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Optimization of electrodialysis process at elevated temperatures
Desalination, 46
(1963) 253-262
253
ElsevierSciencePublishers B.V., Amsterdam-PrintedinTbeNetberlands
OPTIEIZATION OF ELECTRODIALYSIS PROCESS AT ELEVATED TEMPERATURES V.N. SEAGIN, N.N. ZHUROV, D.A. YAROSHEVSKY and O.V. YEVDOKIMOV Yosvodokanalniiproject Institute (The USSR)
ABSTRACT - RESUEB - KURZFASSUEG In order to determine the quantitative characteristics of the temperature effect upon physical and chemical properties of solutions and ion-exchange membrane8 at low ealt concentration8 in the influent water, experimental studies were carried out using laboratory and full-scale equipment. The relationships of the temperature effect8 on the diffusion layer depth, on the value of critical current density and on the parameters of flow hydrodynamics in the experimental cell were obtained. These relationships are taken as a basis for the economic-mathematicalmodel for the optimization of operating parameters and technological scheme8 of high temperature electrodialysis apparatus. Using this model computer-aided technical and economic eetimates were carried out along with the comparison of alternative8 under variable initial conditions. Pour la dbtermination de8 caract&istigues quanitatifs de l'influence de la temperature aur les proprietgs phyeico-chimiques des solutions et de8 membranes & &change d*ions & faibles doncentratione de l'eau de dgpsrt ils ont fait de8 easais exp&rimentaux 8ur de8 installations laboratoffes et industriellea. Lors de8 essais on a ddtermin& de8 fonctions de la temperature, de l'gpaissour de la couche de diffusion, de'la valour de la densitd de courant critique et de8 param&tres de la hydrodynomique du courant dans de cellule d'&lectrodialyse. Ces fonctions font la base de la modele;mathematique-bconom?quepour l'optimisation des aram& tres d'utilisation et de8 chemaa de8 installations pour 1't: lectro. dialyse d hautes temperatures. Les calculs technico-gconomiques et la comparaison de8 variants 1 condition8 de dgpart different8 118 out ete fait au moyen de la simulation sur la machine B calcul Llectronique. Fi,ir die Bestimmung der quantitativen Daten de8 Temperatureinflu 8888 auf phyeiech-chemische Eigenschaften der Lasungen und Ione naustauschermembranen bei niedrigen Salzkonzentration im Ausgangwaeaer wurden experimentelle Untereuchungen,I.inLabor-und Betrieb. sanlagen durchgefiikrt.Es wurden Funktionen feetgeetellt, die die Entealzung mit Temperatur. Diffueionschichtdicke,dem Wert der kritischen Stromdichte und Stromhydrodynamik in der Elektrodialysezelle verbinden. Diese Abhlingigkeitenbilden die Grundlage de8 wirtechaftlichmathematischenhodells fur die Optimierung der Betriebeparameter und Fliessbilder der Hochtemperaturelektrodialyseanlagen. Es wurden wirtechaftlich-techniacheBerechnung und Variantenver gleich bei verschiedenen Auagangsverhliltniseen mit Hilfe diesee Eodelle auf dem Computer durchgefiihrt. OOll-9164/83/$03.00 O1983EhevierSciencePublishe1~B.V.
254 Nowaday there exists a rather urgent problem of the rational utL lization of natural raw material resources, environmental pollution Control, and in connection with this, improvement of the efficiency of existing and development
of new highly efficient
technological processes in all the industries of the national economy associated with output, processing and utilization of the natural resources.
One of the most important and self-independent
trends In theory and practice of natural and sewage water treatment is desalination of aqueous salt solutions and
electrodialys-
is in particular, which has won recognition for several decades. At present there are thousand8 of electrodialysis
apparatus In
operation of various desalinating capacity for the water supply of populated areas, agricultural complexes, mines etc. However, due to some reasons, existing methods of electrodialysis process conducting are used only under specific conditions, mainly because of significant power consumption. One of the lately suggested ways of intensification
and econo-
mical improvement of electrodialysis is conduction of the process at elevated temperature8 of treated water which can be heated either from an external power source or from the heat released in the process of desalination. Data on high-temperature
electrodialysis available in literatu-
re (1,2) do not provide optimal temperature operational conditions for Soviet-made electrodialysis apparatusi. Listed in the paper are the results of theoretical and experimental studies of process temperature influence on the technological and design parameters of electrodialysis apparatus; the results of experimental studies of physical and chemical properties of Soviet-made membranes In relation to the temperature;
and the
results of the optimization of electrodialysis process at elerated temperatures by means of an economic-mathematical Quantitative estimation of polarization, ing badly with, the
model.
