Mathematical Modeling and Simulation of Biodiesel Production in a

Subscriber access provided by University of Sussex Library

Biofuels and Biomass

Mathematical modeling and simulation of biodiesel production in a semi-batch bubble reactor Maxwell Silva, Lucas Rafael Pinto Nobre, Luiz Eduardo Pereira Santiago, Marcell Santana Deus, Anderson Alles Jesus, Jackson Araújo Oliveira, and Domingos Fabiano de Santana Souza Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02196 • Publication Date (Web): 16 Aug 2018 Downloaded from http://pubs.acs.org on August 16, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Mathematical modeling and simulation of biodiesel production in a semi-batch bubble reactor Maxwell G. Silvaa,*, Lucas R. P. Nobrea, Luiz E. P. Santiagoa, Marcell S. Deusa, Anderson A. Jesusa, Jackson A. Oliveiraa, Domingos F. S. Souzaa

a

Chemical Engineering Department, Universidade Federal do Rio Grande do Norte, Senador Salgado Filho Avenue, S/N – Lagoa Nova, Natal, 59078-970, Brazil.

*Corresponding author: E-mail: [email protected] , Phone: +55 84 99140-3371.

Abstract A mathematical model of an isothermal semi-batch bubble reactor has been developed to describe the esterification reaction of free fatty acids with superheated alcohol vapor. The proposed model accounts for the effects of mass transfer followed by chemical reaction in the liquid phase. The fluid physical properties are calculated by published correlations and the partition coefficient of alcohol vapor was estimated based on thermodynamic models of vaporliquid equilibria. Experimental data of acid-catalyzed esterification of oleic acid with superheated ethanol vapor at different conditions of temperature and gas superficial velocities was used to estimate the liquid side mass transfer coefficient and kinetic parameters. The results obtained showed that the model satisfactorily fits the experimental data for all operating conditions and was also able to simulate and predict experimental results for intermediate conditions with a coefficient of determination R2 of 0.987. In addition, the estimated values of the mass transfer coefficient agreed with data reported in literature for gas-liquid reactors.

Keywords: biodiesel, esterification, bubble reactor, mathematical model.

1 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 2 of 32

1. Introduction Multiphase reactors are widely used to carry out gas-liquid and gas-liquid-solid reactions at the most varied operating conditions. This type of reactor is often used in chemical, biochemical and petrochemical industry for different kinds of processes like oxidation, chlorination and CO2 removal1-5. More specifically, gas-liquid reactors present low energy consumption, high operating life, simple construction, design and scale-up. The characteristics of gas-liquid contactors are mainly associated with the phase flow regime and reactor geometry. Bubble column reactors are known to provide high residence time to the gas bubbles, which enhances heat and mass transfer rates 6-8. Likewise, bubble reactors present high mass transfer coefficients due to the excellent mixing characteristics provided by agitation

9,10

. Some authors also report that the spherical geometry presents lower pressure

drops compared to conventional axial flow reactors 11,12. A more recent application of bubble reactors is biodiesel production

13,14

. In this

process, the alcohol is fed to the reactor as superheated vapor bubbles and some of it is transferred to the oil phase to react and form biodiesel by transesterification or esterification reaction, where the last is commonly chosen as the main pretreatment step for feedstocks containing high amounts of free fatty acids, which need to be converted to biodiesel before base-catalyzed transesterification takes place to prevent saponification

15,16,17

. Some studies

have shown that biodiesel production is intensified by using gas-liquid reactors

14,18,19

. The

main aspect related to process intensification in gas-liquid reactors is the effect of the vapor bubbles. In this type of system, each bubble in contact with the liquid phase may be considered as an individual micro-scale gas-liquid contactor where reaction takes place. The reduction of the bubble size increases the interfacial area and provides a higher contact area between the phases of the process. Furthermore, gas-liquid reactors may be operated at


Page 3 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

elevated temperatures, which increases reaction rate, reagents solubility and decreases mass transfer resistance 20,21. For the case of acid-catalyzed esterification, some authors reported that high FFA conversions are achieved in relatively short reaction times when gas-liquid reactors are used instead of the classical homogeneous process

10,13,14

. Since esterification is a reversible

reaction that produces biodiesel and water as by-product, bubble reactors operated at temperatures higher than 100°C may be an excellent choice, since at this operating temperature all the water generated during reaction is continuously removed from the products, which reduces the reverse reaction rate (biodiesel hydrolysis) considerably and shifts the reaction equilibrium towards the products resulting in higher biodiesel yields 13,19,22. Furthermore, this reactor configuration presents some advantages compared to conventional reactors from a technical and economic standpoint. Firstly, since the excess alcohol and byproduct water vapor are continuously removed from the reactor, no additional step to separate these components from the products is required and the cost of downstream processing is reduced

23

. Secondly, for high operating temperatures, the process is not affected by the

presence of water, therefore, the exiting stream containing the by-product water and excess alcohol vapor may return to the system without decreasing reactor performance. Stacy et al. 24 reported that FFA conversions higher than 98% were achieved in a bubble column reactor in less than 2h, including experiments performed with ethanol and methanol vapor containing different percentages of water by volume. Chemical reaction and mass transfer play an important role on bubble reactor performance, and then kinetic and hydrodynamic parameters must be considered to fully understand this type of equipment and find the optimal set of conditions for a specified process. Some works have studied the performance of bubble reactors for biodiesel


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 32

production, however, the experimental results are analyzed based on kinetic effects, disregarding the mass transfer effects or by using simple relationships to describe it 25,26. In this context, mathematical models accounting for both chemical reaction and mass transfer are needed to analyze the process. Moreover, this type of model is required for parameter estimation, simulation and optimization studies, which requires a detailed overview of each phenomenon occurring in the system to find the optimum set of conditions. A phenomenological model of a bubble reactor for biodiesel production has been developed. The model describes the effects of mass transfer accompanied by chemical reaction in the liquid phase. The activation energy, frequency factor and liquid side mass transfer coefficient are estimated from experimental data obtained from the esterification reaction of superheated ethanol vapor and oleic acid (C18:1), which is one of the major free fatty acids found in lipid feedstocks, corresponding to approximately 24 and 53% of soybean and canola oil, respectively 27.

