Effect of process conditions on equilibrium, reaction kinetics and mass transfer for triglyceride transesterification to biodiesel: Experimental and modeling based on fatty acid composition

Fuel Processing Technology 122 (2014) 30–41

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Effect of process conditions on equilibrium, reaction kinetics and mass transfer for triglyceride transesterification to biodiesel: Experimental and modeling based on fatty acid composition B. Likozar ⁎, J. Levec Laboratory of Catalysis and Chemical Reaction Engineering, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia Faculty of Chemistry and Chemical Technology, University Ljubljana, Aškerčeva 5, 1000 Ljubljana, Slovenia

a r t i c l e

i n f o

Article history: Received 25 July 2013 Received in revised form 16 January 2014 Accepted 18 January 2014 Available online 6 February 2014 Keywords: Biodiesel production process optimization/ intensification Reaction mechanism/kinetics Mass transfer/diffusion Renewable energy/fuels

a b s t r a c t Detailed reaction kinetics of oil transesterification were studied based on mechanism and reaction scheme of individual triglyceride, diglyceride, monoglyceride, glycerol and fatty acid methyl ester containing different combinations of gadoleic, linoleic, linolenic, oleic, palmitic and stearic acids determined by high-performance liquid chromatography. Pre-exponential factors and activation energies were correlated with molecular structure in terms of chain lengths and double bonds by response surface models. The activation energies of forward reactions were 47–61 kJ mol−1 with backward ones being 31–49 kJ mol−1, depending on component structure. Mass transfer during initial emulsion phase was acknowledged by determining diffusivities, distribution coefficients, molar volumes, boiling points and viscosities of individual components. Model was validated for a wide range of temperatures, hydrodynamic conditions, dispersed and continuous phase ratios, and methanolysis catalyst concentrations. Rotational speed had the most profound influence on the duration of transport phenomena-limited region spanning the latter to 27 min upon use of 100 rpm. Economics of the process were finally evaluated in terms of alcoholysis cost and price breakdown. Proposed methodology may be usefully applied to transesterification syntheses employing heterogeneous catalysis and enzymes, as well as various renewable resources such as microalgae lipids, waste oils, bioethanol and biobutanol. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Biodiesel, which is composed mainly of fatty acid methyl esters, produced by the transesterification of vegetable oils and animal fats, has become an attractive renewable substitute to the mineral petroleumderived diesel fuel due to its environmental benefits. Mass transfer between two organic phases (methanol and oil) plays a critical role during the transesterification (methanolysis) [1] and in this sense controls the rate at the initial stage [2]. In the studies of the transesterification process rate three regimes are well-recognized, that is an initial mass transfer-controlled regime (slow), followed by a chemically-controlled regime (fast), and a final regime, close to equilibrium (slow) [3]. Therefore, methanol is not effectively used for the reactions due to the interfacial mass transfer resistance [4]. For example, in the transesterification, performed by Sengo et al. [5] in a 30 L reactor under previously optimized conditions, a yield of only 88% fatty acid methyl esters was obtained after 90 min of reaction time, due to the mass transfer limitations. Tsuji et al. [6] noted that a homogeneous

⁎ Corresponding author at: Laboratory of Catalysis and Chemical Reaction Engineering, National Institute of Chemistry, Hajdrihova 19, 1000 Ljubljana, Slovenia. Tel.: +386 1 4760283; fax: +386 1 4760300. E-mail address: [email protected] (B. Likozar). 0378-3820/$ – see front matter © 2014 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.fuproc.2014.01.017

single phase was formed at the 3.9:1 molar ration of methanol to oil (triglyceride) and that the mass transfer resistance between the methanol and oil phases disappeared. Nonetheless, this is seldom reported by other researchers and is rather specific for the utilized reactor system, e.g. the resistance would probably not disappear in a continuous reactor. All three regimes should be in principle correlated into a single model, acknowledging mass transfer, kinetics, and equilibrium [7,8]. The influence of mass transfer on the production of biodiesel may be observed through mixing variation, as the use of different mixing methods (magnetic stirrers, ultrasound, dispersers, etc.) results in different conversions after the transesterification of rapeseed oil with methanol in both acidic and basic systems [9,10]. The production of biodiesel from vegetable oils may thus be assisted by ultrasound, which is a useful tool for strengthening the mass transfer of immiscible liquids [11]. Cavitation mainly affects the mass transfer rates and ensures a uniform distribution of the reactants, as one concludes from the fact that a significant effect on both the reaction rate and the equilibrium conversion is only observed in the later stages of the reactions, when heterogeneity sets in [12]. Some bubbles undergo a sudden expansion to an unstable size and collapse violently, generating the energy for chemical and mechanical effects, and may increase the mass transfer rates by disrupting the interfacial boundary layers (known as the liquid jet effect) [13]. Ultrasound in chemical processing enhances both mass transfer and chemical reactions [14], but noticeably increases the cost of the

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produced biodiesel, rendering the use of ultrasound for liquid fuel production questionable. Mechanical mixing is normally applied to increase contact between the reactants, resulting in an increase in the mass transfer rate [15], consequently; mixing is crucial in the biodiesel synthesis reactions in order to provide a fine dispersion of methanol in oil and therefore to favor the mass transfer rate [16]. The results indicate that under the conditions of sufficient mixing, agitation intensity influences only the initial phase of the transesterification, during which the mass transfer conditions dominate the system, but eventually it develops into a kinetics-controlled process in which agitation intensity has a minimal effect on the rate [17]. Analogously, the main goals of the research, related to continuous reactors, are to investigate the effect of the number of static mixers and of the static mixer superficial velocity on the profiles of oil conversion versus time, with particular focus on the detection of possible mass transfer limitations to the transesterification reactions; and to evaluate the specific energy requirement, associated with the static mixer utilization for biodiesel production, both in the laboratory, pilot, and at the industrial scale [18]. A proposed synthesis process mechanism consists of an initial mass transfer-controlled region, followed by a second-order kineticscontrolled region [19]. Another approach is to use iterative mass transfer and reactor design equations to model the biodiesel conversion in a batch reactor [20]. There are two general disadvantages of previous models. The first one is that mass transfer is not accounted for in the process model [2,4,5,13,15,17,19], although it plays an important role in batch reactors, e.g. at low temperatures, and a predominant one in continuous reactors. The second one is that chemical equilibrium and reaction kinetics are not accounted for [16,18] or oversimplified, i.e. the reversible or consecutive reactions are neglected [3,4,13,20], or that kinetic parameters depend on the resource, e.g. oil [2,5,15,17,19]. The present study is an attempt to develop an overall model, based on the fatty acid composition of species, acknowledging fluid mechanics (mixing), transport phenomena (mass transfer), and reaction kinetics (a single set of kinetic parameters) for an appropriate process sensitivity analysis, monitoring, regulation, optimization, or intensification, regardless of process conditions and resource origin, i.e. vegetable, algal or waste oil, and even oil mixtures.