a phenomenon interfer-
electrodialysi8 process, consists mainly'-of
the determination cf critical current density at various hydrodynamic conditions in the electrodialysis
cell; critical Ourrent
density depending upon the membrane selectivity and mass transfer conditions. The intensity of mass transfer depends, upon the parameters of flow hydrodynamics,
in its turn,
i.e. flow rate, vis-
cosity and diffusion coefficient. Conditions in the eleotrodialysis cell corresponding to the.value are as follows: ZFCD
(1) iLlI??= f ( -t)btim where iLin_critical current density, A/m2; C - concentration of the solution for desalination, g-eq/l; Z - ionic valency; F - Faraday number, A s/g-eq; D - diffusion coefficient, cm2/s; (2 - t) - difference of numbers of ionic transport in the membrane and in the solution;Sl,+,-diffusion layer depth at the membrane surface at the side of desalinated flow according to the critical current density, cm. Reference 3 contains the equation for determining maximum depth of the diffusion layer in the electrodialysis cell. The proposed equation was derived with en account for the summarized experimental results and the following form: stim=
(2)
where 3 - kinematic viscosity, cm2/s; 1 - distance between the turbolator elements cm; dd - thickness of the desalination cell, cm; h - heigh of the turbolator element, cm; K - empirical coefficient characterizing the turbolator; V - desalinated flow rate, cm/s. Any significant increase in critical current density is possible when artificial turbulization of the desalinated flow by means of turbolator jumpers is combined with the decrease of the solution viscosity by heating the solution. Temperature dependence of the water viscosity is the following: (3) ? =%[I + 0,0158 (T - To)]-2 where$,ga- kinematio viscosity; T, To - absolute temperature, The movement of the hydrated ions in the membrane-near desalinated layers may be considered from the point of the hydrodynamic theory of diffusion. In this case the diffusion coefficient is described by the Stocks-Einstein equation: (4) where N - Avogadro number; d - parameter having the length dimen-
tionality; g - coefficient of volume viscosity; Do - diffusion coefficient at 298'K.
The availability of turbolising elements situated in the cells of the electrodialyais apparatus provides the main hydraulic resistance along the flow path. Decrease in the solution viscosity results in the decrease of friction in the system due to the solu tion heating. Liquid flow regime is characterized by the Reinolds number which is included into the expression for estimating head losses caused by the friction along the length and by local resis. tance in the cells with labirynth-netlike spacers. Finally, taking into account equation (3) we receive the expres. sions for estimating the hydraulic resistance along the distance between the turbolator (1) elements and for the local resistance in the turbolator elements:
"LT
0.0092
A=
4vR (I+O.OI% (f-25Wj
2hS2+ 4rR II+o.ow~~-P~~~J~ -
I m
K =*I+ LI ; a - thickness of T the turbolator jumpers along the flow (cm); K - constant, which determines the turbolator design; & - coefficient considering the flow narrowing along the cell thickness at the point of the turbolator jumpers location; Relzma certain Reinolds number which provides for the self-similarity of the free flow in the cell (Rslim = 10000). Thus, we have received the expressions which establish the relation of critical current density and hydraulic resistance to the design parameters of the electrodialysis cell with a labirynth-netlike spacer depending upon the process temperature. The calculation of the diffusion layer depth showed i&,,, increase* with temperature elevating. During the analysis it was established that this phenomenon results from the increase of (+)"3 value, where D is increasing end $ is decreasing according to the temperature increase. This indicated the enlargement of the aone where the rate of mass transfer owing to the molecular diffusion where A=101,2; A*=66,8;
h*= I - %
257
in the membrane-near
leyer excesses over the rate of convectional
mass transfer. Therefore, despite the increase of the diffusion layer depth, critical current density increases.with
temperature
rizeing. In order to check the theoretical preconditions
described ear-
lier, studies have been carried out using laboratory and full-sea. le apparatus. The reaulte of the experimental 8tUdieS of critical current density dependence upon the temperature are given in graphic form in Fig.1. Given for comparison in the same figure are the de8ign value8 of oritical current density.