2. Materials and methods 2.1 Materials

Oleic acid, anhydrous ethanol (99.5 %) and sulfuric acid were purchased from SigmaAldrich (Brazil) and used without any purification. Sodium hydroxide (98.4%) and phenolphthalein were used for base titration to determine the acid content during reaction.

2.2 Experimental Procedures

A round-bottom flask with diameter of 84 mm was placed in a heating mantle and used as the bubble reactor. For all experiments, 150 g of oleic acid was loaded to the reactor and heated to the reaction temperature, which was controlled by the heating mantle. Liquid ethanol was pumped out of a storage glass and passed through a tubular heater to be vaporized and fed to the reactor as superheated vapor bubbles, whose temperature was regulated by a 4 ACS Paragon Plus Environment

Page 5 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

PID controller attached to the alcohol feed line and set to the reactor temperature to avoid temperature changes in the liquid phase. A catalyst solution of sulfuric acid in ethanol (0.765 mol/L) was used in the experiments. The mass of sulfuric acid used to prepare the catalyst solution was equivalent to 0.1% of the oleic acid mass loaded to the reactor. The experiments were performed at temperatures higher than 100°C and all the water generated during reaction was vaporized and collected at the gas exiting stream along with any unreacted ethanol vapor. Three different temperatures (110, 130 and 150°C) and ethanol molar flow rates (0.023, 0.043 and 0.063 mol/min) were used in the esterification experiments.

2.3 FFA conversion analysis

Liquid samples were collected from the reactor at fixed time intervals (10–20 min) and were analyzed by base titration using a solution of sodium hydroxide (0.5 mol/L) and phenolphthalein to indicate the final point. The amount of unreacted oleic acid for each sample was determined and used to calculate the percent conversion (X) based on its initial molar concentration (3.168 mol/L):  [ B ]l ,0 − [ B ]  X =  × 100%  [ B] l ,0  

(1)

where [B]l,0 is the initial FFA acid molar concentration in the reactor and [B] is the FFA molar concentration at each time interval. 3. Mathematical model 3.1 Absorption followed by chemical reaction

Biodiesel production in a semi-batch bubble reactor consists in the chemical absorption of alcohol from a vapor phase followed by the esterification reaction in the liquid phase: 5 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A( g ) → A(l ) ,

A(l ) + B(l )

Page 6 of 32

(2)

C(l ) + D(l )

In Equation (2), the alcohol (A) present in the gas phase is transferred to the liquid phase to react with the free fatty acid (B) and form fatty acid ester (C) and by-product water (D). Since esterification in gas-liquid reactors is commonly conducted under temperatures higher than 100°C to remove all the water formed during reaction through evaporation, the reverse reaction rate becomes negligible and the rate expression may be described as a second order irreversible reaction:

ra = k1[ A][ B]

(3)

where [A], [B], are the molar concentrations of alcohol and free fatty acid, respectively. k1 is the forward rate constant, whose temperature dependence is described by the Arrhenius equation: k1 = k0 e − E1 / RTR

(4)

where E1 is the activation energy, k0 is the frequency factor, R is the ideal gas constant and TR is the reaction temperature.

3.2 Macroscopic Balances

The general material balance for both gas and liquid phase may be represented by the following expression:

dN i , p

dt

= Fi ,inp − Fi ,out p ± Φ i Vl + ri Vl

(5)

where N is the number of moles, F is the molar flow rate, Φi is the interphase mass transfer rate per unit volume of liquid phase Vl, and the subscripts i and p represent the component and phase, respectively. The rate of change of materials is computed by considering the number of moles entering and leaving each phase through material streams, mass transfer, as well as the


Page 7 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

number of moles generated or consumed by chemical reaction. Fig. 1 shows a hypothetical bubble reactor diagram for application of Equation (5).

Figure 1. Hypothetical semi-batch bubble reactor diagram for biodiesel production by esterification reaction.

Since gas phase dynamics is very fast, it is reasonable to assume that accumulation in the gas phase is negligible. In addition, if no reaction occurs in the gas phase and no water vapor is fed to the reactor, application of the general material balance provides the expressions for calculating the molar flow rates of alcohol and water leaving the reactor:

Faout , g = qg ,0 [ A]g ,0 − Φ aVl

(6)

Fdout , g = Φ dVl

(7)

Where qg,0 is the inlet gas volumetric flow rate, [A]g,0 is the inlet gas phase concentration and the terms Φa and Φd are the volumetric mass transfer rates of alcohol and water, respectively. Free fatty acid and fatty acid ester are considered as nonvolatile components for the temperature range adopted, which means that no accumulation of both components in the gas phase is considered in the model. For the liquid phase, the component accumulation depends on the rate of moles entering and leaving liquid phase, as well as the number of moles being formed or consumed


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 32

by chemical reaction. Application of Equation. (5) provides a set of four ordinary differential equations describing the concentration change of each component in the liquid phase:

Vl

Vl

Vl

Vl

d[ A]l ,bulk

dt d[ B]l ,bulk

dt d[C ]l ,bulk

dt

d [ D]l ,bulk

dt

= Φ aVl − raVl − [ A]l ,bulk = −raVl − [ B]l ,bulk = raVl − [C ]l ,bulk

dVl dt

dVl dt

(8)

