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Simulation of Reduction of Cr(VI) by Fe(II) Produced

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Simulation of Reduction of Cr(VI) by Fe(II) Produced Electrochemically in a Parallel-Plate Electrochemical Reactor Sean Rayman * and R. E. White ** ,z Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29028, USA A model is presented for the reduction of hexavalent chromium in a parallel-plate electrochemical reactor via a homogenous reaction between Cr͑VI͒ and Fe͑II͒ generated at the iron anode. The effects of the
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  Simulation of Reduction of Cr(VI) by Fe(II) ProducedElectrochemically in a Parallel-Plate Electrochemical Reactor Sean Rayman *  and R. E. White ** ,z  Department of Chemical Engineering, University of South Carolina, Columbia, South Carolina 29028, USA A model is presented for the reduction of hexavalent chromium in a parallel-plate electrochemical reactor via a homogenousreaction between Cr  VI   and Fe  II   generated at the iron anode. The effects of the space velocity of the feed solution, theconcentration of supporting electrolyte, the distance between the electrodes, and the cell potential on conversion of Cr  VI   toCr  III  , are discussed. This study indicates that for reduction of Cr  VI   using Fe  II  , the space velocity must be maintained below0.02 s −1 or the system becomes limited by the rate of reduction of Cr  VI   by Fe  II  . Increasing the current density by increasingthe cell potential, increasing the amount of supporting electrolyte, and decreasing the distance between the electrodes increasessingle pass conversion of Cr  VI   to Cr  III  ; however, increasing the current density also increases the specific energy required bythe system.© 2009 The Electrochemical Society.   DOI: 10.1149/1.3098476   All rights reserved.Manuscript submitted July 18, 2008; revised manuscript received November 25, 2008. Published April 3, 2009. Hexavalent chromate, Cr  VI  , widely used for the production of stainless steel, textile dyes, wood preservation, and as anticorrosioncoating, is highly toxic to both animals and plants. Concentrations of Cr  VI   as low as 0.5 ppm in solution and 5 ppm in soil can be toxicfor plants; in contrast, the trivalent chromium is generally only toxicto plants at high concentrations and is a necessary micronutrient foranimals. Currently, there are many industrial sites in the world thathave been contaminated with Cr  VI   due to inefficient containmentof process solutions containing Cr  VI  . In the U.S. there has been anongoing effort to clean up these sites by treating the ground water onsite. 1 There are three ways to remove Cr  VI   from the aqueous so-lution: electroreduction, chemical reduction, and electrochemical re-duction   electrocoagulation  . Compared with chemical reduction,where an extra reducing agent   such as ferrous salts   is suppliedfrom outside the system to reduce an ion, and electroreduction,where the ion is reduced directly at the cathode, electrocoagulationuses electricity to produce a reducing agent   ferrous ions from aniron anode   from a sacrificial anode, and then the reducing agent isoxidized via a homogeneous reaction.Several work s have studied Cr  VI   reduction. Fendforf and Li, 2 Buerge and Hug, 3 and Sedlak and Chan 4 studied the chemical re-duction of Cr  VI   in a batch reactor where the hexavalent chromate  Na 2 CrO 4   was reduced by ferrous ion   FeCl 2   rapidly at room tem-perature. Rodriguez-Valdez et al. 5 experimentally studied the elec-trochemical reduction of Cr  VI   on a reticulated vitreous carboncathode. They experimentally show that