1 283 I c, =0,054 r+J;
I
293
I
303
I
I
1
319 329 T, 'K
u, cm/s: i-40; 2-48.0; 3-220 4-40.0;5-50.0
Fig. 1. Critical current density as a fuction of the solution temperature.
258 The type of functional dependence of experimentally determined i c,it_valuesupon the temperature corresponds to the type of the same dependence for theoretically determined i,,(t. values. Critical current density in the temperature range of IO-50°C increases by 2,5-4,2% per l°C, in average. The results of experimental evalution of the hydrodynamic process parameters depending upon the temperature are given in Table 1,which contains also theoretical design values. As is obvious from the following table the experimental results coincide satisfactorily with the design data. Some differences in head losses values (H), hydraulic resistance coefficient values (a) and diffusion layer depth values (8) can be explained by the increase in flow rate (v) values due to the swelling of the membranes and labirynth-netlike spacers. In general it should be noted that hydraulic resistance of labirynth-netlike spacers decreas es by 1% per l°C in average in the mentioned temperature ranges. Studies were carried out using an experimental full-scale apparatus. The main objects of the studies included: establishment of the adequacy of the results received when using a compact apparatus and the results received when using the ssme initial parameters under the conditions close to those of the full-scale apparatus; estimation of the temperature influence on the desalination rate and power consumption per unit of volume of partially desalinated water and salt transported through the membranes; estimation of the temperature influence upon the parameters of the apparatus operating at partial desalination of fresh water with the salinity
of 0,3 - 1,0 g/l; estimation of the temperature influence on the degree of the solution concentration in the saline cells of a fullscale electrodialysis apparatus for desalination. The effciency of electrodialysis process depends upon ,thephysical and chemical properties of the ion-exchange membranes, i.e. conductivity; osmotic, diffusion and hydrodynamic permeability; resistance to the influence of various external factors. While designing and operating the ap aratus for desalination-concentration at elevated temperatures it is necessary to consider the changes in these properties with temperature increase, otherwise considerable mistakes in design and selection of technological parameters as well as in evaluation of the process efficience are
TABLE 1 Comparison of design values and experimental results of investigating hydrodynamic parameters of electrodialysis process at elevated temperatures. T;'K 283 283 313 313 283 283 313 313 ::; 313 313
Re
H,cm/m
164,4 100,4 -"105,o 55,4 321,4 -"55,o 224,9 324,8 -'*238,C 642,9 142.9 -"143,o 398,O ,)@, 487Vo 440,C 964,3 301,7 -"300,o
A 5,94 4,;;" ;:V& 3:46 2,08 2,08 2,57 2,84 I,95 1,94
v,cm/s 990
,n_ n_ ,1)_
18,0 _n, -11, ,)I.. 21r: ,n, ,)),
1 , cm: h/d 8.102,cm 194 ,*I, ..1*_ _1), ,*, ,n,n_n_ ,n, _n, _n_ ,n_
095 ,fi, _fi_ _n_ ,n, ,n,n,w, -u_ _n_ _n_ ,n_
0,854 ?% 1:255 0,646 0,695 0,82 0,887 0,528 X$Z 01724
des. exp. des. exp. des. exy. des. exp. des. exp. des. exe.
