.320.2040.1073819643
0.209133.130.920.330.2090.1122888218
0.214138.060.920.350.2140.1172831293
0.219143.100.920.360.2190.1223633868
0.224148.270.920.370.2240.1275280943
0.229153.560.920.380.2290.1327757518
0.234158.970.920.400.2340.1381048593
0.239164.520.930.410.2390.1435139168
0.244170.190.930.430.2440.1490014243
0.249176.010.930.440.2490.1545658818
0.254181.960.930.450.2540.1602057893
0.259188.060.930.470.2590.1659196468
0.264194.310.930.490.2640.1717059543
0.269200.710.930.500.2690.1775632118
0.274207.270.930.520.2740.1834899193
0.279214.000.930.530.2790.1894845768
0.284220.890.930.550.2840.1955456843
0.289227.960.940.570.2890.2016717418
0.294235.200.940.590.2940.2078612493
0.299242.630.940.610.2990.2141127068
0.304250.250.940.630.3040.2204246143
0.309258.070.940.650.3090.2267954718
0.314266.080.940.670.3140.2332237793
0.319274.310.940.690.3190.2397080368
0.324282.750.940.710.3240.2462467443
0.329291.410.940.730.3290.2528384018
0.334300.300.940.750.3340.2594815093
0.339309.430.940.770.3390.2661745668
0.344318.800.950.800.3440.2729160743
0.349328.420.950.820.3490.2797045318
0.354338.310.950.850.3540.2865384393
0.359348.460.950.870.3590.2934162968
0.364358.900.950.900.3640.3003366043
0.369369.620.950.920.3690.3072978618
0.374380.630.950.950.3740.3142985693
0.379391.960.950.980.3790.3213372268
0.384403.610.951.010.3840.3284123343
0.389415.580.951.040.3890.3355223918
0.394427.900.951.070.3940.3426658993
0.399440.570.951.100.3990.3498413568
0.404453.610.951.130.4040.3570472643
0.409467.030.951.170.4090.3642821218
0.414480.840.961.200.4140.3715444293
0.419495.060.961.240.4190.3788326868
0.424509.700.961.270.4240.3861453943
0.429524.780.961.310.4290.3934810518
0.434540.320.961.350.4340.4008381593
0.439556.330.961.390.4390.4082152168
0.444572.830.961.430.4440.4156107243
0.449589.840.961.470.4490.4230231818
0.454607.380.961.520.4540.4304510893
0.459625.460.961.560.4590.4378929468
0.464644.130.961.610.4640.4453472543
0.469663.380.961.660.4690.4528125118
0.474683.260.961.710.4740.4602872193
0.479703.770.961.760.4790.4677698768
0.484724.960.961.810.4840.4752589843
0.489746.850.961.870.4890.4827530418
0.494769.460.961.920.4940.4902505493
0.499792.840.971.980.4990.4977500068
0.504817.000.972.040.5040.5052499143
0.509841.980.972.100.5090.5127487718
0.514867.830.972.170.5140.5202450793
0.519894.570.972.240.5190.5277373368
0.524922.250.972.310.5240.5352240443
0.529950.910.972.380.5290.5427037018
0.534980.600.972.450.5340.5501748093
0.5391011.350.972.530.5390.5576358668
0.5441043.220.972.610.5440.5650853743
0.5491076.270.972.690.5490.5725218318
0.5541110.540.972.780.5540.5799437393
0.5591146.100.972.870.5590.5873495968
0.5641183.000.972.960.5640.5947379043
0.5691221.320.973.050.5690.6021071618
0.5741261.120.973.150.5740.6094558693
0.5791302.470.973.260.5790.6167825268
0.5841345.460.973.360.5840.6240856343
0.5891390.170.973.480.5890.6313636918
0.5941436.680.973.590.5940.6386151993
0.5991485.090.973.710.5990.6458386568
0.6041535.500.973.840.6040.6530325643
0.6091588.020.983.970.6090.6601954218
0.6141642.770.984.110.6140.6673257293
0.6191699.850.984.250.6190.6744219868
0.6241759.410.984.400.6240.6814826943
0.6291821.580.984.550.6290.6885063518
0.6341886.510.984.720.6340.6954914593
0.6391954.360.984.890.6390.7024365168
0.6442025.300.985.060.6440.7093400243
0.6492099.520.985.250.6490.7162004818
0.6542177.200.985.440.6540.7230163893
0.6592258.570.985.650.6590.7297862468
0.6642343.860.985.860.6640.7365085543
0.6692433.290.986.080.6690.7431818118
0.6742527.150.986.320.6740.7498045193
0.6792625.720.986.560.6790.7563751768
0.6842729.300.986.820.6840.7628922843
0.6892838.230.987.100.6890.7693543418
0.6942952.880.987.380.6940.7757598493
0.6993073.630.987.680.6990.7821073068
0.7043200.920.988.000.7040.7883952143
0.7093335.210.988.340.7090.7946220718
0.7143477.000.988.690.7140.8007863793
0.7193626.850.989.070.7190.8068866368
0.7243785.370.989.460.7240.8129213443
0.7293953.210.989.880.7290.8188890018
0.7344131.100.9810.330.7340.8247881093
0.7394319.830.9810.800.7390.8306171668
0.7444520.290.9911.300.7440.8363746743
0.7494733.430.9911.830.7490.8420591318
0.7544960.320.9912.400.7540.8476690393
0.7595202.130.9913.010.7590.8532028968
0.7645460.180.9913.650.7640.8586592043
0.7695735.900.9914.340.7690.8640364618
0.7746030.920.9915.080.7740.8693331693
0.7796347.040.9915.870.7790.8745478268
0.7846686.260.9916.720.7840.8796789343
