Determination of the Kinetics of the Ethoxylation of Octanol in

Article pubs.acs.org/IECR

Determination of the Kinetics of the Ethoxylation of Octanol in Homogeneous Phase Pascal D. Hermann,† Toine Cents,‡ Elias Klemm,† and Dirk Ziegenbalg*,† †

Institute of Chemical Technology, University of Stuttgart, 70569 Stuttgart Germany Sasol, Group Technology, 1947 Sasolburg, South Africa

‡

S Supporting Information *

ABSTRACT: A two-dimensional computational fluid dynamics model was utilized to test different kinetic models for the description of the anionic polymerization of octanol with ethylene oxide in a microreactor. The reaction was performed as a continuous reaction under elevated pressure and temperatures in a one-phase system. The kinetic parameters were determined with numerical methods by reducing the deviation to experimental data based on the Nelder−Mead method. Four different reaction models with one, two, three, and four different rates for the first propagation steps were tested. The best agreement with the experimental data was found for the four rate model, with a prediction accuracy close to the experimental error. The gathered data suggests an increasing reaction rate for the first four propagation steps, which is in agreement with the Weibull−Törnquist effect [Weibull and Törnquist. Berichte vom VI. Internationalen Kongress für Grenzflächenaktive Stoffe, Zürich, vom 11. bis 15. September 1972; Carl Hanser Verlag: Munich, 1972; p 125; Sallay et al. Tenside Deterg. 1980, 17, 298].

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INTRODUCTION The industrial production of nonionic surfactants is conducted by base-catalyzed reactions of hydrophobic compounds containing an abstractable hydrogen, such as alkylphenols, fatty alcohols, fatty acids, thiols, or alkylamines, with ethylene oxide or propylene oxide.3 As one important product, ethoxylated fatty alcohols were valued to be $5.125 billion with a production of 3.27 million tons in 2014.4 The conventional process is carried out semibatchwise in stirred tank reactors by introducing ethylene oxide into the gas phase or into the liquid reaction mixture with the alcohol/ alcoholate substrate. The usual process conditions are 150− 180 °C and 200−500 kPa with the reaction occurring in the liquid phase.5 However, this type of process can possess masstransfer limitations due to the dissolution process of the gaseous ethylene oxide in the reaction mixture. This process is slow compared to the rapid consumption of the solved ethylene oxide and with this reduces the productivity.5,6 Furthermore, the heat transfer capability of this type of reactor is limited. Hence, it is necessary to slow down the reaction by slowly dosing the ethylene oxide to prevent a thermal runaway of this highly exothermic reaction. Thus, the productivity in a stirred tank reactor can be limited by both the mass transfer limitation and the heat removal capabilities of the vessel. Additionally, the rising pressure during reaction must be handled due to possible safety issues. To intensify the process and improve the safety, the process was transferred to continuous operation in a microreactor in preliminary work by Rupp et al.7−9 Microreactors generally show improved heat transfer capabilities and better resistance to pressure, enabling operation in a single phase system under © XXXX American Chemical Society

elevated pressures and temperatures. However, problems in reaction handling were also found during the experiments for a microstructured reactor: the formation of hot spots was observed.9 For a correct description of this behavior it was necessary to create a robust model with good prediction and extrapolation capabilities. Ethoxylations in two-phase systems are usually modeled by assuming a single propagation rate constant and an equilibrium constant for the proton transfer reaction between the anionic and protonized species for all products and the alcohol as well as considering the dissolution process of ethylene oxide (EO) in the liquid reaction mixture. Temperatures of 180−240 °C and pressures of 9000−10 000 kPa were used in this work and the work of Rupp,9 that share large parts of the experimental data. This exceeds the ranges investigated by the other works. A detailed list of the used process conditions and the resulting phase system of various published work is given in the Supporting Information. Furthermore, it is worth mentioning that the publications utilizing a batch reactor often face the problem of a low number of experiments as a result of the rather long reaction times and larger reactor volumes compared to that of a microreactor. Indeed, benefits of using a microreactor are the possibilities to conduct numerous experiments in a relatively short time and to ensure isothermal conditions by simply using a very small diameter of the reactor. Hence, the number of experiments used for the determination Received: Revised: Accepted: Published: A

