Modeling of a packed-bed electrochemical reactor for producing glyoxylic acid from oxalic acid

Chemical Engineering Science 62 (2007) 6784 – 6793 www.elsevier.com/locate/ces

Modeling of a packed-bed electrochemical reactor for producing glyoxylic acid from oxalic acid Jun Li ∗ , Xiaohui Hu, Yuzhong Su, Qingbiao Li Department of Chemical and Biochemical Engineering, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen, Fujian 361005, PR China Received 24 August 2006; received in revised form 13 February 2007; accepted 13 February 2007 Available online 24 February 2007

Abstract A two-dimensional reactor model was established for a packed-bed electrochemical reactor with cooled cathode (PERCC) for producing glyoxylic acid from oxalic acid based on the system’s reaction kinetics, mass conservation equation, and the equation of charge conservation in terms of solution-cathode potential to describe the distributions of glyoxylic acid concentration and electrolyte potential in the cathode compartment of the PERCC. The equation for a circulating mixer was also presented to account for the accumulation of glyoxylic acid in the catholyte of a batch electroreduction process. Using the orthogonal collocation approach, the partial differential equations of the model could be converted into sets of algebraic equations and be numerically solved. The effects of operating temperature, conductivity of catholyte, operating cathode potential, and volumetric flow rate of the catholyte on the current efficiency and concentration of glyoxylic acid were simulated and discussed, with emphasis on the current densities generated from main and side reactions. The model was used in a batch operation process and a continuous operation process, with the predicted results being generally in good agreement with the experimental data for both the cases. 䉷 2007 Published by Elsevier Ltd. Keywords: Glyoxylic acid; Packed bed; Electrochemical reactor; Cooled cathode; Mathematical modeling; Continuous operation

1. Introduction Glyoxylic acid, the simplest aldehyde acid, is extensively utilized in many fine chemical industries such as perfumery, pharmaceutical, cosmetic, etc. Various reduction or oxidation methods in industrial production of glyoxylic acid have received great attention by many researchers. Among those methods, the electrochemical reduction of oxalic acid to produce glyoxylic acid has been suggested as one of the most acceptable technologies because it meets the increasing and stringent requirements for environmental protection following the rapid development of world economy. It has also many other advantages, such as less investment for the processing plants, low cost of the raw material, and easy separation of the product. Although the production of glyoxylic acid by the electrochemical reduction of oxalic acid has been commercialized for many years, there are still two major problems which remain incompletely solved: the cathode material (lead) can be easily ∗ Corresponding author. Tel./fax: +86 592 2183055.

E-mail address: [email protected] (J. Li). 0009-2509/$ - see front matter 䉷 2007 Published by Elsevier Ltd. doi:10.1016/j.ces.2007.02.021

deactivated due to the presence of metals with low hydrogen overvoltage (Scott, 1986); in addition, the traditional parallel electrode reactor (PER) has usually a low space–time yield (STY). With respect to the former problem, many improvements were proposed either by chemical cleaning (Goodridge et al., 1980) or by use of chemical additives (activators) (Ochoa et al., 1993; Zhou et al., 2003); also it is possible to find some replaceable cathode materials such as platinum-based Pb–Sb catalysts investigated by Xia et al. (2001). For the latter case, we explored the packed-bed electrochemical reactor with cooled cathode (PERCC) (Fan et al., 2004) in an engineering sense based on the concept suggested by Scott (1992) with the purpose to improve the STY of the traditional electrochemical reactors such as PER. Removal of the reaction heat to maintain a constant operating temperature is a key factor for the reduction of oxalic acid in a packed-bed electrochemical reactor. The PERCC is a three-dimensional (3-D) electrochemical reactor installed with cathode packings between series of cathode tubes that act either as heat exchangers or reaction surfaces. For a simple case, Fig. 1 shows a batch operation experiment using PERCC

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

6785

two-dimensional (2-D) PER, the distributions of current, potential, temperature and concentration within the 3-D reactor are more complicated. Meanwhile, the geometry of electrodes, conductivity of electrolytes and electrodes, and hydrodynamics of electrolytes in a 3-D reactor may also obviously influence the distributions of the variables mentioned above. Consequently, theoretical surveys of the reactor in detail are necessary for an optimum operation and a further scale-up of the process. This work is aimed at the modeling of the PERCC, and introduces its applications to both a batch operation process and a continuous operation process for electroreduction of oxalic acid to glyoxylic acid. 2. Reactor model

Fig. 1. Schematic diagram of a batch electroreduction process and the PERCC reactor. (A) Cross-section of the PERCC; (a) anode chamber; (b) cathode chamber; (c) anolyte; (d) catholyte (in a circulating mixer); (e) cathode packings; (f) tube cathodes (cooling medium inside).