0.7897050.840.9917.630.7890.8847249918
0.7947443.320.9918.610.7940.8896844993
0.7997866.560.9919.670.7990.8945559568
0.8048323.780.9920.810.8040.8993378643
0.8098818.660.9922.050.8090.9040287218
0.8149355.350.9923.390.8140.9086270293
0.8199938.600.9924.850.8190.9131312868
0.82410573.880.9926.430.8240.9175399943
0.82911267.410.9928.170.8290.9218516518
0.83412026.440.9930.070.8340.9260647593
0.83912859.320.9932.150.8390.9301778168
0.84413775.790.9934.440.8440.9341893243
0.84914787.220.9936.970.8490.9380977818
0.85415907.000.9939.770.8540.9419016893
0.85917150.920.9942.880.8590.9455995468
0.86418537.750.9946.340.8640.9491898543
0.86920089.920.9950.220.8690.9526711118
0.87421834.430.9954.590.8740.9560418193
0.87923803.960.9959.510.8790.9593004768
0.88426038.420.9965.100.8840.9624455843
0.88928586.940.9971.470.8890.9654756418
0.89431510.500.9978.780.8940.9683891493
0.89934885.580.9987.210.8990.9711846068
0.90438809.100.9997.020.9040.9738605143
0.90943405.301.00108.510.9090.9764153718
0.91448835.581.00122.090.9140.9788476793
0.91955312.581.00138.280.9190.9811559368
0.92463121.021.00157.800.9240.9833386443
0.92972649.031.00181.620.9290.9853943018
0.93484436.661.00211.090.9340.9873214093
0.93999253.091.00248.130.9390.9891184668
0.944118223.821.00295.560.9440.9907839743
0.949143048.361.00357.620.9490.9923164318
0.954176390.331.00440.980.9540.9937143393
0.959222615.761.00556.540.9590.9949761968
0.964289285.041.00723.210.9640.9961005043
0.969390425.801.00976.060.9690.9970857618
0.974554503.381.001386.260.9740.9979304693
0.979846727.961.002116.820.9790.9986331268
0.9841444995.411.003612.490.9840.9991922343
0.9892989792.061.007474.480.9890.9996062918
0.9949405917.161.0023514.790.9940.9998737993
0.999177511111.131.00443777.780.9990.9999932568
&CEQUILIBRE : RESINE Na/Ca
RESINE1
&CEQUILIBRE : RESINE Na / Ca
&CCapacit de la rsine : 2 eq/lr
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Graph1
0
0.1460068354
0.2347265809
0.2972258839
0.3828212828
0.4408260661
0.4838620502
0.5176126671
0.5450975229
0.5681006639
0.5877577905
0.6048331709
0.6198637588
0.6332400237
0.6452540335
0.656129455
0.6660410234
0.6751276058
0.6835012181
0.6912534026
0.6984598382
0.7051837349
0.7114783767
0.7173890548
0.722954557
0.72820833
0.7331793966
0.7378930855
0.7423716195
0.7466345917
0.7506993557
0.7545813467
0.7582943472
0.7618507101
0.7652615446
0.7685368741
0.7831710614
0.7954845072
0.8060503449
0.8152596715
0.823390037
0.8306447778
0.8371768395
0.8431038474
0.8485179952
0.8534927383
0.858087446
0.8623507117
0.8663227565
0.870037207
0.8735224299
0.8768025508
0.8798982404
0.8828273289
0.8856052922
0.8882456388
0.8907602225
0.8931594953
0.8954527151
0.8976481165
0.8997530528
0.9017741143
0.9037172278
0.9055877408
0.9073904926
0.9091298753
0.910809886
0.9124341713
0.9140060665
0.9155286291
0.9170046679
0.9184367688
0.919827317
0.9211785171
0.92249241
0.9237708886
0.9250157115
0.9262285147
0.927410823
0.9285640591
0.9296895526
0.9307885479
0.9318622105
0.9329116343
0.9339378464
0.9349418126
0.9359244423
0.9368865923
0.9378290709
0.9387526414
0.9396580253
0.9405459051
0.9414169272
0.9422717041
0.9431108169
0.9439348173
0.9447442294
0.9455395514
0.9463212578
0.9470897999
0.9478456081
0.9485890927
0.9493206453
0.9500406398
0.9507494332
0.9514473671
0.9521347682
0.9528119492
0.9534792094
0.9541368358
0.9547851036
0.9554242766
0.9560546081
0.9566763413
0.9572897099
0.9578949384
0.9584922428
0.9590818309
0.9596639026
0.9602386505
0.96080626
0.96136691
0.9619207727
0.9624680144
0.9630087955
0.9635432708
0.9640715898
0.9645938968
0.9651103315
0.9656210287
0.9661261188
0.9666257281
0.9671199785
0.9676089883
0.9680928718
0.96857174
0.9690457001
0.9695148563
0.9699793094
0.9704391573
0.9708944947
0.9713454139
0.9717920042
0.9722343522
0.9726725424
0.9731066563
0.9735367737
0.9739629717
0.9743853254
0.9748039078
0.9752187899
0.9756300408
0.9760377278
0.9764419162
0.9768426696
0.9772400501
0.977634118
0.9780249321
0.9784125497
0.9787970266
0.9791784173
0.9795567747
0.9799321505
0.9803045953
0.9806741581
0.9810408871
0.9814048289
0.9817660294
0.9821245331
0.9824803835
0.9828336233
0.9831842939
0.983532436
0.9838780891
0.984221292
0.9845620826
0.9849004979
0.9852365741
0.9855703464
0.9859018496
0.9862311174
0.9865581829
0.9868830786
0.9872058361
0.9875264865
0.98784506
0.9881615863
0.9884760947
0.9887886135
0.9890991707
0.9894077936
0.989714509
0.990019343
0.9903223214