conversion of Cr  VI   toCr  III   increases at lower flowrates, lower initial concentrations, andhigher potentials. Legrand, et al. 6 determined that the formation of Cr  III   monolayers on green rust limits the reduction of Cr  VI   bypermeable reactive barriers. Gheju and Lovi 7 reported that the re-duction of Cr  VI   by iron metal occurs more rapidly at lower pH;however, as time progresses, the iron metal surface becomes passi-vated.Parrish and Newman 8,9 developed a two-dimensional   2D   modelof a parallel-plate electrochemical reactor   PPER   assuming thatthere was a diffusion boundary layer at each electrode and a well-mixed region between the two electrodes. White et al. 10 developed a2D mathematical description of a PPER for the electrowinning of copper on a cathode, relaxing Parrish and Newman’s assumption of a well-mixed region. Alkire and Lisius 11 developed a PPER modelassuming a well-mixed region like Parrish and Newman that in-cluded multiple homogenous reactions in which water was reducedto form OH − and Br − was oxidized, and both electrochemicallygenerated species were reactants in some of the homogenous reac-tions. Mader et al. 12 simplified the PPER model by assuming thatthe axial rate of change of the concentration of every species wasconstant, the “one-step approximation.” The one-step approximationgreatly reduced computational time. Mader and White in a laterpaper 13 modeled a PPER with a separator and a single homogenousequilibrium reaction using the previously developed one-step ap-proximation for the Zn / Br 2  cell. Nguyen et al. 14 showed that whenthe distance between the electrodes is small compared to the lengthof the electrodes, mass transport in the axial direction is dominatedby convection, allowing the axial diffusion and migration terms tobe neglected while maintaining the accuracy of the model. Nguyenet al. 15 modeled a process in which a continuously stirred tank re-actor and PPER were coupled, allowing a homogenous reaction totake place outside of the PPER. Coleman et al. 16 modeled a PPERwith a separator accounting for gas evolution and multiple electro-chemical reactions taking place at both electrodes. Prasad et al. 17 present a PPER model for the electrochemical reduction of nitratesand nitrites, which is based on the boundary-layer model of Parrishand Newman. Georgiadou, 18 using finite-difference formulas,showed that at high Reynolds numbers,  Re  = 1200, the convectionin the axial direction limited the concentration gradients normal tothe electrodes to small distances from the electrodes. Hicks andFedkiw 19 studied experimentally and theoretically the electrolysis of acetate to ethane using a PPER with bulk turbulent flow with diffu-sion boundary layers at each electrode. Drake et al. 20-23 present asteady-state and a transient two-phase PPER model for the Simmonsprocess, assuming that there is a no-slip boundary condition betweenthe liquid and vapor phases. Jha et al. 24-26 expand Drake’s PPERmodel of the Simons process to include both potentiostatic and gal-vanostatic operation, nonsteady-state operation, and slip between theliquid-vapor boundary layer. Neither Drake nor Jha provide concen-tration distributions normal to the bulk fluid flow in the liquid orvapor phases.This paper presents a mathematical model for a PPER that com-bines diffusion and migration throughout the entire subdomain, mul-tiple homogenous reactions, and the oxidation of the anode to formone of the homogenous reactants for the first time. The chemistrypresented in this paper is the reduction of Cr  VI   to Cr  III   by Fe  II  as given by Fendorf. Model The proposed PPER is schematically shown in Fig. 1. The con- taminated solution is fed from the left side at  x   = 0. In order toimprove the conductivity of the aqueous solution, NaCl   supportingelectrolyte   is added to the feed solution. The model is based on thefollowing assumptions:1. Steady-state conditions exist   no time dependence  .2. Isothermal conditions exist.3. Gas evolution and precipitation ef fects are ignored.4. The dilute solution theory applies. 