2. Materials and methods 2.1. Materials Commercial refined and edible-grade canola oil (Tovarna olja Gea, Slovenska Bistrica, Slovenia) was used. The acid, saponification and iodine values of the oil were 0.3 wt.%, 177 mg KOH/g, and 116 g I2/100 g, respectively, determined according to the ISO 660:2009, ISO 3657:2008, and ISO 3961:2000 official methods. For the transesterification, a certified methanol of 99.8 wt.% purity was purchased from Sigma-Aldrich (Steinheim, Germany). KOH pellets of 88 wt.% purity were purchased from J.T. Baker (Deventer, Holland). Solvents, specifically, acetonitrile (gradient grade; 99.9 wt.%), methanol (gradient grade; 99.9 wt.%), n-hexane (for highperformance liquid chromatography (HPLC); 99.9 wt.%), and isopropanol (for HPLC; 99.9 wt.%), all of HPLC grade (Chromasolv) and used without purification, were obtained from Sigma-Aldrich (Steinheim, Germany). The HPLC reference standards for fatty acid methyl esters (FAME) containing methyl, ethyl, isopropyl, butyl, and tert-butyl esters of gadoleic (G), linoleic (L), linolenic (Ln), myristic (M), oleic (O), palmitic (P) and stearic (S) acids (different combinations of esters) and corresponding tri- (trilinolein, trilinolenin, triolein, tripalmitin, and tristearin), di- (1,2dilinolein, 1,3-dilinolein, 1,2-dilinolenin, 1,3-dilinolenin, 1,2-diolein, 1,3diolein, 1,2-dipalmitin, 1,3-dipalmitin, 1,2-distearin, and 1,3-distearin), and monoglycerides (1-monolinolein, 2-monolinolein, 1-monolinolenin, 2-monolinolenin, 1-monoolein, 2-monoolein, 1-monopalmitin, 2monopalmitin, 1-monostearin, and 2-monostearin) were purchased

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from Sigma-Aldrich (Steinheim, Germany) and Nu-Chek Prep (Elysian, MN, USA). 2.2. Batch reactor The reactions were carried out in a 0.6 L glass reactor equipped with the Rushton turbine (a six flat-blade disk turbine) (Fig. SD.1 and Table SD.1, Supplementary data). The impeller diameter and blade width were 25 and 6 mm, respectively. The impeller was centrally placed at 50 mm from the bottom. The reactor was equipped with glassy double jacket filled with silicone oil circulating from a thermostat bath by means of a pump. The reactor was filled with 272 mL of emulsion (the emulsion height was 75 mm). 2.3. Process conditions The 3:1, 4:1, 5:1, 6:1, 7:1, and 8:1 molar ratios of methanol to canola oil were used in different experiments. KOH (0.2, 0.4, 0.6, 0.8, 1.0, and 1.2 g per 100 g of oil) was dissolved into methanol before use (Table SD.2, Supplementary data). The experiments were carried out at 30, 40, 50, 60 or 70 °C, and atmospheric pressure. The impeller speeds of 100, 200, 300, 400, 500, and 600 rpm were applied to produce the dispersions of methanol into the oil of different uniformities. 2.4. Process procedure The transesterification reactions were performed with canola oil and methanol in the proportions of 1:3, 1:4, 1:5, 1:6, 1:7, and 1:8 (mol/mol) using KOH for approximately 25–75 min (depending on process conditions) to obtain a mixture of methyl esters, glycerol, diglycerides, monoglycerides, and unreacted oil and methanol at the temperatures of 30, 40, 50, 60, and 70 °C. The reactor was initially charged with 187–222 g (depending on process conditions) of oil, placed in the reactor and heated to the desired temperature, which was then maintained at a constant value. Methanol (24–54 g; depending on process conditions) with dissolved potassium hydroxide (0.5–2.8 g; depending on process conditions), which was heated separately, was added to the reactor. The mechanical stirrer was turned on during oil heating and as soon as methanol was added to oil, the reactions were timed. For studying the equilibrium, kinetics, and mass transfer, the samples (2 mL) were removed from the reaction mixture during the progress of the reactions, immediately quenched by adding an aqueous hydrochloric acid solution (1.0:1.7 (w/w); 0.02 mL) and vigorously shaken (manually for 1 min). The heating of mixture is presented in Fig. SD.2 (Supplementary data). 2.5. Analytical methods 2.5.1. Determination of concentration of reactants, intermediates and products The samples, removed from reaction mixtures, formed two layers, which were blended by shaking, and a part of the samples was withdrawn and dissolved in isopropanol/n-hexane (5:8 (v/v)) in an appropriate ratio, always obtaining the sample-to-solvent ratio of 1:30 (w/w). This procedure was used in accordance with the rule that the sample must be diluted in the solvent used for elution. The resulting mixture was used to prepare the samples for the tests that is, for HPLC analysis. The composition of the samples of the reaction mixture was determined by HPLC, as described elsewhere [21], using the optimal method, obtained by statistical analysis, setting the parameters each time according to the ones, which were calculated by the full factorial design method [21]. The analyses were conducted with a Agilent (Hewlett Packard) (Santa Clara, CA, USA) 1100 Series HPLC equipped with two G1312A solvent delivery units for binary gradient elution, a model G1315A UV–Vis detector, an automatic G1313A sample injector, a model G1316A column oven for precision temperature control above ambient temperatures, a model SCL-10AVP system controller, and ChemStation for LC 3D

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software. The temperature of the thermostatically controlled compartment of the column was set at 30 °C and the wavelength of the detector at 210 nm without exceeding 220 nm. A Phenomenex (Torrance, CA, USA) Synergi™ 4μ Hydro-RP 80 Å analytical column, with an internal diameter of 4.6 mm, a length of 25 cm, and a particle size of 4 μm was used for the analyses. Chromatograms are presented in Fig. SD.3 (Supplementary data). 2.5.2. Determination of dispersed phase drop size The technique used for drop size measurement was digital image acquisition (Nikon D3100, Tokyo, Japan) and the procedure, image processing and analysis (ImageJ, Bethesda, MA, USA). 25 to 50 drops were digitally measured in photographs with the progress of the methanolysis reactions for each operational condition. The Sauter mean diameter of drops, d32, and the specific surface area, a, were calculated analogously to our other study [22]. 3. Theory The schematic representation of biodiesel production process is shown in Fig. 1. In the beginning and in the end two phases separate upon the absence of mixing, which is methanol and oil phase (beginning) and biodiesel and glycerol phase (end), respectively. During the process, reaction mixture passes through mass transfer-determining

region (emulsion of methanol in oil) to reaction kinetics-determining region (pseudo-homogeneous regime). In the first region, the reactions, represented by the kinetic scheme (Eq. (1); TG, DG, MG, G, M, ME, and OH− are tri-, di- and monoglyceride, glycerol, methanol, methyl ester, and hydroxide ion (catalyst), respectively, while k1–k6 are reaction rate constants), occur only in the methanol phase (m) (where the catalyst is present), while reactants, intermediates, and products diffuse from and to the oil phase (o). The reactions are reversible, consecutive, and parallel. k1

TG þ M ⇌ DG þ ME k2 k3

DG þ M ⇌ MG þ ME k4 k5

ð1Þ

MG þ M ⇌ G þ ME k6

The differential mass balances for the methanol (m) and oil (o) phases for TG, DG, MG, G, M, and ME (OH− is the catalyst) can thus be written as follows, where cx,y, cx,y,i and c⁎x,y denote the bulk, interface and equilibrium concentration of component x in phase y (mol m−3), Kc,x,y the overall mass transfer coefficient of component x, defined for phase y (m s−1), kc,x,y the mass transfer coefficient of component x in phase y (m s−1), Dx,methanol/oil the distribution coefficient of component

Fig. 1. Schematic representation of biodiesel production process with photographs of reaction solutions during batch experiments using homogeneous alkali catalyst and oil/methanol at 50 °C.