(9)

dVl dt

(10)

= raVl − Φ dVl − [ D]l ,bulk

dVl dt

(11)

The liquid volume change in Equations (8)–(11) is obtained by an overall mass balance in the reactor:

ρ

dVl = M a (qg ,0 [ A]g ,0 − Φ aVl ) − M d Φ dVl dt

(12)

where ρ is the liquid phase density, and Ma and Md are the molecular weights of alcohol and water, respectively. Equation (12) is derived by assuming that liquid phase density is constant throughout the process. This assumption is made because liquid phase is mainly composed by unreacted free fatty acid and ester, whose densities are approximately the same. The bubble reactor model is composed by two algebraic equations for the gas phase (6)–(7) and a system of five coupled ordinary differential equations (8)–(12), which require one initial condition for each one of the five dependent variables to be solved uniquely. In the semi-batch operation, the liquid phase is initially composed by the pure Free fatty acid loaded to the reactor. The molar concentrations of alcohol, water and ester at the beginning of reaction are all equal to zero. The initial conditions are represented in Equation (13):


Page 9 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

t = 0,

[ A]l ,bulk = 0

[ B ]l ,bulk = [ B ]l ,0 Vl = Vl ,0

[C ]l ,bulk = 0

[ D ]l ,bulk = 0

(13)

where [B]l,0 and Vl,0 are the molar concentration and volume of free fatty acid at the beginning of reaction, respectively. The gas phase inlet concentration is calculated according to the ideal gas law. 3.3 Volumetric mass transfer rates

The rate of mass transfer of component A is determined by application of the film theory, which postulates the existence of two hypothetical stagnant films (see Fig. 2) responsible for mass transfer resistance 28. The main assumptions of the theory are: i.

Steady state molecular diffusion

ii.

Instantaneous phase equilibrium at the gas-liquid interface

iii.

Stagnant films

Figure 2. Film theory model for steady state mass transfer.

Since gas phase is composed by pure A, resistance to mass transfer in the gas phase is negligible and the total mass transfer resistance of the process is situated in the liquid film. For the film theory, the mass transfer followed by a second order irreversible reaction is described by the following equations: 9 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 32

Da

d 2 [ A] = k1[ A][ B] dz 2

(14)

Db

d 2 [ B] = k1[ A][ B ] dz 2

(15)

where Da and Db are the diffusivities of component A and B, respectively. The two boundary conditions associated with the theory are:

z = 0,

[ A] = [ A]*l

[ B] = [ B]*l

z =δL,

[ A] = [ A]l ,bulk

[ B] = [ B]l ,bulk

(16)

where the first boundary condition in equation (16) describes the phase equilibrium assumption at the gas-liquid interface and the second one states that the concentrations at the end of the liquid film of thickness δL is equal to the liquid bulk concentration. Equations (14) and (15) are coupled nonlinear differential equations and no exact analytical solution is available to express the interfacial flux of component A through the liquid film. However, several approximate analytical solutions have been developed, with emphasis on that of van Krevelen and Hoftijzer

29

who developed an approximate solution for a second order

irreversible reaction based on the film theory. The authors obtained the following expression for the enhancement factor:

Ea =

Ha 2 ( Ei − Ea ) / ( Ei − 1)

tanh

(

Ha 2 ( Ei − Ea ) / ( Ei − 1)

)

(17)

The enhancement factor Ea in Equation (17) depends on the dimensionless Hatta number (Ha) and the instantaneous enhancement factor (Ei). The dimensionless Hatta number represents the ratio of the rate of chemical reaction relative to the physical mass transfer. For a second order irreversible reaction, the Hatta number expression is given by:


Page 11 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Ha =

k1 Da [ B]l ,bulk

(18)

kL

The value of the Hatta number is used for determining whether the reaction occurs entirely in the liquid bulk or in the liquid film 30. For high values of the Hatta number (Ha > 2), the reaction is considered to occur predominantly near the gas-liquid interface (fast reaction regime), while for low values of the Hatta number (Ha < 0.2) the reaction is considered to proceed mainly in the liquid bulk (slow reaction regime)

31

. The asymptotic

instantaneous enhancement factor is calculated by the following expression:

 [ B ]l ,bulk Db   Da  Ei =  1 +   [ A]*l Da   Db  

β

(19)

where [A]l* corresponds to the interface concentration of component A and β is equal to zero for the film theory. The enhancement factor Ea is used to describe the influence of a reaction on the mass transfer rate. The parameter is defined as the ratio of absorption of a gas by a reactive liquid phase (chemical absorption) and the absorption without chemical reaction (physical absorption) with the same driving force

32

. From this definition, the enhancement

factor may be expressed as follows:

Ea =

k L* ([ A]*l − [ A]l ,bulk )

(20)

k L ([ A]*l − [ A]l ,bulk )

where kL and kL* are defined as the physical and chemical absorption coefficients

33

,

respectively. From Equation (20), the volumetric mass transfer rate of component A considering the reaction in the liquid film is calculated by the following expression:


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

 [ A]g ,bulk  Φ a = Ea k L av  − [ A]l ,bulk   ma 

Page 12 of 32

(21)

where av is the average interfacial area of the gas bubbles per unit volume and ma is the partition coefficient of component A, which describes the distribution of a solute between the gas phase and the solvent in the reactor. At low to moderate pressures, ideal behavior of the gas phase may be assumed and the partition coefficient expression is calculated by the vaporliquid equilibrium condition of equal fugacities:

ma =

γ a Pa*

(22)