possible. In order to determine the extent of the changes in the mentioned properties depending upon the temperature an experimental installation was designed. The installation included: a mercury contact cell for the estimation of membrane conductivity; and two cells for determining the osmotic, diffusion and hydrodynamic permeabilities. hathematical processing of the experimental data on U-40 and U-40 membrane properties resulted in the following empirical relationships of the temperature dependence of the membrane characteristics: - of specific membrane conductivity e%= Al(T-273)0'5 + A2Co'35. e (7) z empirical coefficients equal, respeotively,to: where Al, A2, A3 for NA-40 membranes: Al = 46, A2 = 650, A3 = 1210; for hK-40 membranes: A, = 40, A2 = 650, A3 = 1350 - of osmotic membrane permeability: (8) Josm = (A, + A2 C) . e = empirical coefficients equal to: where Al, A2, A3 for U-40 membranes: Al = 15, A2 = 13, A3 = 1575; for UK-40 membranes: Al = 50, A2 = 13, A3 = 1598
- of coefficienttof diffusion through the membranes: Ddi,.= A1. Cn. e k.~*-8
(IO)
where A;, A2 = empirical coefficients equal to: for I&A-40membranesr A, = 12,4; A2 = X,8; n P 0,335; for UK-40 membranes: A, = 1,31; A2 = 28,0; n = 0,348. The checking caiculations of ze, Josm, Jdif, Ddif from the formulas (7.~110) showed satisfactory coincidence of the results with the experimental datav Some deviations (up to 15-18%) are observed at the concentrations equal to the limit of salt solubility and a&othe peak values of the solution temperature range selected for the studies. These deviations can be explained by the activity coefficient variations at high concentrations as well as by the physical and chemical properties disturbance caused by high temperatures. Equations (3-10) determining the changes in technological parameters of the electrodialysis apparatus and variations in physical and chemical membrane properties at temperature fluctuations were introduced into the economic-mathematicalmodel of the electrodialysis process. The model allows to calculate the technological parameters and to select optimal modes of operation of the electrodialysis apparatus. When passing through the electrodialyzer cells desalinated solutions are heated by means of the heat released in the process of electric current passing through the solution. For considering this heat with the aim of subsequent utilization in the process the economic-mathematicalmodel was supplemented by the mathematical description of mass transfer in an electrodialysis cell in the direct current field with an account for temperature fluctuations along the flow path. Using the corrected model calculations and optimization of the electrodialysis process mode were carried out for specific conditions. A predesalination apparatus operating in the scheme of the. mica1 water treatment at one of the hoscow heat power stations was taken as an initial design variant. The capacity of the predesalination apparatus was 100 m3/h at the initial salinity 0,3-0,g g/l and 50% salt removal for a single pass through the apparatus. Calculations were carried out for the two technological schemes of an electrodialysis apparatus - coourrent flow and rececling. The calculation results are given in Table 2.
261
TABLE 2 Temperature Ginit Ti;tit*Topt g/l K
Cfin g/l
Cocurrent flow scheme 293 0,80 0,45 293
553
0,90 ,n_
_ 0:45
s93
553
-"0,60
0:;O
293
553
o"zo
-;30
293
j53
353
A 0,30 ,w_
553
-"0.30
Diffe- DiffeP Ri rence cm/s thousand roubles rence thaias.roubles roubles roubl.
202.6 :;;+ 129:o 201,I 141,3
0,099 0,111
0,086
0,;5 _ A ii"15
86,5
0,135 0,066 0,109 0,052
Recycling echeme 293
0,45
293
O:gO _ :rgO
_w_ 0,23
180.5 141,8 i%:
0,126 0,102 0,199
o,io
0:0
179:9 141,5 ii";5 i76,9 138,8 0,06 417,l ,L_ ,n190,3
"0% 0:102 0,124 0,101
i93
513 ;53
s93
JI3
-"-
%3
0,30 0430 -
s93 293
553
-n_
"o$f ,
IO
5058
0,028
3058
;,016
5958
0,039
3818
;,025
87:6
0,069
6676
0,057
;8,7
0,024
129,2
0,073
;a,4
0,024
%,I
0,023
2;6,!3
0,131
,I*,
24 ,w, IO ,*24 ,~, IO ,R, 24 ,I(24 ,n, ,n_ ,w(, ,f@, ,n,n, ,n-n, ,n-
The calculation results showed that the economic efficiency for one and the same apparatus may be different depending upon the initial and final salinity values of the desalinated water. The greatest effect from the solution heating is observed when desalinating up to very low concentration values; and when the conduc tivity of the solutions is very low at ordinary,temperature, whereas the expenses end power consumption are rather high, The influence of the solution temperature on economic indicators of desalination is shown in Fig.2, where C - capital expenses, E - equated expenses, 0 - operational expenses, P - cost of desalination, N - apparatua quantity. ap
262
Fig. 2. Main technical and economic characteristics of an electrodialysis apparatus as a function of desalinated water tempera ture at cocurrent flow scheme with recuperation of the heat the outcoming fluxee. REFERENCES l.,F.Leits, 5th Inter.Symp.Fresh Water from the Sea,v.3(1976)105 2 Ch.Forgacs, Ith Inter.Symp. Water Desal., (1965) 3 3 V. Smagin and D. Yaroshevcky in book wTheoretica1 Principles of Deminer. of Fresh Water", Moscow "Nauka" (1975).