27 *  Electrochemical Society Student Member. **  Electrochemical Society Fellow. z E-mail: white@engr.sc.edu  Journal of The Electrochemical Society,  156   6   E96-E104   2009  0013-4651/2009/156  6   /E96/9/$25.00 © The Electrochemical Society E96 ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see  128.252.20.193 Downloaded on 2014-08-13 to IP   5. Constant physical and transport parameters exist.6. The Butler–Volmer equation adequately describes the currentdensity of the electrochemical reactions. 27 7. The Nernst–Einstein equation,  u i  =  D i /  RT  , applies. 27 8. The fluid is an incompressible Newtonian fluid in well-developed laminar flow. 10 9. Asmall aspect ratio   S  /  L   exists between the width and lengthof the reactor   S  /  L    1  . 12 The material balance equation of the  i th species is expressed as   ·  N i  =  R i   1  where the flux vector consists of diffusion, migration, and convec-tion terms, respectively N i  = −  D i    c i  −  z i u i c i F       +  c i v   2  For a system with a total number of   N   species, there are  N   materialbalance equations but  N   + 1 variables   the concentration of eachspecies  c i  plus the solution potential    . The electroneutrality con-dition is used as the extra required equation  i =1  N   z i c i  = 0   3  As mentioned above in assumption 8, the velocity distributionwithin the reactor is a well-developed laminar flow and is given as 10 v  x   = 6 v avg   yS  −  y 2 S  2    4  and v  y  = 0   5  In order for the Reynolds number to be greater than 2300, the aver-age velocity of the solution phase in a reactor with a width of 91 cmgiven in this paper and an electrode gap of 3 cm, would be greaterthan 2 cm / s,     0.14 s −1 . If the electrode gap was 0.3 cm, the av-erage velocity would be less than 40 cm / s,     1.3 s −1 , to ensurelaminar flow.In a 2D Cartesian coordinate system, the material balance isderived by substituting Eqs. 4 and 2 into Eq. 1: −  D i   2 c i    x  2  −  z i  D i F  RT      x   c i       x     + 6 v avg   yS  −  y 2 S  2    c i    x  −  D i   2 c i    y 2 −  z i  D i F  RT      y  c i       y    =  R i   6  Next, the following characteristic quantities are defined   = S  L ,    =  x  L ,    =  yS  ,   i  = c i c i ,ref  ,   =   F  RT  , and    =  v avg  L and substituted into Eq. 6 to obtain a material balance with dimen-sionless dependent and independent variables for the  i th species−   2  D i   2  i    2  −   2  z i  D i       i          + 6 v avg  LS  2    −   2     i    −  D i   2  i    2 −  z i  D i       i         = S  2 c i ,ref   R i   7  Using assumption 9, the terms with the coefficient of    2 can beeliminated, which is equivalent to assuming that convection domi-nates migration and dif fusion in the axial direction. 