March 6, 2017 May 5, 2017 May 8, 2017 May 8, 2017 DOI: 10.1021/acs.iecr.7b00948 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research of the kinetics in both the publication of Rupp9 and this work exceeds 200 experiments. For conditions with elevated pressures and high temperatures in a one-phase system, Rupp et al.7−9 used a plug flow reactor (PFR) model to describe the product distribution and determine the kinetic parameters. One disadvantage of this approach is that radial temperature and concentration gradients of the individual species cannot be resolved. Consequently, a computational fluid dynamics (CFD) model was developed to take these influences into account. Due to the higher complexity of a CFD model and the computational effort resulting from this, it was not meaningful to directly implement the kinetic model of the PFR model into the CFD simulation. This applies especially for the assumption of a limiting proton transfer reaction with different proton transfer rate constants for different equivalents of ethylene oxide (equiv EO). A further limitation of the previously used kinetic approach is that this model can not be easily transferred to other equiv EO. To avoid these problems, this work presents a more general kinetic model that includes extrapolation capabilities to different equiv EO. The applicability of the developed more general kinetic models together with a model discrimination will be demonstrated in this publication. For this, four different kinetic models that exclude the influence of a proton transfer were used in CFD simulations and compared by means of statistical numbers. Additionally, the same methods were used for a PFR model to test the necessity of a two-dimensional (2D) CFD model.

Figure 1. The 9° cylinder segment model.

at the pipe wall. This resulted in a pseudo-3D model that shows both good performance and precision and is able to resolve radial gradients. A detailed description of the derivation of all necessary equations and the description of the physical properties has been already published in previous work.11 Furthermore, it could be shown that mass transport limitations in the system will only occur for average chain lengths above 20. The kinetic experiments used in this work used a maximum of 9 equiv of ethylene oxide per octanol. Consequently, mass transfer limitations can be excluded. A further approach to decrease the computational effort was to reduce the number of simulated species because the calculation time scales with the number of simulated species. This was accomplished by introducing a pseudoproduct species that averages the molar mass of all higher ethoxylated products. The average molar mass of the product for a polymerization can be written as11

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MODELING AND SIMULATION Reaction Modeling. The simulations were performed in Ansys CFX 16.1. The set of equations that is used by this software are the unsteady Navier−Stokes equations in their conservative form. The following governing equations for mass, momentum, and energy conservation were used:10

M Ps = (M̅ P −

continuity: ∂ρ + ∇(ρu) = 0 ρ ∂t

∂ρu + ∇(ρu ⊗ u) = −∇p + ∇τstress + SM ∂t

s−1

∑ xiMPi)(1 −

∑ xi)−1

i=0

i=0

(3)

MPs is the molar mass of the pseudoproduct species, that is a sum of all products with a chain length of s and higher, xPi is the mole fraction, and MPi is the molar mass of the i-fold ethoxylated product after removal of EO, with i = 0 being octanol. This molar mass of the pseudoproduct species averages the molar mass of all higher polymerized products and can be used to describe a pseudoproduct species that is the sum of all higher polymerized species. This equation is general and applicable for all polymerizations. The average molar mass M̅ P of the product as a function of the conversion can be written for the ethoxylation of octanol as

(1)

In this equation ρ is the density, u is the velocity, and t is the time. momentum: ρ

s−1

(2)

with the stress tensor being ⎛ ⎞ 2 τstress = μ⎜∇u + (∇u)T − δ∇u⎟ ⎝ ⎠ 3

M̅ P = Moctanol + XEO·equivEO ·MEO

with pressure p and the source of momentum SM. In general, CFD simulations face the problem of a high computational effort especially for three-dimensional (3D) models that is typically not suited for numerical optimizations as used for the determination of the kinetic parameters in this work. Thus, a 9° cylinder segment with one cell width and symmetry boundaries on both sides, as shown in Figure 1, was used to minimize the computational demands of the simulation. This model was used with reactor lengths between 1 and 4 m and a diameter of 250 μm. Due to the small diameter, a laminar flow regime and isothermal conditions were assumed with a fully developed inlet flow. A no-slip boundary condition was set

0

(4)