(Fan et al., 2004).The PERCC was composed of a cathode chamber between two anode chambers, and installed with two cathode tubes in the cathode chamber. Packings were filled into the space between the tubes, with the material of both tubes and packings being made of lead with a purity of 99.99%. The reaction temperature (±0.2 K) could be controlled by adjusting the flow rate and temperature of the coolant ethanol inside the cathode tubes. In the experiment, the catholyte and anolyte were saturated oxalic acid and 20% (in mass) sulfuric acid aqueous solutions, respectively, which were separated by an ion-exchange membrane (CM001) purchased from Shanghai Qiujiang Factory, China, and circulated by two magnetically driven pumps. Before the experiment, the volumetric flow rate of the electrolyte was calibrated by using a stopwatch and graduated cylinders. A PerkinElmer Lambda 35 UV/Vis Spectrometer was used to determine the glyoxylic acid concentration in catholyte at the wavelength of 220 nm.The Cannizzaro reaction (Scott, 1991) was used to detect glyoxal produced from the electroreduction of glyoxylic acid. Cathode potential (±0.01 V), the voltage between a cathode feeder and a saturated calomel electrode (sce), was measured by a digital Ohmmeter and controlled by tuning a power supply provided by Xiamen Rectifier Factory, China. The cathode feeder was connected to the cathode tubes, and the sce was connected with a luggin capillary close to the boundary (x = x0 ) where the ionexchange membranes were installed. Saturated oxalic acid solution of the catholyte was guaranteed by adding excess oxalic acid in the circulating mixer throughout the experiment. Because the PERCC has a relatively large specific area, it is possible to achieve a high STY for electroreduction of oxalic acid, and carry out a continuous operation mode feeding the saturated oxalic acid solution at one side of the reactor and producing glyoxylic acid with the desired concentration at the other side of the reactor. In comparison with the

Fundamentals and applications of the packed-bed electrochemical reactor were intensively studied in the past (Newman and Tobias, 1962; Alkire and Ng, 1977; Storck et al., 1982, Xu et al., 1992, Zhang et al., 1999). Indeed, a mathematical model of a reactor should be capable of describing the distributions of product or reactant concentrations in the reactor, electrolyte temperature and electrolyte potential. The fundamental equations of a model should therefore include: (1) reaction kinetics; (2) equation of conservation of charge; (3) equation of conservation of mass; and (4) equation of conservation of energy. Because we are interested in glyoxylic acid only and the cathode chamber is separated from the anode chamber by an ionexchange membrane for the investigated reactor, the model will be established for the cathodic region only. Since the reaction heat from the reduction of oxalic acid in the cathode chamber can be removed quickly due to the cooled cathodes employed (Fan et al., 2004), the equation of conservation of energy is avoided for an isothermal operation. To simplify the mathematical treatment, further assumptions are required: (1) both the fixed solid phase (cathode) and the liquid phase (catholyte) are continuous; (2) it is a steady plug flow in the reactor for the continuous operation process and also for the batch operation process in a period of differential time; and (3) a flow-by operation mode considering the catholyte flow direction y and the current direction x, as shown in Fig. 1, is adopted because the depth is relatively small compared with the length of the reactor. 2.1. Reaction kinetics The main reaction on the cathode surface is the reduction of oxalic acid into glyoxylic acid: i1

COOHCOOH + 2H+ + 2e− −→ COOHCHO + H2 O.

(1)

The side reactions involve further reduction of glyoxylic acid into glycollic acid or glyoxal and the generation of hydrogen: i2

COOHCHO + 2H+ + 2e− −→ COOHCH2 OH, − i3

2H+ + 2e −→ H2 , +

(2) (3)

− i4

COOHCHO + 2H + 2e −→ CHOCHO + H2 O.

(4)

6786

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

From the analysis of the product in catholyte by the Cannizzaro reaction, glyoxal could not be detected (Fan et al., 2004). Similarly, Goodridge et al. (1980) also indicated that the amount of glyoxal in their product was negligible. Accordingly, reaction (4) can be ignored. The kinetics of reactions (1)–(3) proposed by Scott (1990, 1992) is written as s k 1 k2 cR i1 = s , 2F k2 + k 1 c R

s k1 = 15.85 × 10−12 exp[−8.6E]cH ,

k2 = 2.04 × 10−6 exp[−8.3E], i2 = 2.95 × 106 cPs exp[−2.24E − 9295/T ], 2F i3 s = 7.69 × 10−17 cH exp(−19.95E). 2F

(1)

j2 E a j2 E + = − [i1 (x, y) + i2 (x, y) + i3 (x, y)]. 2 b jx jy 2

(9)

(2) 2.3. Equation of mass conservation (3)

In the equations above, i represents the current density, c is the concentration with subscript R, H, and P being, respectively, reactant (oxalic acid), hydrogen ion, and product (glyoxylic acid). Superscript s denotes the surface of cathode. E (vs normal hydrogen electrode in the equations, nhe) is the difference between the potential of a working electrode and that of a reference electrode; it is a local solution-cathode potential in catholyte, and it can be written as E = M − s (< 0), with s referring to the local potential of catholyte and M referring to the local potential of metal cathode. In addition, T is the operating temperature and F is Faraday constant. To associate the surface concentrations with the bulk concentrations of oxalic acid (cR ), glyoxylic acid (cP ) and hydrogen ion (cH ), the following mass transfer equations are used: s i1 = 2F k LR (cR − cR ),

(4)

i1 − i2 = 2F k LP (cPs − cP ),

(5)

s i1 + i2 + i3 = 2F k LH (cH − cH ),

(6)

where kLi (i = R, P , H ) are the mass transfer coefficients of oxalic acid, glyoxylic acid and hydrogen ion in catholyte, which can be estimated by (Storck et al., 1982) kLi /u = 0.45(Re)−0.41 (Sc)−2/3 ,

where, as before, s is the local potential of catholyte, i1 +i2 +i3 is the overall current density, and b is the effective conductivity of catholyte. Because the conductivity of metal electrode is very large compared with that of the catholyte, the potential change within the lead cathode is neglected, and M is equally distributed in the cathode chamber. Therefore, an alternative charge conservation equation in terms of the solution-cathode potential E(=M − s ) can be obtained from Eq. (8):

(7)

where the Reynolds number is Re = ud e /(> 10) with the equivalent diameter calculated by de = 4/a(1 − ), and the Schmidt number is Sc = /Di . In the expressions of Re, Sc and de , u and  are, respectively, the superficial velocity and the kinematic viscosity of catholyte, Di (i = R, P , H ) are the diffusion coefficients of oxalic acid, glyoxlic acid and hydrogen ion in catholyte, respectively,  is the porosity of the packing cathode, and a is the specific area of the overall cathode.

