COMPARISON OF TANKS-IN-SERIES AND AXIAL DISPERSION MODELS FOR AN ELECTROCHEMICAL REACTOR

R. Saravanathamizhan*, N. Balasubramanian**, C.Srinivasakannan***

*Department of Chemical and Process Engineering technology, Jubail Industrial College, post Box-10099,

Jubail Industrial City, 31961, Saudi Arabia. thamizhan79@rediffmail.com

** Department of Chemical Engineering, Anna University-Chennai, Chennai-600 025, India.

nbsbala@annauniv.edu

*** Chemical Engineering Program, The Petroleum Institute, Abudhabi, UAE. csrinivasakannan@pi.ac.ae

Abstract: In the present investigation it is attempted to compare the color removal of Acid Red 88 dye effluent by tanks-in-series model and an axial dispersion model in Continuous Stirred Tank Electrochemical Reactor (CSTER). The comparison of two modeling approach was made for the color removal of Acid Red 88 synthetic dye effluent with experimental results. The equation Pe= 2(N - 1) is used to correlate the parameter of the dispersion model (Pe) with that of the tanks-in-series model (N). The predictions of the color removal for the tanks in series model and axial dispersion model were compared with experimental color removal. It is observed that the both models were satisfactorily matching the experimental results. Key words: Tanks-in-series model; axial dispersion model; Continuous stirred Tank Electrochemical Reactor; Peclet number; color removal.

NOMENCLATURE

Q : Electrolyte flow rate xA : Fractional conversion CA0 : Initial concentration CA : Final concentration σ : Interfacial area of the electrode N : Number of tanks E(t) : Exit age distribution τ : Residence time A : Surface area of the electrode D1 : Damkohler numbers k : Reaction rate constant km : Mass Transfer coefficient Pe : Peclet Number RTD : Residence Time Distribution CSTER : Continuous Stirred Tank

Electrochemical Reactor CSTR : Continuous Stirred Tank Reactor PFR : Plug Flow Reactor IEC : Initial effluent concentration CD : Current density

1. INTRODUCTION

Reaction kinetics, hydrodynamics, heat and mass transfer is required for the design of electrochemical reactors. The hydrodynamic information can be obtained through the Computational Fluid Dynamics and the Residence Time Distribution.

The residence time distribution is a simple tool to understand the flow behavior and non ideality of any reactor system (Claudel et al., 2003). There are two different ideal reactor models that are used for the description of flow reactors, the continuous stirred tank reactor (CSTR) and plug flow reactor (PFR). The CSTR assumes perfect mixing, whereas PFR assumes no mixing. No real reactor has exactly the characteristics of either of the two ideal reactors. The axial dispersion model and tanks-in-series model are one parameter models that describe the mixing behavior. tanks-in-series model the number of tanks required “N” and in the axial dispersion model “Peclet number” are the parameters. Peclet number that represents the deviation from the ideal behavior such as non uniform mixing velocity or eddies. The Pe number is the single parameter in this model. As Pe increases from 0 to infinity, the flow pattern in the reactor changes from complete mixing (CSTR) to no mixing (PFR). As N increases from 1 to infinity, the flow pattern in the reactor changes from complete mixing (CSTR) to no mixing (PFR). Although the physical basis of the tanks-in-series model is not as clear as that of the axial dispersion model, the tanks-in-series model is simple and can be used with any kinetic equation. The steady-state mathematical model of the tanks-in-series model requires the solution of algebraic equations instead of a differential equation. The two models can be compared quantitatively by equating their variances. This leads to a relationship between their two parameters, Pe and N. (Sahle-Demessie et

al., 2003; Abu Resh and Abu-Sharkh ,2003; Fogler 1999).

Abu Resh and Abu-Sharkh (2003) studied axial dispersion and tanks-in-series model for enzyme reactors. They reported both models fit well at low dimensional residence time and high peclet numbers. Dhamo (1994) studied treatment of dilute solution using an electrochemical hydro cyclone cell. The author observed the batch recycle operation approaches the plug flow model. Turner and Mills (1990) reported that the Tanks-in-series model is more realistic and advantageous compared to the axial dispersion model for simulating the performance of Fischer-Tropsch slurry bubble column reactors. Saravanathamizhan et al., (2008) proposed Tanks-in-series model for the electrolyte flow behavior in a continuous stirred tank electrochemical reactor. In the present investigation Tanks-in-series model and axial dispersion models are compared with experimental color removal of Acid Red 88 dye effluent.

