- Email: [email protected]
Normalized space velocity—a new figure of merit for waste water electrolysis cells
SHORT COMMUNICATION NORMALIZED SPACE VELOCITY-A NEW FIGURE OF MERIT FOR WASTE WATER ELECTROLYSIS CELLS G. KRBYSA Dechema-Institute,
Theodor-Heuss-Alkc
25, D&00
Frankfurt/hi.
97, Federal Republic of Germany
(Received 27 October 1980; in revised from 15 January
metal is generally negligible as compared to the overall purification costs. Considering a waste water puri!ieation process from an eeooomie point of view the specific investment costs per unit volume of waste water are decisive. In the chemical eqinecring a suitable figure of merit relevant to this situation is the space velocity,
NOMENCLATURE specific electrode surface inlet concentration outlet concentration Faraday number current current density limiting current density mass transfer coef6cient mokcular weight conversion degree volume flow rate cell volume charge number current cfliciency space time yield space velocity normalized space velocity normalized molar space velocity residence time, electrolysis time
(cm ‘) (mol cm- 3, (mol cm-x) (Asmol-r) (A) (Acn-a) (A cm-“) (cm s-r) (g mol _ ‘) (1) @rlxs-1) (cm? (I) (I)
p,
=vo VR
which can be calculated in a simple way from the product related space time yield.
:B
P
ps =-=(co -c,)M s
(c, - C,)VRZF
(4)
p, means the volume in cm3 of waste water which can he treated within a ceil volume of I em3 during 1 s. In general, the space velocity is dependent on the inlet concentration and the conversion degree. Therefore, the space velocity does not allow a performance comparison of reactors being independent of waste water properties, Assuming that the whole electrode is working under limiting current density conditions (i 2 &) one can show that the space velocity is independent on the mkt concentration_ The ideal tube reactor theory yields the expression[7]
cgclp-’s;V ;cms ;z’ls’:)
1981)
1
(mol cm-“s-1) (s)
f =zFv,c,[l-exp(-A&r)] During the fast years a large number of new ekctrocbemical cells offering various advantages over cells of traditional design have been suggested in the literature. This develop ment has stimulated the discussion of suitable figures of merit as a basis of an objective performance comparison[ 1,2]. In the case of new electrochemical reactors for the purifrcation of waste waters the general cost situation is characterized by very high investment costs as compared to the running costs[3,4]. This means that the most important figure of merit should be strongly correlated to the investment costs. In electrochemical engineering the space time yield is in general used for this purpose.
(5)
showing that
The same condition also holds for a batch reactor always working under limiting current density conditions. If r means the residence time of an ideal tube reactor or the electrolysis time of a batch reactor, then the conversion degree is given
WI
u, = I -
exp( - A,kr) #/(c,)
(7)
Introducing (co-c1)=u*co The space-time yield is thus the amount of product which can be produced within 1 cm’ of cell volume during 1 s. An alternative way to calculate the space time yield using the inlet and outlet concentrations for the removed species of a waste water was suggested by Gallone[S]. %/Q-l A,kc, p=2,303.Igc,lE,
(2)
Multiplying the right hand expression of this formula with the molecular weight M gives the space time yield iB the same dimension ss (1). Using simple correlations based on the electrochemical ideal tube reactor or the batch reactor theory[6], it can be shown that (1) and (2) are identieal[5]. However, in the case of the purification of waste. waters containing less valuable metals the price of the recovered
(8)
into (4) yields
Conditions (6) and (7) clearly show that the space velocity is independent on the inlet concentration. Substituting u, in (7) by (8) and applying simple algebraic steps yield
W) Since from (3) the space veltity
is equal to l/r it follows that 1 - -. P.
CO
ig-
Cl
1694
G. KREYSA
TIus proportionality suggests the definition of a nor~~lized space velocity being related to an arbitrary fixed conversion degree. It may be appropriate to set u, = 0.9
(12)
since then 1
lgc”= In __ =t. (13) ( 1 -up > Cl If p: means the space velocity related to co/c< = 10 and p, is the space velocity for any c&i then it follows from (I I) 1 P, ~_ Ig@,/c,) -2
(14)
Rearranging and introducing (4) yields
(15) This normalized space veltity means the volume of waste water inem’ for which theconcentration oftheimputitiescan be reduced by a factor of 10 during 1 s in a reactor volume of 1 cm). The more appropriate dimension I/lb results by multiplication with 3.6. 103.