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x between methanol and oil phase (/), jm,x the molar flux of component x (mol s−1 m−2), a the specific surface area (m−1), and t time (s). The component differential mass balances are presented by Eqs. (2)–(13).

Table 1 Distribution coefficients of components between methanol and oil (canola oil, represented as OOL) phases (log(Dx,m/o)) at different temperatures. Component


 dcTG;m  ¼ K c;TG;m a cTG;m −cTG;m −k1 cOH− ;m cTG;m cM;m dt þ k2 cOH− ;m cDG;m cME;m

ð2Þ


 dcDG;m  ¼ K c;DG;m a cDG;m −cDG;m dt þ k1 cOH− ;m cTG;m cM;m −k2 cOH− ;m cDG;m cME;m −k3 cOH− ;m cDG;m cM;m þ k4 cOH− ;m cMG;m cME;m ð3Þ
 dcMG;m  ð4Þ ¼ K c;MG;m a cMG;m −cMG;m dt þk3 cOH− ;m cDG;m cM;m −k4 cOH− ;m cMG;m cME;m −k5 cOH− ;m cMG;m cM;m þk6 cOH− ;m cG;m cME;m


 dcG;m  ¼ ∓K c;G;m a cG;m −cG;m dt þ k5 cOH− ;m cMG;m cM;m −k6 cOH− ;m cG;m cME;m

ð5Þ


 dcM;m  ¼ ∓K c;M;m a cM;m −cM;m −k1 cOH− ;m cTG;m cM;m dt þ k2 cOH− ;m cDG;m cME;m −k3 cOH− ;m cDG;m cM;m þ k4 cOH− ;m cMG;m cME;m −k5 cOH− ;m cMG;m cM;m þ k6 cOH− ;m cG;m cME;m

ð6Þ


 dcME;m  ¼ ∓K c;M;m a cME;m −cME;m dt þ k1 cOH− ;m cTG;m cM;m −k2 cOH− ;m cDG;m cME;m þ k3 cOH− ;m cDG;m cM;m −k4 cOH− ;m cMG;m cME;m þ k5 cOH− ;m cMG;m cM;m −k6 cOH− ;m cG;m cME;m

ð7Þ


 dcTG;o  ¼ ∓K c;TG;o a cTG;o −cTG;o dt

ð8Þ


 dcDG;o  ¼ ∓K c;DG;o a cDG;o −cDG;o dt

ð9Þ


 dcMG;o  ¼ ∓K c;MG;o a cMG;o −cMG;o dt

ð10Þ


 dcG;o  ¼ K c;G;o a cG;o −cG;o dt

ð11Þ


 dcM;o  ¼ K c;M;o a cM;o −cM;o dt

ð12Þ


 dcME;o  ¼ K c;ME;o a cME;o −cME;o dt

ð13Þ

The differential mass balances of components simplify upon the transition to pseudo-homogeneous regime (Eqs. (SD.1–6), Supplementary data) (exclusion of mass transfer resistance terms), where cx denotes the bulk concentration of component x. 4. Results and discussion 4.1. Developing and proofing mass transfer mechanism The overall mass transfer coefficient of component x depends on the mass transfer coefficients of this component in oil and methanol phases and its distribution coefficient between these phases. Since the latter spans from 10−3.59 (SSS) to 101.87 (glycerol) (Table 1), the mass transfer

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Temperature (°C)

OOO OOL OOLn OOP OOG OLL OLLn OLP OLS OLnLn LLL LLLn LLP LLS LLnLn LnLnLn PPP SSS M (methanol) G (glycerol) OO OL OLn OP OG OS LL LLn LP LS LnLn PP SS O L Ln P G S MO ML MLn MP MG MS

30

40

50

60

70

−1.43 −1.27 −1.06 −1.64 −1.52 −1.05 −0.79 −1.32 −1.41 −0.48 −0.78 −0.47 −1.16 −1.25 −0.11 0.29 −2.38 −2.96 1.38 1.87 −0.87 −0.77 −0.62 −0.91 −1.01 −1.12 −0.61 −0.41 −0.72 −0.86 −0.16 −1.10 −1.53 0.33 0.38 0.49 0.44 0.16 0.22 −0.55 −0.45 −0.34 −0.52 −0.76 −0.72

−1.45 −1.11 −0.70 −1.83 −1.51 −0.68 −0.19 −1.38 −1.44 0.17 −0.18 0.18 −1.04 −1.10 0.37 0.62 −2.68 −3.20 1.41 1.77 −0.65 −0.43 −0.24 −0.81 −0.75 −1.00 −0.23 −0.11 −0.53 −0.65 0.0541 −1.07 −1.47 0.46 0.48 0.56 0.57 0.32 0.37 −0.67 −0.54 −0.41 −0.62 −0.89 −0.84

−1.45 −0.95 −0.33 −1.96 −1.48 −0.32 0.20 −1.41 −1.45 0.32 0.21 0.33 −0.92 −0.95 0.51 0.74 −2.88 −3.32 1.43 1.71 −0.41 −0.22 −0.16 −0.70 −0.48 −0.87 −0.15 −0.0398 −0.34 −0.42 0.12 −1.04 −1.40 0.47 0.49 0.57 0.56 0.34 0.38 −0.75 −0.61 −0.46 −0.68 −0.98 −0.92

−1.45 −0.80 0.0150 −2.06 −1.46 0.0322 0.36 −1.44 −1.46 0.46 0.37 0.47 −0.81 −0.81 0.63 0.85 −3.01 −3.47 1.44 1.65 −0.17 −0.14 −0.0897 −0.60 −0.21 −0.74 −0.0786 0.0262 −0.14 −0.19 0.18 −1.01 −1.33 0.47 0.50 0.57 0.56 0.35 0.39 −0.80 −0.65 −0.49 −0.72 −1.03 −0.96

