Energy Conversion and Management 62 (2012) 40–46

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Energy Conversion and Management

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A design algorithm for batch stirred tank transesterification reactors

C.N. Anyanwu a,⇑, C.C. Mbajiorgu b, O.U. Oparaku a, E.U. Odigboh b, U.N. Emmanuel c

a National Centre for Energy Research and Development, University of Nigeria Nsukka, Nigeriab Dept. of Agricultural and Bioresources Engineering, University of Nigeria Nsukka, Nigeriac Dept. of Electronic Engineering, University of Nigeria Nsukka, Nigeria

a r t i c l e i n f o a b s t r a c t

Article history:Received 20 December 2011Received in revised form 30 March 2012Accepted 30 March 2012Available online 25 June 2012

Keywords:BiodieselComputer softwareReactorVegetable oilDesignCI engine

0196-8904/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.enconman.2012.03.027

⇑ Corresponding author. Tel.: +234 805 1980070.E-mail address: cnasofia@yahoo.com (C.N. Anyanw

A 50 L per batch, stirred tank reactor, suitable for carrying out transesterification of vegetable oils wasdesigned and constructed. The major design assumptions included stainless steel plate thickness of2 mm, reaction temperature of 60–65 �C and an initial/final fluid temperature of 25/70 �C. The calculatedimpeller Reynolds number was in the mixed regime zone of 10–104; the power number was variedbetween 1 and 5, while a typical propeller speed of 22.5 rev/s (or 1350 rev/min) was adopted. The lim-iting design conditions were maximum reactor diameter of 1.80 m, straight side height-to-diameter ratioin the range of 0.75–1.5 and minimum agitator motor power of 746 W (1 Hp). Based upon the design, asimple algorithm was developed and interpreted into Microsoft C Sharp computer programming languageto enable scale up of the reactor. Performance testing of the realized reactor was carried out while using itto produce Neem oil biodiesel via base – catalyzed methanolysis, which yielded high quality fuel product.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

With global carbon emissions already in excess of the danger-ously high level of 450 ppm [1], concerted efforts are now gearedtowards reducing the use of fossil fuels by increasing the applica-tion of renewable energy derived fuels, especially in the transportsector. Biodiesel derived from vegetable oils and fats has been dem-onstrated as the best suited alternative fuel for compression igni-tion engines. The biodiesel manufacturing process converts oilsand fats into long chain mono alkyl esters, or fatty acid methylesters (FAMEs), which are utilized as biodiesel fuel after some puri-fication processes. Straight vegetable oils (SVOs) have been used incompression ignition (CI) engines as alternative fuels, starting withRudolph Diesel’s successful trials in the early 19th century when heused peanut oil to power his CI engine. Research has, howevershown that raw vegetable oils are capable of causing problems tothe engine in the long term, owing to their high viscosity [2,3].Transesterification of vegetable oils into biodiesel has, therefore,become a standard way of producing fuel grade products from themby reducing their viscosity to acceptable values of about 3.2 cSt.

Although biodiesel has numerous advantages over fossil-derived diesel fuel such as safety (high flash point, usually above140 �C), environmental friendliness (low greenhouse gas emis-sions), and bio-degradability (low trace metal and sulfur contents);the major factor limiting its widespread utilization is high cost of

ll rights reserved.

u).

production. The production cost of biodiesel is still higher thanthe pump price of diesel in most countries, thereby making it lessattractive to the public, except with government incentives. Thehigh production cost of biodiesel is a direct consequence of thehigh price of vegetable oil raw materials, most of which are edible(first generation biofuel sources) and serve as food for man. For thisreason, it has been adduced that a sustainable biodiesel industrywith vegetable oil starting raw material ought to be based onnon-edible oils [4], often referred to as second generation biofuelsources; or even third generation biofuel resources such as algae.In addition, second generation biofuel resources such as jatropha,castor, rubber seed, and neem oils offer great potentials for thedevelopment of agriculture and light industries.

Apart from high vegetable oil prices, the processing cost of bio-diesel is also high, constituting 20–25% of the total production cost[5]. Arising from the need to continue research work aimed atreducing processing costs, it is necessary to study the transesterifi-cation of oils using uniform bench-scale processors to enable properapplication of obtained optimal results to commercial scale plants.