Under steady-state operation, the mass conservation equation for glyoxylic acid neglecting the axial dispersion is j2 cP (x, y) jcP (x, y) −u jy jx 2 a [i1 (x, y) − i2 (x, y)] = 0. + 2F

DP

2.4. Boundary conditions As Fig. 1 shows, the concentration of glyoxylic acid at the entrance of the reactor (y = 0) is assigned to cin ; both the concentration and the solution potential are symmetrically distributed about the y-axis (x = 0). Further we adopted the continuity assumption (Langlois and Coeuret, 1990) for the potential at the entrance and exit of the reactor. Since no mass transfer of glyoxylic acid proceeds on the boundary (x = x0 ) of the cathode chamber, the solution potential s is a constant (denoted as c ), indicating that Ec = M − c , the solutioncathode potential at x = x0 , is also a constant; this Ec is the socalled cathode potential fixed in experiment for controlling the selectivity of producing glyoxylic acid. Consequently, the use of Eq. (9) instead of Eq. (8) has an evident significance of the direct connection of the model with the experimental operation conditions. In summary, the boundary conditions for potential and concentration (see Fig. 1) are y = 0, 0 < x < x0 , y = y0 , 0 < x < x0 , x = 0, 0 < y < y0 , x = x0 , 0 < y < y0 ,

2.2. Equation of charge conservation

(10)

cP = cin ,

j jE = − s = 0, jy jy

jE j = − s = 0, jy jy jcP = 0, jx jcP = 0, jx

jE j = − s = 0, jx jx

(11a) (11b) (11c)

E =  M − c = Ec . (11d)

In the catholyte phase, the potential field obeys Ohm’s law which gives the charge conservation equation (Alkire and Ng, 1977)

2.5. Nondimensional equations

j2 s j 2 s a + = [i1 (x, y) + i2 (x, y) + i3 (x, y)], 2 2 b jx jy

It is convenient to define the following dimensionless variables: X = x/x0 ; Y = y/y0 ;  = E/Ec ; C = cP /c0 ;

(8)

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

Cri = cis /c0 (i = R, P , H ). With these definitions, the model equations (9) and (10) can be rearranged to a1

j2  j2  + jX 2 jY 2 = a2

1 + 7.7696 × 10−6 CrR CrH c02 exp(−0.3Ec ) (12)

j2 C jC − jY jX 2 = −a5

t = 0,

cin = 0.

(19)

The exit concentration of glyoxylic acid is expressed as cout = c0 × C(Xj , Y8 )

CrR CrH exp(−8.6Ec )

1 + 7.7696 × 10−6 CrR CrH c02 exp(−0.3Ec )

+ a6 CrP exp[−2.24Ec  − 9295/T ]

(13)

and Eqs. (4)–(6) can be reduced to −6

CrR CrH c02 exp(−0.3Ec )

= kLR (cR /c0 − CrR ),

(j = 1, . . . , 8),

(20)

where C is calculated from Eqs. (12) and (13) at a given cin /c0 . The bar above C refers to an average of the calculated concentrations at the eight collocation points as will be specified later. Then, the working equation of the mixer becomes V dcin /dt = Q(c0 × C(Xj , Y8 ) − cin ).

15.85 × 10−12 c0 CrR CrH exp(−8.6Ec ) 1 + 7.7696 × 10

(18)

where V is the mixer volume, Q is the volumetric flow rate of catholyte that relates the superficial velocity u to the cross area A of the cathode chamber by Q = uA. The initial condition of Eq. (18) is

CrR CrH exp(−8.6Ec )

+ a3 CrP exp[−2.24Ec  − 9295/T ]

a4

acid and adding excess oxalic acid. Assuming that the catholyte is fully mixed, the mass conservation for the mixer is V dcin /dt = Q(cout − cin ),

+ a3 CrH (2.607 × 10−23 ) exp[−19.95Ec ],

6787

(21)

4. Simulation (14) 4.1. Simulation conditions and numerical method

15.85 × 10−12 c0 CrR CrH exp(−8.6Ec )

1 + 7.7696 × 10−6 CrR CrH c02 exp(−0.3Ec ) − 2.95 × 10 C exp(−2.24Ec  − 9295/T ) 6

= kLP (CrP − C),

(15)

15.85 × 10−12 c0 CrR CrH exp(−8.6Ec )

1 + 7.7696 × 10−6 CrR CrH c02 exp(−0.3Ec ) + 2.95 × 106 C exp(−2.24Ec  − 9295/T ) + 7.69 × 10−17 CrH exp(−19.95Ec ) = kLH (cH /c0 − CrH ),

(16)

where a1 = y02 /x02 , a2 = −15.85 × 10−12 2F C 20 y02 a/Ec b , a3 = −5.9 × 106 F y 20 ac0 /Ec b , a4 = DP y0 /ux 20 , a5 = 15.85 × 10−12 C0 y0 a/u and a6 = 2.95 × 106 y0 a/u are dimensionless parameters. The corresponding nondimensionlized boundary conditions are j Y = 0, 0 < X < 1, C = cin /c0 , = 0, (17a) jY Y = 1, 0 < X < 1,

j = 0, jY

X = 0, 0 < Y < 1,

jC = 0, jY

j = 0, jY

(17c)

X = 1, 0 < Y < 1,

jC = 0, jX

 = 1.