2. MODELING

2.1 Tanks- in- Series Model

Tanks-in-series model has been proposed to describe the flow characteristics of the electrolyte in a CSTER. It is assumed that the CSTER consists of three tanks connected in series [Figure 1]. Accordingly the tracer material balance for the tank 1 can be written as

Figure 1: Schematic representation of three tanks in

series model

101

1 CCdt

dC−=τ (1)

Where τ1 represents the residence time of electrolyte in the tank1; Co and C1 refer the inlet and outlet tracer concentration of tank 1. Similarly the tracer material balance can be developed for second and third tanks as given below.

The material balance for the tank 2 can be written

as

212

2 CCdt

dC−=τ (2)

The material balance for the tank 3 can be given as

323

3 CCdt

dC−=τ (3)

Where, C2, C3 represent tracer outlet concentration of second and third tanks respectively. While τ2, τ3 represent the residence time of electrolyte in the tanks 2 and 3 respectively. The model is assumed as the volume of tanks 1 and 3 are equal and the volume of tank 2 is higher than the other tanks i.e. 3V,1V2V;3V1V >= ). 2.2 Axial Dispersion Model

When the effluent passes between the electrodes the liquid experiences some degree of back mixing or intermixing. The incoming fluid resides in the reactor for a different length of time. In this case dispersed plug flow behavior is assumed. The model representation is shown in the Figure 2. The material balance has been written as for a small elemental thickness ∆z. The flowing assumptions are made to develop the equation • Process is diffusion controlled. • Mass transfer coefficient is uniform throughout

the reactor. • Dispersion is characterized by the axial

dispersion coefficient. • Temperature and other physical properties of

the electrolyte are constant.

Figure 2: Schematic representation of axial

dispersion model

The differential equation for an axial dispersion

model can be written as

02

2=−−

UAkC

dzAdC

dzACd

U

D (4)

The equation (4) is written in terms of dimensional

quantity as

02

21=−− τψ

λ

ψ

λ

ψk

d

d

d

d

Pe (5)

Where

D

ULPe =

0ACAC

=ψ

L

Z=λ

The above two model equation has been solved.

3. MODEL SOLUTIONS

3.1 Tanks-in-series Model In this case, it is assumed that the tanks 1 and 3 are equal in volume and the volume of tank 2 is higher than the others. Accordingly the equations (1) to (3) are solved for pulse input, i.e.

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ −

−

−

−+

−

−= 12

)21(211

)21(

1)(

ττ

ττ

τττ

ττ

t

e

t

e

t

tetF (6)

The E(t) can be obtained by differentiating equation (6), i.e.

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛ −

−

−

−+

−

−= 12

)21(211

)21(1

1)(

ττ

ττ

τττ

τττ

t

e

t

e

t

tetE (7)

3.2 Axial Dispersion Model The conversion equation for a dispersion model can be written as (Fogler, 1999)

⎟⎟⎠

⎞⎜⎜⎝

⎛

−−−+−=

)2/.exp(2)1()2/.exp(2)1(

)2/exp(41

PeqqPeqq

PeqAX (8)

Where 5.0

41 ⎥⎦

⎤⎢⎣⎡

+=Pe

kq

τ

4. EXPERIMENTAL

The experimental setup consists of a glass beaker of 300ml capacity with PVC lid having provision to fit a cathode and an anode. Ruthineum coated titanium and Stainless steel sheets of 6.5cm×5 cm were used as anode and cathode, respectively. The electrodes are fixed at 3cm inter electrode gap. The uniform electrolyte concentration is achieved by means of magnetic stirrer. Experiments were conducted for both residence time distribution and color removal. The experimental run has been decided by the Box-Behnken design [Table 1]. For RTD studies, the CSTER was operated with water as electrolyte fluid. A tracer of Acid Red 88 dye solution was injected as pulse input and sampled periodically at the outlet of the cell. For electro oxidation, synthetic effluent of Acid Red 88 dye has been prepared at various initial concentrations. The electrolysis was carried out under

galvanostatic conditions using a DC–regulated power source (HIL model 3161). The effluent flow rate has been adjusted by adjusting throat valve and the samples were collected for analysis of color removal at steady state. The samples were analyzed using colorimeter. Table 1. Range of variables chosen for electro oxidation of Acid Red 88 using Box-Behnken method.