−1.44 −0.67 0.34 −2.14 −1.49 0.36 0.52 −1.46 −1.46 0.59 0.52 0.60 −0.72 −0.70 0.74 0.94 −3.09 −3.59 1.44 1.59 −0.0441 −0.0591 −0.0219 −0.49 −0.0865 −0.62 −0.0106 0.0854 0.0272 −0.020 0.23 −0.97 −1.27 0.47 0.51 0.58 0.56 0.37 0.40 −0.82 −0.68 −0.51 −0.74 −1.05 −0.98

resistance in neither the oil nor methanol phase may be neglected, which is almost always the case, and has to be described using Eqs. (15) and (16) [23,24]. Distribution coefficients generally increased with the number of fatty acids, bonded to glycerol; nonetheless, methyl esters had lower values as compared to monoglycerides due to a more hydrophilic nature, resulting from two free hydroxyl groups (e.g. OOO b OO b MO b O). With increasing temperature, methanol solubility is favored for all species, except for methyl esters and a few triglyceride components (with bonded P and S).
−1 K c;x;m ¼ 1=kc;x;m þ Dx;m=o =kc;x;o

kc;x;m ¼

∞ −d32 6 X 1 −4π2 n2 DC e t ln exp 2 2 6t π n¼1 n d32 2 −0:43

kc;x;o ¼ 0:725Re

−0:58

Sc

V t ð1−ϕm Þ

ð14Þ !! ð15Þ ð16Þ

The diffusivities for the concentrated mixtures of x in y (DCxy, Eq. (17)) were calculated from the ones relating to the dilute mixtures (DC0xy, Eq. (18)) according to Siddiqi and Lucas [25]. Vm,x and Vm,y and

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Table 2 Effect of mixture temperature, rotational speed, phase fraction and catalyst content on initial mass transfer resistance characteristics of predominant triglyceride component (OLL) at 50 °C, 400 rpm, 1:6 (mol/mol) (oil to methanol) and 0.8 wt.% catalyst (per canola oil weight) unless specified otherwise. Measurement condition

kc,OLL,m (10−5 m s−1)

kc,OLL,o (10−5 m s−1)

Kc,OLL,m (10−5 m s−1)

d32 (mm)

a (mm−1)

30 °C 40 °C 50 °C 60 °C 70 °C 100 rpm 200 rpm 300 rpm 400 rpm 500 rpm 600 rpm 1:3 (mol/mol) 1:4 (mol/mol) 1:5 (mol/mol) 1:6 (mol/mol) 1:7 (mol/mol) 1:8 (mol/mol) 0.2 wt.% 0.4 wt.% 0.6 wt.% 0.8 wt.% 1.0 wt.% 1.2 wt.%

5.598 3.139 3.216 3.251 3.082 3.986 4.398 3.209 3.216 3.243 3.194 3.263 3.189 3.648 3.216 3.357 4.695 3.640 3.336 3.374 3.216 3.340 3.278

0.115 0.353 0.328 0.315 0.421 0.039 0.074 0.239 0.328 0.408 0.538 0.344 0.367 0.230 0.328 0.268 0.514 0.223 0.284 0.273 0.328 0.283 0.303

0.230 0.597 0.565 0.548 0.684 0.079 0.150 0.432 0.565 0.675 0.831 0.589 0.618 0.424 0.565 0.481 0.875 0.413 0.503 0.488 0.565 0.502 0.530

2.350 2.309 1.781 1.687 0.505 1.964 1.903 1.876 1.781 0.857 0.705 1.082 1.484 1.721 1.781 1.984 3.885 1.089 1.450 1.520 1.781 1.677 1.530

0.519 0.534 0.699 0.745 2.512 0.633 0.654 0.663 0.699 1.452 1.765 0.641 0.600 0.624 0.699 0.707 0.399 1.142 0.858 0.819 0.699 0.742 0.813

Vb,x and Vb,y represent the molar volume at a specific temperature and the boiling point for components x and y, respectively, which were calculated alongside with component viscosities, μy and μo [26–28].
 0 0 DC xy ¼ cx;y V m;x DC yx þ cy;y V m;y DC xy βx

0

DC xy ¼

9:89  10−8 V b;y 0:265 T V b;x 0:45 μ y 0:907

ð17Þ

ð18Þ

L represents turbine diameter, while T, ϕm, Vt, Re, Sc, and βx stand for temperature, the volume fraction of methanol phase, the terminal velocity of methanol drops, the Reynolds and Schmidt numbers for drops, and activity coefficient correction factor (approximated by unity for a constant activity coefficient), respectively. Effective diffusion coefficient within methanol drops (DCe, Eq. (15)) was calculated from DCxm, corrected for the interface adsorption of hydroxyl ions. Initial individual and overall mass transfer coefficients are for the most abundant oil component, OLL, in addition to the Sauter mean diameter and specific surface area of the drops at different process conditions, presented in Table 2. The mass transfer effect during initial emulsion phase may clearly be seen in Figs. 2 and 3 and corresponds to all components. As methanol drops decrease and eventually dissolve through emulsification, reaction kinetics becomes the determining step, which was observed, but not described in several studies (e.g. by Noureddini and Zhu [15]). In Fig. 4, rotational speed is shown to exhibit

Fig. 2. Mass transfer/kinetics/equilibrium modeling curves and experimental points for composition of reaction mixture during transesterification of canola oil at 50 °C, 1:6 (mol/mol) (oil to methanol), 0.8 wt.% catalyst per oil weight and 400 rpm. Different overall and individual predominant components ((a) and (b)) and triglycerides ((c) and (d)).

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Fig. 3. Mass transfer/kinetics/equilibrium modeling curves and experimental points for composition of reaction mixture during transesterification of canola oil at 50 °C, 1:6 (mol/mol) (oil to methanol), 0.8 wt.% catalyst per oil weight and 400 rpm. Diglycerides (a) and monoglycerides and methyl esters (b).

the greatest impact on the initial phase, higher speeds granting an increased interfacial area and consequent mass transfer fluxes and conversion rates. Several mass transfer characteristics are presented in Supplementary data, that is Vm,x, Vm,y, Vb,x, Vb,y, μy and μo are presented in Fig. SD.4, the Reynolds and Schmidt numbers for drops were defined through Eqs. (SD.9) and (SD.12), while the effective diffusion coefficient within methanol drops (DCe, Eq. (15)) was calculated from DCxm, corrected for the interface adsorption of hydroxyl ions (Eqs. (SD.7–SD.11)). If Fig. SD.5 presents analogous results as Fig. 4 for triglyceride conversion, Fig. SD.6 also sheds insights into early stages of the process, temperature having the greatest effect on TG and ME conversion, not only due to increased reaction rates, since concentrations are low, but also due to greater diffusivities and distribution coefficients.

