Politechnika Rzeszowska Wydział Chemiczny Katedra Inżynierii Chemicznej
MODELING OF SORPTION EQUILIBRIUM IN TWO-COMPONENT SYSTEMS
Roman Petrus, Jolanta Warchoł, Miroslav Maliowanyy, Yaroslav Gumnitsky
Experimental part Schematic diagram for the synthesis of silica gel modified with EDTA
Chemicals and equipment: • • • • • • • • •
Silica gel (SG); Ethylenediaminetetraacetic acid (EDTA), Aminopropyl-triethoxysilane (APTES), Double deionized water obtained from SG Ultra Clear Basic (0.055 µS/cm); Acetic acid 100%, Absolute ethanol; ICP-OES (iCAP 6300, Thermo Electron Corporation, USA); Rotary shaker type ST5 (CAT M.Zipperer GmbH, Staufen, Germany); Drying oven, Termaks model TS8000)
Properties
Silica gel LiChroPrep®
Diameter (μm)
5-20
40-63
63-200
Pore volume (g/cm3)
0.84
0.90
0.84
Surface area (m2/g)
540
580
540
One-component isotherm Equilibrium data of Ni(II) and Co(II) sorption on EDSG, pH=3 0,4
-1
qe (mmol g )
0,3
0,2
0,1
EDSG-Cd EDSG-Ni 0,0 0
1
2
3
4
5
-1
Ce (mmol g )
Distribution of various Ni(II) and Co(II) species as a function of pH
Two-component isotherm Under constant mass ratio of Co:Ni ions: 1:1, 1:3, 3:1, 2:3, 3:2, 1:4, 4:1, 1:9, and 9:1 0,35
0,35
0,25
0,20
0,20
0,15 Co EDSG Ni EDSG
0,10
0,15
qe [mmol/g]
0,25
0,15
Co EDSG Ni EDSG
0,00
0,00 0,0
0,5
1,0
1,5
2,0
2,5
-0,5
3,0
0,0
0,5
1,0
2,0
2,5
3,0
3,5
-0,5
4,0
Co:Ni 2:3
0,30
qe [mmol/g]
0,25 0,20 0,15 Co EDSG Ni EDSG
0,10 0,05
1,5
2,0
2,5
0,30
0,25
0,25
0,20
0,20
0,15
Co EDSG Ni EDSG
0,10
0,05
0,05
3,0
3,5
4,0
Co EDSG Ni EDSG
0,00
0,0
0,5
1,0
3
1,5
2,0
2,5
-0,5
3,0
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
4,0
4,5
3
Ce [mmol/dm ]
3
Ce [mmol/dm ]
0,25
2,5
0,15
0,10
3,0
2,0
Co:Ni 1:9
0,30
0,00
0,00
1,5
0,35
qe [mmol/g]
0,35
1,0
1,0
3
Co:Ni 3:2
0,5
0,5
Ce [mmol/dm ]
0,35
0,40
0,0
0,0
Ce [mmol/dm ]
3
qe [mmol/g]
1,5
Co EDSG Ni EDSG
0,00
3
Ce [mmol/dm ]
-0,5
0,10
0,05
0,10 0,05
0,05
-0,5
Co:Ni 4:1
0,30
qe [mmol/g]
qe [mmol/g]
0,30
0,20 Co:Ni 1:4
Co:Ni 1:1
Ce [mmol/dm ]
0,35 Co:Ni 3:1
Co:Ni 1:3
0,30
0,25
0,25
0,20
Co:Ni 9:1
0,10
0,20 qe [mmol/g]
0,15 qe [mmol/g]
qe [mmol/g]
0,20
0,15 0,10
0,05
0,00 -0,5
Co EDSG Ni EDSG
0,00
0,0
0,5
1,0
1,5
2,0
2,5 3
Ce [mmol/dm ]
3,0
3,5
4,0
0,10 0,05
0,05
Co EDSG Ni EDSG
0,15
0,0
0,5
1,0
1,5
2,0 3
Ce [mmol/dm ]
2,5
3,0
3,5
Co EDSG Ni EDSG
0,00 -0,5
0,0
0,5
1,0
1,5
2,0
2,5 3
Ce [mmol/dm ]
3,0
3,5
4,0
4,5
Modeling part BiLangmuir model qe =
q m,1 K1C e 1 + K 1C e
+
q m, 2 K 2 C e 1 + K 2 Ce
where qm,1 and qm,2 are the maximum adsorption capacities of two different adsorption sites: (1) APTSG and (2) EDSG, respectively. K1 and K2 are energies of the adsorption related to adsorption sites (1) APTSG and (2) EDSG, respectively.
Competitive BiLangmuir model q e1 =
q e2 =
q m,1,1 K 1,1C e1 1 + K 1,1C e1 + K 2,1C e2
q m,2,1 K 2,1C e2 1 + K1,1C e1 + K 2,1C e2
+
+
q m,1,2 K 1,2 C e1 1 + K 1,2 C e1 + K 2,2 C e2
q m,2,2 K 2,2 C e2 1 + K1,2 C e1 + K 2,2 C e2
Estimation procedure Nonlinear regression method based on the Levenberg-Marquardt algorithm. The isotherm parameters were determined by minimizing n the Sum of the Squares of the Errors function 2
∑(qe,exp − qe,calc )i i =1
The relationship between experimental and theoretically predicted points was assessed by the coefficient of determination (R2), standard deviation (σ), and mean error (ME).