Variables Unit Range of actual and

coded variables -1 0 +1

Q ml min-1 25 50 75

IEC mg l-1 50 75 100

CD mA cm-2 2 6 10 pH - 4 7 10

5. RESULT AND DISCUSSION

The electrolyte flow behavior in a continuous stirred tank electrochemical reactor has been simulated for pulse tracer input using the model equations developed in the previous section. It is observed that the experimental values are matches well with the model simulation (Saravanathamizhan et al., 2008). Hence model simulation over a period of 30min is considered for the mean residence time calculation. The mean residence time distribution, for CSTER can be given as

∫∞

=0

)( dtttEτ (9)

The variance for CSTER can be written as

dttEt )(0

2)(2∫∞

−= τσ (10)

The number of tanks, N can be given as

2

2

σ

τ=N (11)

The number of tanks in ‘Tanks in Series Model’ can be calculated using the equation (11). The number of Tanks in series and the peclet numbers are related as (Fogler, 1999)

)1(2 −= Npe (12) The color removal of Acid Red 88 dye effluent by an axial dispersion model and tanks in series model

with the experimental color removal values are compared. The conversion equation for a continuous stirred tank electrochemical reactor is written as ( scott 1990)

)11(1

1

1D

kANCANC

++

=− στ

(13)

Where ‘N’ represents the number of tanks in series. The equation (13) can be rearranged as

N

D

k

AiCANC

−

++= ⎟⎟

⎠

⎞⎜⎜⎝

⎛)1(

11

στ (14)

For the above equation, rate constant k value is determined experimentally according the following equation

tV

Amk

ACAC −

=⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

0ln (15)

Where ‘A’ surface area of electrode and ‘V’ is the volume of the reactor. km is the mass transfer coefficient. The slope of the plot ln(CA/CA0) vs electrolysis time gives the value of reaction rate constant and using the value of surface area and volume, mass transfer coefficient is determined. The experiments were designed using Box-Behnken method and the experimental runs are given in the Table 2. In the Box-Behnken method four factors are flow rate, initial effluent concentration; current density and initial pH are selected with three different levels. The experimental color removal was observed for the 27 runs. The mean residence time, Number of tanks is calculated from the simulated exit age distribution. The model information is used in the equation (14) and color removal is calculated and given in the Table 2. The color removal is compared with exit age distribution model. It is observed from the Table the flow rate increase the dispersion coefficient increase. The comparison of experimental color removal with Tanks in series model and axial dispersion model is shown in the Figure 3. It is observed from the Figure 3 the Tanks in series model and axial dispersion model matches well with the experimental observation.

6. CONCLUSION In the present investigation the experimental color removal of Acid Red 88 dye effluent with tanks in series model and axial dispersion model were compared. It was found that the experimental results matches well with tanks in series model and axial dispersion model.

Figure 3 Comparison of model simulation with experimental value. REFERENCES Claudel, S; Fonteix, C; Leclerc J.-P.; Lintz H.-G.

(2003) Application of the possibility theory to the compartment modeling of flow pattern in industrial processes. Chemical Engineering Science. 58, 4005 – 4016.

Dhamo,N. (1994)An electrochemical hydrocyclone cell for the treatment of dilute solutions: approximate plug-flow model for electrodeposition kinetics. Journal of Applied Electrochemistry. 24, 745-750.

Fogler, H. S. Elements of Chemical Reaction Engineering, 3rd ed.; Prentice Hall: Upper Saddle River, NJ, 1999.

Ibrahim M. Abu-Reesh, Basel F. Abu- Sharkh.(2003) Comparison of Axial Dispersion and Tanks-in-Series Models for Simulating the Performance of Enzyme Reactors. Industrial Engineering Chemistry Research. 42, 5495-5505.