15 Applying theone-step approximation 12 for the concentration gradient in the axialconvection term yields6     −   2   i  −   i ,feed   −  D i S  2    2  i    2  +  z i       i          =1 c i ,ref   R i  8  The one-step approximation approximates     i /     as   i    = 1,   −   i    = 0,   / 1 − 0 simplified as     i /        i  −   i ,feed . In essence,there is only one computational element in the axial direction whenthe one-step approximation is applied. Mader 13 uses the one-stepapproximation for a PPER that contains a homogenous equilibriumreaction. By doing so, he is able to eliminate the source terms fromthe material balance equations. As shown later in this work, the firsthomogenous reaction is considered to go to completion, and thus notall the source terms can be eliminated from the set of material bal-ances. Because the equilibrium condition cannot be assumed for thepresent work, the one-step approximation will need to be relaxed infuture work. The length of the reactor,  L , used in this work is30.5 cm. In order to remain within the limits of assumption 9, themaximum distance between the electrodes,  S  , should be no morethan 3 cm. Equation 8 is now a simplified material balance for the i th species in one spatial dimension with the following boundaryconditions: at    = 0   anode  −  N  n , i * =    i    +  z i  i       =   S c i ,ref   D i   j s i ,  j i n ,  j n  j F  , for Fe 2+ 0, for the other species   9  at    = 1   cathode   N  n , i * = −    i    −  z i  i       =   S c i ,ref   D i   j s i ,  j i n ,  j n  j F  , for OH − 0, for the other species   10  and at both    = 0 and    = 1 the electroneutrality condition is satis-fied  i  z i  i c i ,ref   = 0   11  The current that flows through the reactor is a result of the electro-chemical reactions that take place at the anode and cathode. At theanode, the only electrochemical reaction considered is the oxidationof Fe 0 to Fe +2 , described byFe  Fe 2+ + 2e − At the cathode, the only electrochemical reaction considered is thereduction of H 2 O to OH − and H 2 , described by Figure 1.  Schematic of a PPER and fluid velocity profile. E97  Journal of The Electrochemical Society ,  156   6   E96-E104   2009   E97 ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see  128.252.20.193 Downloaded on 2014-08-13 to IP   2H 2 O + 2e −  H 2  + 2OH − In Eq. 10 and 11, the normal component of the current density of  electrochemical reaction  j  can be determined using the Butler–Volmer equation: 27 At the anode i n ,  j  =  i 0,  j ,ref    i  i p ij exp   a ,  j   F  RT V  a  −   a ,0  − F  RT U   j ,ref    −  i  iq ij exp   c ,  j   F  RT V  a  −   a ,0  − F  RT U   j ,ref       12  and at the cathode i n ,  j  =  i 0,  j ,ref    i  i p ij exp   a ,  j   F  RT V  c  −   c ,0  − F  RT U   j ,ref    −  i  iq ij exp   c ,  j   F  RT V  c  −   c ,0  − F  RT U   j ,ref       13  where U   j ,ref   =  U   j  −  RT n  j F   i s ij  ln  c i ,ref   0    14  Tables I-IV provide the values of the constants and the range of  values used for the parameters investigated in this paper. A basecase, represented in Fig. 2-5 as a bold gray line, was established with the following parameters:  v avg  = 0.50 cm / s,  V  a  = 0.60 V,  S  = 0.3175 cm, and  ConcSE   = 1.00  E   − 7 mol / cm 3 . In the case of these simulations, the concentration of the supporting electrolyte, ConcSE  , was changed by changing the concentration of Cl − in thefeed solution. The Na + concentration was calculated by assumingthat the electroneutrality held in the feed solution. The concentrationof most species remained below 10 −3 mol / cm 3 even at the elec-trodes, which indicates that the solution is dilute, assumption 4, andthat the mobility of the ions is proportional to the diffusion coeffi-cient, assumption 7. Source Terms in the Material Balance Equation In the considered system, nine ionic species are included: Na + ,Cl − , Fe 2+ , H + , OH − , CrO 42− , Fe 3+ , and Cr 3+ . All the ionic speciesexcept Na + and Cl − are involved in the homogeneous reactions ex-pressed as Eq. 17-19 below CrO 42− + 3Fe 2+ + 4H 2 O → 3Fe 3+ + Cr 3+ + 8OH −  15  H + + OH −  H 2 O   16  Cr 3+ + 3OH −  Cr  OH  3   17  Fe 3+ + 3OH −  Fe  OH  3   18  Fe 2+ + 2OH −  Fe  OH  2   19  Fendorf and Li 2 determined that Cr  VI   is reduced by Fe  II  according to the kinetic rate expression r  1  =  k  Cr  Fe 2+  0.6  CrO 42−   20  where  k  Cr  = 56.3    3.7   mmol −0.6 min −1 L 0.6 . 