Journal of Food Engineering 97 (2010) 127–134

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Journal of Food Engineering

journal homepage: www.elsevier .com/ locate / j foodeng

Genetic algorithm optimization of supercritical fluid extractionof nimbin from neem seeds

G. Zahedi a,*, A. Elkamel b, A. Lohi c

a Process Systems Engineering Centre (PROSPECT), Faculty of Chemical and Natural Resources Engineering, Universiti Teknologi Malaysia, UTM Skudai,81310 Johor Bahru, Johor, Malaysiab Department of Chemical Engineering, University of Waterloo, Waterloo, Ont., Canada N2L 3G1c Department of Chemical Engineering, University of Ryerson, Toronto, Ont., Canada N2L 3G1

a r t i c l e i n f o

Article history:Received 5 May 2009Received in revised form 4 September 2009Accepted 2 October 2009Available online 12 October 2009

Keywords:Neem extractionSupercritical extractionModelingGenetic algorithmOptimization

0260-8774/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.jfoodeng.2009.10.001

* Corresponding author. Tel.: (60) 7 5535583; fax:E-mail address: grzahedi@fkkksa.utm.my (G. Zahe

a b s t r a c t

The subject of this study is to optimize supercritical extraction of nimbin from neem seeds using aGenetic Algorithm (GA) technique. In order to investigate the effect of parameters on nimbin extractionyield, a partial differential equation model based on mass conservation was developed and solved numer-ically. The results were successfully validated and a parameter estimation problem that employs labora-tory experimental data was solved. Using this validated model and the optimized set of parameters in themodel, another problem was formulated with the aim of optimizing the extraction process. Profit was setas the objective function. Using a GA optimization algorithm, it was found that profit achieves its max-imum when T = 305 k, P = 200 bar, carbon dioxide flow rate = 0.967 cm3/min and dp = 0.1431 cm. Theability of the GA algorithm in optimizing the process was compared with a traditional Gradient Search(GS) optimization technique. THE GA technique proved to be a more efficient technique; especially whenconsidering computational effort in reaching an optimal solution.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Neem with scientific name of ‘‘Azadirachta indica” which hasapplication in agriculture and medicine grows in south, south eastand west of Africa. The seed has approximately 45% oil with com-position of (50–60%) oleic acid, (8–16%) linoleic acid, (13–15%) pal-mitic acid, (14–19%) stearic acid, (8–16%) linoleic acid and (1–3%)arachidic acid. Neem oil is reported to have several usages like,anti-inflammatory, analgesic, antipyretic and anti-malaria drug,cure for syphilitic condition and various skin diseases, antimicro-bial, antifungal and antiviral effects (Okpanyi and Ezeukwu,1981; Johnson and Morgan, 1997).

Since the neem oil is used in pharmaceutical and food industry,its incomplete purification is unacceptable. Using SupercriticalFluid Extraction (SFE) will render this problem. The SFE processeshave at least an order of magnitude higher extraction rate than tra-ditional liquid extraction (Ghoreishi and Sharifi, 2001). Solventrecovery in SFE is easily reached by a small change in the pressureor temperature of the solvent.

Carbon dioxide has a number of favorable characteristics (i.e.low critical point (304 K) inert, non explosive, non-flammable,

ll rights reserved.

(60) 7 5581463.di).

low price, odorless, colorless and non toxic) which makes it aninteresting fluid for SFE applications. Furthermore, the low surfacetension, viscosity and high diffusivity of CO2 provides a high masstransfer coefficient for this fluid (Gopalan et al., 2003; Meireleset al., 2009).