(1963) 253-262
253
ElsevierSciencePublishers B.V., Amsterdam-PrintedinTbeNetberlands
OPTIEIZATION OF ELECTRODIALYSIS PROCESS AT ELEVATED TEMPERATURES V.N. SEAGIN, N.N. ZHUROV, D.A. YAROSHEVSKY and O.V. YEVDOKIMOV Yosvodokanalniiproject Institute (The USSR)
ABSTRACT - RESUEB - KURZFASSUEG In order to determine the quantitative characteristics of the temperature effect upon physical and chemical properties of solutions and ion-exchange membrane8 at low ealt concentration8 in the influent water, experimental studies were carried out using laboratory and full-scale equipment. The relationships of the temperature effect8 on the diffusion layer depth, on the value of critical current density and on the parameters of flow hydrodynamics in the experimental cell were obtained. These relationships are taken as a basis for the economic-mathematicalmodel for the optimization of operating parameters and technological scheme8 of high temperature electrodialysis apparatus. Using this model computer-aided technical and economic eetimates were carried out along with the comparison of alternative8 under variable initial conditions. Pour la dbtermination de8 caract&istigues quanitatifs de l'influence de la temperature aur les proprietgs phyeico-chimiques des solutions et de8 membranes & &change d*ions & faibles doncentratione de l'eau de dgpsrt ils ont fait de8 easais exp&rimentaux 8ur de8 installations laboratoffes et industriellea. Lors de8 essais on a ddtermin& de8 fonctions de la temperature, de l'gpaissour de la couche de diffusion, de'la valour de la densitd de courant critique et de8 param&tres de la hydrodynomique du courant dans de cellule d'&lectrodialyse. Ces fonctions font la base de la modele;mathematique-bconom?quepour l'optimisation des aram& tres d'utilisation et de8 chemaa de8 installations pour 1't: lectro. dialyse d hautes temperatures. Les calculs technico-gconomiques et la comparaison de8 variants 1 condition8 de dgpart different8 118 out ete fait au moyen de la simulation sur la machine B calcul Llectronique. Fi,ir die Bestimmung der quantitativen Daten de8 Temperatureinflu 8888 auf phyeiech-chemische Eigenschaften der Lasungen und Ione naustauschermembranen bei niedrigen Salzkonzentration im Ausgangwaeaer wurden experimentelle Untereuchungen,I.inLabor-und Betrieb. sanlagen durchgefiikrt.Es wurden Funktionen feetgeetellt, die die Entealzung mit Temperatur. Diffueionschichtdicke,dem Wert der kritischen Stromdichte und Stromhydrodynamik in der Elektrodialysezelle verbinden. Diese Abhlingigkeitenbilden die Grundlage de8 wirtechaftlichmathematischenhodells fur die Optimierung der Betriebeparameter und Fliessbilder der Hochtemperaturelektrodialyseanlagen. Es wurden wirtechaftlich-techniacheBerechnung und Variantenver gleich bei verschiedenen Auagangsverhliltniseen mit Hilfe diesee Eodelle auf dem Computer durchgefiihrt. OOll-9164/83/$03.00 O1983EhevierSciencePublishe1~B.V.
254 Nowaday there exists a rather urgent problem of the rational utL lization of natural raw material resources, environmental pollution Control, and in connection with this, improvement of the efficiency of existing and development
of new highly efficient
technological processes in all the industries of the national economy associated with output, processing and utilization of the natural resources.
One of the most important and self-independent
trends In theory and practice of natural and sewage water treatment is desalination of aqueous salt solutions and
electrodialys-
is in particular, which has won recognition for several decades. At present there are thousand8 of electrodialysis
apparatus In
operation of various desalinating capacity for the water supply of populated areas, agricultural complexes, mines etc. However, due to some reasons, existing methods of electrodialysis process conducting are used only under specific conditions, mainly because of significant power consumption. One of the lately suggested ways of intensification
and econo-
mical improvement of electrodialysis is conduction of the process at elevated temperature8 of treated water which can be heated either from an external power source or from the heat released in the process of desalination. Data on high-temperature
electrodialysis available in literatu-
re (1,2) do not provide optimal temperature operational conditions for Soviet-made electrodialysis apparatusi. Listed in the paper are the results of theoretical and experimental studies of process temperature influence on the technological and design parameters of electrodialysis apparatus; the results of experimental studies of physical and chemical properties of Soviet-made membranes In relation to the temperature;
and the
results of the optimization of electrodialysis process at elerated temperatures by means of an economic-mathematical Quantitative estimation of polarization, ing badly with, the
model.