(17d)

(17b)

3. Equation of the circulating mixer A typical batch operation process is shown in Fig. 1, where the catholyte has a circulating mixer for sampling glyoxylic

The cathode chamber previously introduced has a width 2x0 = 0.022 m, length y0 = 0.14 m, and depth z0 = 0.021 m; the tube cathodes have an outer diameter (OD) of about 0.008 m and an inner diameter (ID) of about 0.004 m; the packings are lead wires of 0.001 m diameter and with different lengths. With this arrangement, the overall cathode has a specific area a = 258.7 m2 /m3 , and the packed bed has a porosity of 0.357. The mixer volume (or the volume of the catholyte V ) is 2×10−4 m3 . The cathode potential (Ec =M −c ) is normally fixed between −1.4 and −1.1 V (vs sce), and therefore E in the model equations should be calibrated according to the difference between nhe and sce. Furthermore, the saturated oxalic acid concentration (cR ) is 967 mol/m3 at 293 K ( 1184 mol/m3 at 298 K, 1426 mol/m3 at 303 K); hydrogen ion concentration is equal to that in an aqueous solution with saturated oxalic acid (cH = 7.54 mol/m3 at 293 K, which is obtained from pK√a1 = 1.23 and cR of the saturated oxalic acid solution, namely, Ka1 cR ); the reference concentration c0 is 676 mol/m3 that is equal to 5% (w, mass fraction) for glyoxylic acid in aqueous solution because 5% (or more) glyoxylic acid is usually required in the final catholyte for a commercial plant. The dynamic viscosity of saturated oxalic acid solution is 1.093 × 10−3 Pa s at 293 K (1.024×10−3 Pa s at 298 K and 0.995×10−3 Pa s at 293 K) determined by a Ubbelhode flow viscometer. The density of saturated oxalic acid solution is 1039 kg/m3 at 293 K (1050 kg/m3 at 298 K and 1061 kg/m3 at 303 K) determined by a density bottle. The conductivity of catholyte (b ) is 23.1 S/m obtained by extrapolating the experimental conductivity of oxalic acid solution at 298 K (Darken, 1941) to its saturated concentration cR . The diffusion coefficient of hydrogen ion in water is DH = 7.3 × 10−9 m2 /s (Scott, 1990). In addition, because the molar fraction of saturated oxalic acid in catholyte is less than

6788

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

0.02 at 293 K, the mutual diffusion coefficient usually varies little for the solute molar fraction in the range 0–0.02 based on systems reported elsewhere (Li et al., 2001). DR can therefore be assumed as a mutual diffusion coefficient at infinite dilution by neglecting the effect of oxalic acid concentration; DP can also be assumed as a mutual diffusion coefficient at infinite dilution due to the low molar fraction of glyoxylic acid in catholyte (less than 0.012 in this study). Therefore, DR and DP can be estimated by the Wilke–Chang equation (Wilke and Chang, 1955) Di = 7.4 × 10−15

T (M)0.5 (vi × 106 )0.6

(i = P , R),

(22)

where T is the temperature (K), (=2.6), M(=18 mol/g) and  (Pa s, at T ) are, respectively, the association factor, molar mass and dynamic viscosity of pure water, vi (i =P , R) are the molar volumes of solid glyoxylic and oxalic acids, being 67.3 × 10−6 and 47.4 × 10−6 m3 /mol, respectively. For the partial differential equations (PDEs) (12) and (13) and their auxiliary equations (14)–(16), it is convenient to convert them into sets of algebraic equations by the orthogonal collocation (OC) method (Villadsen and Stewart, 1967) both in the X and in the Y directions. In Eq. (20), j = 1, . . . , 8 come from the OC method using six interior collocation points, with which enough accuracy can be achieved for the calculation (Wang et al., 2006). This transform of the equations brings 320 unknown variables (E(Xi , Yj ), C(Xi , Yj ), CrR (Xi , Yj ), CrP (Xi , Yj ), CrH (Xi , Yj ), i and j = 1, . . . , 8), whilst 320 nonlinear algebraic equations including the boundary conditions can be solved efficiently by the Newton method to obtain these unknowns. Eq. (21) can be solved by the Runge–Kutta–Fehlberg algorithms (Press et al., 1992) for ordinary differential equation (ODE) with an initial value of cin ; a new cin (equal to cout ) can then be obtained through the calculation of cout by using Eqs. (12), (13) and (20). In this way, the accumulated concentration of glyoxylic acid in the mixer at any time can be predicted. The FORTRAN language was used to implement all the calculations aforementioned. 4.2. Results and discussions To optimize the electroreduction process, the effect of four important factors, namely, the operating temperature, the operating cathode potential, the catholyte conductivity, and the catholyte volumetric flow rate, is discussed separately on the simulation results. These four factors can be conveniently controlled over a typical experiment using PERCC. At Q = 0.29 m3 /h (80 ml/s), Ec = −1.2 V and b = 50 S/m, the effect of the operating temperature (from 293 to 303 K) on the current efficiency of glyoxylic acid, i.e., eP = i1 /(i1 + i2 + i3 ), and the concentration of glyoxylic acid (w, mass fraction) in catholyte is simulated. In the calculations, the effect of temperature on the kinetics of reactions (1) and (3) is neglected because they are insensitive to temperature in the investigated range 293–303 K as indicated by Goodridge et al. (1980). As shown in Fig. 2, a high operating temperature can evidently