In this equation equivEO0 is the number of EOs per octanol at the inlet of the reactor and XEO is the conversion of ethylene oxide. In a first step the fatty alcohol, octanol in this work, was partly deprotonized by adding KOH. The water was removed from the alcohol/alcoholate mixture afterward. In various publications it is assumed that for such conditions only the anionic species is responsible for the chain growth reaction or at least the reaction of the nonionic species is negligible.3,7−9,12−17 Thus, it is assumed that only the anionic B

DOI: 10.1021/acs.iecr.7b00948 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research dmP0

species is active for the chain reactions. The reaction chain starts through reaction of octanolate with ethylene oxide to the first product species.

dt

= −k1xcatM P0ρ2

wP0 wEO M P0 MEO

(8)

In this equation P0 represents octanol, P1 is the product with a chain length of one, EO is ethylene oxide, M is the molar mass, w is the mass fraction, and k1 is the rate constant of the first step. For 1 ≤ i < s with s being the chosen highest simulated species and thus defined as a pseudoproduct species, this leads for each species i to the following mass change rate:

Reaction of the anionic species with ethylene oxide continues and results in a growing ether chain.

dmPi dt

= kixcatM Piρ2

wP w wPi−1 wEO − ki + 1xcatM Piρ2 i EO M Pi MEO M Pi−1 MEO (9)

For the pseudoproduct species this results in dmPs

Additionally, there is a proton transfer reaction, which leads to a chain growth at a different chain:

dt

= ksxcatM Psρ2

wP w wPs−1 wEO + ksxcatMEOρ2 s EO M Ps MEO M Ps−1 MEO (10)

with Ms being the molar mass of the pseudoproduct species, calculated with eq 3. The mass change rate for ethylene oxide is s ⎛ dmEO w w ⎞ = −MEOρ2 ∑ ⎜kixcat i EO ⎟ dt Mi MEO ⎠ i=0 ⎝

Most publications state that proton transfer is very fast and thus no limitation of proton transfer exists.3,12,14,15,17 Thus, in this work, it is assumed that proton transfer is not limited. It is assumed that a constant fraction of octanolate in octanol and with this of the anionic species per product exists, that is identical to the molar fraction xcat of octanolate per octanol at the inlet: noct 0− xcat = noctH0 + noct 0− (5)

Determination of Kinetic Models. The experimental data was measured by Rupp et al. in a lab-scale reactor.9 The experiments were performed at four temperatures (180, 200, 220, 240 °C) with 3, 6, and 9 equiv EO and a concentration of 0.66 mol % octanolate in octanol. The reactions were conducted in a tempered capillary reactor with a length of 4 m. To ensure isothermal behavior, the experiments were performed in a reactor with an inner diameter of 250 μm.9 The experimental data contains information on the molar fraction of octanol and the products after removal of EO: nP x Pi = s i ∑ j = 0 nPj (12)

This was implemented as a constant factor for all products and octanol. This assumption is possible because water was removed from the reaction mixture previously and the absence of a solvent. Four different kinetic models were tested. The one-rate model assumes a constant rate constant for all steps (k1 = k2 = k3 = kp). The two-rate model assumes a different rate constant for the first step and a constant for all following steps (k1; k2 = k3 = kp); the three-rate model assumes different rate constants for the first two steps and a constant rate constant for the third and all following steps ((k1; k2; k3 = kp). Consequently, the four-rate model assumes a different rate constant for the first three reaction steps and a constant rate constant for all following reaction steps (k1; k2; k3; kp). To implement the concentration change in the CFD model, the rate of concentration change was transferred into mass change rates: dmPi

nPi is the amount of the i-fold ethoxylated product with P0 = octanol and s is the highest ethoxylated product measured. The experimental data was measured up to s = 14. In this work, the kinetic parameters were numerically determined by utilizing the described CFD model. This was done by minimizing the deviations between simulated and experimental data. More precisely, the sum of the relative squared error RSSE was minimized with a Python based script using the Nelder−Mead algorithm.18 The sum of the relative squared error was calculated as shown in eq 13: 2⎞ ⎛ l ⎛ x Pisimn − x Piexpn ⎞ ⎟ ⎜1 ⎟ RSSE = ∑ ⎜ ∑ ⎜⎜ ⎟ ⎟⎟ ⎜l x Piexpn ⎠⎠ i=0 ⎝ n=1 ⎝ s

dci (6) dt dt For a second order reaction the change in concentration can be written as = M Pi

dci = kpic1c 2 dt

(11)