[ L]RT

where γa is the activity coefficient of the liquid phase, Pa* is the saturation pressure of component A at the reaction temperature and [L] is the total liquid phase concentration. Equation (22) was obtained by considering the interfacial gas concentration equal to the gas bulk concentration. This assumption is made because mass transfer resistance in the gas phase is negligible. One must note that Equation (17) is implicit in Ea and then the enhancement factor must be determined iteratively. 3.4 Evaporation rate of water

The molecules of water generated during the reaction between the dissolved alcohol and FFA are completely immersed in a fluid whose temperature is above 100°C. Therefore, it is reasonable to assume that all molecules of water reach thermal equilibrium with the liquid phase and evaporates instantaneously after being formed in the liquid phase. This assumption simplifies the evaluation of the volumetric mass transfer rate of water, which is now assumed to be equal to its rate of formation by chemical reaction at each time:

Φd = rd

(23)


Page 13 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

3.5 Mass Transfer Coefficient

The mass transfer coefficient is an important hydrodynamic parameter in gas-liquid reactors, being responsible for most of equipment performance

5–7,10

. The mass transfer

coefficient is mainly influenced by the physical properties of the fluids, velocity of the phases and reactor geometry. Dimensionless groups are often used to predict the effects of the mass transfer coefficient in gas-liquid reactors, where most of the correlations found in literature are expressed in terms of the Sherwood (Sh), Reynolds (Re) and Schmidt (Sc) numbers 10,34:

Sh =

ρU g DR  µ  k L DR = f  Re = , Sc =  Da µ ρ Da  

(24)

where µ is the liquid phase dynamic viscosity, Ug is the gas phase superficial velocity in the reactor and DR is the reactor diameter. The mass transfer coefficients are frequently correlated with the dimensionless numbers by the following mathematical relationship 10,34–39: c

b

 ρU g DR   µ   Da  kL = a ⋅        µ   ρ Da   DR 

(25)

where a, b and c are adjustable parameters of Equation (25) associated with the process. Therefore, the liquid side volumetric mass transfer coefficient may be estimated based on Equation (25) using different experimental data sets obtained at different temperatures and gas phase superficial velocities. 3.6 Physical Properties and model parameters

The temperature dependence of oleic acid density and dynamic viscosity are calculated by the correlations reported by Noureddini et al. 40 and Pratas et al. 41, respectively. The diffusion coefficients of the components are estimated by the equation proposed by Wilke and Chang

42

. The vapor pressure of ethanol is calculated by the Antoine’s equation


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 14 of 32

43

with coefficients calculated from data reported by Ambrose et al. Wiebe

and Kretschmer and

44

. The average interfacial area of the bubbles was estimated by the correlation

proposed by Akita and Yoshida 37, whose equations are displayed in Table 1.

Table 1. Hydrodynamic parameters used in the model (Akita & Yoshida37) Parameter

Equation

average interfacial area

av = 6ε g / d vs

volume-surface mean

 g D 2ρ  d vs = 26 DR  c R   σ 

bubble diameter

−0.5

 ρ 2 g c DR 3    2  µ  1/8

−0.12

 Ug     gD   c R 1/12

εg  g c DR 2 ρ   ρ 2 g c DR 3  = 0.20     2 (1 − ε g ) 4  σ   µ 

gas hold up

−0.12

 Ug     gD  c R  

The activity coefficient of ethanol in the liquid mixture was estimated by the UNIFAC method, where the volume (Rk), surface area (Qk) and interaction parameters (Aij) were taken from data reported in the literature

45–50

. The UNIFAC parameters and number of subgroups

(vk) used to model the molecules of ethanol (A), oleic acid (B), ethyl oleate (C) and water (D) are shown in Tables 2–3: Table 2. UNIFAC volume parameter, surface area parameter and number of subgroups used to model ethanol (A), oleic acid (B), ethyl oleate (C), and water (D) Subgroups

Main groups

k

Rk

Qk

vk(A)

vk(B)

vk(C)

vk(D)

CH3 CH2 CH=CH OH H2O CH2-COO COOH

1 1 2 5 7 11 20

1 2 6 14 16 22 42

0.9011 0.6744 1.1167 1.0000 0.9200 1.6764 1.3013

0.848 0.540 0.867 1.200 1.400 1.420 1.224

1 1 0 1 0 0 0

1 14 1 0 0 0 1

2 13 1 0 0 1 0

0 0 0 0 1 0 0


Page 15 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Table 3. UNIFAC main group interaction parameters Aij (K) used in the model

j i

1

2

5

7

11

20

1

0

86.02

986.5

1318.0

232.1

663.5

2

-35.36

0

524.1

270.60

37.80

318.9

5

156.40

457.0

0

353.50

101.1

199.0

7

300.00

496.1

-229.1

0

72.87

-14.09

11

114.80

132.1

245.4

200.80

0

660.2

20

315.30

1264.0

-151.0

-66.170

-256.3

0

3.7 Numerical Solution and parameter estimation

The combined system of differential equations was numerically integrated by the solver ode15s available in MATLAB, which is a variable-step solver indicated to handle problems that exhibit some stiffness. The enhancement factor was determined by employing the Newton-Raphson iterative scheme with suitable initial estimates (Ea ≥1) for solving Equation (17). The experimental data obtained for the esterification reaction of oleic acid was used to estimate the mass transfer coefficient parameters in Equation (25), activation energy and frequency factor of the forward reaction rate constant. The parameters were estimated by minimizing the sum of squared errors (SSE) between experimental (Xexp) and calculated (Xcalc) oleic acid conversions:

SSE = ∑∑ ( X ijcalc - X ijexp ) 2 i

(29)

j

where i and j are the counters for experiment number and experimental data point, respectively. The Particle Swarm optimization

51

algorithm was implemented in MATLAB

and used to minimize Equation (29) in order to find the optimal set of parameters. Table 4


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 32

shows the experimental conditions of each experiment used for parameter estimation and validation of the model. Table 4. Experimental conditions used for parameter estimation and model validation Experiment number 1 2 3 4 5(*) 6 7 8 9

Reactor temperature, TR (°C) 110 110 110 130 130 130 150 150 150

Inlet gas phase temperature Tg0 (°C) 110 110 110 130 130 130 150 150 150

Gas superficial velocity Ug (m/s) 0.092 0.169 0.246 0.096 0.178 0.259 0.101 0.186 0.272

Final oleic acid conversion (**) XF (%) 98.60 97.18 97.48 98.87 97.75 98.17 97.66 98.95 97.25

Time to final conversion, tF (min) 110 80 70 100 70 50 90 60 50

(*) Validation experiment not included in parameter estimation, (**) AAD = 1.73%.