0.9906234693
0.9909228115
0.9912203722
0.9915161749
0.9918102431
0.9921025996
0.9923932665
0.992682266
0.9929696196
0.9932553482
0.9935394728
0.9938220134
0.9941029903
0.9943824228
0.9946603302
0.9949367313
0.9952116448
0.9954850888
0.9957570811
0.9960276392
0.9962967805
0.9965645218
0.9968308797
0.9970958706
0.9973595106
0.9976218153
0.9978828004
0.9981424809
0.998400872
0.9986579883
0.9989138444
0.9991684543
0.9994218322
0.9996739917
0.9999249465
Feuil1
320
111
0.1250.251
1.5-440-2
-1.756-613
0.25-120.50.0
RESINE1
T10.005T224.88E-031.97E+004.98E-01
xay
0.0000.000.000.000.0000
0.0010.200.150.000.0010.0000007498a0.00000.00050.00100.00150.00200.00250.00300.00350.00400.00410.00420.00430.00440.00450.00460.00470.00480.00490.00500.00510.00520.00530.00540.00550.00560.00570.00580.00590.00600.00610.00620.00630.00640.00650.00660.00710.00760.00810.00860.00910.00960.01010.01060.01110.01160.01210.01260.01310.01360.01410.01460.01510.01560.01610.01660.01710.01760.01810.01860.01910.01960.02010.02060.0211
0.0010.400.230.000.0010.000002998Equation 3.2-0.01-0.0081224875-0.0064799-0.0050571625-0.0038392-0.0028109375-0.0019573-0.0012632125-0.0007136-0.0006196879-0.0005308312-0.0004469093-0.0003678016-0.0002933875-0.0002235464-0.0001581577-0.0000971008-0.00004025511.25E-056.13E-051.06E-041.47E-041.85E-042.19E-042.50E-042.77E-040.00030175120.00032311790.00034160.00035731810.00037039280.00038094470.00038909440.00039496250.00039866960.00038901110.00034341760.00027696410.00020472560.00014177710.00010319360.00010405010.00015942160.00028438310.00049400960.00080337610.00122755760.00178162910.00248066560.00333974210.00437393360.00559831510.00702796160.00867794810.01056334960.01269924110.01510069760.01778279410.02076060560.02404920710.02766367360.03161908010.03593050160.0406130131
0.0020.600.300.000.0020.0000067433
0.0031.010.380.000.0030.0000187188
0.0041.410.440.000.0040.0000366643
0.0051.820.480.000.0050.0000605678
0.0062.220.520.010.0060.0000904173
0.0072.630.550.010.0070.0001262008
0.0083.050.570.010.0080.0001679063
0.0093.460.590.010.0090.0002155218
0.00953.870.600.010.0100.0002690353
0.0114.290.620.010.0110.0003284348
0.0124.710.630.010.0120.0003937083
0.0135.130.650.010.0130.0004648438
0.0145.550.660.010.0140.0005418293
0.0155.970.670.010.0150.0006246528
0.0166.400.680.020.0160.0007133023
0.0176.820.680.020.0170.0008077658Txy
0.0187.250.690.020.0180.00090803130.54.7500003.6
0.0197.680.700.020.0190.00101408680.252.3750006.7
0.0208.110.710.020.0200.00112592030.10.95000014.2
0.0218.550.710.020.0210.00124351980.050.47500023.0
0.0228.980.720.020.0220.00136687330.010.09500049.5
0.0239.420.720.020.0230.00149596880.0050.04750060.5
0.0249.860.730.020.0240.00163079430.0010.009579.7
0.02510.300.730.030.0250.0017713378
0.02610.740.740.030.0260.001917587310.10000.250.170.1
0.02711.180.740.030.0270.00206953080.90.10000.270.180.09
0.02811.630.750.030.0280.00222715630.80.10000.310.200.08
0.02912.080.750.030.0290.00239045180.70.10000.350.220.07
0.03012.530.750.030.0300.00255940530.60.10000.410.240.06
0.03112.980.760.030.0310.00273400480.50.10000.490.270.05
0.03213.430.760.030.0320.00291423830.40.10000.620.300.04
0.03313.890.770.030.0330.00310009380.30.10000.820.350.03
0.03414.350.770.040.0340.00329155930.20.10001.230.420.02
0.03916.660.780.040.0390.00433261680.150.10001.650.470.015
0.04419.020.800.050.0440.00551212430.10.10002.470.530.01
0.04921.430.810.050.0490.00682858180.050.10004.940.640.005
0.05423.890.820.060.0540.00828048930.040.10006.170.670.004
0.05926.400.820.070.0590.00986634680.030.10008.230.710.003
0.06428.960.830.070.0640.01158465430.020.100012.350.750.002
0.06931.580.840.080.0690.01343391180.010.100024.690.820.001
0.07434.250.840.090.0740.01541261930.0090.100027.430.830.0009
0.07936.980.850.090.0790.01751927680.0080.100030.860.840.0008
0.08439.760.850.100.0840.01975238430.0070.100035.270.850.0007
0.08942.610.860.110.0890.02211044180.0060.100041.150.860.0006
0.09445.510.860.110.0940.02459194930.0050.100049.380.870.0005
0.09948.480.870.120.0990.02719540680.0040.100061.730.880.0004
0.10451.510.870.130.1040.02991931430.0030.100082.300.900.0003
0.10954.610.870.140.1090.03276217180.0020.1000123.460.910.0002
0.11457.770.880.140.1140.03572247930.0010.1000246.910.940.0001
0.11961.000.880.150.1190.03879873680.00050.1000493.830.960.00005
0.12464.300.880.160.1240.04198944430.00040.1000617.280.960.00004
0.12967.680.890.170.1290.04529310180.00030.1000823.050.970.00003