Fig. 2. Simulated current efficiency (eP , solid lines) and concentration (w, dashed lines) of glyoxylic acid following the electroreduction of oxalic acid under different temperatures at Q=0.29 m3 /h, Ec =−1.2 V, and b =50 S/m.

Fig. 3. Simulated current densities following the electroreduction of oxalic acid under different temperatures at Q=0.29 m3 /h, Ec =−1.2 V, and b =50 S/m. Solid lines: T = 303 K; dashed lines: T = 293 K.

decrease the current efficiency of glyoxylic acid, and slightly increases the glyoxylic acid concentration at the beginning of the reaction, but quickly decreases the glyoxylic acid concentration after about 30 min of reaction, particularly, at 303 K. Fig. 3 shows the current densities (i1 , i2 , and i3 ) of reactions (1)–(3) under two different temperatures. The same figure indicates that i2 , the current density of the side reaction (2) for producing glycollic acid, highly increases at high temperature because of the proposed CE reaction mechanism (Scott, 1990), while i1 , the current density of reaction (1) for producing glyoxylic acid, and i3 , the current density of reaction (3) for hydrogen generation, change little (due to the couple effect of the three reactions and the changes of cR and cH at different temperatures) compared to the change of i2 . Even though, the relatively fast drop of i1 explains the decrease in concentration of glyoxylic acid at 303 K after a period of reaction. At T = 293 K, Q = 0.29 m3 /h and b = 50 S/m, the effect of the operating cathode potential from −1.3 to −1.1 V on

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

6789

Fig. 4. Simulated current efficiency (eP , solid lines) and concentration (w, dashed lines) of glyoxylic acid following the electroreduction of oxalic acid under different cathode potentials at T = 293 K, Q = 0.29 m3 /h, and b = 50 S/m.

Fig. 6. Simulated current efficiency (eP , solid lines) and concentration (w, dashed lines) of glyoxylic acid following the electroreduction of oxalic acid under different catholyte conductivities at T = 293 K, Ec = −1.2 V, and Q = 0.29 m3 /h.

Fig. 5. Simulated current densities following the electroreduction of oxalic acid under different cathode potentials at T = 293 K, Q = 0.29 m3 /h, and b = 50 S/m. Solid lines: Ec = −1.3 V; dashed lines: Ec = −1.1 V.

Fig. 7. Simulated current densities following the electroreduction of oxalic acid under different catholyte conductivities at T = 293 K, Ec = −1.2 V, and Q = 0.29 m3 /h. Solid lines: b = 90 S/m; dashed lines: b = 10 S/m.

the current efficiency and concentration of glyoxylic acid is simulated. As shown in Fig. 4, a high Ec reduces the current efficiency of glyoxylic acid, but increases the glyoxylic acid concentration. This reverse effect can be illustrated with the current densities under different Ec as shown in Fig. 5: a high Ec can slightly increase i1 , hence increases the concentration of glyoxylic acid; on the contrary, a high Ec can highly increase i3 and causes a moderate increase in i2 , making i3 be comparable to i2 and decreasing quickly the current efficiency of glyoxylic acid. From this consideration, Ec is an important factor for adjusting the reaction selectivity to obtain an optimum current efficiency and an optimum concentration of glyoxylic acid. At T = 293 K, Ec = −1.2 V and Q = 0.29 m3 /h, the effect of the conductivity of catholyte from 10 to 90 S/m on the current efficiency and concentration of glyoxylic acid is simulated. As shown in Fig. 6, a high b slightly decreases the current

efficiency, but highly increases the concentration of glyoxylic acid from 10 to 50 S/m, manifesting the importance of maintaining the saturated solution of oxalic acid in the electroreduction process. As shown in Fig. 7, current densities under different b illustrate that a high b can increase i1 , hence increases the concentration of glyoxylic acid; but a high b can also increase the i2 and i3 , causing a decrease in the current efficiency of glyoxylic acid. On the other hand, the simulated results show that E(0, Y ) ranges from −0.765 to −1.2 V at b = 10 S/m (t = 5 min, T = 293 K, Q = 0.29 m3 /h), but it varies from −1.051 to −1.2 V at b = 90 S/m. This explains that b is sensitive to the catholyte potential distribution, so that it affects the current density and current efficiency of glyoxylic acid through the charge conservation equation, and finally affects the concentration of glyoxylic acid due to the couple effect of the charge conservation equation and the mass conservation equation.

6790

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

Fig. 8. Simulated current efficiency (eP , solid lines) and concentration (w, dashed lines) of glyoxylic acid following the electroreduction of oxalic acid under different catholyte volumetric flow rates at T =293 K, Ec =−1.2 V, and b = 50 S/m.