4.2. Finding reaction rate constants, activation energies and pre-exponential factors The activation energies and pre-exponential factors of the three reversible transesterification reactions (Eq. (1)) were determined by nonlinear regression (Levenberg–Marquardt algorithm, 10− 5 tolerance). The concentrations, predicted by the model, embodied in Eqs. (2)–(18) for the initial emulsion and without mass transfer terms for the pseudo-homogeneous regime (Fig. 1) (solved by the Runge– Kutta method with a time step of 0.05 min) were fitted simultaneously to the measured values of different TG, DG, MG and ME of variable fatty

35

acid composition, determined by HPLC. This was performed simultaneously for all mixture temperatures (30–70 °C), rotational speeds (100–600 rpm), phase fractions (1:3–1:8 (mol/mol) oil to methanol) and catalyst concentrations (0.2–1.2 wt.% (per oil weight)). A genetic algorithm was utilized to determine the globally optimal parameter values, considering firstly the three reversible transesterification reactions in series equivalently due to the same type of reaction and regressing only the two ratios, A1/A2 and Ea1/Ea2. Secondly, 1000 regressed sets exhibiting the lowest residual were subjected to further simultaneous regression of A1, A2, Ea1 and Ea2 and then the latter 100 regressed sets with the lowest residual to the simultaneous regression of A1–A6 and Ea1–Ea6. Finally, the 10 regressed sets exhibiting the lowest residual were subjected to the regression of the parameters for all components with different fatty acid composition. All pre-exponential factors and activation energies in Tables 3 and 4 were determined within the approximation error of 10%, while most of the studies do not present the approximation errors of kinetic parameters [2,7,8,15,17,19]. The activation energies of forward transesterification reactions are relatively similar regardless of transesterification step that is for TG, DG and MG transesterification, which may not be claimed for the pre-exponential factors, which clearly increase through the decrease of the steric hindrance in DG and later MG, as compared to TG, even for as much as two orders of magnitude. The latter is in accordance with the collision theory, as the ester group in TG is less susceptible for the attack of the methoxide ion due to the long chains of bonded fatty acids, which is reflected through the steric factor determining the value of preexponential factor, while the activation energy is less affected, because of the same reaction mechanism and rate-determining steps. Analogous findings may be observed for the backward reactions, nonetheless, electronic effects seem to predominantly affect the pre-exponential factors with the decrease of steric hindrance, considering backward reactions of DG, MG and G. For all three reversible transesterification reactions in series, the forward reaction pre-exponential factors by far surpass their backward counterparts, methoxide ion possessing a relative good mobility and accessibility of the reactive sites in reactions with TG, DG and MG in comparison to the backward reactions of two long-chained reactants, specifically, ME reactions with DG, MG or G. Since most of the studies are relatively system-specific (transesterifications of oils varying in fatty acid composition at different process conditions), the paralleling of the kinetic parameters is rather difficult as well with some additional complications arising due to the unorthodox coupling of mass transfer and reaction kinetics, e.g. the activation energies of transesterification being dependent on Reynolds number [15] or the reaction rate constants of transesterification varying with the rotational speed of impeller and the molar ratio of reactants [17]. Omitting the mass transfer in the process model and not accounting for the distribution of bonded fatty acids thus result in a wide range of reported activation energies for the same type of reactions. Therefore, Ea values were 31– 105 kJ mol −1 (Ea1), 31–242 kJ mol −1 (Ea2), 41–93 kJ mol −1 (Ea3), 41– 87 kJ mol −1 (Ea4), 6–74 kJ mol −1 (Ea5), and 21–64 kJ mol −1 (Ea6) [2,7,15,17,19]. The determined pre-exponential factors and activation energies were consequently related to the molecular structure through the number of carbons and double bonds using response surface models. The agreement, upon neglecting the concomitant influence of chain lengths and their rigidity due to double bonds, is worsened. Moreover, the electronic effects may not be considered minute in comparison to the steric hindrance, as the impact of the number of carbons and double bonds varies with the type of the reversible transesterification reaction in series. These correlations employing the constant, linear and mixed terms are presented in Figs. SD.6 and SD.7 and only constant and linear terms in Fig. SD.8. Supplementary data also lists additional equations, which complement the model, embodied in Eqs. (2)–(18) and (SD.7– 12) for the initial emulsion and Eqs. (SD.1–6) for the pseudohomogeneous regime.

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Fig. 4. Effect of mixing intensity (a), molar ratio (b), catalyst concentration (c), reaction temperature (d) and reaction time on dependence of overall conversion to methyl esters (FAME) for base-catalyzed oil transesterification reactions at 50 °C, 400 rpm, 1:6 (mol/mol) (oil to methanol) and 0.8 wt.% catalyst per oil weight unless specified otherwise.

4.3. Modeling concentrations and conversions during the course of reactions The determined equilibrium, kinetics and diffusion parameters (Tables 1, 3 and 4, and Fig. SD.4) were consequently utilized to predict the concentrations and conversions of all components (TG, DG, MG and ME) differing in bonded fatty acid composition (O, L, Ln, P, G and S), the depletion and evolution of reactants, intermediates and products being presented in Figs. 2–4, SD.5 and SD.6 and Table 5. Fig. 2a and b presents the variation of the overall components with time, which is rather similar to the dependencies, available in the existing literature [2,7,15,17,19] with the exception of the initial mass transfer-determining region. Additionally, the variation is presented for the most abundant species in the examined canola oil, accounting for the presence of diglycerides in the initial oil resource (induction phase plateau prior to DG maximum). What is more, Fig. 2c and d reveals that specific TG reactions are responsible for the slow consumption of the overall TG components, which may be seen through a minute decrease in OOP species in comparison to the others, e.g. OLL, and is reflected in a comparatively high activation energy of its forward reaction (Ea1) and low counterpart pertinent to the backward reaction (Ea2) in Table 4. The latter and analogous limiting components are to be avoided in oil resources (when this is possible, for example in algae) to shift the chemical equilibrium towards ME and to comply to biodiesel purity standards in terms of TG, DG and MG with less required downstream purification. The overall diglyceride concentration ordinarily exhibits a maximum, as DG components are intermediates during the transesterification [2,7,15,17,19], but Fig. 3a reveals that this is not necessarily the case, since the concentration of OO, which is relatively high in the initial oil resource, steadily decreases over the course of reactions.

Analogous findings may be observed for OP, nonetheless, the latter is related to rather slow consumption of OOP seen in Fig. 2c, as the conversion of OOP to OP represents the rate-determining step. Fig. 4 presents the overall conversion of ME and TG at different process conditions, as predicted by the model. TG exhibits an initial conversion higher than zero due to the presence of DG in the initial oil resource. More turbulent hydrodynamic conditions decrease the mass transfer-determining region with the consequent achievement of the same equilibrium conversion at shorter process times. Methanol phase fraction, catalyst content and temperature, nevertheless, noticeably affect both the reaction kinetics and the final equilibrium conversion. The initial region is the least influenced by the methanol phase fraction, as the limiting factor seems to be the mass transfer coefficient and not the interfacial area between both phases in the emulsion.

4.4. Effect of temperature on biodiesel production process The effect of the temperature on the reaction rate and chemical equilibrium of transesterification is predominant as may be seen in Figs. 4, SD.5 (Supplementary data) and Table 5 and may only be paralleled by methanol phase fraction. A higher temperature intensifies mass transfer through larger overall mass transfer coefficients and reaction kinetics via larger reaction rate constants. Despite the lower activation energies of backward reactions in Table 4, which would favor higher temperatures, the rate constants of forward reactions dominate over the backward ones in the pertinent range of process temperatures due to the values of pre-exponential factors (Table 3). Noureddini and Zhu [15], Vicente et al. [2,19] and Bambase et al. [17] came to similar conclusion, yet only regarding overall methanolysis kinetics and equilibrium.