Modeling of one-component equilibrium
0,4
0,4
Co EDSG
Ni EDSG 0,3
-1
qe (mmol g )
-1
qe (mmol g )
0,3
0,2
0,2
0,1
0,1
exp set A set B
0,0 0
1
2
3
4
exp set A set B
0,0 5
0
1
2
Guess value A
ion
q m,exp mmol/g
Co Ni
0.302 0.329
Co Ni
0.302 0.329
B
qm1 KBiL1 q m2 K BiL2 mmol/g L/g mmol/g L/g 0.3 1.0 0.3 1.0 0.132 1.883 0.193 110.671 0.142 2.328 0.215 118.205 0.1 1.0 1.0 1.0 9 0.274 1.568 0.102 1.75*10 9 0.111 1.67*10 0.303 1.750
3 -1
-1
Ce (mmol L )
Ce (mmol L )
R2
Ďƒ
ME %
0.9962 0.9869
0.009 0.019
20.827 46.605
0.9161 0.9153
0.040 0.046
79.447 93.546
4
5
Modeling of two-component equilibrium Two-parameters estimated Co:Ni 1:3 EDSG qm,i estimeted
0,35
0,30
0,30
0,25
0,25
0,20
0,20
qe [mmol/g]
qe [mmol/g]
0,35
Four-parameters estimated
0,15 0,10
0,15 0,10
Co - exp. Ni - exp. Co - model Ni - model
0,05 0,00 -0,5
Co:Ni 1:3 EDSG Ki, qm,i estimeted
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
3
K BiLCo1 KBiLCo2 ( L/g) n.e. n.e. n.e. n.e. 0.529 70.084
n.e. non estimated
0,00 -0,5
0,0
0,5
1,0
1,5
2,0
2,5
3,0
3,5
3
Ce [mmol/dm ]
qmCo1 qmCo2 (mmol/g) n.e. n.e. 0.047 0.158 0.099 0.238
Co - exp. Ni - exp. Co - model Ni - model
0,05
Ce [mmol/dm ]
qm Ni1 qm Ni2 (mmol/g) n.e. n.e. 0.220 0.238 0.098 0.229
KBiLNi1 KBiLNi 2 R2 Ďƒ ME ( L/g) (%) n.e. n.e. 0.7639 0.074 138.983 n.e. n.e. 0.8565 0.060 110.941 13.907 492.982 0.9864 0.018 106.953
Co EDSG
3D graphs
0.25 0.2 0.15 0.1 0.05 0 4 3
Co EDSG
4 3
2
2
1 Ce,Ni (mmol/l)
1 0
0
Ce,Co (mmol/l) 0.3 qe,Co (mmol/g)
qe,Co (mmol/g)
0.3
0.25 0.2 0.15 0.1 0.05 0 0 1 2 3 4 Ce,Ni (mmol/l)
0
1
2
Ce,Co (mmol/l)
3
4
Ni EDSG
3D graphs
0.25 0.2 0.15 0.1 0.05 0 4 3
4 3
2 Ce,Ni (mmol/l)
Ni EDSG
2
1
1 0
0
0.35
Ce,Co (mmol/l) 0.3
0.25 qe,Ni (mmol/g)
qe,Ni (mmol/g)
0.3
0.2
0.15
0.1
0.05
0 0
1
2
3 Ce,Ni (mmol/l)
4
4
3 C
e,Co
2 (mmol/l)
1
0
2D graphs
0,3
0,4 EDSG Co:Ni 1:9
EDSG Co:Ni 9:1
0,3
-1
qe (mmol g )
-1
qe (mmol g )
0,2 0,2
exp Co exp Ni model Co model Ni
0,1
0,02
0,15
exp Co exp Ni model Co model Ni
0,1
0,01
0,0
0
1
0,05 0,00
0,00
0,0
0,10
2
0,5
3 -1
Ce (mmol L )
4
0,0
0,0
0
1
2
0,1
3 -1
Ce (mmol L )
0,2
4
Conclusions The validation of the parameter values cannot be totally proven by nonlinear regression and corresponded to the global minimum of the objective function. The best correlation with the experimental data was obtained using initial guesses of maximum adsorption capacities (qm) corresponding to the experimentally obtained ones. The application of the extended Bilangmuir model confirmed the coexistence of low- (APTES) and high (EDTA) -energy active sites on sorbent surface that showed an unequal ability for Co(II) and Ni(II) adsorption. However, the overlapping parts of the resulting isotherms presented in the three-dimensional graphs could not provide a useful evaluation of the accuracy of the fit.
Acknowledgements The authors gratefully acknowledge the State Committee for Scientific Research (Poland) (KBN N N209 760140) for the financial support.