(13)

l is the number of experiments used, xPisimn is the simulated mole fraction of product i after removal of EO for experiment n and species i, and xPiexpn is the experimental mole fraction. The model for the determination of the kinetic constants used s = 4; thus the 4-fold ethoxylated product is a pseudospecies. The reaction rate is calculated with the Arrhenius equation:

(7)

ρwiMi−1,

For octanol, this results with ci = together with eq 6 and inserting eq 5 in the following equation for the rate of mass change:

ki = k 0i e−EAi / RT C

(14) DOI: 10.1021/acs.iecr.7b00948 Ind. Eng. Chem. Res. XXXX, XXX, XXX−XXX

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Industrial & Engineering Chemistry Research Table 1. Determined Arrhenius Parameters for the Four Different Models k0p (m3 mol−1 s−1) EAp (kJ mol−1) k01 (m3 mol−1 s−1) EA1 (kJ mol−1) k02 (m3 mol−1 s−1) EA2 (kJ mol−1) k03 (m3 mol−1 s−1) EA3 (kJ mol−1)

one-rate model

two-rate model

three-rate model

four-rate model

(35 ± 67) × 104 80.5 ± 4 k0p EAp k0p EAp k0p EAp

(1.5 ± 0.5) × 104 62.6 ± 0.5 (20 ± 7) × 104 78.0 ± 0.6 k0p EAp k0p EAp

(5.3 ± 2.9) × 104 66.3 ± 2 (11 ± 17) × 104 75 ± 4 (1.7 ± 0.5) × 104 64 ± 1 k0p EAp

(7.4 ± 0.7) × 104 67.5 ± 0.2 (7 ± 1) × 104 73.2 ± 0.6 (1.3 ± 0.1) × 104 62.6 ± 0.3 (6.9 ± 0.8) × 104 68.3 ± 0.4

with k0i being the preexponential factor, EA being the activation energy, R being the universal gas constant, and T being the temperature in kelvin. During the determination process k0i and EA were varied. To improve numerical stability of the optimization algorithm, the Arrhenius equation was used in a reparametrized form for the optimization. Additionally, this way the high error of the determination of k0i is reduced. A reduced set of 37 experiments measured in the 4 m capillary was used for the determination of the kinetic parameters and afterward validated by 188 experiments measured with capillary lengths of 1, 1.5, 3, 3.5, and 4 m by Rupp.9 To evaluate which model gives the best precision without overfitting, the Akaike information criteria (AIC) was used.19 For a set of models for the same data, the preferred model is the one with the minimum AIC value. ⎛ ⎞ SSE ⎟ AIC = qexp ln⎜⎜ ⎟ + 4rrates ⎝ qexp ⎠

relative mean difference (RMD): −1 ⎛ ∑l (|x ⎞ Pnsimi − xnexpi|xnexpi) ⎟ −1 i=0 ⎜ RMD = ∑ ⎜ ⎟s l ⎠ n=0 ⎝ s

sum of the squared error (SSE): SSE =

■

s

⎛ ∑l

∑ ⎜⎜ n=0

⎝

i=0

(|x Pnsimi − xnexpi|) ⎞ −1 ⎟s ⎟ l ⎠

⎛1

l

i=0

⎝l

n=1

i simn

⎞ − x Piexpn)2 ⎟⎟ ⎠

(19)

RMSE =

RSSE

(20)