Fig. 9. Simulated current densities following the electroreduction of oxalic acid under different catholyte volumetric flow rates at T =293 K, Ec =−1.2 V, and b = 50 S/m. Solid lines: Q = 0.29 m3 /h; dashed lines: Q = 0.072 m3 /h.

Finally, the effect of the catholyte volumetric flow rate ranged from 0.072 m3 /h (20 ml/s) to 0.29 m3 /h (80 ml/s) on the current efficiency and concentration of glyoxylic acid is simulated at T = 293 K, Ec = −1.2 V and b = 50 S/m. As shown in Fig. 8, increasing the flow rate can slightly enhance the current efficiency and obviously increases the concentration of glyoxylic acid. The current densities under different Q as shown in Fig. 9 indicate that a high Q can increase simultaneously the current densities of reactions (1)–(3), and the increase in i1 is relatively larger than that of i2 and i3 , illustrating that the main reaction from oxalic acid to glyoxylic acid is mainly in mass transfer control in the studied range of catholyte flow rate. Moreover, flow rate up to 0.18 m3 /h (50 ml/s) with respect to a superficial velocity 0.1 m/s (or an interstitial velocity, i.e., u/ = 0.28 m/s) has significant effect on the current efficiency of glyoxylic acid. Yet, a high flow rate is still beneficial

Fig. 10. Simulated instantaneous distribution of solution-cathode potential along X with fixed Y (solid lines) and along Y with fixed X (dashed lines)) at T = 293 K, Q = 0.29 m3 /h, Ec = −1.2 V, b = 50 S/m, and t = 5 min.

to reaction (1) to increase the concentration of glyoxylic acid due to the control step of mass transfer, for example, KL1 increases from 6.14 × 10−5 to 1.92 × 10−4 m/s when Q changes from 0.072 to 0.5 m3 /h at T = 293 K, while KL3 increases from 1.79 × 10−4 to 5.62 × 10−4 m/s with the same change of Q. From the comparison of the simulated results shown in Figs. 2–9, we concluded that all four factors have an effective impact on the current efficiency and concentration of glyoxylic acid, among them the operating temperature and cathode potential are more sensitive to the current efficiency than other two factors in the investigated ranges. Furthermore, decreasing the operating temperature (after a short period of reaction) and increasing the electrolyte flow rate are positive to both the current efficiency and the concentration of glyoxylic acid; but the cathode potential and the conductivity of catholyte have a reverse effect on them, and should therefore be carefully selected for obtaining a high current efficency and a high concentration of glyoxylic acid. In addition, Fig. 10 shows the instantaneous distribution of solution-cathode potential along X with fixed Y (solid lines) and along Y with fixed X (dashed lines) in the reactor at T = 293 K, Q = 0.29 m3 /h, Ec = −1.2 V, b = 50 S/m and t = 5 min. It is observed that the potential does not change along X at fixed Y, while the potential is uniformly distributed along Y although it changes rapidly at about X = 0.5 and slowly around X = 0 or X = 1, indicating that the luggin capillary should be located at least at X > 0.9 to obtain a correct Ec . Fig. 11 shows the distribution of glyoxylic acid concentration along X (solid lines) and along Y (dashed lines) under the same conditions aforementioned. It is observed that the concentration changes little along X at fixed Y, and changes much along Y at a fixed Cin (here Cin = cin /c0 is not zero because of the instantaneous distribution at t = 5 min) and different X, manifesting the reaction is proceeding along Y.

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

6791

Fig. 11. Simulated instantaneous distribution of glyoxylic acid concentration along X (solid lines) and along Y (dashed lines) at T = 293 K, Q = 0.29 m3 /h, Ec = −1.2 V, b = 50 S/m, and t = 5 min.

5. Applications of the model 5.1. A batch operation process At T =293 K, Q=0.42 m3 /h (116.7 ml/s) and Ec =−1.23 V, a batch operation experiment was carried out (Fan et al., 2004). The mathematical model including the reactor model and the working equation of the circulating mixer is applied to predict the concentration and current efficiency of glyoxylic acid under the same conditions used in the experiment. As shown in Fig. 12, the predicted results are generally in good agreement with the experimental data although both the predicted current efficiency (Fig. 12a) and the predicted concentration (Fig. 12b) slightly underestimate the experimental data at the late stage of the reaction. In view of the discussions of the four factors, and assuming the equations adopted for the kinetics as accurate, the difference between the predicted data and the experimental data may most possibly result from the used average temperature (293 K) because the surface of the cathode tube has a relatively low temperature when the coolant (usually at about 283 K) flows inside. This suggests that the temperature distribution inside the reactor should also be important to accurately account for the experimental results. 5.2. A continuous operation process For a continuous operation process using PERCC, the model established can give the prediction of the length of the reactor required to achieve a desired concentration of glyoxylic acid at the exit of the reactor with feeding the saturated oxalic acid solution at the entrance of the reactor. To increase the cathode surface, the cathode chamber is designed as 0.017 m (2x0 ) × 0.12 m(4z0 )×L(y0 ) (the reactor length L needs to be predicted); four cathode chambers (each has z0 = 0.03 m) are assembled together with four cathode tubes (OD of about 0.011 m and ID of about 0.006 m). The specific area of the overall cathode including the cathode tubes and packings is 368.8 m2 /m3 (assuming it is independent of the length of the reactor) which was