As the investment to build a SFE is high compared with conven-tional methods, optimization of these plants is of great importance.Consequently the accurate modeling of the process is necessary.Some authors have studied SFE of nimbin with CO2 (Johnson andMorgan, 1997; Tonthubthimthong et al., 2001; Mongkholkhajorn-slip et al., 2005). Among the works only Mongkholkhajornslipet al. have proposed a model for SFE of nimbin with CO2. This mod-el has some assumptions to convert governing Partial DifferentialEquation (PDEs) to ordinary differential equation, which leads toerrors in estimation. For optimization purposes, a more accuratemodel of the SFE process is necessary. No works were found inthe literatures on optimization of nimbin SFE except our GradientSearch (GS) work (Zahedi et al., 2009). To the best of our knowl-edge, the application of Genetic Algorithms (GA) in SFE optimiza-tion is a new endeavor which has not been undertaken before forneem seed extraction. In the current study, a detailed model forSFE of nimbin is first presented. The model which is a set of PDEsis solved numerically and then compared with experimental data.In the next step of the study, the model is employed within an

Nomenclature

Bi Biot number (ðkf RpÞ=Dp)Cp

molcm3

� �neem oil concentration in the neem particle pore

Cpsmolcm3

� �neem oil concentration at the surface of the neem parti-cle pore

C molcm3

� �neem oil concentration in the supercritical phase

C0molcm3

� �initial neem concentration

C1 ($) nimbin profitC2 ($) compressing costC3 ($) cooling costC4 ($) carbon dioxide costC5 ($) neem seeds cost

D1cm2

s

� �axial dispersion coefficient

DABcm2

s

� �diffusivity of neem oil in supercritical CO2

Dpcm2

s

� �effective diffusivity in the neem particle pore

dp (cm) neem particle diameterF(t) cumulative nimbin productionG randomly generated standard Gaussian variableKf

cms

� �mass transfer coefficient

K equilibrium constantL (cm) length of packed bedn constant of Freundlich equationP1 (Pa) pressurePeb Peclet number for the bed, ðLmÞ=D1, m is the bed fluid

kinematic viscosity

Pep Peclet number for the particle, ðdPmÞ=D1, m is the bedfluid kinematic viscosity

pwc (w) real compressor workPwcoo (w) carbon dioxide cooling work

Q cm3

s

� �carbon dioxide flow rate

q molcm3

� �neem oil concentration in the neem particle phase

r (cm) radial coordinate in the neem particleRp (cm) neem particle radiusRe Reynolds number(ð2Rpmqf Þ=lf )Sc Schmidt number (lf ðqf DmÞ)Sh Sherwood number (ð2Rpkf Þ=Dp)w (g) neem seed weightx variable for mutation in genetic algorithmZ1, Z2 compressibility factorsz dimensionless axial coordinate along the bed (x/L)

Greek lettersq dimensionless radial coordinate in the neem particle (r/

Rp)s dimensionless time ((tm)/L)st dimensionless bed filling timee void fraction of packed bedeb void fraction of the bedep void fraction of neem particleqf

gcm3

� �supercritical fluid density

lfg:cm

s

� �supercritical fluid viscosity

128 G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134

optimization strategy to find the optimum operating values oftemperature, pressure, carbon dioxide flow rate and particle sizeusing a GA optimization routine. Finally, the GA ability in optimi-zation is compared with GS method.

2. Modeling

Mathematically the overall extraction rate of nimbin from neemseeds can be described by a set of PDEs. Fig. 1 depicts a schematicof an extractor and Fig. 2 shows a hypothetical element for theextractor modeling. The extractor is assumed to be a fixed bed ofneem seeds as the stationary phase while the supercritical carbondioxide as the mobile phase (Fig. 2). In order to provide a meaning-ful model, radial dispersion is neglected. Axial dispersion has beentaken into account through Peb. It is assumed that the whole col-umn operates in the same pressure and temperature (due to thesmall length of the extractor). Axial concentration gradients areimportant and radial concentration gradients are neglected. As aresult, the physical properties of the supercritical CO2 do notchange significantly.

Based on these assumptions and applying conservation of mass,the model of the extractor can be written as given below:

@C@s� 1

Peb

@2C@z2 þ

@C@zþ 1� e

e3LRp

BiPepðC � CpsÞ ¼ 0 ð1Þ

ep þ ð1� epÞ@q@cp

� �@Cp

@s¼ 1

Pep

LRp

1q2

@

@qq2 @Cp

@q

� �ð2Þ

ð1� epÞ @q@t is concentration change in nimbin which is equivalent

to concentration change in the solid part of the neem seed.Where,

q ¼ KCn ð3Þ

The boundary and initial conditions for Eqs. (1)–(3) are:

