Mathematical Model of a Falling Film Reactorfor Methyl Ester Sulfonation
Jesús Alfonso Torres Ortega, Universidad de La SalleGiovanni Morales Medina, Universidad Industrial de
SantanderOscar Yesid Suárez Palacios, Universidad Nacional de
ColombiaFrancisco José Sánchez Castellanos, Universidad Nacional
de Colombia
Recommended Citation:Torres Ortega, Jesús Alfonso; Morales Medina, Giovanni; Suárez Palacios, Oscar Yesid; andSánchez Castellanos, Francisco José (2009) "Mathematical Model of a Falling Film Reactor forMethyl Ester Sulfonation," Chemical Product and Process Modeling: Vol. 4 : Iss. 5, Article 12.Available at: http://www.bepress.com/cppm/vol4/iss5/12DOI: 10.2202/1934-2659.1393
Mathematical Model of a Falling Film Reactorfor Methyl Ester Sulfonation
Jesús Alfonso Torres Ortega, Giovanni Morales Medina, Oscar Yesid SuárezPalacios, and Francisco José Sánchez Castellanos
Abstract
Methyl ester sulfonation with sulfur trioxide derived from oleum is possible under specialconditions on a pilot plant scale. Quantum chemical calculations were used to study the relativestability between intermediates in the proposed mechanism. In this report an analysis of amathematical model for a falling film sulfonation reactor is presented. It aims to estimate thetemperature and conversion profiles of the thin film. The model treats the heat released and thetrioxide sulfur dissolution assuming that the film theory is applicable. The temperature andconcentration gradients can exist across the film during the chemical reaction. The equations weresolved using finite differences. The most important data obtained by the mathematical model for asubsequent correlation with the properties of the reagents and product are the conversion, thedensity and viscosity of the sulfonic product. The results indicate an increase in the axialtemperature of the liquid film and the conversion from the top reactor in accordance with theexperimental results. It considers that at the upper section of the reactor the reaction is controlledby means of mass transfer due to gas phase turbulence. A mild conversion on the reactor bottommeans that the liquid phase controls the mass transfer due to the amounts of sulfur trioxidetransferred into the film which produces changes in the film composition.
KEYWORDS: modelling, film reactor, sulfonation, methyl stearate, sulfur trioxide
Author Notes: We gratefully acknowledge Prof. Federico Ignacio Talens Alesson fromUniversity of Nottingham (England). During this study the authors were beneficiaries of a doctoralgrant from COLCIENCIAS (Departamento Administrativo de Ciencia, Tecnología e Innovación).
Erratum
Page 11, Figure 9 should appear as follows:
01020304050607080
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7
Act
ive
mat
ter
perc
enta
ge
Lenght, m
Active matter reactor Mater active model
Introduction Falling film reactor (FFR) is widely used for exothermic gas–liquid reactions such as sulfonation. Methyl esters sulfonate (MES) has a wide range of application and important biological properties; it is an interesting class of anionic surfactant (Ahmad et al., 2007). Post-sulfonic reactions have been extensively studied, mainly the kinetics for ageing (stabilization/digestion), bleaching and neutralization stages (Kapur et al., 1978; Lim and Ahmad, 2001; Roberts, 2007; Roberts et al., 2008). However, the process inside the FFR has not been well understood. Therefore, it is considered of special interest for the current research.
This paper presents a review of events that occur downstream in a FFR: convection, diffusion, reaction and the hydrodynamic process, applied to SO3–absorption on the methyl esters mixture. Phenomenological descriptions of mass, momentum and heat balances are developed herein. The mathematical modeling relates several process variables with the conversion expressed as molar fraction of the sulfonated product. In this case a mixture of methyl esters (ME) composed mainly of methyl palmitate and methyl stearate is used (Torres et al., 2005). The composition of SO3 as a sulfonation agent derived from oleum was determined empirically by absorbing on a sulfuric acid solution (Torres et al., 2008b).
The characterization of anionic surfactants was applied on the sulfonated product. The content of active matter or active ingredient was determined using a two-phase titration technique with Hyamine 1622 as a titrant and methylene blue as an indicator. Unsulfonated matter was measured by extraction with petroleum ether, followed by evaporation and weighing of dry residue and finally the total acidity was determined with the potentiometric titration (Ahmad et al., 1998). The results from the mathematical model were validated using physicochemical properties of the reactants and product. Some physicochemical properties are listed in Table 1. Reaction scheme of methyl ester sulfonation At the beginning of the reaction, the SO3 is absorbed by the liquid and an irreversible reaction occurs. The chemistry of the methyl ester sulfonation is complex and is not yet fully elucidated, but may be summarized in Figure 1. Here, the third reaction stage is considerably slower than the previous one, where an SO3 group is liberated (on ageing). That SO3 group would be especially active and therefore capable of sulfonating directly another methyl ester molecule in an alpha position (Stein and Baumann, 1975; de Groot, 1991; Roberts, 2001).