4. Results and discussion 4.1 Data Fitting

In this work, a total of 59 experimental conversion points at different temperatures and ethanol superficial velocities were used for parameter estimation and model validation. Fig. 3(a)-(c) shows the fit of the bubble reactor model for the set of conversion data obtained in this work. The model shows an excellent description of the experimental data in the whole range of temperature and superficial gas velocity studied. The bubble reactor model fitting obtained an R² coefficient of 0.987 with a minimum value of SSE of 0.089. A comparison between experimental and calculated conversions is showed in Fig. 4, while the estimated values of the model parameters are displayed in Table 5.


Page 17 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 3. Model fitting for experimental conversion data: a) experiments 1, 2 and 3, b) experiments 4,6 and c) experiments 6,7 and 8.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 32

Table 5. Estimated parameters of the model k0 (m³ mol-1 s-1) 5.489×10

3

E1 (kJ mol-1)

a

b

c

69.534

0.0708

0.7854

0.2810

Figure 4. Equality diagram of the calculated and experimental values of FFA conversion for bubble reactor model.

According to Equation (25), kL is proportional to Da1-c, as well as the rate of mass transfer (Equation (21)). Analyzing the results in Table 5, the estimated value of parameter c shows that the rate of mass transfer is dependent on Da0.719. This result agrees with experimental data reported in literature, which indicates a dependence of Dan, where n varies from 0.50 to 0.75 52. 4.2 Model validation and analysis

For validation of the model, the estimated parameters displayed in Table 5 were used to calculate the reaction rate constant and mass transfer coefficient of ethanol at 130°C and superficial gas velocity of 0.178 m/s. The calculated parameters were used to predict the oleic acid concentration change in the reactor with time. Fig. 5 shows the concentration profile of


Page 19 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

each component in the liquid phase obtained during simulation at the operating conditions of experiment 5 (Table 4).

Figure 5. Liquid phase concentration profiles obtained during simulation of experiment 5.

The results showed in Fig. 5 demonstrates the predictive capability of the model, which could predict the experimental change in concentration of oleic acid with excellent precision, as well as the exact time needed to reach the final steady state concentration obtained experimentally. The amount of oleic acid decreases exponentially with time, while the amount of ester increases in a similar manner. Furthermore, it is observed that the rate of disappearance of oleic acid is faster during the first 35 minutes of reaction and then becomes slower as it approaches the steady state region (t = 70 min). A comparison between the volumetric mass transfer and chemical reaction rates with time for experiment 5 is shown in Fig. 6.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 32

Figure 6. Mass transfer and reaction rate of ethanol obtained during simulation of experiment 5.

At the maximum driving force of the process (t = 0, [A]l,bulk = 0), the highest rate of mass transfer per unit volume is observed. As time proceeds, the rate of reaction reaches a maximum value and then decreases along with the mass transfer rate. It is observed that rate of mass transfer and chemical reaction have approximately the same values throughout the whole process. The influence of the chemical reaction on the rate of mass transfer of ethanol was analyzed according to the calculated values of the Hatta number (Ha) and enhancement factor (Ea). Since the process is operated in the semi-batch mode, the liquid phase concentration in the reactor changes with time, which means that the Hatta number (Equation (18)) and the reaction regime may change during the process 53. Fig. 7 shows the change of the Hatta number and enhancement factor with time obtained for each experiment.


Page 21 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Fugure 7. Dimensionless Hatta number and enhancement factor as function of time: (a) experiments 1-3 (110°C), (b) experiments 4-6 (130°C) and (c) experiments 7-9 (150°C).

According to the results displayed in Fig. 7(a)-(c), the Hatta number for all 9 experiments are lower than 0.2 during the entire time, which means that the process is operated under the “slow reaction regime”, in other words, the conversion in the liquid film is negligible and chemical reaction is considered to occur predominantly in the liquid bulk. Since chemical reaction does not take place inside the liquid film, the mass transfer flux of ethanol coming from the gas-liquid interface through a reactive liquid phase is essentially the same that would be obtained by physical absorption (no chemical reaction) with the same driving force. This may be verified by the calculated values of the enhancement factor, which were found to be close to one for all experiments throughout the process (Fig. 7(a)-(c)). In 21 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 32

addition, according to the mathematical definition of the enhancement factor given in Equation (20), the chemical and physical absorption constants have no distinction in values for the specified reaction regime. Fig. 8 shows the calculated values of the mass transfer coefficients for the operating conditions presented in Table 4.

Figure 8. Calculated liquid side mass transfer coefficient at different inlet gas phase temperatures and superficial velocities.

The calculated values obtained for the mass transfer coefficients in the temperature range studied seems to agree with the reported order of magnitude for agitated gas-liquid reactors, which ranges from 10-6 to 10-5 m/s 54. It is observed that the mass transfer coefficient increases almost linearly with superficial gas velocity, which may be explained by the estimated exponent of the Reynolds number in Equation (25) being close to unity. In addition, the slopes of the curves presented in Fig. 8 increases with the inlet gas phase temperature, which means that mass transfer resistance in the liquid phase (ma/kL) might be reduced by increasing the temperature and flow rate of the superheated ethanol vapor feed stream.