0.13471.120.890.180.1340.04870820930.00020.10001234.570.970.00002
0.13974.640.890.190.1390.05223326680.00010.10002469.140.980.00001
0.14478.250.890.200.1440.0558667743
0.14981.930.900.200.1490.0596072318
0.15485.690.900.210.1540.0634531393
0.15989.530.900.220.1590.0674029968
0.16493.460.900.230.1640.0714553043
0.16997.480.900.240.1690.0756085618
0.174101.600.910.250.1740.0798612693
0.179105.800.910.260.1790.0842119268
0.184110.100.910.280.1840.0886590343
0.189114.500.910.290.1890.0932010918
0.194119.000.910.300.1940.0978365993
0.199123.600.910.310.1990.1025640568
0.204128.310.920.320.2040.1073819643
0.209133.130.920.330.2090.1122888218
0.214138.060.920.350.2140.1172831293
0.219143.100.920.360.2190.1223633868
0.224148.270.920.370.2240.1275280943
0.229153.560.920.380.2290.1327757518
0.234158.970.920.400.2340.1381048593
0.239164.520.930.410.2390.1435139168
0.244170.190.930.430.2440.1490014243
0.249176.010.930.440.2490.1545658818
0.254181.960.930.450.2540.1602057893
0.259188.060.930.470.2590.1659196468
0.264194.310.930.490.2640.1717059543
0.269200.710.930.500.2690.1775632118
0.274207.270.930.520.2740.1834899193
0.279214.000.930.530.2790.1894845768
0.284220.890.930.550.2840.1955456843
0.289227.960.940.570.2890.2016717418
0.294235.200.940.590.2940.2078612493
0.299242.630.940.610.2990.2141127068
0.304250.250.940.630.3040.2204246143
0.309258.070.940.650.3090.2267954718
0.314266.080.940.670.3140.2332237793
0.319274.310.940.690.3190.2397080368
0.324282.750.940.710.3240.2462467443
0.329291.410.940.730.3290.2528384018
0.334300.300.940.750.3340.2594815093
0.339309.430.940.770.3390.2661745668
0.344318.800.950.800.3440.2729160743
0.349328.420.950.820.3490.2797045318
0.354338.310.950.850.3540.2865384393
0.359348.460.950.870.3590.2934162968
0.364358.900.950.900.3640.3003366043
0.369369.620.950.920.3690.3072978618
0.374380.630.950.950.3740.3142985693
0.379391.960.950.980.3790.3213372268
0.384403.610.951.010.3840.3284123343
0.389415.580.951.040.3890.3355223918
0.394427.900.951.070.3940.3426658993
0.399440.570.951.100.3990.3498413568
0.404453.610.951.130.4040.3570472643
0.409467.030.951.170.4090.3642821218
0.414480.840.961.200.4140.3715444293
0.419495.060.961.240.4190.3788326868
0.424509.700.961.270.4240.3861453943
0.429524.780.961.310.4290.3934810518
0.434540.320.961.350.4340.4008381593
0.439556.330.961.390.4390.4082152168
0.444572.830.961.430.4440.4156107243
0.449589.840.961.470.4490.4230231818
0.454607.380.961.520.4540.4304510893
0.459625.460.961.560.4590.4378929468
0.464644.130.961.610.4640.4453472543
0.469663.380.961.660.4690.4528125118
0.474683.260.961.710.4740.4602872193
0.479703.770.961.760.4790.4677698768
0.484724.960.961.810.4840.4752589843
0.489746.850.961.870.4890.4827530418
0.494769.460.961.920.4940.4902505493
0.499792.840.971.980.4990.4977500068
0.504817.000.972.040.5040.5052499143
0.509841.980.972.100.5090.5127487718
0.514867.830.972.170.5140.5202450793
0.519894.570.972.240.5190.5277373368
0.524922.250.972.310.5240.5352240443
0.529950.910.972.380.5290.5427037018
0.534980.600.972.450.5340.5501748093
0.5391011.350.972.530.5390.5576358668
0.5441043.220.972.610.5440.5650853743
0.5491076.270.972.690.5490.5725218318
0.5541110.540.972.780.5540.5799437393
0.5591146.100.972.870.5590.5873495968
0.5641183.000.972.960.5640.5947379043
0.5691221.320.973.050.5690.6021071618
0.5741261.120.973.150.5740.6094558693
0.5791302.470.973.260.5790.6167825268
0.5841345.460.973.360.5840.6240856343
0.5891390.170.973.480.5890.6313636918
0.5941436.680.973.590.5940.6386151993
0.5991485.090.973.710.5990.6458386568
0.6041535.500.973.840.6040.6530325643
0.6091588.020.983.970.6090.6601954218
0.6141642.770.984.110.6140.6673257293
0.6191699.850.984.250.6190.6744219868
0.6241759.410.984.400.6240.6814826943
0.6291821.580.984.550.6290.6885063518
0.6341886.510.984.720.6340.6954914593
0.6391954.360.984.890.6390.7024365168
0.6442025.300.985.060.6440.7093400243
0.6492099.520.985.250.6490.7162004818
0.6542177.200.985.440.6540.7230163893
0.6592258.570.985.650.6590.7297862468
0.6642343.860.985.860.6640.7365085543
0.6692433.290.986.080.6690.7431818118
0.6742527.150.986.320.6740.7498045193
0.6792625.720.986.560.6790.7563751768
0.6842729.300.986.820.6840.7628922843
0.6892838.230.987.100.6890.7693543418
0.6942952.880.987.380.6940.7757598493
0.6993073.630.987.680.6990.7821073068
0.7043200.920.988.000.7040.7883952143
0.7093335.210.988.340.7090.7946220718