2 The products of Re-action 1, Cr 3+ , Fe 3+ , and Fe 2+ , react with OH − to form Cr  OH  3 ,Fe  OH  3 , and Fe  OH  2  as described by Eq. 17-19, respectively. For Eq. 16-19, the kinetic reaction rates are expressed as fast equilibrium reactions r  2  =  k  2,  f  c H + c OH −  −  k  2, b c H 2 O r  3  =  k  3,  f  c Cr 3+ c OH − 3 −  k  3, b c Cr  OH  3 r  4  =  k  4,  f  c Fe 3+ c OH − 3 −  k  4, b c Fe  OH  3 r  5  =  k  5,  f  c Fe 2+ c OH − 2 −  k  5, b c Fe  OH  2 where the backward and forward rate constants are related by thefollowing dissociation constants K  w  = k  2, b k  2,  f  ,  K  Cr  OH  3 = k  3, b k  3,  f  ,  K  Fe  OH  3 = k  4, b k  4,  f  ,  K  Fe  OH  2 = k  5, b k  5,  f  For the purpose of this work, the authors assumed that the dissolu-tion of the solid products was extremely slow compared to the for-mation of the solid products, i.e., the forward reactions progressedmuch faster than the backward reactions. Equations 16-19 allow for the formation of solids in the solution phase; however, it is assumed Table II. Kinetic and thermodynamic properties of electrochemi-cal reactions. Reaction    j  10 8 i 0,  j ,ref   A / cm 2    a ,  j   c ,  j  n  j  U   jo –   V  29 1 1.0 0.5 0.5 1.0 −0.4402 300.0 0.5 0.5 1.0 −0.828 Table III. Stoichiometry of the electrochemical reactions. Reaction Species  s ij  p ij  q ij 1 Fe 2+ −0.5 0.0 0.52 OH − 1.0 1.0 0.0 Table IV. Operation conditions and other parameters. Parameter Value Unit T   298.15 K S   0.05–3.0 cm V  a  0.11–6.0 V v avg  0.01–10 3 cm/s V  c  0.0 V  0  1.0 g / cm 3 K  w  1.0    10 −20  mol / cm 3  2 K  Fe  OH  3  2.79    10 −3928  mol / cm 3  4 K  Cr  OH  3  6.3    10 −43  mol / cm 3  4 K  Fe  OH  2  4.87    10 −1728  mol / cm 3  3 k  Cr  3.735    10 32  cm 3 / mol  0.6 / s k  2,b  1.0    10 −10a cm 3 / mol / s k  3,b  1.0    10 −20a  cm 3 / mol  3 / s k  4,b  1.0    10 −21a  cm 3 / mol  3 / s k  5,b  1.0    10 −8a  cm 3 / mol  2 / s a Chosen arbitrarily. Table I. Transport properties and reference concentration. Species10 5  D i  cm 2 / sec  28  z i 10 7 c i ,ref   mol / cm 3  c i ,feed  mol / cm 3  Na + 1.334 +1 1.0  Adjusted to maintainelectroneutrality of the feed Cl − 2.032 −1 1.0 0–5    10 −3 Fe 2+ 0.719 +2 1.0 0.0H + 9.311 +1 1.0 1.0    10 −10 OH − 5.273 −1 1.0 1.0    10 −10 CrO 42− 1.132 −2 4.0 6.17    10 −9 Fe 3+ 0.604 +3 1.0 0.0Cr 3+ 0.595 +3 1.0 0.0 E98  Journal of The Electrochemical Society ,  156   6   E96-E104   2009  E98 ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see  128.252.20.193 Downloaded on 2014-08-13 to IP   that none of the solid particles coagulate inside of the reactor   as-sumption 3  .By taking into account the homogenous reactions, the sourceterm in the material balance equation for each species is specified as  R Na +  = 0   21   R Cl −  = 0   22   R Fe 2+  = − 3 r  1  −  r  5   23   R H +  = −  r  2   24   R OH −  = 8 r  1  −  r  2  − 3 r  3  − 3 r  4  − 2 r  5   25   R CrO 42−  = −  r  1   26   R Fe 3+  = −  r  4   27   R Cr 3+  = −  r  3   28  Figure 2.  Dimensionless concentrationprofile of Cr  VI   as current density in-creases. Figure 3.  Dimensionless concentrationprofile of Cr  VI   as concentration of sup-porting electrolyte increases. E99  Journal of The Electrochemical Society ,  156   6   E96-E104   2009   E99 ) unless CC License in place (see abstract). ecsdl.org/site/terms_use address. Redistribution subject to ECS terms of use (see  128.252.20.193 Downloaded on 2014-08-13 to IP 
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