Table 1. Normalized space velocities of various electrochemical waste water cells cell type Eco-CelI[tl] Beat rod all[9] Swiss roll cell (anial)[3] Swiss roll cdl (radii)[S] Porous flow-through ccU[lO] Packed bad cell[ll] Fluidized bed rxll[ 121 Rotating packed bed cell[ 133 Rolling tube ceU[9]
reactant feed instead of the reaction mixture feed volume. This normalized molar space velocity,
p:/I/lh 20 0.2 20 12 0.9 28 ZO 0.4
scale iod. ind. lab. lab. lab. ind. ind. lab. ind.
For electrochemical production cells it may be convenient to express the normalized space velocity in terms of the molar
means the moles of reactant which can uudergo a conversion of 90 per Cent during I s in a reactor vohune of 1 cm3. With respect to the fact, that the conversion degree strongly influences the specific raw materials costs and the costs of product purification this figure may be of more economic relevance than the space time yield. In Table 1 the normalized space velocities calculated from literature data on various modem electrochemical reactor systems tested for purification of metal containing waste waters both in industrial and kboratory scale are summarized. REFERENCES 1. N. Ibl, 31st ISE-Meeting, Venice, September (1980). 2. F. Goodridge, 3lst ISE-Meeting, Venice, September (1980). 3. P. M. Robertson and N. Ibl, J. appl. Electrockem. 7,323 (1977). 4. G. Kreysa, Annual Meeting of Dechema, Frankfurt/M., June (1980). 5. P. Gallone, P. L. I% Anna and P. L. Bonora, Moreriots Chem. 3.285 (1978). 6. E. Heitr and G. Kreysa, Grundlagen der Technischen Elektrochemie, Verlag Chemie, Weinheim, New York (1977). 7. G. Kreysa, Habilitationssehrift, Universitat Dortmund (1978). 8. F. S. Holland, Chem. Ind. 453 (1978). 9. R. Kammel and H.-W. Lieber, Galuonotechnik 69, 687 (19783; W. Gotzelmann, Galvanorechnik 70, 569 (1979). 10. R. S. Wenger and D. N. Bennion, J. appt. Electrochem. 6, 385 (1976). 11.G. Kreysa, Deehema-Monographie Nr. 1775-1801, Vol. 86/H, p. 757 (1980). 12. G. van der Heiden. personal communication. 13. G. Kreysa and R. Brandner, 3lsl ISE-Meeting. Venice, September (1980).
Theodor-Heuss-Alkc
25, D&00
Frankfurt/hi.
97, Federal Republic of Germany
(Received 27 October 1980; in revised from 15 January
metal is generally negligible as compared to the overall purification costs. Considering a waste water puri!ieation process from an eeooomie point of view the specific investment costs per unit volume of waste water are decisive. In the chemical eqinecring a suitable figure of merit relevant to this situation is the space velocity,
NOMENCLATURE specific electrode surface inlet concentration outlet concentration Faraday number current current density limiting current density mass transfer coef6cient mokcular weight conversion degree volume flow rate cell volume charge number current cfliciency space time yield space velocity normalized space velocity normalized molar space velocity residence time, electrolysis time
(cm ‘) (mol cm- 3, (mol cm-x) (Asmol-r) (A) (Acn-a) (A cm-“) (cm s-r) (g mol _ ‘) (1) @rlxs-1) (cm? (I) (I)
p,
=vo VR
which can be calculated in a simple way from the product related space time yield.
:B
P
ps =-=(co -c,)M s
(c, - C,)VRZF
(4)
p, means the volume in cm3 of waste water which can he treated within a ceil volume of I em3 during 1 s. In general, the space velocity is dependent on the inlet concentration and the conversion degree. Therefore, the space velocity does not allow a performance comparison of reactors being independent of waste water properties, Assuming that the whole electrode is working under limiting current density conditions (i 2 &) one can show that the space velocity is independent on the mkt concentration_ The ideal tube reactor theory yields the expression[7]
cgclp-’s;V ;cms ;z’ls’:)
1981)
1
(mol cm-“s-1) (s)
f =zFv,c,[l-exp(-A&r)] During the fast years a large number of new ekctrocbemical cells offering various advantages over cells of traditional design have been suggested in the literature. This develop ment has stimulated the discussion of suitable figures of merit as a basis of an objective performance comparison[ 1,2]. In the case of new electrochemical reactors for the purifrcation of waste waters the general cost situation is characterized by very high investment costs as compared to the running costs[3,4]. This means that the most important figure of merit should be strongly correlated to the investment costs. In electrochemical engineering the space time yield is in general used for this purpose.