0.7143477.000.988.690.7140.8007863793
0.7193626.850.989.070.7190.8068866368
0.7243785.370.989.460.7240.8129213443
0.7293953.210.989.880.7290.8188890018
0.7344131.100.9810.330.7340.8247881093
0.7394319.830.9810.800.7390.8306171668
0.7444520.290.9911.300.7440.8363746743
0.7494733.430.9911.830.7490.8420591318
0.7544960.320.9912.400.7540.8476690393
0.7595202.130.9913.010.7590.8532028968
0.7645460.180.9913.650.7640.8586592043
0.7695735.900.9914.340.7690.8640364618
0.7746030.920.9915.080.7740.8693331693
0.7796347.040.9915.870.7790.8745478268
0.7846686.260.9916.720.7840.8796789343
0.7897050.840.9917.630.7890.8847249918
0.7947443.320.9918.610.7940.8896844993
0.7997866.560.9919.670.7990.8945559568
0.8048323.780.9920.810.8040.8993378643
0.8098818.660.9922.050.8090.9040287218
0.8149355.350.9923.390.8140.9086270293
0.8199938.600.9924.850.8190.9131312868
0.82410573.880.9926.430.8240.9175399943
0.82911267.410.9928.170.8290.9218516518
0.83412026.440.9930.070.8340.9260647593
0.83912859.320.9932.150.8390.9301778168
0.84413775.790.9934.440.8440.9341893243
0.84914787.220.9936.970.8490.9380977818
0.85415907.000.9939.770.8540.9419016893
0.85917150.920.9942.880.8590.9455995468
0.86418537.750.9946.340.8640.9491898543
0.86920089.920.9950.220.8690.9526711118
0.87421834.430.9954.590.8740.9560418193
0.87923803.960.9959.510.8790.9593004768
0.88426038.420.9965.100.8840.9624455843
0.88928586.940.9971.470.8890.9654756418
0.89431510.500.9978.780.8940.9683891493
0.89934885.580.9987.210.8990.9711846068
0.90438809.100.9997.020.9040.9738605143
0.90943405.301.00108.510.9090.9764153718
0.91448835.581.00122.090.9140.9788476793
0.91955312.581.00138.280.9190.9811559368
0.92463121.021.00157.800.9240.9833386443
0.92972649.031.00181.620.9290.9853943018
0.93484436.661.00211.090.9340.9873214093
0.93999253.091.00248.130.9390.9891184668
0.944118223.821.00295.560.9440.9907839743
0.949143048.361.00357.620.9490.9923164318
0.954176390.331.00440.980.9540.9937143393
0.959222615.761.00556.540.9590.9949761968
0.964289285.041.00723.210.9640.9961005043
0.969390425.801.00976.060.9690.9970857618
0.974554503.381.001386.260.9740.9979304693
0.979846727.961.002116.820.9790.9986331268
0.9841444995.411.003612.490.9840.9991922343
0.9892989792.061.007474.480.9890.9996062918
0.9949405917.161.0023514.790.9940.9998737993
0.999177511111.131.00443777.780.9990.9999932568
&CEQUILIBRE : RESINE Na/Ca
RESINE1
&CEQUILIBRE : RESINE Na / Ca
&CCapacit de la rsine : 2 eq/lr
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1 : la mise en contact la rsine contient un nombre de moles de sodium gale son volume que multiplie la concentration en sodium dans la rsine soit Vr.Na, de mme pour le volume d'eau Ve.2 : partir du moment o il y a contact entre l'eau et la rsine le calcium de l'eau migre vers la rsine jusqu' atteindre un tat d'quilibre pour lequel un nombre de moles "a" de calcium a t absorb. D'o le nombre de moles de calcium restant dans l'eau : Ve.Ca-a. Dans le mme temps "a" moles de calcium sont passes dans la rsine (5me colonne)De mme il a disparu de la rsine un nombre de moles de sodium "2.a" qui ont migr dans l'eau (colonnes 2 et 6).3.) Cette ligne permet de traduire en activits la ligne prcdente en divisant par le volume intress (Ve pour l'eau, Vr pour la rsine) le nombre de moles prcdemment obtenu.On peut partir de la dernire ligne appliquer la loi d'action de masse (la constante d'quilibre K=1) :
Le dveloppement permet de se ramener :
Remarque : Na et Ca sont exprimes en mole par litre.
Application numrique : Ca=2,5 mmol.l-1 ; Na=2 mol.l-1 ; Ve=2 litres ; Vr=10-2 litre, L'quation devient :
A l'aide d'une mthode numrique on trouve a=4,98.10-3 2R-, 2.Na+Ca2+
(R-)2, Ca2+2.Na+=1,00=1,22.10-5
=0,498=4,98.10-3Quant aux fractions quivalentes on les calcule partir des rsultats ci-dessus en les crivant en quivalents par litre.
= 4,88.10-3 et =0,5
La concentration en calcium dissous au sein de l'eau en F s'exprime directement partir du tableau prcdent : THCa= 1,22.10-5x2x1000x5=0,12F, l'eau est nettement adoucie puisque le THCa de dpart tait de 25F.Si l'on accepte une eau adoucie 0,5F de calcium la fraction quivalente en calcium dans l'eau sera : qui correspond une fraction quivalente dans la rsine de l'ordre de 0,71 (par le calcul vu en 3.3)On peut aisment vrifier que les fractions quivalentes en calcium s'crivent : et
On peut ainsi dterminer "a" et Ve : a=7,08.10-3 et Ve=2,89 l.