The main objective of the present work is to develop a computerprogram based on the design algorithm of a batch biodiesel reactor.Specifically, it describes the development of a C Sharp computerprogram for design of batch stirred tank transesterification reactors.

2. Technology and kinetics of transesterification

There are five major technological means used to obtain fuelgrade products from vegetable oils, namely dilution, pyrolysis,

Fig. 1. Schematic of acid/base transesterification process. Source: [5].

C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46 41

micro-emulsification, catalytic cracking and transesterification [6].Among these, transesterification is the most commonly appliedtechnique in view of its comparative cost advantage and conve-nience [7,8]. Among other methods of transesterification, such asthe acid [9,10] and enzyme catalyzed processes, and (non-cata-lytic) supercritical methanol process [11–14]; base catalysis hasfound widespread industrial application owing to the fact that itproduces greater yield, is simple and can be scaled up easily beinga more flexible process. However, a major requirement towards thefeedstock for the base catalyzed process is that it should containless than 0.05 wt.% of water and less than 0.5 wt.% free fatty acid[15]. According to Canakci and Van Gerpen [16], transesterificationwill not occur when the FFA content is above 3%. A schematic flowdiagram of the transesterification process is presented in Fig. 1.

In the batch-scale base process, most of the steps are usuallyundertaken separately. The catalyst promotes an increase in solu-bility to allow the reaction to proceed at a reasonable rate [17],and is required because the alcohol is sparingly soluble in theoil phase. The most common catalysts used are strong mineralbases such as sodium hydroxide and potassium hydroxide. Firstly,the catalyst (usually 0.5–1.5% w/w) is mixed with the methanol(6:1 ratio to the oil, i.e. 100% excess) in a smaller container (theactual catalyst sodium or potassium methoxide is produced dur-ing this step). This mixture is then transferred into the transeste-rification reactor, where the vegetable oil has been charged andpreheated. The reactor is covered tightly and heated to 60–65 �Cfor duration ranging from 30 to 120 min with agitation for opti-mal results. The mixture is then transfered into a settling tank(separator) with a high height-to-diameter ratio. Two phases ofglycerol (lower) and biodiesel (upper) begin to emerge after afew minutes, but complete phase separation is only possible aftera period of 2–8 h. The glycerol phase with a specific gravity ofabout 1.25 settles at the bottom, whereas the biodiesel remainson top.

3. Reactors for transesterification

Both batch and flow reactors are used for transesterification ofvegetable oils, but batch reactors are usually more adapted for re-search and testing activities, since they are more flexible and easyto control. Stirred, batch reactors for the purpose are often unbaf-fled tank vessels made of stainless steel plates and mounted on asuitable stand.

3.1. Chemical design of the reactor

The relationship between reaction time and reactor volume (V)in the case of batch reactors is given by the equation [18]:

t ¼ NA0

Z x

0

dx�rAV

ð1Þ

where t is the time (s), NA0 the initial number of moles of reactant A,rA the reaction rate, and x is the conversion.

According to some authors [19,20], the acid- and base-catalyzedtransesterification of vegetable oils follow a pseudo second orderchemical reaction mechanism, combined with a shunt reactionscheme at lower alcohol-to-oil ratios such as 6:1. Since the reac-tion time is a function of the desired conversion (x), it is possibleto link a given reactor volume to degree of conversion once thereaction time is specified. A typical value of k is of the order of0.001–0.01 d m3 mol�1 s�1. However, since the reactor is intendedfor transesterification studies at different temperatures and reac-tion durations, greater emphasis has been placed on the mechani-cal design aspects.

3.2. Mechanical design of the reactor

3.2.1. Description of the reactorThe reactor for the present work was a Batch Stirred Tank

(BSTR), unbaffled cylindrical vessel with conical bottom. It washeated with an electrical coil and agitated by means of a straightentering stirrer, powered by a single phase AC motor. The choiceof a batch reactor is supported by literature [21], which indicatesthat they are more flexible and produce higher yield of productin comparison with continuous flow reactors, although the latterare often associated with lower operating costs and high through-puts. A batch reactor is often preferred for research work and in sit-uations where the down-time is much less than the reaction time,especially for slow reactions like transesterification, which requireup to 1 h. A flexible thermo-regulator capable of maintaining thetemperature of a given medium within ±0.5 �C was fabricatedbased on the LM35 integrated circuit to enhance accurate temper-ature control during the transesterification process.