Fig. 12. Comparison of experimental current efficiency (a) and concentration (b) of glyoxylic acid with predicted values at T = 293 K, Q = 0.42 m3 /h, b = 32.1 S/m and Ec = −1.23 V.

deliberately determined with L=1 m. For comparison, the same size (0.017 m × 0.12 m × L) of the reactor is applied to a traditional PER which has a cathode specific area a = 86.2 m2 /m3 . Other conditions are the same as those mentioned in Section 4.1. With the conditions above and at T = 293 K, Ec = −1.3 V, b =50 S/m and Q=0.18 m3 /h, the model provides the relation of glyoxylic acid concentration vs the length of PERCC or PER as indicated in Fig. 13. This figure shows that the concentration of glyoxylic acid is only 1.3% at L=60 m for the PER due to the low specific area of cathode of the reactor, while it is 4.7% for the PERCC. The same figure also shows that the concentration of glyoxylic acid reaches a plateau around L = 60 m, indicating that it cannot be effectively increased by a further increase in the length of the reactor. Considering this point, a stepvaried temperature along the reactor or a partial reflux of the catholyte is suggested to overcome the drawback. For example, a variation of temperature (from T = 298 K at L 30 m to T = 293 K at 30 < L 60 m) at Ec = −1.3 V, b = 50 S/m and Q = 0.18 m3 /h gives w = 4.4% at L = 60 m, while w = 3.4% at L = 60 m and at T = 298 K; in the other case, when part of the

6792

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

experimental points. It should be noted that the present reactor was not easy to construct, and the plug flow of the catholyte in the reactor could not be guaranteed completely because the short-cut flow may exist, which reduces the concentration of glyoxylic acid in catholyte. 6. Conclusions

Fig. 13. Simulated glyoxylic acid concentration vs reactor length for PER and PERCC with a continuous operation process at T = 293 K, Q = 0.18 m3 /h, b = 50 S/m and Ec = −1.3 V.

Fig. 14. Comparison of experimental concentration of glyoxylic acid with predicted values for a continuous operation process by using PERCC at T = 293 K, Q = 0.42 m3 /h, b = 32.1 S/m and Ec = −1.30 V.

catholyte (a constant w =4.7% inside the catholyte is assumed) with half of the overall volumetric flow rate is refluxed from the position at L = 60 m to the entrance of the PERCC, it gives a new w = 5.2% at L = 60 m. We also note that the volumetric flow rate in a continous operation case affects the residence time (or the reaction time) for the bulk catholyte; a large flow rate can assure a better current efficiency for producing glyoxylic acid but reduce the reaction time of the catholyte, and then the final concentration of glyoxylic acid. As a tentative experiment, a PERCC with dimension 0.017 m × 0.12 m × 3.1m was constructed for the continuous operation. At T = 293 ± 0.5 K, Q = 0.42 m3 /h and Ec = −1.23 V, three experimental data were obtained by recycling the catholyte four times for each experimental point, corresponding to L = 12.4, 24.8 and 37.2 m, respectively. As shown in Fig. 14, the predicted results generally agree with the experimental data, although the predicted data overestimate the

This work established a 2-D model for calculating the distributions of the glyoxylic acid concentration and of the catholyte potential in PERCC based on the system’s reaction kinetics, mass conservation equation, and charge conservation equation in terms of the solution-cathode potential. The difference of the model established in this work from those previously reported (Newman and Tobias, 1962; Alkire and Ng, 1977; Storck et al., 1982; Xu et al., 1992, Zhang et al., 1999) lies in that the model combines the operation equation of a circulating mixer to be suitable for two cases: a batch operation process and a continuous operation process, and that the charge conservation of the model uses the cathode-solution potential which directly associates with the operating cathode potential controlled in experiments for the selectivity of the reactions. Using the OC method, the model equations were conveniently converted into sets of algebraic equations for obtaining numerical results. The effect of operating temperature, operating cathode potential, conductivity of catholyte, and volumetric flow rate of catholyte on the current efficiency and concentration of glyoxylic acid was discussed. From the simulation and comparison of the predicted and experimental results, we conclude: (a) The operating temperature, the operating cathode potential, the catholyte conductivity and the catholyte volumetric flow rate have an effective influence on the current efficiency and concentration of the product glyoxylic acid. This influence can be conveniently explained by the effect of those factors on the current densities of producing glyoxylic acid, forming glycollic acid and hydrogen evolution. (b) In the ranges investigated, operating temperature and cathode potential are more sensitive to the current efficiency than other studied factors. A decrease in operating temperature (after a short period of reaction) and an increase in the electrolyte volumetric flow rate can increase the current efficiency and concentration of glyoxylic acid. The cathode potential and the electrolyte conductivity have a reverse effect on the current efficiency and on the concentration of glyoxylic acid, indicating they need to be optimized for practical application. (c) For a continuous operation, when the concentration of glyoxylic acid in catholyte arrives at about 5% using PERCC, it is less than one-third of that using PER due to its low specific area of cathode. The concentration of glyoxylic acid can increase quickly following the increase in the length of the PERCC, but it wears off when the length of the reactor is further increased. To solve this problem, modifications in technology such as utilizing a step-varied operating temperature or adopting a partial reflux of the catholyte should be considered.