1.5) Si l'on remplace l'eau adoucie 0,5F par une saumure 117 grammes de NaCl par litre quel va tre le rsultat produit (rpondre qualitativement).
Si l'on remplace l'eau adoucie 0,5F par une saumure 117 grammes de NaCl par litre le rsultat produit va tre l'inverse de l'opration prcdente.En effet une saumure 117 grammes de sel est une solution 2 quivalents de sodium, on va donc trouver le point d'quilibre sur la seconde courbe. Si l'on suppose partir d'une rsine sature en calcium (fraction quivalente dans la rsine gale 1), on voit que celle-ci sera en quilibre avec une eau contenant 100% de calcium or la saumure (dans l'hypothse impose) n'en contient pas : on va donc assister un relargage du calcium de la rsine vers l'eau jusqu' arriver un nouveau point d'quilibre.Cette opration est appele rgnration de la rsine et pour les rsines fonctionnant avec l'ion mobile sodium : saumurage du fait de l'utilisation d'une solution sature en NaCl.On pourra vrifier (le calcul propos l'esquisse) que les volumes d'eau adoucie productibles diminuent si l'on dsire obtenir une excellente qualit de l'eau. On fixe donc un point d'arrt : dans notre exemple 0,5F et l'on rgnre ; de mme la rgnration sera interrompue bien avant d'atteindre une fraction quivalente dans la rsine gale 0 (en calcium) car il faudrait utiliser des volumes de saumure trs important ou des concentrations en sodium trs leves (qui sont forcment limites par le produit de solubilit du NaCl : de l'ordre de 330 g par litre de saumure). On ne pourra donc exploiter qu'une part de la capacit de la rsine, ici de l'ordre de 40%.On ne peut donc liminer totalement le calcium : cette fuite calcique sera choisie en fonction du process utilisateur : 0,2F pour une chaudire vapeur 10 bars, 0,5F voire plus pour des eaux chaudes sanitaires, infrieur 0,2 micro-gramme par litre pour une eau ultra-pure, ... Remarques : Dans la pratique la capacit utile dpend d'autres paramtres, en particulier nous nous sommes placs dans un cadre statique o les cintiques de raction n'interviennent pas.De plus la forme des courbes dtermines n'est qu'une approximation : pour les fortes concentrations (pour des saumures), les courbes prsentent un point d'inflexion.Graph2
00
0.00050.1460068354
0.0010.2347265809
0.00150.2972258839
0.00250.3828212828
0.00350.4408260661
0.00450.4838620502
0.00550.5176126671
0.00650.5450975229
0.00750.5681006639
0.00850.5877577905
0.00950.6048331709
0.01050.6198637588
0.01150.6332400237
0.01250.6452540335
0.01350.656129455
0.01450.6660410234
0.01550.6751276058
0.01650.6835012181
0.01750.6912534026
0.01850.6984598382
0.01950.7051837349
0.02050.7114783767
0.02150.7173890548
0.02250.722954557
0.02350.72820833
0.02450.7331793966
0.02550.7378930855
0.02650.7423716195
0.02750.7466345917
0.02850.7506993557
0.02950.7545813467
0.03050.7582943472
0.03150.7618507101
0.03250.7652615446
0.03350.7685368741
0.03850.7831710614
0.04350.7954845072
0.04850.8060503449
0.05350.8152596715
0.05850.823390037
0.06350.8306447778
0.06850.8371768395
0.07350.8431038474
0.07850.8485179952
0.08350.8534927383
0.08850.858087446
0.09350.8623507117
0.09850.8663227565
0.10350.870037207
0.10850.8735224299
0.11350.8768025508
0.11850.8798982404
0.12350.8828273289
0.12850.8856052922
0.13350.8882456388
0.13850.8907602225
0.14350.8931594953
0.14850.8954527151
0.15350.8976481165
0.15850.8997530528
0.16350.9017741143
0.16850.9037172278
0.17350.9055877408
0.17850.9073904926
0.18350.9091298753
0.18850.910809886
0.19350.9124341713
0.19850.9140060665
0.20350.9155286291
0.20850.9170046679
0.21350.9184367688
0.21850.919827317
0.22350.9211785171
0.22850.92249241
0.23350.9237708886
0.23850.9250157115
0.24350.9262285147
0.24850.927410823
0.25350.9285640591
0.25850.9296895526
0.26350.9307885479
0.26850.9318622105
0.27350.9329116343
0.27850.9339378464
0.28350.9349418126
0.28850.9359244423
0.29350.9368865923
0.39350.9528119492
0.49350.9645938968
0.59350.9739629717
0.69350.9817660294
0.79350.9884760947
0.89350.9943824228
0.99350.9996739917
0.99450.9997242786
0.99550.9997745175
0.99650.9998247083
RESINE1
T10.005T224.88E-031.97E+004.98E-01
xay
0.0000.000.000.000.000
0.0010.200.150.000.001a0.00000.00050.00100.00150.00200.00250.00300.00350.00400.00410.00420.00430.00440.00450.00460.00470.00480.00490.00500.00510.00520.00530.00540.00550.00560.00570.00580.00590.00600.00610.00620.00630.00640.00650.00660.00710.00760.00810.00860.00910.00960.01010.01060.01110.01160.01210.01260.01310.01360.01410.01460.01510.01560.01610.01660.01710.01760.01810.01860.01910.01960.02010.02060.0211