B. Likozar, J. Levec / Fuel Processing Technology 122 (2014) 30–41 Table 3 Pre-exponential factors of reaction rate constants for catalyzed transesterification reactions of TG, DG and MG, regressed for different temperatures, mixing intensities, phase fractions and catalyst contents. Pre-exponential factor A1 (107 m6 kmol−2 min−1) OOO → OO OOL → OL OOL → OO OOLn → OLn OOLn → OO OOP → OP OOP → OO OOG → OG OOG → OO OLL → LL OLL → OL OLLn → LLn OLLn → OLn OLLn → OL OLP → LP OLP → OP OLP → OL OLS → LS OLS → OS OLS → OL OLnLn → LnLn OLnLn → OLn LLL → LL LLLn → LLn LLLn → LL LLP → LP LLP → LL LLS → LS LLS → LL LLnLn → LnLn LLnLn → LLn LnLnLn → LnLn PPP → PP SSS → SS

5.7 ± 0.5 6.0 ± 0.5 6.9 ± 0.3 7.2 ± 0.4 7.1 ± 0.2 5.2 ± 0.3 4.45 ± 0.07 7.7 ± 0.3 4.93 ± 0.01 6.90 ± 0.02 7.2 ± 0.3 7.0 ± 0.2 7.5 ± 0.3 6.8 ± 0.4 4.7 ± 0.1 4.1 ± 0.4 4.08 ± 0.08 6.6 ± 0.4 6.18 ± 0.08 5.9 ± 0.3 7.9 ± 0.4 8.0 ± 0.5 7.9 ± 0.7 7.1 ± 0.5 8.0 ± 0.4 4.0 ± 0.2 3.55 ± 0.08 6.5 ± 0.1 6.9 ± 0.4 7.4 ± 0.5 7.8 ± 0.1 7.9 ± 0.3 5.82 ± 0.07 5.28 ± 0.04

A2 (106 m6 kmol−2 min−1) OO → OOO OL → OOL OO → OOL OLn → OOLn OO → OOLn OP → OOP OO → OOP OG → OOG OO → OOG LL → OLL OL → OLL LLn → OLLn OLn → OLLn OL → OLLn LP → OLP OP → OLP OL → OLP LS → OLS OS → OLS OL → OLS LnLn → OLnLn OLn → OLnLn LL → LLL LLn → LLLn LL → LLLn LP → LLP LL → LLP LS → LLS LL → LLS LnLn → LLnLn LLn → LLnLn LnLn → LnLnLn PP → PPP SS → SSS

4.2 ± 0.2 3.75 ± 0.01 4.54 ± 0.01 3.4 ± 0.3 4.5 ± 0.2 5.0 ± 0.3 2.3 ± 0.1 4.6 ± 0.4 2.51 ± 0.01 3.13 ± 0.01 4.4 ± 0.5 2.4 ± 0.1 3.25 ± 0.05 4.0 ± 0.1 3.6 ± 0.1 4.2 ± 0.3 1.06 ± 0.06 4.2 ± 0.2 5.6 ± 0.5 3.4 ± 0.1 1.96 ± 0.07 3.7 ± 0.2 3.6 ± 0.3 2.9 ± 0.2 3.40 ± 0.08 3.3 ± 0.2 0.07 ± 0.02 4.62 ± 0.08 2.87 ± 0.08 1.99 ± 0.07 2.7 ± 0.2 2.17 ± 0.07 5.36 ± 0.07 5.6 ± 0.2 (continued on next page)

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Table 3 (continued) Pre-exponential factor A3 (108 m6 kmol−2 min−1) OO → O OL → L OL → O OLn → Ln OLn → O OP → P OP → O OG → G OG → O OS → S OS → O LL → L LLn → Ln LLn → L LP → P LP → L LS → S LS → L LnLn → Ln PP → P SS → S

4.92 ± 0.01 3.56 ± 0.05 5.6 ± 0.2 2.2 ± 0.2 6.5 ± 0.6 5.80 ± 0.04 2.24 ± 0.01 5.1 ± 0.3 0.42 ± 0.01 6.0 ± 0.2 4.51 ± 0.05 4.3 ± 0.2 2.6 ± 0.2 4.8 ± 0.3 5.9 ± 0.3 0.83 ± 0.01 6.4 ± 0.3 3.5 ± 0.4 2.9 ± 0.4 3.34 ± 0.01 6.0 ± 0.2

A4 (105 m6 kmol−2 min−1) O → OO L → OL O → OL Ln → OLn O → OLn P → OP O → OP G → OG O → OG S → OS O → OS L → LL Ln → LLn L → LLn P → LP L → LP S → LS L → LS Ln → LnLn P → PP S → SS

5.4 ± 0.2 4.5 ± 0.2 7.30 ± 0.08 3.8 ± 0.5 8.8 ± 0.4 3.3 ± 0.2 5.84 ± 0.03 7.9 ± 0.4 5.75 ± 0.01 6.2 ± 0.6 3.0 ± 0.1 7.3 ± 0.5 6.35 ± 0.09 9.5 ± 0.7 4.2 ± 0.3 4.28 ± 0.06 7.4 ± 0.3 2.8 ± 0.2 8.2 ± 0.2 6.18 ± 0.04 3.8 ± 0.2

A5 (108 m6 kmol−2 min−1) O → MO L → ML Ln → MLn P → MP G → MG S → MS

7.5 ± 0.7 7.3 ± 0.3 5.7 ± 0.1 0.43 ± 0.01 6.52 ± 0.01 8.8 ± 0.6

A6 (105 m6 kmol−2 min−1) MO → O ML → L MLn → Ln MP → P MG → G MS → S

1.7 ± 0.1 1.37 ± 0.07 0.80 ± 0.03 8.65 ± 0.01 4.61 ± 0.01 1.86 ± 0.08

4.5. Economics of biodiesel production process The economics of the transesterification of triglycerides to biodiesel were evaluated in terms of overall costs (C) being broken down to the cost of heating, mixing, oil, alcohol and catalyst. This was achieved using Eq. (19), in which Cenergy, Coil, Cmethanol and CKOH represent the corresponding costs of 0.08 $/kW h, 1.09 $/kg, 0.48 $/kg and 1.10 $/kg [29–31], woil, wmethanol and wKOH the mass fractions, Cp,oil and Cp,methanol the heat capacities, ΔT the temperature difference between reaction and

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Table 4 Activation energies of reaction rate constants for catalyzed transesterification reactions of TG, DG and MG, regressed for different temperatures, mixing intensities, phase fractions and catalyst contents. Activation energy, (kJ/mol) Ea1 OOO → OO OOL → OL OOL → OO OOLn → OLn OOLn → OO OOP → OP OOP → OO OOG → OG OOG → OO OLL → LL OLL → OL OLLn → LLn OLLn → OLn OLLn → OL OLP → LP OLP → OP OLP → OL OLS → LS OLS → OS OLS → OL OLnLn → LnLn OLnLn → OLn LLL → LL LLLn → LLn LLLn → LL LLP → LP LLP → LL LLS → LS LLS → LL LLnLn → LnLn LLnLn → LLn LnLnLn → LnLn PPP → PP SSS → SS