RESULTS AND DISCUSSION Kinetic Parameters. The determined activation energies (EAi) and preexponential factors (k0i) for the temperature dependency of the rate constants described with the Arrhenius equation (see eq 14) are listed for the four different tested models in Table 1. Model Evaluation. The parity plots in Figure 2 show the precision of the different models for all data used for the determination of the kinetic parameters. In these figures xsim is the simulated mole fraction after removal of EO and xexp is the experimentally measured mole fraction. The one-rate model shows a large deviation from the experimental data for all products. Additionally, all products except octanol show a wrong trend that clearly indicates wrong model assumptions. The two-rate model shows an improved precision but still significant trends in the deviations to the experimental data for product 1 and product 3. The three-rate model and four-rate model both show a good precision with smaller differences. The four-rate model shows a slightly improved precision for product 2 compared to the three-rate model. To decide which model shows the best prediction without overfitting the data, it is possible to calculate different typical error numbers and the Akaike information criteria. These values are listed in Tables 2 and 3. In these tables, e.g., “1r-4p” means the one-rate model with the fourth product as pseudoproduct species and “4r-14p” means the four-rate model with the 14th product as pseudoproduct species. As shown in Table 2, the one-rate model (1r-4p) and tworate model (2r-4p) show large errors and values for AIC as well as a negligible likelihood compared to the three-rate model and four-rate model. Hence, these models can be rejected. Comparing the 3r-4p and 4r-4p models gives a different situation. The four-rate model shows a slightly lower AIC; the likelihood of the three-rate model is 70% compared to the fourrate model. Still, the likelihood is too high for rejecting the

(15)

(16)

AICmin is the smallest AIC of all models and AICn is the AIC of model n. In addition, different numbers were calculated to statistically evaluate the errors of the investigated models: mean difference (MD): MD =

s

∑ ⎜⎜ ∑ (xP

and the relative root mean squared error RMSE that is the root of the sum of the relative squared error (RSSE) as described in eq 13:

In this equation qexp is the number of used experiments, SSE is the sum of the squared deviations in mole percent between the simulated and experimentally measured values, and rrates is the number of different rates used for modeling the reaction (1 for the one-rate model, 2 for the two-rate model, etc.). The AIC rewards the goodness of fit but also includes a penalty that is increased with the number of used fitting parameters because an increased number of parameters in the model almost always improves the calculated goodness of a fit. The relative likelihood L of a model n compared to the model with the lowest AIC can be determined with the following equation:

Ln = e((AICmin − AICn)/2)

(18)

(17)

In this equation xPnsimi is the simulated mole fraction of product n in experiment i, xnexpi is the experimental value of experiment i, s is the number of simulated species with species s being the pseudoproduct species, and l is the number of used experiments. D


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Figure 2. Parity plots for octanol, product 1, product 2, product 3, and the pseudoproduct species for all higher ethoxylated products. The black dotted lines give the ±10% error.

model. The mean difference MD of the four-rate model is slightly better, but the relative mean difference RMD is worse.

The sum of the squared error (SSE), the sum of the relative squared error (RSSE), and the relative root mean squared error E


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Industrial & Engineering Chemistry Research Table 2. Errors and Likelihood of the Four Tested Models 1r-4p to 4r-4p or the Four Product Species Modela model 1r-4p 2r-4p 3r-4p 4r-4p a

nexp

xA− (mol %)

37 37 37 37

AIC

0.66 0.66 0.66 0.66

68.67 4.89 −18.10 −18.82

Li (%) −17

1.01 × 10 7.09 × 10−4 70 100

MD (mol %)

RMD (%)

SSE

RSSE (%2)

RMSE (%)

8.1 3.4 2.2 2.0

19 11 8.4 9.7

2.3 0.58 0.36 0.35

45 12 7.2 7.0

6.7 3.4 2.7 2.6

nexp is the number of used experiments; xA− is the molar fraction of anionic species in octanol.

Table 3. Errors and Likelihood of the 14-Species Model model

nexp

xA− (mol %)

AIC

Li (%)

MD (mol %)

RMD (%)

SSE

RSSE (%2)

RMSE (%)

3r-14p 4r-14p

37 37

0.66 0.66

−22.29 −25.46

21 100

0.90 0.79

7.65 9.78

4.59 4.28

30.63 28.54

5.53 5.34

Figure 3. Parity plots for the four-rate model with octanol, product 1, product 2, product 3, and the pseudoproduct species for all higher ethoxylated products. The blue data points were used for fitting, while all red crosses are predicted. The black dotted lines give the ±10% error.