5. Conclusions A semi-batch bubble reactor model was developed for the esterification reaction of FFA with superheated alcohol vapor. A phenomenological approach was used to develop the 22 ACS Paragon Plus Environment

Page 23 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

model considering the effects of both mass transfer and chemical reaction. The frequency factor, activation energy and liquid side mass transfer coefficient were estimated by minimizing the sum of squared errors (SSE) between calculated and experimental conversion data of oleic acid esterification with superheated ethanol vapor. The model exhibited an excellent fit and the estimated values of the mass transfer parameters agreed with experimental data reported in literature. The proposed model showed to be very effective in describing the performance of bubble reactors for esterification reactions and was able to describe the limitations of the process due to mass transfer and reaction. In addition, the phenomenological approach, theoretical considerations and dimensional analysis used to evaluate the effects of mass transfer makes the model a suitable choice for parameter estimation, design and process scaleup.

Acknowledgements The authors gratefully acknowledge the financial support by CAPES and CNPq.

Nomenclature A

alcohol

[]

molar concentration (mol·m-3)

a

parameter of mass transfer coefficient correlation

av

average interfacial area of gas bubbles per unit volume (m-1)

b


B

free fatty acid

c


C

fatty acid ester


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

D

water

Da

diffusivity coefficient of component A (m2 ·s-1)

Db

diffusivity coefficient of component B (m2 ·s-1)

DR

reactor diameter (m)

dvs

Volume-surface mean bubble diameter (m)

E1

activation energy of the forward reaction (kJ·mol-1)

Ea

enhancement factor

Ei

instantaneous enhancement factor

gc

gravitational constant (m· s-2)

Ha

Hatta number

k0

frequency factor (m³·mol-1·s-1)

k1

forward reaction rate constant (m³·mol-1·s-1)

kL

liquid side mass transfer coefficient (m·s-1)

L

total liquid phase concentration (mol·m-3)

M

molecular weight (kg·mol-1)

ma

partition coefficient of component A

P*

saturation pressure (Pa)

qg

gas phase volumetric flow rate (m³·s)

r

reaction rate (mol·m-3· s-1)

R

universal gas constant (J·mol-1 ·K-1)

R2

coefficient of determination

Re

Reynolds number

Sc

Schmidt number

Sh

Sherwood number

t

time (min)

Page 24 of 32


Page 25 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Tg

gas phase temperature (°C)

TR

reaction temperature (°C)

Ug

superficial gas velocity (m·s-1)

Vl

liquid volume (L)

X

free fatty acid conversion

z

spatial coordinate (m)

Greek Symbols γ

activity coefficient

δ

film thickness (m)

εg

gas holdup

µ

dynamic viscosity (kg·m-1·s-1)

ρ

density (kg·m-3)

σ

surface tension (kg·s-2)

Φ

volumetric mass transfer rate (mol·m-3·s-1)

Subscripts l

liquid phase

0

initial

bulk

bulk phase

g

gas phase

p

component phase

R

reactor


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 26 of 32

Superscripts calc

calculated

*

interface/equilibrium

exp

experimental

in

inlet

out

outlet

References (1)

Leonard, C.; Ferrasse, J.-H.; Boutin, O.; Lefevre, S.; Viand, A. Bubble Column

Reactors for High Pressures and High Temperatures Operation. Chem. Eng. Res. Des. 2015, 100, 391–421. (2)

Konsowa, A. H. Decolorization of Wastewater Containing Direct Dye by Ozonation in

a Batch Bubble Column Reactor. Desalination 2003, 158 (1), 233–240. (3)

M. Navaza, J.; Gómez-Díaz, D.; La Rubia García, M. D. Removal Process of CO2

Using MDEA Aqueous Solutions in a Bubble Column Reactor; 2009; Vol. 146. (4)

Folgueira, I.; Teijido, I.; García-Abuín, A.; Gómez-Díaz, D.; Rumbo, A. 2-

(Methylamino)Ethanol for CO2 Absorption in a Bubble Reactor. Energy & Fuels 2014, 28 (7), 4737–4745. (5)

Blanco, A.; García-Abuín, A.; Gómez-Díaz, D.; Navaza, J. M. Hydrodynamic and

Absorption Studies of Carbon Dioxide Absorption in Aqueous Amide Solutions Using a Bubble Column Contactor . Brazilian Journal of Chemical Engineering . scielo 2013, pp 801– 809. 26 ACS Paragon Plus Environment

Page 27 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(6)

Kantarci, N.; Borak, F.; Ulgen, K. Bubble Column Reactors; 2005; Vol. 40.

(7)

Deckwer, W.-D.; Schumpe, A. Improved Tools for Bubble Column Reactor Design

and Scale-Up. Chem. Eng. Sci. 1993, 48 (5), 889–911. (8)

Shah, Y.; G. Kelkar, B.; P. Godbole, S.; Deckwer, W.-D. Design Parameters

Estimations for Bubble Column Reactors; 1982; Vol. 28. (9)

Schäfer, R.; Merten, C.; Eigenberger, G. Bubble Size Distributions in a Bubble

Column Reactor under Industrial Conditions. Exp. Therm. Fluid Sci. 2002, 26 (6), 595–604. (10)

Behkish, A.; Men, Z.; Inga, J.; Morsi, B. Mass Transfer Characteristics in a Large-

Scale Slurry Bubble Column Reactor with Organic Liquid Mixtures; 2002; Vol. 57. (11)