1
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Table 1. The correlations used for the falling film reactor calculations. Parameter Correlation Method
ME density kg/m3 ρME = 881.31–0.8214TL (1) Torres et al. (2005)
Film density, kg/m3 ρL = 980 + 192x – 0.66TL (2) Talens and Gutiérrez (1995)1
Diffusivity, m2/s
DMES-ME = 321110123 /
L
LT.μ
−× (3)
DME-MES = 3211102886 /
L
LT.μ
−× (4)
DSO3= 3210
1000100312 /
L
LT.μ
−× (5)
Reid et al., (1987)2
Gas conductivity, J/msK kG = 0.0279 Davis et al., (1979) Heat capacity of liquid, J/kmolK cL = 507.300 + 101.010x (6) Reid et al., (1987)3
Heat capacity of gas mix, J/kmolK cG = 29.82 Some at nitrogen
Liquid conductivity, J/msK kL = 0.276 Davis et al., (1979) Surface tension, N/m σ = 0.046 de Groot (1991)
Methyl ester viscosity, kg/ms μME = LTe6.1949
6108 −× (7) Torres et al. (2005)
Methyl ester sulfonic viscosity, kg/ms 885
5700810361 .LT
MES e. +−×=μ (8) Talens and
Gutiérrez (1995)1
Gas viscosity, kg/ms μG = 1.9×10-5 Some at nitrogen
Viscosity of the film, kg/ms
a) 0< x ≤ 0.25: (9)
xTL
Le 86.32980
71072.2 +−×=μ b) 0.25 < x ≤ 0.6: (10)
003.0107.3 035.14850
10 +×= +− xTL
Leμ c) 0.6 < x < 1: (11)
003.0107.3 22.54850
10 +×= +− xTL
Leμ
Talens and Gutiérrez (1995)1
Wall thermal conductivity, J/msK kw = 16.3 Davis et al., (1979) 1 Same methodology used by Broström (1975). 2 The diffusivities are estimated of a modified form of equation Wilke and Chang (1955) and
Hiss and Cussler (1973), they measured diffusion coefficients and report that D~µ–2/3. Concentration dependence of binary liquid diffusion coefficient may be estimated through of equation Vignes (Vignes, 1966).
3 Calculated for each segment by the method of group contributions (Aspen Engineering SuiteTM V11.1).
2
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
Thermodynamics of the stable compounds for the reaction of methyl ester sulfonation was studied between methyl stearate and SO3, using the Density Functional Theory (Young, 2001; Cramer, 2002). The B3LYP functional and 6-31G(d) basis set were used for calculating frequencies and geometries. Calculations were carried out in the Gaussian 03W program (Frisch et al. 2004).
(a) The first stage: sulfonation (very fast)
Intermediate I Intermediate II Intermediate III
(b) The second and third stage: over-sulfonation (even faster than the first)
(c) The ageing stage Figure 1. Mechanism proposed for methyl ester sulfonation
The reactivity of the ME due to its aliphatic chains is less than the
aromatic compounds, these reactions are highly exothermic: 150 – 170 kJ/mol, including 25 kJ/mol of the absorption heat of gaseous SO3 (Roberts, 2003). The formation of intermediates is relatively fast. That is in agreement with the results showed in Figure 2(a). The intermediate III is very stable according to the Gibbs diagram (ΔG < 0) as shown in Figure 2(b), here the spontaneity is favored because of negative value of enthalpy.
According to the results of the thermodynamic ground, the intermediates in the sulfonation and over-sulfonation steps were found to have the same relative stability. This fact disregards the inclusion of these intermediates into the kinetic model and allows the use of a second order equation for the reaction progress. Thus, the reaction kinetics in the reactor (FFR) was determined using the following rate law:
r = MESO CkC 3− , Tek14350
191014.1−
×= m3/kmol (12) The activation energy is 30377 J/mol (Torres et al., 2008a).