Table 4. Prediction Precision of the Four-Rate Models with Four Product Species (4p) and 14 Product Species (14p) Compared to the Experimental Error (exp) model

nexp

xA− (mol %)

MD (mol %)

RMD (%)

SSE

RSSE (%2)

RMSE (%)

4r-4p 4r-14p exp-4p exp-14p 4p-4p 4r-14p

188 188 11 11 22 22

0.66 0.66 0.66 0.66 0.83 0.83

2.79 0.98 0.95 0.32 4.07 5.60

12.74 18.40 22.33 14.00 0.99 10.36

0.57 4.63 0.54 8.42 0.62 0.90

11.38 30.85 10.75 56.16 12.46 43.82

3.37 5.55 3.28 7.49 3.53 6.62

(RMSE) are slightly better for the four-rate model. But the differences between these two models are too small to discriminate between them. Thus, a more detailed investigation is necessary to make a decision. In comparison to the determined experimental error, both models show an even lower value. To decide if the three-rate model is sufficient, the number of simulated species was increased to product 14, with product 14 being the pseudoproduct species. The results are summarized in Table 3. The parity plots can be found in the Supporting Information. Even for these models the AIC and the error values, except for the RMD, are improved for the four-rate

model and the likeliness of the three-rate model further decreases to 21%. Thus, it can be assumed that the four-rate model is the best model. Prediction Capabilities. To test the prediction capabilities of the developed model, the number of simulated experiments was increased by 151 experiments in reactors with the same diameter but lengths of 1, 1.5, 2.5, and 3.5 m resulting in 188 simulated experiments in total. The results are shown in Figure 3 and Table 4. The experimental error was calculated by 11 reproduction experiments (exp-4p and exp-14p). If the experimental error is compared to the error of the simulation, it is obvious that for all used error values the experimental error F


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Figure 4. Parity plots for the four-rate model with four product species for a different concentration of the anionic species (0.83 mol %). The black dotted lines give ±10% error.

Figure 5. Temperature dependency between 180 and 240 °C of all rate constants for the three-rate model and four-rate model.

be explained by the complexation of the cation K+ by the oxygen of the ether chain of the product, as exemplary shown for P4 in Figure 6. This complex causes a weakening of the ion

is similar to the prediction error of the simulation. Hence, it can be concluded that the model has good prediction capabilities. Additionally, the assumption of a constant molar fraction of the active anionic species in each product species and octanol was tested by comparing the simulated values with 22 experiments performed with a different catalyst concentration (0.83 mol %) with a reactor length of 2.5 m and a diameter of 250 μm (same as before). The results are shown in Figure 4 and in Table 4. Again, the relative errors are comparable to the experimental error and the general trends are correct with a somewhat higher absolute spreading than for a lower catalyst concentration of xA− = 0.66 mol %. However, this was expected due to the faster reaction rate for a higher catalyst concentration and thus higher conversion rate and mole fractions of the individual species leading to a higher absolute difference. It can be concluded that the assumption of a constant fraction of active anionic species seems to be correct and the model can be transferred to a different concentration of anionic species. Increase of Rate Constants. For both the three-rate and the four-rate model, an increase of the rate constants for every reaction step can be observed (see Figure 5). This finding can

Figure 6. Weibull−Törnquist complex.

pair bond between the cation and alkoxylate, making the alkoxylates more reactive. The reactivity increases with the increasing chelate effect, which is observed for an increasing chain length. This effect is known as the Weibull−Törnquist effect, which typically leads to an increasing propagation rate for the first six products.1,2,20 It is also responsible for the typical broadening of the product distribution. The general acceleration of the reaction rate by complexation was experimentally validated by Rupp et al.9 by adding crown ether to the reaction mixture. Indeed, a significant increase of G


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Industrial & Engineering Chemistry Research Table 5. Precision of the PFR Models Compared to the Favored CFD Model model

nexp

xA− (mol %)

AIC

MD (mol %)

RMD (%)

SSE

RSSE (%2)

RMSE (%)

PFR 1r-14p PFR 2r-14p PFR 3r-14p PFR 4r-14p PFR 5r-14p PFR 6r-14p PFR 7r-14p PFR 8r-14p CFD 4r-14p

