simulation of a cstr model for thevetia peruviana oil transesterification in the

8/10/2019 Simulation of a Cstr Model for Thevetia Peruviana Oil Transesterification in The

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International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 6480(Print), ISSN 0976 6499(Online) Volume 5, Issue 7, July (2014), pp. 103-115 IAEME

103

SIMULATION OF A CSTR MODEL FOR THEVETIA PERUVIANA OILTRANSESTERIFICATION IN THE PRODUCTION OF BIODIESEL

Olatunji, O. M., Ayotamuno, M. J.

1Department of Agricultural and Environmental EngineeringRivers State University of Science and Technology, PMB 5080, Port Harcourt, Nigeria

ABSTRACT

In this research work, a mathematical model was simulated for Continuous Stirred TankReactor (CSTR) as an extension of the work of Abowei et al ., (2013) exploiting thetransesterification kinetic of Olatunji et. al., (2012) at an isothermal condition. The Kinetic model of

Olatunji et. al., (2012) was obtained through laboratory experiment on which ester was producedusing alcohol to oil molar ratios of 6:1, 9:1 and 12:1 at isothermal reaction temperature of 50 oC. Thesimulated model equations was able show reactor dimensions as a function of Olatunji et. al., (2012)kinetic parameters. The model equations were further analyzed with MATLAB programmingtechnique, and results obtained for reactor dimensions can be used to predict the volume to beproduced at different time intervals and reaction rate which demonstrated high dependencyfunctionality of Olatunji et. al., (2012) proposed kinetic model parameters.

Keywords: Model Simulation, Continuous Stirred Tank Reactor (CSTR), Thevetia peruviana ,Transesterification, Biodiesel Production.

INTRODUCTION

In the process of searching for an alternative energy sources, a special attention is focused onthe Chemical Kinetics of Milk bush (Thevetia peruviana) oil transesterification process in theproduction of biodiesel (Olatunji et. al .,2013). From the work of Olatunji et. al., (2012) the reactionkinetics of esters was proposed as follows:

INTERNATIONAL JOURNAL OF ADVANCED RESEARCHIN ENGINEERING AND TECHNOLOGY (IJARET)

ISSN 0976 - 6480 (Print)ISSN 0976 - 6499 (Online)Volume 5, Issue 7, July (2014), pp. 103-115 IAEME: http://www.iaeme.com/IJARET.aspJournal Impact Factor (2014): 7.8273 (Calculated by GISI)www.jifactor.com

IJARET

I A E M E


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1 Where,

CTG = Concentration of TriglycerideCA = Concentration of AlcoholCDG = Concentration of DiglycerideK = Rate Constant.But,K1CA = K

1

2 Where,

K

1 = effective rate constantCE = concentration of Ester

In order to find a solution to equation (6) there is need to express C D and C E as a function oftime. At the initial period when the reaction start to the final period (ie. time t i to t f , t i = 0 and t f =t DG1 ). The diglyceride concentration was increased and then decreased.Applying the equation proposed by Fogler (Fogler, 1999).

The suggested formula for this type of change in concentration is composed of twoexponential terms.

3

Where,

1 , 2 and 3 are constants

t = time

4 Where,

CDGO = Initial concentration of Diglyceride

After the final period, ie. t f = t dg1, diglyceride concentration went below its initial value,hence, equation (8) cannot be used to predict the final concentration of Diglyceride at this period.Therefore equation 8 may be written as equation 9.

5


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Also,

6 Substituting equation (9) and (10) into equation 6, taking the Laplace of the new equation

developed; also by applying the partial fraction technique, and taking the inverse Laplace of the finalequation.CTG , C DG, and C MG final equations were developed.

(7)


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Where,K = rate constants

The final concentration of Diglyceride, Monoglyceride, Ester (Biodiesel) and Glycerol werederived in the same manner.

Where, i , i, i, are constants derived from Foglers equation to calculate the change inconcentration of Tri, Di, Mono glycerides, Ester and glycerol.

These constants are determined using initial guess values. From Linear Regression methodusing MATLAB programming which was written to validate the model.The aspect of modelling reactor functional parameters for large scale production of ester using theproposed Chemical Kinetic expression need to be proposed.

MATERIALS AND METHODS

The reaction mechanism demonstrated Isothermal Characteristics and the resulting designequation for a Continuous Stirred Tank Reactor (CSTR) is described as:

8 For CSTR operating in Isothermal Condition is given:

9 1 10

Where,

Considering the Cylinder shape of the reactor type, thus:

2 11Where, = Volume of the CSTR; , = Rate Constants = Space velocityDetermination of the Length, of the CSTR

1 12 Similarly, in order to establish the performance levels of the reactor, space time and space velocityare vital ingredients and developed as thus,

13


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Where,= Space time (sec)

From equation 13

1 14

Where = Volumetric flow of the reacting substance in the vein.