O + SO3
O SO3–
+
SO3H O SO3– SO3H
+ k2
k’2
k3
O
SO3H
+ SO3
α-sulfo methyl ester acid
353K Ageing
RCH2CO2CH3 + SO3 k1
Methyl ester
R – CH2 – C – O – CH3 R – CH = C – O – CH3 R – CH – C – O – CH3
O SO3–
+ R – CH2 – C – O – CH3
O SO3– SO3H
+ R – CH – C – O – CH3 R – CH – C – O – CH3
Intermediate III
3
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
ΔH (kJ/mol)
Reaction
–116.65 –158.69
Reaction
ΔG (kJ/mol)
–470.91 –449.15
Figure 2. Thermodynamic for the initial reaction between ME and SO3 at the
B3LYP/6-31G(d) level
The experimental apparatus utilized is presented in Figure 3. The SO3 vapor was generated through distillation from oleum and diluted to the desired concentration with nitrogen before entering in FFR (Moretti and Adami, 2002).
Figure 3. Experimental setup for methyl ester sulfonation using FFR
(a) Heat of reaction, ΔH (b) Gibbs energy, ΔG
515.63 119.03
.
Analysis
Analysis
Wat
er in
let
Falli
ng F
ilm R
eact
or
Methyl esters storage
Heating circuit
Des
icca
n
Ageing reactor
Column of absorption
Store of Oleum
Heating Circuit
Water
Air
Nitrogen
Atmosphere
Water outlet
NaOH
H2SO4
H2SO4
Humidity remover
SO3storage
tank
PT
T
P
T
P
Dry Air
Heater W
ater
inle
t
Water outlet
Water outlet
Heater
Filter
Methyl esters
Des
icca
n
Oleum
Wat
er in
let
Analysis
Exhaust gases
Mass flow controller
Liquid feed
SO3 and dry air (N2)
Treatment of gases
4
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
Experiments were performed in three film reactors with different lengths: 0.25, 0.40 and 0.75 meters. All of them with ½ inch inner diameter. For industrial or commercial level the whole sulfonation process includes the neutralization stage to form the sulfo methyl ester monosodium salt as final product (Figure 4).
Figure 4. Neutralization chemistry Mathematical model Previous models for FFR have been proposed by several authors for the tridecylbenzene and dodecylbenzene sulfonation (Johnson and Crynes, 1974; Davis et al., 1979; Gutiérrez et al., 1988; Dabir et al., 1996; Talens, 1999 and Akanksha et al., 2007). Some of their assumptions are questionable as they consider that the reaction occurs at the gas–liquid interface and SO3 chemisorptions and velocity profiles are assumed laminar.
In the reactor the feedstock is injected upper section and the organic liquid is distributed as a thin film on the inner wall of the reactor tube. Here the SO3/N2 stream occupies the core of the tube (Figure 5).
Figure 5. Schematic view of the monotubular falling film reactor
The principal assumptions made in our mathematical model are: Steady-state system. Rectangular coordinate system.
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
The liquid film is symmetric in regards to the reactor axis. The liquid film and the gas mixture circulate simultaneously as a turbulent
flow. No access of liquid droplets into the gas core, neither access of gas bubbles
into the liquid film. Fully developed thin film (entrance and exit effects to reactor are neglected). The SO3 radial diffuses from the core of the tube to the liquid–gas interface. Condensation and evaporation do not occur on the surface of the liquid film. The film thickness is small compared to the column radius. The reaction occurs in the film thickness with rapid changes of composition. SO3 solubility in the liquid reactant and in the reaction product is ideal
according to Henry’s law. The mono-sulfonation of methyl esters produces mainly MES. The liquid reactant (ME) and the product (MES) are non-volatile at working
temperatures.
Strong changes in conversion on upper reactor region due to the turbulence of the gas are enough to transport fresh liquid to the interface (Knaggs, 2004). Hence the gas phase is entirely controlling the resistance to mass transfer. The rate is limited by the SO3 that can be supplied to the liquid interface. A mild conversion on the bottom reactor means that the liquid phase controls the mass transfer due to the high amount of SO3 transferred into the film, which induces a change in the composition. The reaction heat must be removed to prevent degradation of the product into three statements: A portion of the reaction heat raises the temperature of the liquid film. Another portion of the reaction heat is transferred into the moving gas stream
and raises the temperature of the gas phase. A third portion of the reaction heat is transferred through the liquid film into
the wall.
The model proposed in this paper is appropriate for turbulent flows and considers effects of wavy film flow by using eddy diffusivity parameter. Effects of interfacial drag at the gas–liquid interface and the gas–phase heat and mass transfer resistance have been also considered. The model predicts conversions, gas–liquid interface temperature along the reactor length and it is applicable to any falling film reactor. Knowledge of temperature distribution along the reactor is important for product quality control, since degradation of the products may occur under certain conditions.