a phenomenon interfer-
electrodialysi8 process, consists mainly'-of
the determination cf critical current density at various hydrodynamic conditions in the electrodialysis
cell; critical Ourrent
density depending upon the membrane selectivity and mass transfer conditions. The intensity of mass transfer depends, upon the parameters of flow hydrodynamics,
in its turn,
i.e. flow rate, vis-
cosity and diffusion coefficient. Conditions in the eleotrodialysis cell corresponding to the.value are as follows: ZFCD
(1) iLlI??= f ( -t)btim where iLin_critical current density, A/m2; C - concentration of the solution for desalination, g-eq/l; Z - ionic valency; F - Faraday number, A s/g-eq; D - diffusion coefficient, cm2/s; (2 - t) - difference of numbers of ionic transport in the membrane and in the solution;Sl,+,-diffusion layer depth at the membrane surface at the side of desalinated flow according to the critical current density, cm. Reference 3 contains the equation for determining maximum depth of the diffusion layer in the electrodialysis cell. The proposed equation was derived with en account for the summarized experimental results and the following form: stim=
(2)
where 3 - kinematic viscosity, cm2/s; 1 - distance between the turbolator elements cm; dd - thickness of the desalination cell, cm; h - heigh of the turbolator element, cm; K - empirical coefficient characterizing the turbolator; V - desalinated flow rate, cm/s. Any significant increase in critical current density is possible when artificial turbulization of the desalinated flow by means of turbolator jumpers is combined with the decrease of the solution viscosity by heating the solution. Temperature dependence of the water viscosity is the following: (3) ? =%[I + 0,0158 (T - To)]-2 where$,ga- kinematio viscosity; T, To - absolute temperature, The movement of the hydrated ions in the membrane-near desalinated layers may be considered from the point of the hydrodynamic theory of diffusion. In this case the diffusion coefficient is described by the Stocks-Einstein equation: (4) where N - Avogadro number; d - parameter having the length dimen-
tionality; g - coefficient of volume viscosity; Do - diffusion coefficient at 298'K.
The availability of turbolising elements situated in the cells of the electrodialyais apparatus provides the main hydraulic resistance along the flow path. Decrease in the solution viscosity results in the decrease of friction in the system due to the solu tion heating. Liquid flow regime is characterized by the Reinolds number which is included into the expression for estimating head losses caused by the friction along the length and by local resis. tance in the cells with labirynth-netlike spacers. Finally, taking into account equation (3) we receive the expres. sions for estimating the hydraulic resistance along the distance between the turbolator (1) elements and for the local resistance in the turbolator elements:
"LT
0.0092
A=
4vR (I+O.OI% (f-25Wj
2hS2+ 4rR II+o.ow~~-P~~~J~ -
I m
K =*I+ LI ; a - thickness of T the turbolator jumpers along the flow (cm); K - constant, which determines the turbolator design; & - coefficient considering the flow narrowing along the cell thickness at the point of the turbolator jumpers location; Relzma certain Reinolds number which provides for the self-similarity of the free flow in the cell (Rslim = 10000). Thus, we have received the expressions which establish the relation of critical current density and hydraulic resistance to the design parameters of the electrodialysis cell with a labirynth-netlike spacer depending upon the process temperature. The calculation of the diffusion layer depth showed i&,,, increase* with temperature elevating. During the analysis it was established that this phenomenon results from the increase of (+)"3 value, where D is increasing end $ is decreasing according to the temperature increase. This indicated the enlargement of the aone where the rate of mass transfer owing to the molecular diffusion where A=101,2; A*=66,8;
h*= I - %
257
in the membrane-near
leyer excesses over the rate of convectional
mass transfer. Therefore, despite the increase of the diffusion layer depth, critical current density increases.with
temperature
rizeing. In order to check the theoretical preconditions
described ear-
lier, studies have been carried out using laboratory and full-sea. le apparatus. The reaulte of the experimental 8tUdieS of critical current density dependence upon the temperature are given in graphic form in Fig.1. Given for comparison in the same figure are the de8ign value8 of oritical current density.