B:Cat z ¼ 0 C ¼ C0

at z ¼ 1 @C@z ¼ 0

at s ¼ 0 C ¼ C0

8<: ð4Þ

B:C

at q ¼ 1 BiðC � CpsÞ ¼ @Cp

@q

at q ¼ 0 @Cp

@q ¼ 0

at s ¼ 0 Cp ¼ C0

8>><>>: ð5Þ

The above model is solved numerically using the MATLAB 7.4software. In this case, Eqs. (1)–(3) are discritized in the z directionand the resulting ODE sets are solved simultaneously. Since in aprevious study (Tonthubthimthong et al., 2001) cumulative nimbinproduction was measured up to time t, hence we also employ thisquantity:

FðtÞ ¼ eð1� eÞð1� ebÞÞC0st

Z s

0Cds ð6Þ

3. Auxiliary equations

Some parameters in the model are obtained from correlationsand from our previous work (Mongkholkhajornslip et al., 2005;Meireles et al., 2009) as given below:

3.1. External mass transfer coefficient

External mass transfer coefficient, Kf was calculated from theSherwood number (Sh):

Kf ¼DABSh

dpð7Þ

Collection tube

CO2 Cyliner

Extractor

H/X

P

Pressure gauge

Gascompressor

CO2 Ventilation

Nimbin

Nimbin + CO2 (high P)

Neempacked bed

Fig. 1. Schematic diagram of supercritical CO2 extraction system.

Fig. 2. Bed of particles streamed by the solvent.

Fig. 3. Comparison of model results with experimental data at P = 200 bar,Q = 0.62 cm3/min and dp = 0.06 cm.

Fig. 4. Comparison of model results with experimental data at P = 200 bar,T = 328 K and dp = 0.06 cm.

G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134 129

Sherwood number has been obtained from our previous corre-lation (Mongkholkhajornslip et al., 2005):

Sh ¼ 0:135 ðRe0:5Sc0:33Þ ð8Þ

The density of CO2 was calculated by the Modified Peng–Rabin-son equation of state. The viscosity of CO2 at high pressure wasestimated by the residual viscosity correlation of Stiel and Thodos(Poling et al., 2001) using the low-pressure gas estimated by meth-od of Chung (Poling et al., 2001). The binary diffusion coefficient ofnimbin–CO2 at supercritical condition was obtained by the methodof Riazi and Whitson (Poling et al., 2001) based on low-pressurevalues from the Fuller’s equation (Poling et al., 2001). The criticalproperties of nimbin (C30H36O9) were calculated by using the Jo-back modification of Lydersen’s method (Tonthubthimthong,2004) (Tc = 1512.23 K, Pc = 9.99 bar, vc = 1513.5 cm3/mol andTb = 1235.12 K).

4. Modeling results

Figs. 3–6 provide comparisons of the model and laboratoryexperimental data (Tonthubthimthong, 2004). The model capabil-

ity in accurately estimating the experimental observations is illus-trated by these figures. Fig. 7 shows the variation of extractionyield as a function of temperature and pressure. Figs. 8–11 depictthe model response. It is obvious as much as pressure increases,extraction yield increases. For higher pressures (more than200 bar), increasing pressure doesn’t change the extraction yield

Fig. 5. Comparison of model results with experimental data at T = 328 K,Q = 0.62 cm3/min and dp = 0.06 cm.

Fig. 6. Comparison of model results with experimental data at T = 328 K,Q = 0.62 cm3/min and P = 200 bar.

Fig. 7. Variation of efficiency with temperature and pressure at Q = 0.62 cm3/minand dp = 0.06 cm.

Fig. 8. Effect of pressure on extraction rate at T = 305 K, dp = 0.0575 andQ = 0.24cm3/min.

Fig. 9. Effect of CO2 flow rate on extraction rate at T = 305 K, dp = 0.0575 andP = 260 bar.

130 G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134

significantly. Fig. 9 shows a positive effect of carbon dioxide flowrate on extraction. It is interesting that temperature has a negativeeffect on nimbin extraction (Fig. 10). Small particle sizes providehigh surface area which causes high mass transfer coefficients.Fig. 11 shows this fact. For a realistic judgment about the extrac-tion process, the effect of operating parameters on process profitwas investigated. Fig. 12 provides the variation of neem concentra-tion along the SFE bed as a function of time.