15 Hence,

16 Therefore, 17 Heat generated per unit volume,

18 To determine the heat generation per unit volume of CSTR Reactor , both sides of equation

18 above is divided by

19

Therefore,

20

1 21 RESULTS AND DISCUSSIONS

Process optimizationThe objective of this study was to optimize the conditions for transesterification of Milk bush

(Thevetia peruviana ) oil for higher ester yield. The effects of catalyst concentration, reactiontemperature, and alcohol-to-oil molar ratio were included in this study. Stirring speed of allexperiments was fixed at 600 rpm. Table 1.0 summarized the effects of catalyst concentration,reaction temperature, and alcohol-to-oil molar ratio in terms of conversion.


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Effect of catalyst loading The catalyst loading (KOH) was varied from 0.5 to 1.5 wt.% in this study. The reaction

temperature was maintained at 50 oC. The experimental results shows similar trend with thecalculated results which shows that there was an increase in ester concentrations with catalystloading. This is a typical observation which agrees with the findings of Zhous et al. (2003).

However, the rate of the increase in ester concentration dropped when catalyst concentration wasincreased beyond 1 wt. %. In addition, the conversion increased as catalyst concentration increased.Potassium Hydroxide ions react with the methanol molecule to produce methoxide ions, and the rateof reaction increased when hydroxide concentration was increased.

Table 1.0 : The percentage conversion of alkali-catalyzed transesterification of Milk bush oil

Effect of alcohol-to-oil molar ratioThe effect of alcohol to oil molar ratio (6:1, 9:1, and 12:1) on ester concentration was studiedat 50 oC. From the results obtained ester concentration as well as the % conversion decreased as thealcohol-to-oil molar ratio was increased. This can be explained on the basis of the reactant (oil)concentration in the reaction mixture. By increasing alcohol to oil molar ratio, the amount of alcoholwas increased, therefore the Milk bush and catalyst concentrations were diminished, which reducedthe rate of reaction. Results published by Boocock et al . (1998) showed a similar trend in which themethyl ester percentage decreased as the alcohol-to-oil molar ratio was increased.

Replication

Catalystconcentration

(wt. %)

Temperature(oC)

Alcohol tooil molar

ratio

Conversion,mol %1 min 5 min 10 min

1 0.5 50 6:1 16.5 44.5 53.6

2 0.5 50 6:1 27.5 61.8 66.0

3 0.5 50 6:1 34.6 66.6 71.6

4 1.0 50 6:1 61.5 76.8 84.3

5 1.0 50 6:1 72.5 81.9 83.6

6 1.0 50 6:1 75.4 82.2 84.1

7 1.5 50 6:1 81.7 86.8 90.1

8 1.5 50 6:1 78.9 87.3 90.1

9 1.5 50 6:1 81.5 90.4 99.910 1.0 50 9:1 35.8 65.4 78.0

11 1.0 50 9:1 42.4 78.0 86.1

12 1.0 50 9:1 55.3 83.7 89.5

13 1.0 50 12:1 21.0 48.2 70.2

14 1.0 50 12:1 45.2 73.6 83.7

15 1.0 50 12:1 52.5 52.5 92.7


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Table 1: Values of V r, S v, S t and V o obtained from the Numerical SimulationS/n Volume, Vr

(m3)Space velocity, S

(sec. -1)Space tim, S T

(Sec.)Volumetric

flowrate, Vo,(m 3 /s)

1 0.1000 0.0014 720.0000 0.0111e-03

2 0.3500 5.5555e-04 1800.0000 0.0389e-03

3 0.7000 2.7778e-04 3600.0000 0.0778e-03

4 1.2000 1.1111e-04 9000.0000 0.1333e-03

5 1.4500 9.2593e-05 10800.0000 0.1611e-03

Table 2: Values of V r, -R a, 1/R a, F ao and Conversion Rate obtained from the Numerical Simulation S/n Volume, Vr

(m3)Reaction

rate,-Ra

1/-Ra Fao/-Ra %Conversion,

X1 0.1000 4.3826 0.2282 0.7758 0

2 0.3500 1.2522 0.7986 2.7152 0.2

3 0.7000 0.6261 1.5972 5.4304 0.4

4 1.2000 0.3652 2.7381 9.3100 0.6

5 1.4500 0.3022 3.3085 11.2504 0.8

Table 3: Design Parameters for a Cylindrical shape CSTRS/N Volume, Vr

(m3)Radius, R (m) Height of

Cylinder, h (m)Area, A (m 2)

1 0.1000 0.2940 0.4060 0.2463

2 0.3500 0.4040 0.6025 0.5809

3 0.7000 0.5580 0.7366 0.9503

4 1.2000 0.6780 0.8309 1.4441

5 1.4500 0.6880 0.9751 1.4871

V total = V 1 + V 2 + V 3 + V 4 + V 5 = 3.8m3

Radius of the total volume = 0.9643m, Area =2.9212m 2 and Length of tube =1.3mThe results above was obtained from Numerical Simulation of model equation using MATLAB2013a, from series of iterations using initial guess values with boundary conditions.