The equations are explained below according to the mass, momentum and heat transfer. In these equations the turbulent diffusivity for mass transfer with chemical reaction was considered. The model simulates the variations in physical
6
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
properties with temperature and predicts conversion and temperature of the liquid in the axial and transversal directions. Here, we consider a system in which a liquid (initially free of the absorbing species at z = 0) falls into the surface of a vertical and impermeable wall under the influence of gravity and gas mixture with y varies from y = 0 (at the wall surface) to y = δ (at the liquid free surface). The mathematical model equations are:
Figure 6. Mass balance on finite volume includes the boundary conditions at the solid wall and gas/liquid interface
As shown in Figure 6, three components are considered in the liquid phase: methyl ester (ME), methyl ester sulfonic acid (MES) and sulfur trioxide (SO3). Then two microscopic balances are sufficient to determine the concentration profiles. The differential equation for diffusion in fully developed, two-dimensional flow may be written in terms of the eddy diffusivity as:
( ) MESOSO
TSOSO
z CkCy
CDD
yz
Cv 3
33
3 −⎥⎥⎦
⎤
⎢⎢⎣
⎡
∂
∂+
∂∂
=∂
∂ 0 ≤ y ≤ δ (13)
( ) MESOME
TMEME
z CkCy
CDD
yzC
v 3−⎥⎦
⎤⎢⎣
⎡∂
∂+
∂∂
=∂
∂ 0 ≤ y ≤ δ (14)
Gutiérrez et al. (1988) reported that due to the high Schmidt number and wavy film flow, DT cannot be neglected. Equations for turbulent diffusivity and turbulent viscosity in the liquid phase were suggested by Yih and Liu (1983).
5.02)/(
2
5.0
164.015.05.0⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡−×++−= +
+−+ A
y
w
Tw
eyττ
ττ
νν (15)
where, τ/τw = 1 – (τL/(τG + τL))3(y+/δ+) (16)
y z = 0
y = 0 y = δ y = d/2
z
z = L
y y+Δy
z
z+Δz
0y
C3SO =
∂
∂
0y
CME =∂
∂
RTD
Pk
yC
ME
*SOGME 3=
∂∂
Liqu
id /
Gas
inte
rfac
e SO3 (G) N2 (G) Liquid film
Tube
wal
l
Tube
cor
e
yCD∂∂
−
0
0y
C3SO =
∂
∂( )iSOSO
SO
GSO mCCDk
yC
333
3 −=∂
∂
Liquid phase Gas phase
7
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Equations for turbulent diffusivity in the liquid phase follow the Cebeci’s modification of the van Driest model and were modified in this paper to include the effect of shear variable:
For non–volatility liquids such as methyl stearate the vapor pressure is zero at working temperatures. At the interface, it is assumed that Henry’s and Raoult laws are applicable to determine the SO3 solubility. The Henry constant m, is determined from the SO3 vapor pressure:
( )iSO
GSOG
GSO mCCkN
333−= (19)
704.08.0 −= ScukG (McCready and Hanratty, 1984) (20)
Where the turbulent velocity is defined as: 21
⎟⎟⎠
⎞⎜⎜⎝
⎛=
G
Guρτ (21)
The axial liquid velocity vz, can be derived from the momentum equation after neglecting the pressure gradient and axial terms (see Figure 7).
L
G
L
Lz
yyyg
vμτ
δμρ
+⎥⎥⎦
⎤
⎢⎢⎣
⎡−=
2
2 (22)
Figure 7. Boundary conditions at the solid wall and gas/liquid interface by momentum balance
y = 0, v = 0
vi
vz
y z = 0
y = 0 y = δ y = d/2
u du/dy = 0
z
z = L
Liquid / Gas interface
SO3 (G) N2 (G) Liquid film Tube wall
Tube
cor
e
Liquid phase Gas phase
8
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
The flow profile of the liquid falling and gas is predominantly turbulent. Consequently the SO3 is absorbed at the gas/liquid interface. For relative high gas flow rates where the shear force predominates over the gravitational force, the linear velocity distribution is:
L
Gz
yvμτ
= . (23)
Calculation of τG based on the relations proposed by Riazi and Faghri (1986) shows that gas flow is turbulent. Thereby in most cases for FFR interfacial drag effects cannot be neglected. For film sulfonation, flow parameters can be introduced and adjusted to minimize the deviation from a data set (Talens, 1999):
L
G
L
L gμδτδ
μρ
23
23 −= (24)
2uC GfG ρτ = (25)
( ) ( )⎪⎭
⎪⎬⎫
⎪⎩
⎪⎨⎧
⎟⎟⎠
⎞⎜⎜⎝
⎛+−−=
GG2f Re.
d/LogRe.