5. Genetic algorithm method

A GA program was developed in order to optimize the extrac-tion process. The manipulated variables were allowed to vary withtime. The method starts with a population of random regimes.Each of these regimes (also called a member of the population),consists of a vector x of the dependent variable at equally spacedtime intervals, from which its values at other times are found bylinear interpolation. Smoother relationships can be found by usingother interpolation methods, such as a polynomial (Lagrangian)

Fig. 10. Effect of temperature on extraction rate at dp = 0.0575, Q = 0.24 cm3/minand P = 260 bar.

Fig. 11. Effect of particle diameter on extraction rate at T = 305 K, Q = 0.24 cm3/minand P = 260 bar.

Fig. 12. Variation of neem concentration along the SFE bed at dp = 0.0575 cm,T = 305 K and P = 230 bar.

G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134 131

interpolation or a cubic spline. However, the type of interpolationused is irrelevant to our discussion.

A new member or ‘‘offspring” is generated from one or two ran-domly-chosen parents are added to the population pool. This iscalled the reproduction step. Next, two members are taken at ran-dom out of the pool. The less optimal of these is removed fromthe population. This elimination process ensures that the generalfitness of the population keeps increasing. The process is repeateduntil a satisfactory regime is found among the existing population,or until no further improvement has been obtained for a pre-spec-ified number of cycles. Fig. 13 shows a schematic of the GA used inthis study.

Because a member is eliminated as soon as a new one is gener-ated, this method is said to use a steady-state strategy. Othermethods may generate a whole new population before carryingout the elimination step, or an intermediate strategy betweenthese extremes. The details of the reproduction step are the keyto the success of the method. The reproductive methods must besufficiently powerful to theoretically generate all possible solu-tions; otherwise the global optimum cannot be guaranteed even

after an infinite number of cycles. The reproduction rules calledmutation.

Mutation generates an offspring from a parent member by caus-ing a large change in one element xi of the x vector:

XiNEW ¼ xiþ Dxmaxð1� expð�absjGjÞÞ ð9Þ

where Dxmax is the maximum possible change, i.e. distance betweenxi and the maximum possible of x (in our study, constrains limit Dxfor temperature, pressure, particle size and CO2 flow rate), and G is arandomly generated standard Gaussian variable. The exponent var-ies from 0 to 1, ensuring that the maximum value is not exceeded.The expression also ensures that small changes are more likely thanlarge ones.

Mutation causes a small change in all of the x-values. Obviouslythere are a large number of parameters that can be changed to im-prove the performance of the optimization method: the size of thepopulation, the relative frequency of each operator and the param-eters of the mutation, creep, smooth, and interpolation and extrap-olation operators. The optimal values of these parameters can befound by trial and error, but the process is time consuming andthe results are problem-dependent. Alternatively, a competitiveevolution strategy can be used in which several populations, eachwith different parameter tunings, fight to compete for computertime. However, it was found that the optimal ‘‘tuning” of the meth-od is relatively independent of the problem, and only a rough man-ual tuning was performed.

6. Optimization

Based on our experience and understanding of changes in pro-cess parameters; temperature, pressure, carbon dioxide flow rateand particle size were selected as the optimization parameters.The objective function is profit which is more comprehensive thancumulative neem production rate. The profit consists of five parts:

Profit ¼ C1 � C2 � C3 � C4 � C5 ð10Þ

C1 ¼ yield� Cost1; ð11Þ

C2 ¼ Pwc � time� Cost2; ð12Þ

C3 ¼ Pwcoo � time� Cost2; ð13Þ

Fig. 13. Flow chart of GA optimization.

Fig. 14. Effect of pressure on process profit at T = 305 K, dp = 0.0575 andQ = 0.24 cm3/min.