0.0010.400.230.000.001Equation 3.2-0.01-0.0081224875-0.0064799-0.0050571625-0.0038392-0.0028109375-0.0019573-0.0012632125-0.0007136-0.0006196879-0.0005308312-0.0004469093-0.0003678016-0.0002933875-0.0002235464-0.0001581577-0.0000971008-0.00004025511.25E-056.13E-051.06E-041.47E-041.85E-042.19E-042.50E-042.77E-040.00030175120.00032311790.00034160.00035731810.00037039280.00038094470.00038909440.00039496250.00039866960.00038901110.00034341760.00027696410.00020472560.00014177710.00010319360.00010405010.00015942160.00028438310.00049400960.00080337610.00122755760.00178162910.00248066560.00333974210.00437393360.00559831510.00702796160.00867794810.01056334960.01269924110.01510069760.01778279410.02076060560.02404920710.02766367360.03161908010.03593050160.0406130131
0.0020.600.300.000.002
0.0031.010.380.000.003
0.0041.410.440.000.004
0.0051.820.480.000.005
0.0062.220.520.010.006
0.0072.630.550.010.007
0.0083.050.570.010.008
0.0093.460.590.010.009
0.0103.870.600.010.010
0.0114.290.620.010.011
0.0124.710.630.010.012
0.0135.130.650.010.013
0.0145.550.660.010.014
0.0155.970.670.010.015
0.0166.400.680.020.016
0.0176.820.680.020.017
0.0187.250.690.020.018
0.0197.680.700.020.019
0.0208.110.710.020.020
0.0218.550.710.020.021
0.0228.980.720.020.022
0.0239.420.720.020.023
0.0249.860.730.020.024
0.02510.300.730.030.025
0.02610.740.740.030.026
0.02711.180.740.030.027
0.02811.630.750.030.028
0.02912.080.750.030.029
0.03012.530.750.030.030
0.03112.980.760.030.031
0.03213.430.760.030.032
0.03313.890.770.030.033
0.03414.350.770.040.034
0.03916.660.780.040.039
0.04419.020.800.050.044
0.04921.430.810.050.049
0.05423.890.820.060.054
0.05926.400.820.070.059
0.06428.960.830.070.064
0.06931.580.840.080.069
0.07434.250.840.090.074
0.07936.980.850.090.079
0.08439.760.850.100.084
0.08942.610.860.110.089
0.09445.510.860.110.094
0.09948.480.870.120.099
0.10451.510.870.130.104
0.10954.610.870.140.109
0.11457.770.880.140.114
0.11961.000.880.150.119
0.12464.300.880.160.124
0.12967.680.890.170.129
0.13471.120.890.180.134
0.13974.640.890.190.139
0.14478.250.890.200.144
0.14981.930.900.200.149
0.15485.690.900.210.154
0.15989.530.900.220.159
0.16493.460.900.230.164
0.16997.480.900.240.169
0.174101.600.910.250.174
0.179105.800.910.260.179
0.184110.100.910.280.184
0.189114.500.910.290.189
0.194119.000.910.300.194
0.199123.600.910.310.199
0.204128.310.920.320.204
0.209133.130.920.330.209
0.214138.060.920.350.214
0.219143.100.920.360.219
0.224148.270.920.370.224
0.229153.560.920.380.229
0.234158.970.920.400.234
0.239164.520.930.410.239
0.244170.190.930.430.244
0.249176.010.930.440.249
0.254181.960.930.450.254
0.259188.060.930.470.259
0.264194.310.930.490.264
0.269200.710.930.500.269
0.274207.270.930.520.274
0.279214.000.930.530.279
0.284220.890.930.550.284
0.289227.960.940.570.289
0.294235.200.940.590.294
0.394427.900.951.070.394
0.494769.460.961.920.494
0.5941436.680.973.590.594
0.6942952.880.987.380.694
0.7947443.320.9918.610.794
0.89431510.500.9978.780.894
0.9949405917.161.0023514.790.994
0.99513150413.221.0032876.030.995
0.99619664197.531.0049160.490.996
0.99732538775.511.0081346.940.997
&CEQUILIBRE : RESINE Na/Ca
RESINE1
&CEQUILIBRE : RESINE Na / Ca
&CCapacit de la rsine : 2 eq/lr
Graph2
00
0.00050.1460068354
0.0010.2347265809
0.00150.2972258839
0.00250.3828212828
0.00350.4408260661
0.00450.4838620502
0.00550.5176126671
0.00650.5450975229
0.00750.5681006639
0.00850.5877577905
0.00950.6048331709
0.01050.6198637588
0.01150.6332400237
0.01250.6452540335
0.01350.656129455
0.01450.6660410234
0.01550.6751276058
0.01650.6835012181
0.01750.6912534026
0.01850.6984598382
0.01950.7051837349
0.02050.7114783767
0.02150.7173890548
0.02250.722954557
0.02350.72820833
0.02450.7331793966
0.02550.7378930855
0.02650.7423716195
0.02750.7466345917
0.02850.7506993557
0.02950.7545813467
0.03050.7582943472
0.03150.7618507101
0.03250.7652615446
0.03350.7685368741
0.03850.7831710614
0.04350.7954845072
0.04850.8060503449
0.05350.8152596715
0.05850.823390037
0.06350.8306447778
0.06850.8371768395
0.07350.8431038474
0.07850.8485179952
0.08350.8534927383
0.08850.858087446
0.09350.8623507117
0.09850.8663227565
0.10350.870037207
0.10850.8735224299
0.11350.8768025508
0.11850.8798982404
0.12350.8828273289
0.12850.8856052922
0.13350.8882456388
0.13850.8907602225
0.14350.8931594953
0.14850.8954527151
0.15350.8976481165
0.15850.8997530528
0.16350.9017741143
0.16850.9037172278