Farsi, M.; Asemani, M.; Rahimpour, M. R. Mathematical Modeling and Optimization

of Multi-Stage Spherical Reactor Configurations for Large Scale Dimethyl Ether Production. Fuel Process. Technol. 2014, 126, 207–214. (12)

Samimi, F.; Bayat, M.; Karimipourfard, D.; Rahimpour, M. R.; Keshavarz, P. A Novel

Axial-Flow Spherical Packed-Bed Membrane Reactor for Dimethyl Ether Synthesis: Simulation and Optimization. J. Nat. Gas Sci. Eng. 2013, 13, 42–51. (13)

Joelianingsih; Tambunan, A. H.; Nabetani, H. Reactivity of Palm Fatty Acids for the

Non-Catalytic Esterification in a Bubble Column Reactor at Atmospheric Pressure. Procedia Chem. 2014, 9, 182–193. (14)

Nakajima, S. H. and H. N. and M. Non-Catalytic Alcoholysis Process for Production

of Biodiesel Fuel by Using Bubble Column Reactor. J. Phys. Conf. Ser. 2015, 596 (1), 12017. (15)

Chai, M.; Tu, Q.; Lu, M.; Yang, Y. J. Esterification Pretreatment of Free Fatty Acid in

Biodiesel Production, from Laboratory to Industry. Fuel Process. Technol. 2014, 125, 106– 113. 27 ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(16)

Page 28 of 32

Chen, L.; Liu, T.; Zhang, W.; Chen, X.; Wang, J. Biodiesel Production from Algae Oil

in Free Acids by Two-Step Catalytic Conversion; 2012; Vol. 111. (17)

Wang, Y.; Pengzhan Liu, S. O.; Zhang, Z. Preparation of Biodiesel from Waste

Cooking Oil via Two-Step Catalyzed Process. Energy Convers. Manag. 2007, 48 (1), 184– 188. (18)

Joelianingsih; Nabetani, H.; Sagara, Y.; Tambunan, A. H.; Abdullah, K. A

Continuous-Flow Bubble Column Reactor for Biodiesel Production by Non-Catalytic Transesterification. Fuel 2012, 96, 595–599. (19)

Wulandani, D.; Ilham, F.; Fitriyan, Y.; Siswantara, A. I.; Nabetani, H.; Hagiwara, S.

Modification of Biodiesel Reactor by Using of Triple Obstacle within the Bubble Column Reactor. Energy Procedia 2015, 65, 83–89. (20)

Čerče, T.; Peter, S.; Weidner, E. Biodiesel-Transesterification of Biological Oils with

Liquid Catalysts: Thermodynamic Properties of Oil−Methanol−Amine Mixtures. Ind. Eng. Chem. Res. 2005, 44 (25), 9535–9541. (21)

Noureddini, H.; Zhu, D. Kinetics of Transesterification of Soybean Oil. J. Am. Oil

Chem. Soc. 1997, 74 (11), 1457–1463. (22)

Lucena, I. L.; Saboya, R. M. A.; Oliveira, J. F. G.; Rodrigues, M. L.; Torres, A. E. B.;

Cavalcante, C. L.; Parente, E. J. S.; Silva, G. F.; Fernandes, F. A. N. Oleic Acid Esterification with Ethanol under Continuous Water Removal Conditions. Fuel 2011, 90 (2), 902–904. (23)

Marchetti, J. M.; Miguel, V. U.; Errazu, A. F. Heterogeneous Esterification of Oil with

High Amount of Free Fatty Acids. Fuel 2007, 86 (5), 906–910.


Page 29 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(24)

Stacy, C. J.; Melick, C. A.; Cairncross, R. A. Esterification of Free Fatty Acids to

Fatty Acid Alkyl Esters in a Bubble Column Reactor for Use as Biodiesel. Fuel Process. Technol. 2014, 124, 70–77. (25)

Khuenpetch, A.; Siripatana, C.; Kooamornpattana, W.; Nuithitikul, K. Biodiesel

Production from Palm Oil Using a Downflow Bubble Column Reactor; 2017; Vol. 12. (26)

Joelianingsih; Maeda, H.; Hagiwara, S.; Nabetani, H.; Sagara, Y.; Soerawidjaya, T.

H.; Tambunan, A. H.; Abdullah, K. Biodiesel Fuels from Palm Oil via the Non-Catalytic Transesterification in a Bubble Column Reactor at Atmospheric Pressure: A Kinetic Study. Renew. Energy 2008, 33 (7), 1629–1636. (27)

Cao, P.; Dubé, M. A.; Tremblay, A. Y. High-Purity Fatty Acid Methyl Ester

Production from Canola, Soybean, Palm, and Yellow Grease Lipids by Means of a Membrane Reactor. Biomass and Bioenergy 2008, 32 (11), 1028–1036. (28)

Theorie Der Reaktionsgeschwindigkeit in Heterogenen Systemen . Zeitschrift für

Physikalische Chemie . 1904, p 52. (29)

W. van Krevelen, D.; J. Hoftijzer, P. Kinetics of Gas-Liquid Reactions. Part I. General

Theory; 2010; Vol. 67. (30)

Kierzkowska-Pawlak, H. Determination of Kinetics in Gas-Liquid Reaction Systems.