.d/Log
C13
73025
7341 ϕδϕδ (26)
If viL < 0.175 ms–1, Ln(φ) = 3.59 – 5.14 viL, else Ln(φ) = 20.55 viL – 0.93. The initial value of the film thickness δ can be obtained from:
31
Lg ⎟⎟⎠
⎞⎜⎜⎝
⎛ Γ=
ρμδ 3 (27)
Later the δ value can be calculated by iteration through equation 24. In exothermic reactions, an amount of heat is released and in this case an
The heat transport equations follow the Prandtl analogy and are equivalent to that used for mass transfer: 704080 .G Sc.
uh −= . (30)
Numerical scheme The model developed has the following sequence: the film thickness is determined by iteration with the mass flow per unit perimeter. Then the turbulent viscosity, the diffusivity and the reactant mass balance are calculated. On the basis SO3 concentrations, the profile of MES concentrations is estimated.
Γ
9
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Figure 8. Sketch of the symbols used for heat balance on the segment
That provides the new profile of SO3 concentrations. By an iteration process, the discrepancy is reduced to a certain value. Then the overall conversion in the segment is now estimated and the energy balance is solved. The concentration values are corrected to determine the velocity profile and film thickness before making the calculations for the next stage. Mass and heat transfer coefficients in the gas phase are calculated using empirical equations proposed by McCready and Hanratty (1984) and Gutiérrez et al. (1988).
The proposed model is a special case for exothermic gas absorption. This study uses the film theory to evaluate the consequences of intense heat effects during absorption and chemical reaction. Microscopic mass and energy balances are calculated using solving equations in partial derivatives for the liquid phase. This set of equations is numerically solved using the linearization of finite differences by Laasonen implicit forms for first and second order derivates.
The linear stability problem associated with a vertical liquid flowing under the action of gravity has been solved in terms of a numerical solution of the Orr-Sommerfeld equation. The physical properties as well as the radial heat and mass transfer rates are assumed constant in each segment. However they are adjusted for the next segment according to the output temperatures from each previous segment. The crucial variables for the process are: the length and diameter of the FFR, the flow of liquid reactant, the molar ratio between SO3 and organic liquid, and the mole fraction of SO3 in the gas phase and the temperature of the reactor jacket. To ensure convergence of the system the transformation of the equations proposed by Agrawal and Peckoever (1980) was chosen following the same development by Talens (1999).
Liquid – Gas interface
Liquid film SO3 (G) N2 (G)
Q
Ti1
Ti2
Tw1
Tw2
TL1
TL2
Q
y z = 0
y = 0 y = δ y = d/2
z
z = L
y y+Δy
( )wyL TTUyTk −=∂∂
=0 ( )GyGL TThyTk −=∂∂
− =δ
Tube
cor
e
Liquid phase Gas phase
Tube wall
10
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
Results This mathematical model allows one to calculate the longitudinal profiles of temperatures for any column height. It also may be suitable for the design and operation of industrial falling film reactors. The model was constructed to predict the sharp increase during the conversion that takes place in the first stage inside the FFR. It confirms that mass transfer is initially controlled by the resistance in the gas phase. Later the resistance occurs in the liquid phase.
An example of the longitudinal profile on the degree of sulfonation expressed as percentage of active matter is presented in Figure 9. A fast conversion at the top of the reactor (linked with gas phase control) and slow conversion at the bottom (linked with liquid phase control) was observed. The progress of the reaction is decisive for the sulfonation degree expressed as the amount of active matter. For ME sulfonation several experiments were conducted varying different process factors: the mole ratio between methyl ester and SO3, the percentage of SO3 in the gaseous mixture, reagents inlet temperatures and jack temperature. The operating conditions are listed in Table 2.
Figure 9. An example of longitudinal conversion profile for ME sulfonation Table 2. Base conditions used in the methyl ester sulfonation.