0.17350.9055877408
0.17850.9073904926
0.18350.9091298753
0.18850.910809886
0.19350.9124341713
0.19850.9140060665
0.20350.9155286291
0.20850.9170046679
0.21350.9184367688
0.21850.919827317
0.22350.9211785171
0.22850.92249241
0.23350.9237708886
0.23850.9250157115
0.24350.9262285147
0.24850.927410823
0.25350.9285640591
0.25850.9296895526
0.26350.9307885479
0.26850.9318622105
0.27350.9329116343
0.27850.9339378464
0.28350.9349418126
0.28850.9359244423
0.29350.9368865923
0.39350.9528119492
0.49350.9645938968
0.59350.9739629717
0.69350.9817660294
0.79350.9884760947
0.89350.9943824228
0.99350.9996739917
0.99450.9997242786
0.99550.9997745175
0.99650.9998247083
RESINE1
T10.005T224.88E-031.97E+004.98E-01
xay
0.0000.000.000.000.000
0.0010.200.150.000.001a0.00000.00050.00100.00150.00200.00250.00300.00350.00400.00410.00420.00430.00440.00450.00460.00470.00480.00490.00500.00510.00520.00530.00540.00550.00560.00570.00580.00590.00600.00610.00620.00630.00640.00650.00660.00710.00760.00810.00860.00910.00960.01010.01060.01110.01160.01210.01260.01310.01360.01410.01460.01510.01560.01610.01660.01710.01760.01810.01860.01910.01960.02010.02060.0211
0.0010.400.230.000.001Equation 3.2-0.01-0.0081224875-0.0064799-0.0050571625-0.0038392-0.0028109375-0.0019573-0.0012632125-0.0007136-0.0006196879-0.0005308312-0.0004469093-0.0003678016-0.0002933875-0.0002235464-0.0001581577-0.0000971008-0.00004025511.25E-056.13E-051.06E-041.47E-041.85E-042.19E-042.50E-042.77E-040.00030175120.00032311790.00034160.00035731810.00037039280.00038094470.00038909440.00039496250.00039866960.00038901110.00034341760.00027696410.00020472560.00014177710.00010319360.00010405010.00015942160.00028438310.00049400960.00080337610.00122755760.00178162910.00248066560.00333974210.00437393360.00559831510.00702796160.00867794810.01056334960.01269924110.01510069760.01778279410.02076060560.02404920710.02766367360.03161908010.03593050160.0406130131
0.0020.600.300.000.002
0.0031.010.380.000.003
0.0041.410.440.000.004
0.0051.820.480.000.005
0.0062.220.520.010.006
0.0072.630.550.010.007
0.0083.050.570.010.008
0.0093.460.590.010.009
0.0103.870.600.010.010
0.0114.290.620.010.011
0.0124.710.630.010.012
0.0135.130.650.010.013
0.0145.550.660.010.014
0.0155.970.670.010.015
0.0166.400.680.020.016
0.0176.820.680.020.017
0.0187.250.690.020.018
0.0197.680.700.020.019
0.0208.110.710.020.020
0.0218.550.710.020.021
0.0228.980.720.020.022
0.0239.420.720.020.023
0.0249.860.730.020.024
0.02510.300.730.030.025
0.02610.740.740.030.026
0.02711.180.740.030.027
0.02811.630.750.030.028
0.02912.080.750.030.029
0.03012.530.750.030.030
0.03112.980.760.030.031
0.03213.430.760.030.032
0.03313.890.770.030.033
0.03414.350.770.040.034
0.03916.660.780.040.039
0.04419.020.800.050.044
0.04921.430.810.050.049
0.05423.890.820.060.054
0.05926.400.820.070.059
0.06428.960.830.070.064
0.06931.580.840.080.069
0.07434.250.840.090.074
0.07936.980.850.090.079
0.08439.760.850.100.084
0.08942.610.860.110.089
0.09445.510.860.110.094
0.09948.480.870.120.099
0.10451.510.870.130.104
0.10954.610.870.140.109
0.11457.770.880.140.114
0.11961.000.880.150.119
0.12464.300.880.160.124
0.12967.680.890.170.129
0.13471.120.890.180.134
0.13974.640.890.190.139
0.14478.250.890.200.144
0.14981.930.900.200.149
0.15485.690.900.210.154
0.15989.530.900.220.159
0.16493.460.900.230.164
0.16997.480.900.240.169
0.174101.600.910.250.174
0.179105.800.910.260.179
0.184110.100.910.280.184
0.189114.500.910.290.189
0.194119.000.910.300.194
0.199123.600.910.310.199
0.204128.310.920.320.204
0.209133.130.920.330.209
0.214138.060.920.350.214
0.219143.100.920.360.219
0.224148.270.920.370.224
0.229153.560.920.380.229
0.234158.970.920.400.234
0.239164.520.930.410.239
0.244170.190.930.430.244
0.249176.010.930.440.249
0.254181.960.930.450.254
0.259188.060.930.470.259
0.264194.310.930.490.264
0.269200.710.930.500.269
0.274207.270.930.520.274
0.279214.000.930.530.279
0.284220.890.930.550.284
0.289227.960.940.570.289
0.294235.200.940.590.294
0.394427.900.951.070.394
0.494769.460.961.920.494
0.5941436.680.973.590.594
0.6942952.880.987.380.694
0.7947443.320.9918.610.794
0.89431510.500.9978.780.894
0.9949405917.161.0023514.790.994
0.99513150413.221.0032876.030.995
0.99619664197.531.0049160.490.996
0.99732538775.511.0081346.940.997
&CEQUILIBRE : RESINE Na/Ca
RESINE1
&CEQUILIBRE : RESINE Na / Ca
&CCapacit de la rsine : 2 eq/lr
Phase de service : adoucissementBascule en phase de rgnrationPhase de rgnrationBascule en phase de serviceCapacit d'change utile