37 37 37 37 37 37 37 37 37

0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66 0.66

121 95 95 98 102 105 109 113 −25.46

20.14 8.19 2.36 1.76 1.85 2.23 2.43 2.18 0.79

61.95 35.46 32.11 30.60 30.11 30.17 30.23 30.48 9.78

302.17 122.87 35.36 26.44 27.73 33.40 36.40 32.70 4.28

867.11 384.44 352.17 343.45 337.72 334.41 331.27 329.80 28.54

29.45 19.61 18.77 18.53 18.38 18.29 18.20 18.16 5.34

the reaction rate was found as a consequence of complexation by the crown ether. The kinetic model of this work is limited to four rates, although the Weibull−Törnquist effect predicts an influence up to six species. In fact, it is likely to find an increased rate for the first six propagation steps. Despite this, the fraction of highly ethoxylated products is small in the experimental data measured. Including this data point in the calculation lowers the accuracy of the model. Furthermore, increasing the number of parameters together with the necessary higher number of simulated species would significantly increase the calculation time with no superior improvement of prediction. In fact, even the increase of prediction precision from the three-rate model to the four-rate model was only moderate. However, for investigations more focusing on long chained products, it might be necessary to increase the number of different rate constants up to six. Comparison CFD to PFR. The study to determine the kinetic parameters was also conducted with a PFR model using the same experimental data set with a 14-product model and with a possible larger number of reaction rates up to eight. The precision of each of the models is shown in Table 5. Detailed results for the kinetic parameters are available in the Supporting Informations. Compared to the CFD model, the PFR model shows a considerably worse precision even with a larger number of different propagation rates. However, for a PFR approach, a two- or three-rate model is favored by AIC. A significant improvement by using more than four rates was not observed. As shown in Figure 7, the PFR model also shows the best performance for an increase of the propagation rate with the chain length. Comparison to Other Work. The propagation rate constants of various publications are shown in Figure 8. Detailed data of the propagation rates are listed in Table 6.

Figure 8. Plot of the temperature dependency of various published propagation rates.3,9,13−17 The blue graphs represent ethoxylations of octanol, red graphs represent ethoxylations of dodecanol in semibatch, purple graphs represent ethoxylations of dodecanol in other reactor types, and green graphs represent this work.

Most of the published reaction models assume the same reaction rate constant for the first and the following steps. With the exception of Hall and Agrawal13,16 and Rupp et al.,9 the kinetics are measured in a semibatch reactor in a two-phase system. In most publications it is assumed that the solubility is not limiting for temperatures below 200 °C. The propagation rate constant determined in this work is slightly larger than most published rates. This directly results from the kinetic model used in this work, which uses four rate constants to describe the reaction. If a smaller number of rate constants is used, these rate constants mathematically compensate all the rate constants that were not implemented in the model but are relevant in reality. The large deviation of the rate constant determined by Fan et al.,16 which is the only work for a continuous process in a small pipe reactor, is attributed to the nonisothermal kinetic measurements. The authors used a reactor with a diameter of 4 mm and assume a one-phase system at 35 bar. As could be shown recently, such large reactor diameters face problems in heat management even for one-phase systems.11 Fan et al.16 also show in their work that the internal temperature rises above 200 °C at cooling temperatures of 110 °C. Rupp9 showed that a mixture of octanol and ethylene oxide needs 65−70 bar to mix in a single phase at 200 °C. Thus, it is most likely that Fan et al.16 could not ensure measurements under one-phase conditions, leading to mass transfer limitation between the two phases. This can explain the lower rate constant compared to other publications. In summary, the propagation rate constant determined in this work is in the same region as already published results, but slightly faster. The rate constants for the three first steps k1−k3 determined in this work also span the region of published values.

Figure 7. Temperature dependency between 180 and 240 °C of all rate constants for the six-rate PFR model. H


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Industrial & Engineering Chemistry Research Table 6. Overview of Published Propagation Rates for the Ethoxylation of Fatty Alcohola 13

Hall (1990) Santacesaria (1992)3 Di Serio (1995)14 Di Serio (1996)15 Fan (2000)16 Amaral (2011)17 Rupp (2015)9 Hermann (2017) a

alcohol

k0ip (m3 mol−1 s−1)

error + (m3 mol−1 s−1)

error − (m3 mol−1 s−1)

EAp (kJ mol−1)

error (kJ mol−1)

dodecanol dodecanol octanol dodecanol dodecanol dodecanol octanol octanol

4024 660 820 600 1967 79580 199000 74000

n.a. 230 230 210 n.a. n.a. 44000 7000

n.a. 170 180 150 n.a. n.a. 36000 7000

55.2 55.6 54.4 55.3 82.8 71.61 73.0 67.5

n.a. 1.0 7.5 1.3 n.a. n.a. 0.7 0.2

In this table k0ip is the preexponential factor and EAp is the activation energy as described in eq 14.