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Fig. 1: The reciprocal of reaction rate versus percentage conversion of the biodiesel

Fig. 2: Volume of Reactor versus Conversion rate

Fig. 3: The Percentage Conversion of the Oil in a given Volume

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.5

1

1.5

2

2.5

3

X, Conversion

1 / - R a

1/-Ra versus X

Reaction rate vs % Conversion

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

0.2

0.4

0.6

0.8

1

1.2

1.4

X, % Conversion

V r

( c u b

i c m e t e r

)

Vr vs. X

Volume versus % Conversion

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

2

4

6

8

10

X, % Conversion

F a o

/ - R a ( c u b

i c m e

t e r s

)

Fao/-Ra versus X


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Fig. 4: Volumetric Flow Rate versus Volume of CSTR

Fig. 5: Reactor Volume versus Space Time

From the Fig. 5 above General model for the volume versus space time,f(x) = a*exp(b*x), Coefficients (with 95% confidence bounds): a = 0.2899 (-0.003071, 0.5828),b = 0.0001524 (4.692e-05, 0.0002579).

Fig. 6: Volume of CSTR versus Space time

0.2 0.4 0.6 0.8 1 1.2 1.4

2

4

6

8

10

12

14

16

x 10-5

Volume of CSTR (cubic meter)

V o l u m e t r i c

f l o w r a

t e ( c u b

i c m

/ s )

y = 0.00011*x + 8e-09

2000 4000 6000 8000 10000

0.2

0.4

0.6

0.8

1

1.2

1.4

St (sec.)

V r

( c u b

i c m e t e r )

Vr vs. StVolume of CSTR versus space time

2000 4000 6000 8000 10000

0.2

0.4

0.6

0.8

1

1.2

1.4

St (sec.)

V r

( c u b i c m e t e r

)

Vr vs. St Volume of CSTR versus space time


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The Fig. 7 above show the equation for the prediction of Space time at different sizing of thevolume of CSTR using a Smoothing spline: f(x) = piecewise polynomial computed from p,Smoothing parameter: p = 8.9306127e-10, Goodness of fit: SSE: 0.001847, R-square: 0.9986.

Fig. 7: Space velocity versus Volume and Space time

Fig. 8: The Inverse of Reaction Rate versus Space Time

Fig. 9: The Reaction Rate versus Space Time

2000 40006000 8000

10000

2468

101214

x 10-4

0.5

1

1.5

St (sec.)Sv (1/sec.)

V r

( c u

b i c m

)

Vr vs. St, Sv

2000 4000 6000 8000 10000

0.5

1

1.5

2

2.5

3

St (sec.)

1 / - R a

1/-Ra versus St

2000 4000 6000 8000 10000

1

2

3

4

St (sec.)

- R a

-Ra vs. StReaction rate vs Space time


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Fig. 10: Reactor Volume versus Reactor Radius

Effect of Space Time and Space VelocityFrom the results obtained, it could be observed that as the space time and space velocity

increased, the concentration of ester produced also increased, this is in agreement with the findingsof Olatunji et al ., (2011) and Suppes et al., (2004).

CONCLUSION

The model equations developed can be used to design a CSTR with different dimensions thatcan be used to produced a known volume of the Milk bush ( Thevetia peruviana) oil at isothermalreaction temperature of 50 oC and 1.0 wt % KOH. The 6:1 alcohol-to-oil molar ratio was found to beoptimum at low reaction temperature below 50 oC. At high reaction temperature (50 oC), 12:1 alcohol-

to-oil molar ratio is recommended.

PART MATLAB PROGRAMME

%for 100L of CSTR; Computation of Space velocity%Radius of the reactor using initial guess values %of the space velocity, Let St= space time (sec.)

%Input Variables % Cao=8.523096; % initial conc. of triglyceride(mol/L) Cbo=1.955362; % initial conc.of ester(mol/L)

Cyo=Cao*Cbo

%Equation(9);CSTR in isothermal codition V=100; %where Vr=100L Fao=3.4; %mol/sec Xa=0.1289; %Unit=mol/L Ra=-(Fao*Xa)/V% %A cylindrical reactor design

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

R a d

i u s

( m )

Volume (cubic meter)

y = 0.44*x + 0.25

data1 linear


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[10] Olatunji, O.M., Akor, A.J., and Abowei, M.F.N. (2012). Modelling The Chemical Kinetics ofMilk Bush ( Thevetia peruviana ) Oil Transesterification Process for Biodiesel Production.Continental Journal Of Engineering Sciences. 7 (3): 40-48.

[11] Abowei, M.F.N., Olatunji O.M., and Akor, A.J. (2013). Modelling Batch Reactor for MilkBush ( Thevetia peruviana ) Oil Transesterification in the Production of Biodiesel.

International Journal of Scientific and Engineering Research, 4 (4) :952-967.[12] Suppes, G.J., Dasari, E.J., Doskosil, E.J., Mankidy, P.J. and Goff, M.J, (2004).

Transesterification of Soyabean oil with zeolite and metal catalysis. Appl. Catal. A: Gen.,257(2): 213-223.

[13] Dr. V.Balaji and E.Maheswari, Model Predictive Control Techniques for CSTR usingMATLAB, International Journal of Electrical Engineering & Technology (IJEET) ,Volume 3, Issue 3, 2012, pp. 121 - 129, ISSN Print : 0976-6545, ISSN Online: 0976-6553.

simulation of a cstr model for thevetia peruviana oil transesterification in the

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