3.2.2. Sizing of the reactorPreliminary experiments carried out using conventional labora-

tory equipment (hot plate, equipped with magnetic stirrer andtemperature sensor) corroborated literature data [22–24], which

42 C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46

show that the expected reaction time for the transesterification ofNeem oil ranges between 0.5 and 2.0 h, depending on other reac-tion conditions such as temperature, alcohol-to-oil ratio and cata-lyst amount. In the present work, 1 h was taken as the designreaction time, whereas the reactor was assumed to work for 10 hper day.

3.2.3. Reactor batch sizeA 500 L per day batch reactor operating for 10 h each day with

an average reaction time (including down-time) of 1 h would havea batch volume given by the expression

Vbt ¼Rcp

104 ¼500104 ¼ 0:05 ½m3� ð2Þ

where Vbt is the batch volume, and Rcp is the capacity of the reactor,liters per day.

3.2.4. Diameter and height of reactorThe reactor would not be filled to the brim due to safety consid-

erations. It was assumed that the volume of conical section of thevessel is equal to the difference between the total volume and theeffective volume. Thus,

pDT H ¼ 4Vbt ð3Þ

where DT is the diameter of vessel, m and H is the straight sideheight, m.

According to Knudsen et al. [25], the height to diameter ratio ofan unbaffled reactor should lie between 0.75 and 1.5. Therefore weassumed 1.3 times the diameter as height

H ¼ 1:3DT

Then 1:3pD3T ¼ 4VBt

DT ¼ffiffiffiffiffiffiffiffiffiffiffi4VBt

1:3p3

r¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4 � 0:05

1:3p3

r¼ 0:37 m ð4Þ

and H = 1.3DT = 0.48 m.

3.2.5. Volume of conical section, Vc

The volume of conical section (Vc) of the cylindrical vessel(where r1 and r2 are the radii of the reactor and outlet tap, respec-tively) was given by the expression:

Vc ¼ p hc

3

� �r2

1 þ r1r2 þ r22

� �ð5Þ

In Eq. (5), hc is the height of the conical section of the reactor asshown in Fig. 2.

Hence,

Vc ¼ 0:17DTp 0:25D2T þ 0:0125DT þ 0:000625

� �¼ 0:0078 m3 ð6Þ

With an effective volume of 50 L, the reactor should thereforebe filled up to the 40 cm mark on the straight height.

3.2.6. The propeller shaft and paddleA straight-entering propeller, which is recommended for ves-

sels with diameters less than 6 ft (1.80 m) or 1000 gallons (4 m3),was chosen for the unbaffled stainless steel tank. This was done

r2

r1

hc

Fig. 2. Conical section of the reactor.

to enable its use even in scaled-up versions of the equipment.According to Priday et al. [26], slanting propellers are not suitablefor agitators requiring more than 3 Hp (2.24 kW). The designrequirement is that the straight entering paddle should bemounted at a distance of DT/4 from the bottom of the reactor foreffective mixing.

3.2.6.1. Length of propeller. A distance of 10 cm was allowed be-tween the agitator motor mounting and the top of the reactor forease of maintenance. Therefore, the total length of the propellershaft (Lp) was calculated as per the expression:

Lp ¼ H þ hc � 0:25DT þ 0:10 ½m� ð7Þ

Since hc = 0.5DT the conical section was welded to the base at anangle of 135� with respect to the straight side. The outlet tap diam-eter was 2.5 cm (but could be up to 5.0 cm in larger tanks, suchthat hc was taken to be equal to the reactor radius).

Lp ¼ H þ 0:25DT þ 0:1 ½m�

3.2.6.2. Diameter of propeller (Da). Tilton [27] recommended thatthe propeller diameter should be within (0.3–0.6)DT. In order tosave materials and also operating costs since power, P = f(Da); Dawas chosen as 0.4DT in the present work, such that Da = 0.148 m.

3.2.7. Power requirement of agitator motorThe degree of laminarity or turbulence within the reactor was

defined by the impeller Reynolds number, given by the expression[28]:

NRe ¼Da2Nq

lð8Þ

where NRe is the Reynolds number (which is less than 10 for laminarand above 104 for turbulent flow regimes), Da the propeller diame-ter (0.15 m), N the rotational speed (22.5 rev/s), q the fluid density(900 kg/m3), and M is the fluid viscosity (0.2 Pa s).