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The work of Rupp et al.,8 which shared large parts of the experimental data, assumes a coupled first rate constant to the propagation rate constant (k1 = 0.55kp). The results for 3, 6, and 9 equiv EO were corrected by different rate constants for the proton transfer. However, the results presented in this work indicate that it is possible to describe the product distribution correctly without a limiting proton transfer equilibrium and with a more general model with prediction capabilities. This could be achieved by use of independent rate constants for the first four propagation steps. The product distribution can be described by an increase of the rate constants for the first four steps. The observed Weibull−Törnquist effect, which is wellknown for ethoxylations with KOH, but was not explicitly implemented in the kinetic model presented here, additionally supports the suitability of the developed model for the description of ethoxylations.8

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CONCLUSION The results presented in this work indicate that a four-rate model describes the reaction the best without overfitting. The commonly used approach to describe the kinetics of ethoxylations with a proton transfer equilibrium and one propagation step may be sufficient to describe the reaction in a two-phase system with comparable low temperatures. Nevertheless, for one-phase systems with elevated pressures and temperatures this is not the case. Furthermore, the increasing rate constants explain the experimentally observed difficulties in preventing hot spots. Overall, the slow initial step limits the productivity of the whole process. Increasing the productivity by use of a larger amount of anionic species may easily lead to thermal runaway as a result of the faster reaction rate. With this, heat management might be the most crucial point, which should be considered during the reactor design.

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REFERENCES

(1) Weibull, B.; Törnquist, J. Distribution of Polymer Homologues in Ethylene Oxide Adducts. Berichte vom VI. Internationalen Kongress für Grenzflächenaktive Stoffe, Zürich, vom 11. bis 15. September 1972; Carl Hanser Verlag: Munich, 1972; pp 125−138. (2) Sallay, P.; Morgos, J.; Farkas, L.; Rusznak, I.; Veress, G.; Bartha, B. Complex forming effect of the product in ethoxylation in the presence of sodium hydroxide. Verification and theoretical interpretation of the Weibull-Toernquist effect. Tenside Deterg. 1980, 17, 298−300. (3) Santacesaria, E.; Di Serio, M.; Garaffa, R.; Addino, G. Kinetics and mechanisms of fatty alcohol polyethoxylation. 2. Narrow-range ethoxylation obtained with barium catalysts. Ind. Eng. Chem. Res. 1992, 31, 2419−2421. (4) Alcohol Ethoxylate Market by Application (Household & Personal Care, Pharmaceutical, Oilfield, Agrochemicals, and Others) & Geographies - Global Market Trends, Forecasts to 2019; 2015. http://www.researchandmarkets.com/reports/3292449/alcoholethoxylate-market-by-application. (5) Di Serio, M.; Tesser, R.; Santacesaria, E. Comparison of Different Reactor Types Used in the Manufacture of Ethoxylated, Propoxylated Products. Ind. Eng. Chem. Res. 2005, 44, 9482−9489.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.iecr.7b00948. List of reaction conditions in different published works; parity plots of CFD 14p models; kinetic data and parity plots of PFR 14p models (PDF)

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SYMBOLS AND ABBREVIATIONS CFD = computational fluid dynamics EO = ethylene oxide eg = ethoxylation grade equiv = equivalents c = concentration (mol m−3) i = chain length i j = highest ethoxylated product in the reaction mixture k = reaction rate (mol s−1 m−3) l = number of used experiments MD = mean difference ṁ = mass flow rate (kg h−1) M = molar mass (g mol−1) n = amount of substance (mol) Pi = product with chain length i PFR = plug flow reactor RMD = relative mean difference RSSE = sum of relative squared error SSE = sum of squared error s = defined highest simulated species, averages s-times and higher ethoxylated products u = velocity (m s−1) w = mass fraction x = mole fraction XEO = conversion of ethylene oxide Δ = difference (variable) ∇ = nabla operator η = dynamic viscosity (Pa s)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Dirk Ziegenbalg: 0000-0001-6104-4953 Notes

The authors declare no competing financial interest. I


Article

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Determination of the Kinetics of the Ethoxylation of Octanol in

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