Conditions Reactor SO3 in nitrogen (gaseous sulfonate mixture), % v/v 3 – 7 Methyl esters inlet temperature, K 313 – 343 SO3/N2 inlet temperature, K 343 – 353 SO3/methyl esters mole ratio 1 – 1.2 Wall temperature, K 313 – 333
Active matter modelActive matter reactor
11
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Figure 10 shows model results for different variations between SO3 in the gas mixture with the liquid interface temperature versus the reactor length. As observed, an increase of the liquid temperature according to the excess of SO3 in the gas flow occurs. The temperature of the reagents is controlled to avoid undesirable effects which could reduce the selectivity, purity and yield of the main product.
Figure 10. Liquid temperature profiles along the reactor
Figure 11 presents the conversion profile in the film reactor at the same previous conditions. The inlet temperatures for methyl ester are invariant (the mixture at 343 K and the wall temperature at 333 K). Conversions in the reactor are lower than those calculated by the model for the 25 cm reactor. This can be explained due to late effects in the reactor. By contrast, for 40 and 75 cm reactors, the correlation between the values predicted by the model and those obtained experimentally is excellent with variations under 10%. The jump conversion occurs in the top of the reactor and the temperature rises considerably reducing the viscosity of the liquid. Later, the temperature decreases while the viscosity increases.
The raise of SO3/ME mole ratio or the SO3 percentage in the sulfonate stream produces a temperature increase at the entrance of the reactor which results in a decrease of the film viscosity. Viscosity presents variations as the result of an abrupt change in composition and release of energy in the initial part of the
333
338
343
348
353
358
0,0 0,2 0,4 0,6
Tem
pera
ture
, K
Lenght, m%SO3=7, mole ratio=1.1, model %SO3=7, mole ratio=1.1, reactor
%SO3=3, mole ratio=1.1, model %SO3=3, mole ratio=1.1, reactor
%SO3=7
%SO3=3%SO3=7%SO3=3
0.0 0.60.4 0.2
Tem
pera
ture
, K
12
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
Film density model Film viscosity model Film density reactor Film viscosity reactor
0.7 0.60.50.40.30.20.1 0.0
reactor which produces an increment in the temperature of this area. Consequently the interfacial velocity increases and the film thickness decreases (due to turbulent gas phase). Finally, these situations improve the SO3 absorption on the thin film.
Figure 11. Conversion profiles calculated along the reactor
At the end of the reactor, there is a small jump in the conversion due to
kinetic effects that achieve importance for the consumption of reactants. This confirms that the model includes the presence of SO3 absorbed by the film. The estimated density of the sulfonic product downstream of the reactor is similar to the determined by that experimental result (Figure 12).
Figure 12. Density and viscosity calculated along the reactor
%SO3=7
%SO3=3
%SO3=7
%SO3=3
13
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Conclusions An analysis of the reaction mechanism to methyl ester sulfonation was performed using modern techniques of simulation and molecular modeling. The stability of the intermediate species was verified experimentally as predicted with the Density Functional Theory B3LYP and the 6-31G(d) basis set.
Considering that the liquid film and gas phase are turbulent, we conclude that mainly the reaction can occur at the interface gas/liquid. However it can also occur inside the liquid.
The model predicts two distinct transfer areas. The first is characterized by an abrupt increase in conversion in which the controlling step initially depends on the gas phase. In the second area, the viscosity fluid and the film thickness increase, elsewhere the film velocity decreases, then the liquid phase becomes the controlling stage with a mild increase of conversion.