An Overview; 2012; Vol. 19. (31)

Roizard, C.; Wild, G. Mass Transfer with Chemical Reaction: The Slow Reaction

Regime Revisited. Chem. Eng. Sci. 2002, 57 (16), 3479–3484. (32)

Hogendoorn, J. A.; Vas Bhat, R. D.; Kuipers, J. A. M.; van Swaaij, W. P. M.;

Versteeg, G. F. Approximation for the Enhancement Factor Applicable to Reversible


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 32

Reactions of Finite Rate in Chemically Loaded Solutions. Chem. Eng. Sci. 1997, 52 (24), 4547–4559. (33)

M. Wellek, R.; J. Brunson, R.; H. Law, F. Enhancement Factors for Gas-Absorption

with Second-Order Irreversible Chemical Reaction; 1978; Vol. 56. (34)

Hikita, H.; Asai, S.; Tanigawa, K.; Segawa, K.; Kitao, M. The Volumetric Liquid-

Phase Mass Transfer Coefficient in Bubble Columns. Chem. Eng. J. 1981, 22 (1), 61–69. (35)

Li, C.; Zhu, C.; Ma, Y.; Liu, D.; Gao, X. Experimental Study on Volumetric Mass

Transfer Coefficient of CO2 Absorption into MEA Aqueous Solution in a Rectangular Microchannel Reactor. Int. J. Heat Mass Transf. 2014, 78, 1055–1059. (36)

Kashid, M. N.; Renken, A.; Kiwi-Minsker, L. Gas–liquid and Liquid–liquid Mass

Transfer in Microstructured Reactors. Chem. Eng. Sci. 2011, 66 (17), 3876–3897. (37)

Akita, K.; Yoshida, F. Bubble Size, Interfacial Area, and Liquid-Phase Mass Transfer

Coefficient in Bubble Columns. Ind. Eng. Chem. Process Des. Dev. 1974, 13 (1), 84–91. (38)

Akita, K.; Yoshida, F. Gas Holdup and Volumetric Mass Transfer Coefficient in

Bubble Columns. Effects of Liquid Properties. Ind. Eng. Chem. Process Des. Dev. 1973, 12 (1), 76–80. (39)

Calderbank, P. H.; Moo-Young, M. B. The Continuous Phase Heat and Mass-Transfer

Properties of Dispersions. Chem. Eng. Sci. 1961, 16 (1), 39–54. (40)

Noureddini, H.; Teoh, B. C.; Davis Clements, L. Densities of Vegetable Oils and Fatty

Acids. J. Am. Oil Chem. Soc. 1992, 69 (12), 1184–1188. (41)

Pratas, M. J.; Freitas, S.; Oliveira, M. B.; Monteiro, S. C.; Lima, A. S.; Coutinho, J. A.

P. Densities and Viscosities of Fatty Acid Methyl and Ethyl Esters. J. Chem. Eng. Data 2010, 55 (9), 3983–3990. 30 ACS Paragon Plus Environment

Page 31 of 32 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(42)

R., W. C.; Pin, C. Correlation of Diffusion Coefficients in Dilute Solutions. AIChE J.

2018, 1 (2), 264–270. (43)

Ambrose, D.; Sprake, C. H. S.; Townsend, R. Thermodynamic Properties of Organic

Oxygen Compounds XXXVII. Vapour Pressures of Methanol, Ethanol, Pentan-1-Ol, and Octan-1-Ol from the Normal Boiling Temperature to the Critical Temperature. J. Chem. Thermodyn. 1975, 7 (2), 185–190. (44)

Kretschmer, C. B.; Wiebe, R. Liquid-Vapor Equilibrium of Ethanol--Toluene

Solutions. J. Am. Chem. Soc. 1949, 71 (5), 1793–1797. (45)

Skjold-Jorgensen, S.; Kolbe, B.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria

by UNIFAC Group Contribution. Revision and Extension. Ind. Eng. Chem. Process Des. Dev.

1979, 18 (4), 714–722. (46)

Gmehling, J.; Rasmussen, P.; Fredenslund, A. Vapor-Liquid Equilibriums by

UNIFAC Group Contribution. Revision and Extension. 2. Ind. Eng. Chem. Process Des. Dev.

1982, 21 (1), 118–127. (47)

Macedo, E. A.; Weidlich, U.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibriums

by UNIFAC Group Contribution. Revision and Extension. 3. Ind. Eng. Chem. Process Des. Dev. 1983, 22 (4), 676–678. (48)

Tiegs, D.; Rasmussen, P.; Gmehling, J.; Fredenslund, A. Vapor-Liquid Equilibria by

UNIFAC Group Contribution. 4. Revision and Extension. Ind. Eng. Chem. Res. 1987, 26 (1), 159–161. (49)

Hansen, H. K.; Rasmussen, P.; Fredenslund, A.; Schiller, M.; Gmehling, J. Vapor-

Liquid Equilibria by UNIFAC Group Contribution. 5. Revision and Extension. Ind. Eng. Chem. Res. 1991, 30 (10), 2352–2355.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(50)

Page 32 of 32

Wittig, R.; Lohmann, J.; Gmehling, J. Vapor−Liquid Equilibria by UNIFAC Group

Contribution. 6. Revision and Extension. Ind. Eng. Chem. Res. 2003, 42 (1), 183–188. (51)

Kennedy, J.; Eberhart, R. Particle Swarm Optimization; 1995; Vol. 4.

(52)

Charpentier, J.-C. Mass-Transfer Rates in Gas-Liquid Absorbers and Reactors; Drew,

T. B., Cokelet, G. R., Hoopes, J. W., Vermeulen, T. B. T.-A. in C. E., Eds.; Academic Press, 1981; Vol. 11, pp 1–133. (53)

Bin, A.; Roustan, M. Basic Chemical Engineering Concepts for the Design of Ozone

Gas-Liquid Reactors; 2005. (54)

Ganapathy, H.; Shooshtari, A.; Dessiatoun, S.; Alshehhi, M.; Ohadi, M. Fluid Flow

and Mass Transfer Characteristics of Enhanced CO2 Capture in a Minichannel Reactor. Appl. Energy 2014, 119, 43–56.


Mathematical Modeling and Simulation of Biodiesel Production in a

Recommend Documents