A typical value of N in single phase motors is 1350 rpm(22.5 rev/s) and was taken as design value for the agitator motor.For most vegetable oils, the density and viscosity are in the range900 kg/m3 and 0.2 Pa s, respectively. These values were adoptedin the design, leading to a Reynolds number of 2278.

The power requirement of the agitator motor, P in watts wasobtained from the expression [28]:

P ¼ NpqDa5N3 ð9Þ

where Np is the power number, which depends on the Reynoldsnumber and was obtained from Nomographs as given in [26]. Othersymbols have the same meaning as in Eq. (8).

The relationship expressed in Eq. (9) is given by plots of powernumber versus Reynolds as presented for different types of propel-lers in [27]. The Power number corresponding to a Reynolds num-ber of 2278 for a propeller with few blades varies between 1 and 5,hence the power requirement could vary between 746.4 W and3112 W. A 1 Hp motor was chosen for the present work as thiswould reduce initial and running costs.

3.2.8. Power requirement of heating coilThe heat supplied by the electrical coil (Qcoil) is absorbed by the

reactants, the stainless steel tank and the agitator. The balance islost heat. Thus

Q coil ¼ Q oil þ Q steel þ Q ag þ losses ð10Þ

where Qoil is the heat absorbed by oil; Qsteel the heat absorbed bythe stainless steel vessel; Qag the heat absorbed by the agitator;and Losses is the heat losses.

X1 X3X2

θ1

θ 2

θ 3

θ 4

Fig. 3. Temperature profile of the wall of the reactor.

C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46 43

These heat losses are often within 5–7% of the heat supplied. Forthe present design, a worst-case value of 10% was adopted,whereas initial and reaction temperatures of 25 �C and 70 �C,respectively for all the fluid reactants were used. Thus

0:9Q coil ¼ 45½ðCpVqÞoil þ ðCpVqÞsteel þ ðCpVqÞag� ð11Þ

Q coil ¼ 50½ðCpVqÞoil þ ðCpVqÞsteel þ ðCpVqÞag� ð12Þ

where Voil = Vbt is the volume of oil (reactants) = 0.05 m3, Vsteel thevolume of stainless steel vessel, Vag the volume of agitator; Cp oil

the heat capacity of reactants (oil), Cp steel the heat capacity of stain-less steel = 0.5 kJ/kg K, Cp ag the heat capacity of cast iron agita-tor = 0.6 kJ/kg K, qoil the density of oil = 900 kg/m3, qsteel thedensity of steel = 7800 kg/m3, and qag is the density of cast iron(agitator) = 7200 kg/m3.

According to Liley et al. [28], the specific heat capacity of vege-table oils may be obtained from the expression

Cp ¼0:5ffiffiffiffiffiffiffi

d154

q þ 0:007ðt � 15Þ; ð13Þ

where d is the density (g/cm3), Cp the Specific heat capacity (Cal/g �C),and t is the temperature (�C).

3.2.8.1. Volume of stainless steel material. The volume of materialused to construct the conical section of the cylinder was taken as5% of the entire material (as confirmed through practical calcula-tions). Therefore, the volume of the steel material was calculatedas follows:

V steel ¼ 1:05pDT Hd ð14Þ

where DT is the reactor diameter; H the straight side height of thereactor; and d is the thickness of the steel plate (m).

3.2.8.2. Volume of cast iron agitator. The volume of material neededto fabricate the padle was taken as 10% of the volume of cast ironneeded to fabricate the entire propeller. Therefore,

VCastIron ¼ 0:275pDa2LP ð15Þ

Hence

Q coil ¼ 50 900 � 2:15VBtð Þ þ 7800 � 0:5V steelð Þ½þ 7200 � 0:6VCastIronð Þ�

Q coil ¼ 5� 104½1:935VBt þ 4:095pDT Hdþ 1:188pDa2LP�; kJ ð16Þ

The value obtained for coil energy using Eq. (16) was 5279 kJ.This quantity of heat energy must be supplied during the pre-heat-ing period. Assuming a pre-heating period of 30 min, then the coilpower amounts to 2.93 kW, including losses. The actual power rat-ing of the heating coil used in the present design was 2.5 kW.