The mathematical model proposed agreed with the trend of the experimental results. The profiles of temperature, density, viscosity and conversion are consistent with the experimental results and satisfy the conditions to minimize the mathematical mistakes made due to the usage of numerical solutions. This fact suggests that the methodology here proposed can be used to predict conversions in any film reactor. Nomenclature C = Concentration, kmol/m3
c = Heat capacity, J/kmol K Cf = Friction factor D = Diffusivity, m2/s DT = Turbulent diffusivity, m2/s d = Reactor diameter, m g = Acceleration of gravity, m/s2
h = Heat transfer coefficient, J/m2 s K k = Thermal conductivity, J/m s K; Reaction rate constant, m3/kmol s L = Reactor length, m m = Henry constant, kmol of SO3/m3 of gas/kmol of SO3/m3 of liquid P = Pressure, atm Pr = Prandtl number cμ/k, dimensionless Q = Heat of reaction, J/mol R = Aliphatic chain Re = Reynolds number, ReG = ρu(d – 2δ)/μ; ReL = 4Г/μ. Sc = Schmidt number μ/DρL, dimensionless T = Temperature, K
14
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
U = Global heat transfer coefficient, J/m2 s K u = Turbulence characteristic velocity of gas, m/s x = Conversion expressed as molar fraction of the acid, dimensionless v = Axial velocity of liquid film, m/s y = Transversal coordinate (from wall toward the liquid free surface) y+ = Non-dimensional distance to the wall: y(τwgρ)½/μ z = Axial coordinate Greek Symbols Γ = Volumetric flow rate of the liquid per unit wetted perimeter, m2/s δ = Film thickness, m δ+ = Dimensionless film thickness, δu/ ν φ = Roughness enhancement factor, dimensionless μ = Liquid viscosity, kg/m s ρ = Liquid density, kg/m3
τ = Interfacial shear stress, N/m2
Subscripts ex = Exterior G = In gas phase i = In the interface in = Interior L = In the liquid phase lm = Logarithmic mean w = In the wall
layer problems. Computer Physics Communications, 19: 171-178. Ahmad S., Ismail Z., Samsi J. 1998. Palm based sulphonated methyl esters and
soap. Journal of Oil Palm Research, 10(1): 15-34. Ahmad S., Siwayanan P., Abd Murad Z., Abd Aziz H., Seng Soi H. 2007. Beyond
Biodiesel. Methyl Esters as the Route for the production of Surfactants Feedstock. International News on Fats, Oils and Related Materials, 18: 216-220.
Akanksha, Pant K.K., Srivastava V.K. 2007. Modeling of sulphonation of tridecylbenzene in a falling film reactor. Mathematical and Computer Modelling, 46: 1332-1344.
15
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Broström A. 1975. A mathematical model for simulating the sulphonation of dodecylbenzene with gaseous sulphur trioxide in an industrial reactor of votator type. Chemical Engineering Research and Design, 53: 29-33.
Cramer J.C. 2002. Essentials of Computational Chemistry. Theories and Models. John Wiley & Sons, Ltd. USA.
Dabir B., Riazi M.R., Davoudirad H.R. 1996. Modeling of falling film reactors. Chemical Engineering Science, 51: 2553-2558.
Davis E.J., Van Ouwerkerk M., Venkatesh S. 1979. An analysis of falling film gas–liquid reactor. Chemical Engineering Science, 34: 539-550.
de Groot W.H. 1991. Sulphonation technology in the detergent industry. Kluwer Academic Publisher. Dordrecht, The Netherlands.
Frisch M.J., Trucks G.W., Schlegel H.B., Scuseria G.E., Robb M.A., Cheeseman J.R., Montgomery J.A. Jr., Vreven T., Kudin K.N., Burant J.C., Millam J.M., Iyengar S.S., Tomasi J., Barone V., Mennucci B., Cossi M., Scalmani G., Rega N., Petersson G.A., Nakatsuji H., Hada M., Ehara M., Toyota K., Fukuda R., Hasegawa J., Ishida M., Nakajima T., Honda Y., Kitao O., Nakai H., Klene M., Li X., Knox J.E., Hratchian H.P., Cross J.B., Adamo C., Jaramillo J., Gomperts R., Stratmann R.E., Yazyev O., Austin A.J., Cammi R., Pomelli C., Ochterski J.W., Ayala P.Y., Morokuma K., Voth G.A., Salvador P., Dannenberg J.J., Zakrzewski V.G., Dapprich S., Daniels A.D., Strain M.C., Farkas O., Malick D.K., Rabuck A.D., Raghavachari K., Foresman J.B., Ortiz J.V., Cui Q., Baboul A.G., Clifford S., Cioslowski J., Stefanov B.B., Liu G., Liashenko A., Piskorz P., Komaromi I., Martin R.L., Fox D.J., Keith T., Al-Laham M.A., Peng C.Y., Nanayakkara A., Challacombe M., Gill P.M.W., Johnson B., Chen W., Wong M.W., González C., Pople J.A., Gaussian Inc., Wallingford CT. 2004. Gaussian 03, Revision C.02.
Gutiérrez G.J., Mans T.C., Costa L.J. 1988. Improved mathematical model for a falling sulfonation reactor. Industrial and Engineering Chemistry Research, 27 (9): 1710-1707.
Habib I.S., Na T.P. 1974. Prediction of heat transfer in turbulent pipe flow with constant wall temperature. Journal of Heat Transfer, Transactions of the ASME, 96C:253.
Hiss T.G., Cussler E.L. 1973. Diffusion in high viscosity liquids. AIChE Journal, 19(4):698-703.
Johnson G.R., Crynes B.L. 1974. Modelling of a thin–film sulfur trioxide sulfonation reactor. Industrial and Engineering Chemistry Process Design and Development, 13(1): 6-14.