J. Li et al. / Chemical Engineering Science 62 (2007) 6784 – 6793

(d) The current efficiency and glyoxylic acid concentration predicted by the model are generally in good agreement with the experimental data obtained from a batch operation process and a continous operation process using PERCC. Notation a A c de Di E Ec F i kLi M Q t T u V v w x0 y0 z0

specific area, m2 /m3 cross area of cathode chamber, m2 concentration, mol/m3 equivalent diameter, m diffusion coefficient, m2 /s solution-cathode potential, V cathode potential, V Faraday constant, C/mol current density, A/m2 mass transfer coefficient, m/s molecular weight, g/mol flow rate, m3 /h time, min operating temperature, K superficial velocity, m/s mixer volume, m3 solid molar volume, m3 /mol mass fraction, % width of cathode chamber, m length of cathode chamber, m depth of cathode chamber, m

Greek letters     b   eP

porosity association factor dynamic viscosity, Pa s kinematic visocosity, m2 /s conductivity, S/m potential, V E/Ec current efficiency, %

Dimensionless parameters Re Sc X Y C Cri

ud e / /Di x/x0 y/y0 cP /c0 cis /c0 i = R, P , H

Superscript s

cathode surface

Subscript H in M out P R

hydrogen ion entrance of reactor metal exit of reactor product (glyoxylic acid) reactant (oxalic acid)

s 0

6793

solution reference

Acknowledgment The authors are grateful to the Natural Science Foundation of Fujian Province of China (Scientific Project 2003H045) for the financial support. References Alkire, R., Ng, P.K., 1977. Studies on flow-by porous electrodes having perpendicular directions of current and electrolyte flow. Journal of Electrochemical Society 124, 1220–1227. Darken, L.S., 1941. The ionization constants of oxalic acid at 25 ◦ C from conductance measurements. Journal of the American Chemical Society 63 (4), 1007–1011. Fan, J.H., Hu, X.H., Su, Y.Z., Li, J., 2004. Electrosynthesis of glyoxylic acid in a packed-bed reactor with cooled cathode. Applied Chemical Industry 33, 24–27 (in Chinese). Goodridge, F., Lister, K., Plimley, R.E., Scott, K., 1980. Scale-up studies of the electrolytic reduction of oxalic to glyoxylic acid. Journal of Applied Electrochemistry 10, 55–60. Langlois, S., Coeuret, F., 1990. Flow-through and flow-by porous electrodes of nickel foam, Part III: theoretical electrode potential distribution in the flow-by configuration. Journal of Applied Electrochemistry 20, 740–748. Li, J., Liu, H.L., Hu, Y., 2001. A mutual-diffusion-coefficient model based on local composition. Fluid Phase Equilibria 187–188, 193–208. Newman, J., Tobias, C.W., 1962. Theoretical analysis of current distribution in porous electrodes. Journal of Electrochemical Society 109, 1183–1191. Ochoa, J.R., De Diego, A., Santa-Olalla, J., 1993. Electrosynthesis of glyoxylic acid using a continuously electrogenerated lead cathode. Journal of Applied Electrochemistry 23, 905–909. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P., 1992. Numerical Recipes. second ed. Cambridge University Press, Cambridge. Scott, K., 1986. Electrolytic reduction of oxalic acid to glyoxylic acid: a problem of electrode deactivation. Chemical Engineering Research & Design 64, 266–271. Scott, K., 1990. The influence of adsorption in electrochemical reaction modelling. Chemical Engineering Research & Design 68, 537–546. Scott, K., 1991. A preliminary investigation of the simultaneous anodic and cathodic production of glyoxylic acid. Electrochimica Acta 36, 1447–1452. Scott, K., 1992. The role of temperature in oxalic acid electroreduction. Electrochimica Acta 37, 1381–1388. Storck, A., Enriquez-Granados, M.A., Roger, M.A., 1982. The behavior of porous electrodes in a flow-by regime-I. Theoretical study. Electrochimica Acta 27, 293–301. Villadsen, J.V., Stewart, W.E., 1967. Solution of boundary-value problems by orthogonal collocation. Chemical Engineering Science 22, 1483–1501. Wang, F.S., Li, J., Wang, J.R., Gao, H.Q., 2006. Adsorption of acrylonitrile and methyl acrylate on activated carbon in a packed bed column. Adsorption 12, 213–220. Wilke, C.R., Chang, P., 1955. Correlation of diffusion coefficients in dilute solutions. A.I.Ch.E. Journal 1 (2), 264–270. Xia, S.Q., Chen, S.P., Sun, S.G., 2001. Electrocatalytic reduction of oxalic acid on platinum based Pb–Sb surface alloy electrode. Acta PhysicoChimica Sinica 17, 140–143. Xu, W.L., Ding, P., Yuan, W.K., 1992. The behavior of packed bed electrode reactor. Chemical Engineering Science 47, 2307–2312. Zhang, X.S., Wu, G.B., Ding, P., Zhou, X.G., Yuan, W.K., 1999. Studies on paired packed-bed electrode reactor: modeling and experiments. Chemical Engineering Science 54, 2969–2977. Zhou, Y.L., Zhang, X.S., Dai, Y.C., Yuan, W.K., 2003. Studies on chemical activators for electrode I: Electrochemical activation of deactivating cathode for oxalic acid reduction. Chemical Engineering Science 58, 1021–1027.