3.2.9. The thermoregulatorA thermoregulator is a feedback mechanism used to monitor

the reactor temperature and control it within a pre-set range orpoint. A linear type thermoregulator was fabricated based on theLM35 integrated circuit and used to control the heating element.Since the sensor circuit cannot be immersed in the liquid reactantphase, it was encased in a water-tight aluminum container and cal-ibrated against the readings obtained from a K-type thermocouple(BK Precision), made in Taiwan.

3.2.10. Thickness and type of insulationTo reduce heat losses from the reactor, it was necessary to insu-

late the vessel with properly selected and sized material. The insu-lation material was glass wool with thermal conductivity

k = 0.03 W/mK. Assuming the average temperature of the reactorto be 70 �C, whereas the outer wall temperature should not exceed25 �C; then, applying Fourier’s conduction heat transfer equation[25] to Fig. 3:

dQdh¼ �kA

dtdx

� �ð17Þ

or

q ¼ � h1 � h4x1

k1A1þ x2

k2A2þ x3

k3A3

where dQ/dh = q is the heat power (flux) (W), x1 = x3 the thickness ofsteel plate (0.002 m), x2 the thickness of insulator, m, x3 the thick-ness of leather covering (0.001 m), k1 the heat transfer coefficientof steel (45 w/mK), k2 the heat transfer coefficient of glass wool(0.03 W/mK), k3 the heat transfer coefficient of leather (0.03 W/mK), A1 the Area of steel plate (m2), A2 (A3) the area of glass woolinsulator (leather material) (m2), h1 the reactor temperature(70 �C), h2 the temperature at the inner metal/insulator boundary(�C), h3 the temperature at the leather/insulator boundary (�C),and h4 the outer wall temperature (25 �C).

Obviously,

x2 ¼ �k2A2h1 � h4

q� 2x1

k1A1

� �ð18Þ

The heat flux (power), q was obtained from the initial consider-ations and substituted in Eq. (17) such that x2 = 0.3 mm was foundto be adequate glass wool insulation for the present design. The ac-tual thickness of insulation used was 5.0 mm, considering avail-ability of construction materials. The front and top views of therealized reactor are presented in Figs. 4 and 5, respectively.

4. Performance evaluation

4.1. Testing of the reactor

This was carried out by using the reactor to produce biodieselfrom 50 L of Neem oil. The temperature was maintained at 50 �C,using the fabricated thermoregulator. Alcohol to oil ratio of 6:1was applied, while using 1% w/w NaOH as the catalyst. Neem oilpurchased from a farm in Katsina State of Nigeria was degummedat 60 �C using 10% v/v (i.e. 5 L) of water heated to 70 �C. The mix-ture was then allowed to separate by gravity and the top (oil)phase was collected and subjected to acid esterification in orderto reduce its FFA content. Acid esterification was carried out byheating the oil to 50 �C and adding 20% v/v (i.e. 10 L) of methanolslowly into the oil with agitation. The agitation was continuedfor a few minutes, after which 5% (i.e. 2.5 L) of concentrated sulfu-ric acid was added. Stirring was continued for another 30 min, afterwhich the mixture was transferred into a settling tank and allowedto separate. The bottom (oil) phase was then collected into in aclean container and the free fatty acid content tested. The oil (with

Fig. 4. Front view of the reactor.

Fig. 5. Top view of the reactor.

44 C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46

a water content of 0.2%), was charged into the reactor and pre-heated to 50 �C (Optimum reaction temperature was determinedbased on reactions conducted using conventional laboratory hot-plate equipped with thermoregulator.) The pre-determined quan-tity of NaOH was dissolved in the methanol and transferred intothe reactor and the reactor was closed and maintained at 50 �Cwith agitation. At the end of 1 h, heating and stirring were stoppedand the mixture transferred into a separating column, where it wasallowed to stand for about 4 h for complete gravity separation ofthe biodiesel and glycerol. Thereafter, the supernatant (biodiesel)phase was decanted, washed several times with tap water until apH value of 7.0 was obtained. The product was then subjected toquality control characterization tests, results of which are pre-sented in Table 2. Flash point was determined using the PenskyMartens Closed cup method as per ASTM D-93 A. Kinematic viscos-ity was measured using the Canon Fenske Viscometer according to

ASTM ASTM D 445-04, while Acid number was determined accord-ing to ASTM D 664 method.