(5)
showing that
The same condition also holds for a batch reactor always working under limiting current density conditions. If r means the residence time of an ideal tube reactor or the electrolysis time of a batch reactor, then the conversion degree is given
WI
u, = I -
exp( - A,kr) #/(c,)
(7)
Introducing (co-c1)=u*co The space-time yield is thus the amount of product which can be produced within 1 cm’ of cell volume during 1 s. An alternative way to calculate the space time yield using the inlet and outlet concentrations for the removed species of a waste water was suggested by Gallone[S]. %/Q-l A,kc, p=2,303.Igc,lE,
(2)
Multiplying the right hand expression of this formula with the molecular weight M gives the space time yield iB the same dimension ss (1). Using simple correlations based on the electrochemical ideal tube reactor or the batch reactor theory[6], it can be shown that (1) and (2) are identieal[5]. However, in the case of the purification of waste. waters containing less valuable metals the price of the recovered
(8)
into (4) yields
Conditions (6) and (7) clearly show that the space velocity is independent on the inlet concentration. Substituting u, in (7) by (8) and applying simple algebraic steps yield
W) Since from (3) the space veltity
is equal to l/r it follows that 1 - -. P.
CO
ig-
Cl
1694
G. KREYSA
TIus proportionality suggests the definition of a nor~~lized space velocity being related to an arbitrary fixed conversion degree. It may be appropriate to set u, = 0.9
(12)
since then 1
lgc”= In __ =t. (13) ( 1 -up > Cl If p: means the space velocity related to co/c< = 10 and p, is the space velocity for any c&i then it follows from (I I) 1 P, ~_ Ig@,/c,) -2
(14)
Rearranging and introducing (4) yields
(15) This normalized space veltity means the volume of waste water inem’ for which theconcentration oftheimputitiescan be reduced by a factor of 10 during 1 s in a reactor volume of 1 cm). The more appropriate dimension I/lb results by multiplication with 3.6. 103.
Table 1. Normalized space velocities of various electrochemical waste water cells cell type Eco-CelI[tl] Beat rod all[9] Swiss roll cell (anial)[3] Swiss roll cdl (radii)[S] Porous flow-through ccU[lO] Packed bad cell[ll] Fluidized bed rxll[ 121 Rotating packed bed cell[ 133 Rolling tube ceU[9]
reactant feed instead of the reaction mixture feed volume. This normalized molar space velocity,
p:/I/lh 20 0.2 20 12 0.9 28 ZO 0.4
scale iod. ind. lab. lab. lab. ind. ind. lab. ind.
For electrochemical production cells it may be convenient to express the normalized space velocity in terms of the molar
means the moles of reactant which can uudergo a conversion of 90 per Cent during I s in a reactor vohune of 1 cm3. With respect to the fact, that the conversion degree strongly influences the specific raw materials costs and the costs of product purification this figure may be of more economic relevance than the space time yield. In Table 1 the normalized space velocities calculated from literature data on various modem electrochemical reactor systems tested for purification of metal containing waste waters both in industrial and kboratory scale are summarized. REFERENCES 1. N. Ibl, 31st ISE-Meeting, Venice, September (1980). 2. F. Goodridge, 3lst ISE-Meeting, Venice, September (1980). 3. P. M. Robertson and N. Ibl, J. appl. Electrockem. 7,323 (1977). 4. G. Kreysa, Annual Meeting of Dechema, Frankfurt/M., June (1980). 5. P. Gallone, P. L. I% Anna and P. L. Bonora, Moreriots Chem. 3.285 (1978). 6. E. Heitr and G. Kreysa, Grundlagen der Technischen Elektrochemie, Verlag Chemie, Weinheim, New York (1977). 7. G. Kreysa, Habilitationssehrift, Universitat Dortmund (1978). 8. F. S. Holland, Chem. Ind. 453 (1978). 9. R. Kammel and H.-W. Lieber, Galuonotechnik 69, 687 (19783; W. Gotzelmann, Galvanorechnik 70, 569 (1979). 10. R. S. Wenger and D. N. Bennion, J. appt. Electrochem. 6, 385 (1976). 11.G. Kreysa, Deehema-Monographie Nr. 1775-1801, Vol. 86/H, p. 757 (1980). 12. G. van der Heiden. personal communication. 13. G. Kreysa and R. Brandner, 3lsl ISE-Meeting. Venice, September (1980).