Sahle-Demessie E.; Siefu Bekele; Pillai,U.R. (2003) Residence time distribution of fluids in stirred annular photo reactor. Catalysis Today. 88, 61–72

Saravanathamizhan,R.;Paranthaman,R.; Balasubramanian, N; Ahmed Basha, C. (2008).Tanks in Series Model for Continuous Stirred Tank Electrochemical Reactor. Industrial Engineering Chemistry Research. 47, 2976-2984.

Scott. K. (1990). The continuous stirred tank electrochemical reactor. An overview of dynamic and steady state analysis for design and modeling. Journal of Applied Electrochemistry, 21, 945-960.

Turner, J. R.; Mills, P. L.(1990) Comparison of axial dispersion and mixing cell models for design and simulation of Fischer-Tropsch slurry bubble column reactors. Chemical Engineering Science. 45, 2317-2324.

Table 2. Comparison of Acid Red 88 dye effluent color removal with tanks in series model and axial dispersion model.

S. No

Q

IEC

CD

pH

Color removal

exp (%)

km

(m min-1)

k ( min-1)

Tanks-in -series Model

Dispersion Model

τ

(min) N

Color removal

(%)

Pe Color removal

%

1 25 50 6 7 61.15 0.0183 0.1982 9.53 1.8 70.06 1.6 72.592 75 50 6 7 35.25 0.0183 0.1982 3.99 1.42 37.69 0.84 46.383 25 100 6 7 45.05 0.0185 0.2004 9.53 1.8 70.3 1.6 72.884 75 100 6 7 32.00 0.0185 0.2004 3.99 1.42 37.92 0.84 46.675 50 75 2 4 28.05 0.0076 0.0823 5.9 1.51 27.9 1.02 34.126 50 75 10 4 58.75 0.0329 0.3563 5.9 1.51 66.19 1.02 73.387 50 75 2 10 52.99 0.014 0.1516 5.9 1.51 42.84 1.02 50.168 50 75 10 10 87.53 0.0533 0.5772 5.9 1.51 77.73 1.02 83.959 25 75 2 7 37.12 0.0083 0.0899 9.53 1.8 47.69 1.6 50.05

10 75 75 2 7 15.08 0.0083 0.0899 3.99 1.42 20.9 0.84 27.211 25 75 10 7 57.58 0.0391 0.4235 9.53 1.8 86.48 1.6 88.9712 75 75 10 7 47.50 0.0533 0.5772 3.99 1.42 66.33 0.84 74.8113 50 50 6 4 55.00 0.0144 0.156 5.9 1.51 43.54 1.02 50.9514 50 100 6 4 43.00 0.011 0.1191 5.9 1.51 36.53 1.02 43.5515 50 50 6 10 75.53 0.0254 0.2751 5.9 1.51 59.22 1.02 66.7116 50 100 6 10 51.47 0.0166 0.1798 5.9 1.51 47.44 1.02 54.9417 25 75 6 4 45.21 0.0146 0.1581 9.53 1.8 63.83 1.6 66.4218 75 75 6 4 35.21 0.0146 0.1581 3.99 1.42 32.19 0.84 40.419 25 75 6 10 85.2 0.0177 0.1917 9.53 1.8 69.13 1.6 71.7120 75 75 6 10 32.85 0.0177 0.1917 3.99 1.42 36.81 0.84 45.4821 50 50 2 7 30.00 0.0111 0.1202 5.9 1.51 36.72 1.02 43.7922 50 100 2 7 24.37 0.0074 0.0801 5.9 1.51 27.38 1.02 33.4923 50 50 10 7 58.00 0.036 0.3899 5.9 1.51 68.53 1.02 75.5624 50 100 10 7 55.00 0.0502 0.5437 5.9 1.51 76.42 1.02 82.7925 50 75 6 7 45.23 0.0172 0.1863 5.9 1.51 48.34 1.02 55.9426 50 75 6 7 45.23 0.0172 0.1863 5.9 1.51 48.34 1.02 55.9427 50 75 6 7 45.23 0.0172 0.1863 5.9 1.51 48.34 1.02 55.94