1 283 I c, =0,054 r+J;
I
293
I
303
I
I
1
319 329 T, 'K
u, cm/s: i-40; 2-48.0; 3-220 4-40.0;5-50.0
Fig. 1. Critical current density as a fuction of the solution temperature.
258 The type of functional dependence of experimentally determined i c,it_valuesupon the temperature corresponds to the type of the same dependence for theoretically determined i,,(t. values. Critical current density in the temperature range of IO-50°C increases by 2,5-4,2% per l°C, in average. The results of experimental evalution of the hydrodynamic process parameters depending upon the temperature are given in Table 1,which contains also theoretical design values. As is obvious from the following table the experimental results coincide satisfactorily with the design data. Some differences in head losses values (H), hydraulic resistance coefficient values (a) and diffusion layer depth values (8) can be explained by the increase in flow rate (v) values due to the swelling of the membranes and labirynth-netlike spacers. In general it should be noted that hydraulic resistance of labirynth-netlike spacers decreas es by 1% per l°C in average in the mentioned temperature ranges. Studies were carried out using an experimental full-scale apparatus. The main objects of the studies included: establishment of the adequacy of the results received when using a compact apparatus and the results received when using the ssme initial parameters under the conditions close to those of the full-scale apparatus; estimation of the temperature influence on the desalination rate and power consumption per unit of volume of partially desalinated water and salt transported through the membranes; estimation of the temperature influence upon the parameters of the apparatus operating at partial desalination of fresh water with the salinity
of 0,3 - 1,0 g/l; estimation of the temperature influence on the degree of the solution concentration in the saline cells of a fullscale electrodialysis apparatus for desalination. The effciency of electrodialysis process depends upon ,thephysical and chemical properties of the ion-exchange membranes, i.e. conductivity; osmotic, diffusion and hydrodynamic permeability; resistance to the influence of various external factors. While designing and operating the ap aratus for desalination-concentration at elevated temperatures it is necessary to consider the changes in these properties with temperature increase, otherwise considerable mistakes in design and selection of technological parameters as well as in evaluation of the process efficience are
TABLE 1 Comparison of design values and experimental results of investigating hydrodynamic parameters of electrodialysis process at elevated temperatures. T;'K 283 283 313 313 283 283 313 313 ::; 313 313
Re
H,cm/m
164,4 100,4 -"105,o 55,4 321,4 -"55,o 224,9 324,8 -'*238,C 642,9 142.9 -"143,o 398,O ,)@, 487Vo 440,C 964,3 301,7 -"300,o
A 5,94 4,;;" ;:V& 3:46 2,08 2,08 2,57 2,84 I,95 1,94
v,cm/s 990
,n_ n_ ,1)_
18,0 _n, -11, ,)I.. 21r: ,n, ,)),
1 , cm: h/d 8.102,cm 194 ,*I, ..1*_ _1), ,*, ,n,n_n_ ,n, _n, _n_ ,n_
095 ,fi, _fi_ _n_ ,n, ,n,n,w, -u_ _n_ _n_ ,n_
0,854 ?% 1:255 0,646 0,695 0,82 0,887 0,528 X$Z 01724
des. exp. des. exp. des. exy. des. exp. des. exp. des. exe.