132 G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134

C4 ¼ Cost3� Qm� time; ð14Þ

C5 ¼ Cost4�wt: ð15Þ

Yield is mass of nimbin extracted (g). This quantity can be cal-culated from F. Cost1 is nimbin price which has been found to be40000 $/g. Pwc is real compressor work to provide supercritical car-bon dioxide and circulate it (Fig. 1). This quantity was calculatedusing Eq. (16) as:

Pwc ¼1

440c

c� 1ffiffiffiffiffiffiffiffiffiz1z2p

NsP1V1P2

P1

� �c�1cNs

� 1

" #ð16Þ

Cost 2 is price of electricity (i.e. in Ontario, Canada) which is1.38888 � 106/30 $/Ws. Pwcoo is the work which is necessary to coolCO2. This process is necessary to remove extracted nimbin from car-bon dioxide.

Pwcoo ¼1

440c

c� 1ffiffiffiffiffiffiffiffiffiz1z2p

P1V1P2

P1

� �c�1c

� 1

" #ð17Þ

Cost 3 is price of liquid CO2, which was found to be 350 $/18 kg.Cost4 is neem seed price which is equal to 0.1/30 $/g.

Fig. 15. Effect of CO2 flow rate on process profit at T = 305 K, dp = 0.0575 andP = 260 bar.

Fig. 16. Effect of temperature on process profit at, dp = 0.0575, Q = 0.24 cm3/minand P = 260 bar.

Fig. 17. Effect of particle diameter on process profit at T = 305 K, Q = 0.24 cm3/minand P = 260 bar.

Table 1Operating variables and their bounding in maximum extraction yield.

Independent variables Lower–upper bounded variable

Pressure (bar) 100–260Temperature (K) 305–340CO2 flow rate (cm3/min) 0.24–1.24Particle size (cm) 0.0575–0.1850Amount of neem used (g) 1–2.5Extraction time (min) P0

Table 2GA optimum values for nimbin extraction.

Quantity Value

The optimum temperature (K) 305The optimum pressure (bar) 260.00The optimum time for extraction (min) 240.00The optimum particle diameter(cm) 0.0575The optimum carbon dioxide flow rate (cm3/min) 1.24The maximum yield 1.00The maximum weight of extracted nimbin (g) 2The number of generations 25The number of function evaluations 50344

G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134 133

Fig. 14 illustrates the effect of pressure on process economy.Higher pressures provide a more economical operation. The effectof carbon dioxide flow rate on process profit is interesting. At lowerextraction times, high CO2 flow should be used, but after about250 min a lower carbon dioxide flow should be used to improveprofit (Fig. 15). Fig. 16 emphases again that for higher profits,extraction should be carried out at lower temperatures. FinallyFig. 17 again shows the authenticity of the proposed model andindicates that to gain higher profits as much as possible, small par-ticle sizes are necessary.

Obj ¼Max½profit� ð18Þ

Table 1 shows the parameters’ ranges for the extraction process.The Matlab genetic algorithm toolbox has been used to imple-

ment the GA optimization routines (Mathwork, 2009). Neemextraction yield has been set as the fitness function. A populationsize of 10 was set for generation. Using the GA technique, the opti-mum values for suitable operation of process were found. Table 2represents these values. Unlike previous works, we investigated

here optimization of a variety of extraction parameters (fiveparameters simultaneously) as optimization variables. Consideringprofit as the objective function, the following optimum conditionswere found: T = 305 k, P = 200 bar, carbon dioxide flowrate = 0.967 cm3/min and dp = 0.1431 cm. The particle size in thisresult is somewhat large. The program responds in 50.23 s secondon a Pentium IV computer with 3.06 GHz, CPU. Comparing to theGS method from our previous work (Zahedi et al., 2009), whichprovide results in 230 s, the GA is 4.6 times faster than the GSmethod.

7. Conclusions and remarks

Optimization of nimbin extraction from neem seed has been thesubject of the current study. Temperature, pressure, CO2 flow rateand particle size have been set as optimization variables. Processlimitations have been considered as constraints in the optimizationroutines. GA and GS methods both were used to optimize the pro-

134 G. Zahedi et al. / Journal of Food Engineering 97 (2010) 127–134

cess. The GA method proved to be more computational efficientthan the GS method and can be useful in tuning control parametersof the supercritical extraction process.

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