56.3 ± 0.9 54 ± 2 55.4 ± 0.3 56.1 ± 0.8 56.7 ± 0.6 54 ± 2 61 ± 2 57 ± 2 48.1 ± 0.1 57 ± 2 56.0 ± 0.3 60 ± 5 55.4 ± 0.3 56.4 ± 0.4 47 ± 4 52.0 ± 0.5 55 ± 3 59 ± 3 55.5 ± 0.3 53 ± 2 52 ± 4 55.7 ± 0.3 57 ± 2 57 ± 1 58 ± 2 54 ± 2 58 ± 1 55.8 ± 0.1 58 ± 3 53 ± 3 53 ± 3 55.6 ± 0.4 56.3 ± 0.1 52 ± 3

Ea2 OO → OOO OL → OOL OO → OOL OLn → OOLn OO → OOLn OP → OOP OO → OOP OG → OOG OO → OOG LL → OLL OL → OLL LLn → OLLn OLn → OLLn OL → OLLn LP → OLP OP → OLP OL → OLP LS → OLS OS → OLS OL → OLS LnLn → OLnLn OLn → OLnLn LL → LLL LLn → LLLn LL → LLLn LP → LLP LL → LLP LS → LLS LL → LLS LnLn → LLnLn LLn → LLnLn LnLn → LnLnLn PP → PPP SS → SSS

40.0 ± 0.1 36 ± 4 38 ± 2 40.2 ± 0.1 37 ± 3 40.4 ± 0.7 37 ± 1 40.5 ± 0.2 31.5 ± 0.1 43 ± 3 39.0 ± 0.8 40.4 ± 0.1 38 ± 2 39.7 ± 0.1 39.0 ± 0.1 38.6 ± 0.1 37.2 ± 0.3 40.7 ± 0.9 40.3 ± 0.8 39.8 ± 0.3 38 ± 2 42 ± 2 40.3 ± 0.2 44 ± 4 42 ± 2 37 ± 1 38 ± 2 41 ± 1 38 ± 2 43 ± 2 38 ± 2 39.8 ± 0.4 43.1 ± 0.1 42 ± 3

Table 4 (continued) Activation energy, (kJ/mol) Ea3 OO → O OL → L OL → O OLn → Ln OLn → O OP → P OP → O OG → G OG → O OS → S OS → O LL → L LLn → Ln LLn → L LP → P LP → L LS → S LS → L LnLn → Ln PP → P SS → S

55.8 ± 0.7 58 ± 1 55.4 ± 0.9 61 ± 4 56.4 ± 0.2 53.8 ± 0.3 56.6 ± 0.2 58.5 ± 0.5 49.8 ± 0.0 60 ± 4 54 ± 3 56.2 ± 0.5 57.8 ± 0.8 56.2 ± 0.3 52.9 ± 0.6 56.8 ± 0.1 57 ± 1 55 ± 2 55 ± 2 52.7 ± 0.1 56.2 ± 0.1

Ea4 O → OO L → OL O → OL Ln → OLn O → OLn P → OP O → OP G → OG O → OG S → OS O → OS L → LL Ln → LLn L → LLn P → LP L → LP S → LS L → LS Ln → LnLn P → PP S → SS

38 ± 3 42.7 ± 0.4 40 ± 1 46 ± 1 40.2 ± 0.2 40 ± 1 40 ± 3 35 ± 2 39.0 ± 0.1 42 ± 3 44 ± 3 40 ± 2 49 ± 4 42.1 ± 0.4 42.8 ± 0.3 39 ± 3 41 ± 2 42 ± 2 44.4 ± 0.1 32.4 ± 0.5 38.8 ± 0.5

Ea5 O → MO L → ML Ln → MLn P → MP G → MG S → MS

56.1 ± 0.5 56.4 ± 0.9 55.1 ± 0.5 55.3 ± 0.1 57.0 ± 0.1 55 ± 1

Ea6 MO → O ML → L MLn → Ln MP → P MG → G MS → S

41 ± 2 40 ± 2 40.7 ± 0.8 41.4 ± 0.1 44.8 ± 0.1 46 ± 3

room temperatures, m the weight of a batch, t99% conversion the time to reach 99% of equilibrium TG conversion, and P mixing power, derived from the dependency of power number (Po) on Reynolds number (Re), mixture densities and viscosities [32].
 C ¼ woil C p;oil þ wmethanol C p;methanol ΔTC energy þ ðP=mÞt 99% equilibrium C energy þ woil C oil þ wmethanol C methanol þ wKOH C KOH

ð19Þ

The costs of the transesterification process (excluding preparatory and final purification and recycling separations) are presented in Fig. 5. Oil resource price de facto dictates the costs of biodiesel, the

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39

Table 5 Effect of mixture temperature, rotational speed, phase fraction and catalyst content on equilibrium transesterification of canola oil at 50 °C, 400 rpm, 1:6 (mol/mol) (oil to methanol) and 0.8 wt.% catalyst (per canola oil weight) unless specified otherwise. Measurement condition

TG (wt.%)

DG (wt.%)

MG (wt.%)

ME (wt.%)

TG conversion (%)

ME conversion (%)

pKa

30 °C 40 °C 50 °C 60 °C 70 °C 100 rpm 200 rpm 300 rpm 400 rpm 500 rpm 600 rpm 1:3 (mol/mol) 1:4 (mol/mol) 1:5 (mol/mol) 1:6 (mol/mol) 1:7 (mol/mol) 1:8 (mol/mol) 0.2 wt.% 0.4 wt.% 0.6 wt.% 0.8 wt.% 1.0 wt.% 1.2 wt.%

21.9 12.5 8.1 5.8 4.3 8.1 8.1 8.1 8.1 8.1 8.1 33.2 21.4 13.3 8.1 5.0 3.2 16.8 9.9 8.4 8.1 8.1 8.2

1.6 1.1 0.9 0.7 0.7 0.9 0.9 0.9 0.9 0.9 0.9 2.0 1.6 1.2 0.9 0.6 0.5 1.4 0.9 0.9 0.9 0.9 0.9

3.3 3.6 3.8 4.0 4.2 3.8 3.8 3.8 3.8 3.8 3.8 4.2 4.4 4.2 3.8 3.4 3.0 3.0 3.3 3.6 3.8 4.0 4.2

73.2 82.8 87.3 89.4 90.8 87.3 87.3 87.3 87.3 87.3 87.3 60.6 72.6 81.4 87.3 91.0 93.4 78.8 85.9 87.2 87.3 87.0 86.7

77.9 87.4 91.9 94.1 95.6 91.9 91.9 91.9 91.9 91.9 91.9 66.5 78.3 86.6 91.9 95.0 96.8 83.4 90.2 91.6 91.9 91.8 91.7

73.2 82.9 87.4 89.7 91.5 87.4 87.4 87.4 87.4 87.4 87.4 20.0 25.1 28.0 87.4 34.6 35.5 77.7 85.2 86.9 87.4 87.6 87.7

15.55 15.21 14.89 14.60 14.32 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89 14.89

cost of methanol being approximately one order of magnitude lower, even for large phase fractions (1:8 (mol/mol)). Overall operating costs (including upstream and downstream) represent less than 10% [29] and are even lower for the transesterification process itself. Reaction mixture heating cost surpasses the one pertinent to mixing, but the latter may also be seen to be dependent on other process conditions beside

the rotational speed, as for example larger catalyst content decreases the process time, and thus the required energy input for a given extent of transesterification (99%) is lower. Analogous process economics apply for the case of the reactor in a scaled-up biodiesel plant. Evidently, the only term that would differ in Eq. (19) is the contribution of mixing, which is comparatively the

Fig. 5. Average oil transesterification cost breakdown at 50 °C, 400 rpm, 1:6 (mol/mol) and 0.8 wt.% catalyst (per oil weight) unless specified otherwise.