possible. In order to determine the extent of the changes in the mentioned properties depending upon the temperature an experimental installation was designed. The installation included: a mercury contact cell for the estimation of membrane conductivity; and two cells for determining the osmotic, diffusion and hydrodynamic permeabilities. hathematical processing of the experimental data on U-40 and U-40 membrane properties resulted in the following empirical relationships of the temperature dependence of the membrane characteristics: - of specific membrane conductivity e%= Al(T-273)0'5 + A2Co'35. e (7) z empirical coefficients equal, respeotively,to: where Al, A2, A3 for NA-40 membranes: Al = 46, A2 = 650, A3 = 1210; for hK-40 membranes: A, = 40, A2 = 650, A3 = 1350 - of osmotic membrane permeability: (8) Josm = (A, + A2 C) . e = empirical coefficients equal to: where Al, A2, A3 for U-40 membranes: Al = 15, A2 = 13, A3 = 1575; for UK-40 membranes: Al = 50, A2 = 13, A3 = 1598
- of coefficienttof diffusion through the membranes: Ddi,.= A1. Cn. e k.~*-8
(IO)
where A;, A2 = empirical coefficients equal to: for I&A-40membranesr A, = 12,4; A2 = X,8; n P 0,335; for UK-40 membranes: A, = 1,31; A2 = 28,0; n = 0,348. The checking caiculations of ze, Josm, Jdif, Ddif from the formulas (7.~110) showed satisfactory coincidence of the results with the experimental datav Some deviations (up to 15-18%) are observed at the concentrations equal to the limit of salt solubility and a&othe peak values of the solution temperature range selected for the studies. These deviations can be explained by the activity coefficient variations at high concentrations as well as by the physical and chemical properties disturbance caused by high temperatures. Equations (3-10) determining the changes in technological parameters of the electrodialysis apparatus and variations in physical and chemical membrane properties at temperature fluctuations were introduced into the economic-mathematicalmodel of the electrodialysis process. The model allows to calculate the technological parameters and to select optimal modes of operation of the electrodialysis apparatus. When passing through the electrodialyzer cells desalinated solutions are heated by means of the heat released in the process of electric current passing through the solution. For considering this heat with the aim of subsequent utilization in the process the economic-mathematicalmodel was supplemented by the mathematical description of mass transfer in an electrodialysis cell in the direct current field with an account for temperature fluctuations along the flow path. Using the corrected model calculations and optimization of the electrodialysis process mode were carried out for specific conditions. A predesalination apparatus operating in the scheme of the. mica1 water treatment at one of the hoscow heat power stations was taken as an initial design variant. The capacity of the predesalination apparatus was 100 m3/h at the initial salinity 0,3-0,g g/l and 50% salt removal for a single pass through the apparatus. Calculations were carried out for the two technological schemes of an electrodialysis apparatus - coourrent flow and rececling. The calculation results are given in Table 2.
261
TABLE 2 Temperature Ginit Ti;tit*Topt g/l K
Cfin g/l
Cocurrent flow scheme 293 0,80 0,45 293
553
0,90 ,n_
_ 0:45
s93
553
-"0,60
0:;O
293
553
o"zo
-;30
293
j53
353
A 0,30 ,w_
553
-"0.30
Diffe- DiffeP Ri rence cm/s thousand roubles rence thaias.roubles roubles roubl.
202.6 :;;+ 129:o 201,I 141,3
0,099 0,111
0,086
0,;5 _ A ii"15
86,5
0,135 0,066 0,109 0,052
Recycling echeme 293
0,45
293
O:gO _ :rgO
_w_ 0,23
180.5 141,8 i%:
0,126 0,102 0,199
o,io
0:0
179:9 141,5 ii";5 i76,9 138,8 0,06 417,l ,L_ ,n190,3
"0% 0:102 0,124 0,101
i93
513 ;53
s93
JI3
-"-
%3
0,30 0430 -
s93 293
553
-n_
"o$f ,
IO
5058
0,028
3058
;,016
5958
0,039
3818
;,025
87:6
0,069
6676
0,057
;8,7
0,024
129,2
0,073
;a,4
0,024
%,I
0,023
2;6,!3
0,131
,I*,
24 ,w, IO ,*24 ,~, IO ,R, 24 ,I(24 ,n, ,n_ ,w(, ,f@, ,n,n, ,n-n, ,n-
The calculation results showed that the economic efficiency for one and the same apparatus may be different depending upon the initial and final salinity values of the desalinated water. The greatest effect from the solution heating is observed when desalinating up to very low concentration values; and when the conduc tivity of the solutions is very low at ordinary,temperature, whereas the expenses end power consumption are rather high, The influence of the solution temperature on economic indicators of desalination is shown in Fig.2, where C - capital expenses, E - equated expenses, 0 - operational expenses, P - cost of desalination, N - apparatua quantity. ap
262
Fig. 2. Main technical and economic characteristics of an electrodialysis apparatus as a function of desalinated water tempera ture at cocurrent flow scheme with recuperation of the heat the outcoming fluxee. REFERENCES l.,F.Leits, 5th Inter.Symp.Fresh Water from the Sea,v.3(1976)105 2 Ch.Forgacs, Ith Inter.Symp. Water Desal., (1965) 3 3 V. Smagin and D. Yaroshevcky in book wTheoretica1 Principles of Deminer. of Fresh Water", Moscow "Nauka" (1975).