Kapur B.L., Solomon J.M., Bluestein B.R. 1978. Summary of the technology for the manufacture of higher alpha–sulfo fatty acid esters. Journal of the American Oil Chemists’ Society, 55: 549-557.
16
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
Knaggs E. 2004. Comment on “Optimization of the linear alkyl benzene sulfonation process for surfactant manufacture” and “Sulfonation technology for anionic surfactant manufacture”: Falling Film SO3 Sulfonation – Laminar or Turbulent Flow Controversy. Organic Process Research and Development, 8(6): 1079-1080.
Lim W.H., Ahmad S. 2001. Surface tension, foaming and detergency properties of mixed alpha-sulphonated methyl esters derived from palm stearin with some commercial surfactants. Journal of Oil Palm Research, 13(1): 75-83.
McCready M.J., Hanratty T.J. 1984. Gas transfer at water surfaces. Vol. 283. D. Reidel Dordrecht, Holland: Publishing Company.
Moretti G.F., Adami I. 2002. SO3-sulphonation: Evolution of process design as a function of update feedstock and surfactant quality specifications. R&D Department – Ballestra S.p.A.
Reid R.C., Prausnitz J.M., Poling B.E. 1987. The properties of gases and liquids. Fourth Edition. McGraw-Hill Book Company, New York.
Riazi M.R., Faghri A. 1986. Effect of the interfacial drag on gas absorption with chemical reaction in a vertical tube. AIChE Journal, 32(4): 696-699.
Roberts D.W. 2001. Chapter 3: Manufacture of anionic surfactants. Oleochemical Manufacture and Applications. Edited by Frank D. Gustone and R. J. Hamilton. Sheffield Academic Press. CRC Press UK. 55-73. Roberts D.W. 2003. Optimization of linear alkyl benzene sulfonation process for
surfactant manufacture. Organic Process Research and Development, 7(2): 172-184.
Roberts D.W. 2007. The origin of colour formation in methyl ester sulfonation. Comunicaciones presentadas a las Jornadas del Comité Español de la Detergencia, 37: 153-159.
Roberts D.W, Giusti L., Forcella A. 2008. Chemistry of methyl ester sulfonates. A supplement special: Surfantant from Biorenewable Resourses. International News on Fats, Oils and Related Materials, 5: 2-9.
Stein W., Baumann H. 1975. α-sulfonated fatty acids and esters: manufacturing process, properties and applications. Journal of the American Oil Chemists’ Society, 52: 323-329.
Talens A.F.I. 1999. The modelling of falling film chemical reactor. Chemical Engineering Science, 54: 1871-1881.
Talens F.I., Gutiérrez J.M. 1995. Shorter communication: Estimation of the viscosity and density of lauryl alcohol/laurylsulphuric acid mixtures as a function of the temperature and laurylsulphuric acid molar fraction. Chemical Engineering Research and Design, 73 Part A: 206-207.
Torres O.J.A., Díaz A.L.A., Sánchez C.F.J. 2008a. Kinetic study of the sulfonation of methyl esters derived from palm stearin. Revista Corpoica, 9(2): 88-95.
17
Torres Ortega et al.: Mathematical Model of Falling Film Reactor
Published by The Berkeley Electronic Press, 2009
Torres O.J.A., Narváez R.P.C., Suárez P.O.Y., Sánchez C.F.J. 2008b. Sulfonation of methyl esters derived from palm oil. Revista Corpoica, 9(2): 77-87.
Torres O.J.A., Narváez R.P.C., Ponce de León Q.L.F., Sánchez C.F.J. 2005. Production of methyl stearate derived of hydrogenated stearin palm. Revista de Investigaciones de la Unad, 4(2):150-162.
Vignes A. 1966. Diffusion in binary solutions: Variation of diffusion coefficient with composition. Industrial and Engineering Chemistry Fundamentals, 5: 189-199.
Wilke C.R., Chang P. 1955. Correlation of diffusion coefficients in dilute solutions. AIChE Journal, 1(2): 264-270.
Yih S.M., Liu J.L. 1983. Prediction of heat transfer in turbulent falling liquid films with or without interfacial shear. AIChE Journal, 29(6): 903-909.
Young D.C. 2001. Computacional Chemitry. Chapter 35. Wiley-Interscience. Jhon Wiley & Sons, Inc. New York.
18
Chemical Product and Process Modeling, Vol. 4 [2009], Iss. 5, Art. 12