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lowest, as seen in Fig. 5. On one hand, the mixing power per batch weight (P/m) is ordinarily lower, but correspondingly, process takes longer to reach 99% conversion (t99% conversion), since mass transfer resistance is much greater in industrial scale (lower specific surface area). An additional term in Eq. (19), which has to be taken into account in industrial scale, is energy losses as well as up- and downstream processing, negligible in laboratory scale, but gaining importance with the increase of reactor size; nonetheless, even this contribution is according to current market prices [29–31] dwarfed by the cost of resources (e.g. oil). Additionally, one has to acknowledge are due to lower yields of the main product (biodiesel) due to the presence of unwanted side reactions (e.g. saponification), which are easily quenched in laboratory scale (by using water-free chemicals), nevertheless, are much more difficult to circumvent in realistic scales, water being present in resources themselves, and its removal by heating or drying being completely cost-ineffective. 5. Conclusions Transesterification was studied by inherently relating mass transfer, reaction kinetics and chemical equilibrium in order to describe the transition from biphasic system to the homogeneous one. Both the mass transfer and reaction kinetics were examined at a detailed level of each species composition in terms of gadoleic, linoleic, linolenic, oleic, palmitic and stearic fatty acids. The pre-exponential factors/activation energies of triglyceride, diglyceride and monoglyceride forward reactions were determined at 3–8 × 107 m6 kmol−2 min−1/47–61 kJ mol−1, 1–7 × 108 m6 kmol−2 min−1/50–61 kJ mol−1, and 1–9 × 108 m6 kmol−2 min−1/ 55–57 kJ mol−1, confirming the existence of the same mechanism for all three transesterification steps, but a decrease of the steric hindrance with a lesser number of bonded fatty acids. Analogous findings were obtained for backward reactions. The decrease of rotational speed (from 600 to 100 rpm) resulted in the prolongation of mass transferdetermined region from 1 to 27 min, whereas the variation in the fraction of alcohol exerted almost no impact on its length. Several physicochemical properties were determined for different tri-, di- and monoglycerides, glycerol, and fatty acid methyl esters, which may be used in other applicative fields, for example biodiesel fuel combustion. The proposed methodology may be extended to transesterification processes employing heterogeneous catalysis and immobilized enzymes.

List of symbols (continued) Dx,methanol/oil Ea1 Ea2 Ea3 Ea4 Ea5 Ea6 jm,x k1 k2 k3 k4 k5 k6 Kc,x,y kc,x,y L m P pKa Po Re Sc T ΔT t t99% conversion Vb,x Vb,y Vm,x Vm,y Vt wKOH wmethanol woil α βx μo μy ρm ρo ϕm

Distribution coefficient of component x between methanol and oil phase Activation energy of forward TG reaction Activation energy of backward TG reaction Activation energy of forward DG reaction Activation energy of backward DG reaction Activation energy of forward MG reaction Activation energy of backward MG reaction Molar flux of component x Rate constant of forward TG reaction Rate constant of backward TG reaction Rate constant of forward DG reaction Rate constant of backward DG reaction Rate constant of forward MG reaction Rate constant of backward MG reaction Overall mass transfer coefficient of component x, defined for phase y Mass transfer coefficient of component x in phase y Turbine diameter Batch weight Mixing power Negative logarithm of acid dissociation constant Power number Reynolds number for drops Schmidt number for drops Temperature Temperature difference between reaction and room temperatures Time Time to reach 99% of equilibrium TG conversion Molar volume at boiling point for component x Molar volume at boiling point for component y Molar volume at specific temperature for component x Molar volume at specific temperature for component y Terminal velocity of drops Mass fraction of catalyst Mass fraction of methanol Mass fraction of oil Retardation coefficient of adsorbing components Activity coefficient correction factor for component x Viscosity of oil Viscosity of component y Methanol density Oil density Volume fraction of methanol phase

/ m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 kmol s−1 m−2 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m s −1 m s−1 m kg W / / / / K K s s m3 kmol−1 m3 kmol−1 m3 kmol−1 m3 kmol−1 m s−1 / / / / / Pa s Pa s kg m−3 kg m−3 /

List of symbols

a A1 A2 A3 A4 A5 A6 ac C Cenergy CKOH Cmethanol CNx Coil Cp,methanol Cp,oil cx cx,y cx,y,i c⁎x,y d32 DBx DCe DCxy, DC0xy

Specific surface area of drops Pre-exponential factor of forward TG reaction Pre-exponential factor of backward TG reaction Pre-exponential factor of forward DG reaction Pre-exponential factor of backward DG reaction Pre-exponential factor of forward MG reaction Pre-exponential factor of backward MG reaction Acceleration of drops Overall costs Costs of energy Costs of catalyst Costs of methanol Number of carbons in component x Costs of oil Heat capacity of methanol Heat capacity of oil Bulk concentration of component x Bulk concentration of component x in phase y Interface concentration of component x in phase y Equilibrium concentration of component x in phase y Sauter mean diameter of drops Number of double bonds in component x Effective diffusion coefficient within drops Diffusivities for concentrated mixtures of x in y Diffusivities for diluted mixtures of x in y

m−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m6 kmol−2 s−1 m s−2 $/kg $/kWh $/kg $/kg / $ kg−1 J K−1 J K−1 kmol m−3 kmol m−3 kmol m−3 kmol m−3 m / m2 s−1 m2 s−1 m2 s−1

Acknowledgments The provision of financial support for the conduct of the research and preparation of the article by Slovenian Research Agency (ARRS) (Program P2-0152) is gratefully acknowledged. The authors would also like to thank Ana Butara and Matic Skornšek for providing experimental help during research. Appendix A. Supplementary data Supplementary data to this article can be found online at http:// dx.doi.org/10.1016/j.fuproc.2014.01.017. References [1] Y. Zhang, M. Stanciulescu, M. Ikura, Rapid transesterification of soybean oil with phase transfer catalysts, Applied Catalysis A: General 366 (2009) 176–183. [2] G. Vicente, M. Marchtinez, J. Aracil, Kinetics of Brassica carinata oil methanolysis, Energy and Fuels 20 (2006) 1722–1726. [3] O.S. Stamenković, Z.B. Todorović, M.L. Lazić, V.B. Veljković, D.U. Skala, Kinetics of sunflower oil methanolysis at low temperatures, Bioresource Technology 99 (2008) 1131–1140.

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