4.2. Testing of the C Sharp software

The software was tested while using it to carry out designcalculations for different sizes of batch stirred tank reactors withsimilar features to the one already constructed. Reactors withbatch size of between 2 L and 10,000 L were sized using the pro-gramme. These results are presented in Appendices A–E.

5. Results and discussion

The fabricated 50 L batch, stirred tank, reactor was used to pro-cess neem oil biodiesel, after acid esterification of the feedstock to

Table 1Properties of the pretreated neem oil.

S/No Property Value Units

1 Water content 0.20 %2 Density 881 kg/m3

3 Free fatty acid 0.13 %

Table 2Determined properties of the biodiesel.

S/No Property Values ASTM limits* Units

1 Flash point 168 >130 �C2 Kinematic viscosity 3.7 1.9–6.0 mm2/s3 Water and sediments 0.03 <0.05 %4 Acid number 0.24 0.50 max mg KOH/g5 Free glycerol 0.012 0.020 wt.%6 Total glycerol 0.016 0.024 wt.%

* As per ASTM D6751 requirements. Source: [17].

C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46 45

reduce its FFA content to 0.13%. The methyl ester yield obtained atthe end of washing was 84.6%, which is comparable with resultsreported elsewhere [24]. The properties of the pretreated neemoil are presented in Table 1. Values obtained for all the parametersof the produced methyl ester (Table 2) were within ASTM D6751standard stipulated limits, an indication that the product can beused as fuel grade biodiesel.

It was observed that agitation alone required 0.75 kW h duringthe reaction, compared to heating that consumed about 1.96 kW hsince the total heating power was for pre-heating (which lasted for22.5 min) and reaction (24.6 min). Although the energy requiredfor agitation was only 27.6% of the processing costs (excludingpre-treatment), it could be reduced further if a 0.5 Hp (374 W) cen-trifugal pump had been employed to circulate the reactantsthrough the reactor.

Using the developed C Sharp software for reactor design is atime-saving measure, which also reduces the incidence of humanerrors in the design calculations. Tests carried out using the soft-ware also indicated that it can be used by professionals who havelittle or no in-depth knowledge of reactor design practice.

Nonetheless, it is clear that reactor scale-up is not a purelymechanical design problem, considering the fact that the mechan-ical aspects have a great influence on diffusion, heat transfer andchemical kinetics; which determine the reactor’s overall perfor-mance. Adeyemi et al. [29], who studied the effect of certain vari-ables on FAME yield concluded that there is high correlationbetween FAME yield, peak time and reaction temperature;although wide impeller speed variations for Rushton and Elephantear types gave rise to only little difference in FAME yield between89% and 94%. Future research work would investigate the influenceof reactor size and degree of agitation on transesterification kinet-ics and quality of final biodiesel product.

6. Conclusion

A design algorithm for batch stirred tank transesterificationreactors was developed. On the basis of the algorithm, a genericMS C Sharp programme was developed and tested by using it toscale up the designed reactor. Performance evaluation of the con-structed reactor, which was also carried out, showed good results.

Acknowledgments

The authors are grateful to the Management of the NationalCentre for Energy Research and Development, University of Nigeria

Nsukka for funding support provided for this research work. Con-tributions made by Prof. C.A. Nwadinigwe, technical staff ofN.C.E.R.D. and colleagues in the Department of Agricultural andBioresources Engineering are highly acknowledged.

Appendix A

A.1. Computation details

Reactor capacity, Rcp: 20 L.Batch size of reactor, Vbt: 0.002 m3.Diameter of vessel, DT: 0.1221 m.Straight side height, H: 0.1587 m.Volume of conical section, Vc: 0.0004 m3.Safe loading mark, h: 0.0342 m.Length of propeller: 0.3892 m.Reynolds number, NRe: 241.1208.Power requirement of the agitator motor: 2.8368 W.Thickness of stainless steel sheet: 0.002 m.Diameter of propeller, Da: 0.0366 m.Length of propeller, Lp: 0.3892 m.Pre-heating time, t: 30 min.Qcoil: 195.9459 J.Power requirement of heating coil: 0.1089 kW.

Appendix B

B.1. Computation details

Reactor capacity, Rcp: 500 L.Batch size of reactor, Vbt: 0.05 m3.Diameter of vessel, DT: 0.3569 m.Straight side height, H: 0.464 m.Volume of conical section, Vc: 0.007 m3.Safe loading mark, h: 0.07 m.Length of propeller: 0.7532 m.Reynolds number, NRe: 2064.6738.Power requirement of the agitator motor: 608.6462 W.Thickness of stainless steel sheet: 0.002 m.Diameter of propeller, Da: 0.1071 m.Length of propeller, Lp: 0.7532 m.Pre-heating time, t: 30 min.Qcoil: 4874.0195 J.Power requirement of heating coil: 2.7078 kW.

Appendix C

C.1. Computation details

Reactor capacity, Rcp: 5000 L.Batch size of reactor, Vbt: 0.5 m3.Diameter of vessel DT: 0.769 m.Straight side height, H: 0.9997 m.Volume of conical section, Vc: 0.0649 m3.Safe loading mark, h: 0.1397 m.Length of propeller: 1.392 m.Reynolds number, NRe: 9580.0482.Power requirement of the agitator motor: 28226.4019 W.Thickness of stainless steel sheet: 0.002 m.Diameter of propeller, Da: 0.2307 m.Length of propeller, Lp: 1.392 m.Pre-heating time, t: 30 min.Qcoil: 48671.3591 J.Power requirement of heating coil: 27.0396 kW.

46 C.N. Anyanwu et al. / Energy Conversion and Management 62 (2012) 40–46

Appendix D

D.1. Computation details

Reactor capacity, Rcp: 10,000 L.Batch size of reactor, Vbt: 1 m3.Diameter of vessel, DT: 0.9689 m.Straight side height, H: 1.2596 m.Volume of conical section, Vc: 0.128 m3.Safe loading mark, h: 0.1736.Length of propeller: 1.7018 m.Reynolds number, NRe: 15211.1682.Power requirement of the agitator motor: 89669.0786 W.Thickness of stainless steel sheet: 0.020 m.Diameter of propeller, Da: 0.2907 m.Length of propeller, Lp: 1.7018 m.Pre-heating time, t: 30 min.Qcoil: 97318.2696 J.Power requirement of heating coil: 54.0657 kW.

Appendix E

E.1. Computation details

Reactor capacity, Rcp: 20,000 L.Batch size of reactor, Vbt: 2 m3.Diameter of vessel, DT: 1.2207 m.Straight side height, H: 1.5869 m.Volume of conical section, Vc: 0.2532 m3.Safe loading mark, h: 0.2163 m.Length of propeller: 2.0921 m.Reynolds number, NRe: 24141.7351.Power requirement of the agitator motor: 284549.2772 W.Thickness of stainless steel sheet: 0.020 m.Diameter of propeller, Da: 0.3662 m.Length of propeller, Lp: 2.0921 m.Pre-heating time, t: 30 min.Qcoil: 194597.1521 J.Power requirement of heating coil: 108.1095 kW.

References

[1] Schenk PM, Thomas-Hall SR, Stephens E, Marx UC, Mussgnug JH, Posten C.Second generation biofuels: high-efficiency microalgae for biodieselproduction. Bioenergy Resour 2008;1:20–43.

[2] Schuchardt U, Sercheli R, Vargas RM. Transesterification of vegetable oils: areview. J Braz Chem Soc 1998;9(3):1–27.

[3] Nwafor OMl. Emission characteristics of diesel engine running on vegetable oilwith elevated fuel inlet temperature. Int J Biomass Bioenergy 2004;27:507–11.

[4] Balat M. Potential alternatives to edible oils for biodiesel production – a reviewof current work. Energy Convers Manage 2011;52(2):1479–92.

[5] Tyson KS. Biodiesel handling and use guidelines. US Department of Energy; 2004.[6] Yusuf NNAN, Kamarudin SK, Yaakub Z. Overview of the current trends in

biodiesel production. Energy Convers Manage 2011;52(7):2741–51.[7] Anyanwu CN, Sharma VK, Braccio G, Nanna F, Akubuo CO. Palm oil (Elaeis

guiniensis) plantations: a potential biomass resource for biodiesel productionin Nigeria. Int Energy J 2005;6(2):69–82.

[8] Demirbas A. Biodiesel production from vegetable oils by supercriticalmethanol. J Sci Indust Res 2005:858–65.

[9] Miao X, Li R, Yao H. Effective acid-catalyzed transesterification for biodieselproduction. Energy Convers Manage 2009;50(10):2680–4.

[10] Samart C, Chaiya C, Reubroychareon P. Biodiesel production by methanolysisof soybean oil using calcium supported on mesophorus silica catalyst. EnergyConvers Manage 2010;51(7):1428–31.

[11] Baroutian S, Aroua MK, Abdul Aziz AR, Sulaiman NMN. TiO2/Al2O3 membranereactor equipment with a methanol recovery unit to produce palm oilbiodiesel. Int J Energy Res 2012;36::120–129. John Wiley.

[12] Demirbas A. Recent trends in biodiesel fuels. Energy Convers Manage2009;50(1):14–34.

[13] Hanh HD, Dong NT, Starvarche C, Okitsu K, Maeda Y, Nishimura R.Methanolysis of triolein by low frequency ultrasonic irradiation. EnergyConvers Manage 2008;49(2):276–80.

[14] Demirbas A. Biodiesel production via non-catalytic SCF methanol and biodieselfuel characteristics. Energy Convers Manage 2006;47(15–16):2271–82.

[15] Marchetti JM. The effect of economic variables over biodiesel production plant.Energy Convers Manage 2011;52(10):3227–33.

[16] Canakci M, Van Gerpen J. Biodiesel production from oils and fats with high freefatty acids. Trans ASAE 2001;44:1429–36.

[17] Van Gerpen J, Shanks B, Pruszko R, Clements D, Knothe G. Biodiesel analyticalmethods August 2002–January 2004. National Renewable Energy LaboratorySubcontractor Report NREL/SR-510-36240, Colorado, USA; July, 2004.

[18] Fogler HS. Elements of chemical reaction engineering. 4th ed. Prentice HallInt’l Series in Chemical Engineering; 2006.

[19] Noureddini H, Zhu D. Kinetics of transesterification of soybean oil. J Am OilChem Assoc 1997;74:1457–63.

[20] Freedman B, Kwoiek WF, Pryde EH. Quantitation in the analysis oftransesterified soybean oil by capillary gas chromatography. J Am Oil ChemSoc 1989;63:1370–5.

[21] Lin K, Van Ness HC, Abbott MM. Reaction kinetics, reactor design andthermodynamics. In: Perry RH, Chilton CH, editors. Chemical engineers’handbook. McGraw-Hill; 1973 [Chapter 4].

[22] Sekhar MC, Mamilla VR, Mallikarjuan MV, Reddy KVK. Biodiesel productionfrom neem oil. Int J Eng Stud 2009;1:295–302.

[23] Galadima A, Garba ZN. Catalytic synthesis of ethyl ester from some commonoils. Sci World J 2009;4:1–5.

[24] Eevera T, Rajendran K, Saradha S. Biodiesel production process optimizationand characterization to assess the suitability of the product for variousenvironmental conditions. Renew Energy 2009;34:762–5.

[25] Knudsen JG, Hottel HC, Sarofim AF, Wankart PC, Kneabel KS. Heat and masstransfer. In: Perry RH, Green DW, Maloney JO, editors. Perry’s chemicalengineers’ handbook. NY: McGraw-Hill; 1999 [Section 5].

[26] Priday G, Silverblatt CE, Slottee JS, Smith JC, Todd DB. Liquid–solid operationsand equipment. In: Perry RH, Green DW, Maloney JO, editors. Perry’s chemicalengineers’ handbook. NY: McGraw-Hill Book Company; 1999 [Chapter 18].

[27] Tilton JN. Fluid and particle dynamics. In: Perry RH, Green DW, Maloney JO,editors. Perry’s chemical engineers’ handbook. NY: McGraw-Hill; 1999[Section 6].

[28] Liley PE, Thomson GH, Friend DG, Daubert TE, Buck E. Physical and chemicaldata. In: Perry RH, Green DW, Maloney JO, editors. Perry’s chemical engineers’handbook. NY: McGraw-Hill; 1999 [Section 2].

[29] Adeyemi NA, Mohiuddin A, Jameel T. Waste cooking oil transesterification:influence of impeller type, temperature, speed and bottom clearance on FAMEyield. Afr J Biotechnol 2011;10(44):8914–29.