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Effective and Intrinsic Kinetics of the Two-Phase Alkylation of i‑Paraffins with Olefins Using Chloroaluminate Ionic Liquids As Catalyst Stephan Josef Aschauer† and Andreas Jess*,† †

Department of Chemical Engineering, University of Bayreuth, Universitätsstrasse 30, 95440 Bayreuth, Germany ABSTRACT: Acidic ionic liquids (IL) are attractive alternative catalysts in refinery alkylation of i-paraffins with light olefins, but the intrinsic kinetics and influence of mass transfer on the effective kinetics in this biphasic system is still unknown. Solubility measurements were conducted (largely with neutral, nonacidic ILs) using mixtures of i-hexane/2-hexene and i-pentane/ 2-pentene, respectively, to determine the Nernst partition coefficient and thus the maximum concentration of olefins and paraffins in the IL. Thereafter, kinetic studies were carried out both in a stirred and nonstirred batch reactor using i-hexane/ 1-hexene and i-pentane/1-pentene. In the static system, the concentration profile of the particular olefin in the organic phase was measured. The experimental results are in good agreement with the simulation based on the interplay of the chemical reaction in the ionic liquid as well as of the external and internal mass transfer to the interface and into the IL. The effective reaction rate of alkylation is proportional to the interfacial surface area between organic and IL phase: The intrinsic chemical reaction is very fast which leads to a strong mass transfer limitation of the olefin into the IL phase. Hence, the effectiveness (compared to utilization of the entire IL phase) is very low, and the alkylation reaction takes place in a very thin layer with a thickness of only around 5 μm.

1. INTRODUCTION The alkylation of i-paraffins with light olefins (e.g., 1- and 2-butene with i-butane) forming highly branched paraffins (e.g., 2,2,4-trimethylpentane) is an important refinery process since the products of this reaction provide a high octane number and can be considered to be free of sulfur and aromatics.1,2 In the future, the importance of alkylation may even grow: Catalytic reforming of heavy naphtha, which is today still the most important process for high octane gasoline production, yields a gasoline rich in aromatics, but their content in gasoline for sale is more and more limited. Hence, processes like alkylation and isomerization may become increasingly important. To date, the alkylation catalysts used in industry are sulfuric acid or hydrogen fluoride. Both catalysts have significant drawbacks.3 HF is a very efficient catalyst but extremely toxic. So alkylation plants using HF have to be provided with strict and eleborated safety equipment. Sulfuric acid is environmentally less hazardous compared to HF but considerably consumed during the reaction (about 0.1 t/talkylate) and very corrosive. So, alternative less toxic and hazardous catalysts are of great interest for the alkylation process. Promising new alkylation catalysts are highly Lewis acidic ionic liquids (ILs), mainly chloroaluminate based ionic liquids,4−6 where a Lewis acid is dissolved in the ionic liquid. A retrofitted sulfuric acid alkylation unit in China7 and patents disclosed by Chevron describing the use of ILs8−12 and their regeneration13,14 show that IL alkylation is or will probably be applied on a large industrial scale in the near future. While HF and sulfuric acid catalysts are well-described in the literature,1,2 there have been no publications regarding the kinetics and the role of mass transfer on the effective reaction rate in i-paraffin/olefin alkylation with ionic liquids. However the kinetics of alkylating aromats with olefins (Friedel−CraftsAlkylation) without mass transfer limitation are reported by Joni et al.15 In contrast, our contribution reports on effective and © 2012 American Chemical Society

intrinsic reaction rate in aliphatic-alkylation and gives a closer insight into mass transfer of the organic/ionic liquid system. An important parameter to improve the alkylation with ionic liquids is the use of tert-butyl sources (e.g. tert-butylhalides) as described by Rosenbach et al.,16,17 patents disclosed by Chevron,10 and publications from our group.18,19 These promoters enhance the reaction rate by forming the active species, the tert-butyl cation, directly by abstraction of the halide and by suppressing side reactions such as formation of undesired methylheptanes and dimethylhexanes. Chloroaluminate ionic liquids are also applied in other reactions such as the dimerization of propene or 1-butene20,21 or the Difasol Process.22 But in most of these reactions, when a fast homogeneous two-phase reaction is observed, the intrinsic chemical reaction rate and the role of mass transport is not satisfactorily described yet. The kinetics in the biphasic system cumene-[C2mim][Al2Cl7] measured by Joni et al.15 are limited to the chemical reaction rate, thus the mass transfer was not examined. In order to gain more insight into the i-paraffin alkylation reaction and to describe the mass transport of the olefin both in the organic and IL phase, experiments in a stirred and nonstirred (static) reactor were conducted in this work. First, the solubility of olefins and i-paraffins in the IL was measured. Second, the effective reaction rate was determined both in a stirred and not-stirred system. In the latter case, the concentration profile in the organic phase was also measured and simulated by numerical solution of the respective differential equation to deduce the intrinsic and effective reaction rate for different amounts of promoter (tert-butyl chloride). Finally, the Received: Revised: Accepted: Published: 16288

August 23, 2012 October 4, 2012 November 26, 2012 November 26, 2012 dx.doi.org/10.1021/ie302259j | Ind. Eng. Chem. Res. 2012, 51, 16288−16298

Industrial & Engineering Chemistry Research

Article

fraction in the organic phase: wi ,IL,GG K w,i = wi ,org,GG

effectiveness factor was calculated, i.e. the ratio of the effective reaction rate and maximum rate without any diffusional resistance in the IL phase. Although refinery alkylation is mainly done with C4 hydrocarbons as feedstock, the experiments in this work were carried out either with mixtures of i-hexane/2-hexene or i-pentane/2-pentene. This enables liquid phase experiments at atmospheric pressure.

A more detailed description of the experimental procedure is given elsewhere.24 The samples were analyzed using a Varian CP-3800 gas chromatograph (Table 2). 2.3. Measurement of Effective Alkylation Kinetics in a Stirred Batch Reactor. At first, kinetic studies were

2. EXPERIMENTAL SECTION All chemicals were purchased from the suppliers shown in Table 1 and used as obtained. The ionic liquid 1-butyl-3methylimidazolium tetrachloroaluminate [C4mim][AlCl4], cy-

Table 2. Parameters of the Analysis by Gas Chromatography parameter

Table 1. Purity of the Used Chemicals chemical

purity in %

supplier

[C4mim][AlCl4] cyclohexane AlCl3 tert-butyl chloride i-pentane 2-pentene 2,2,4-trimethylpentane 2,3,4-trimethylpentane 2,2-dimethylhexane i-hexane 2-hexene n-pentane n-hexane n-heptane n-octane n-nonane n-decane

95.00 99.90 99.90 99.00 99.00 98.50 99.00 97.00 99.00 95.00 95.00 99.00 97.20 99.99 95.00 99.00 95.00

Sigma-Aldrich Sigma-Aldrich Fluka Sigma-Aldrich Fluka Fluka Riedel-de Haen Fluka Fluka Merck Fluka Grüssing Prolabo Fisher-Scientific Fluka Acros Fluka

(2)

comments

carrier gas detector capillary column oxygen inlet pressure hydrogen inlet pressure helium inlet pressure split flow carrier gas flow injector temperature detector temperature column length inner column diameter film thickness sample pressure sample volume running time

He 4.6 FID Varian CP-Sil CB/MS bar 2.41 bar 1.24 bar 4.13 mL min−1 40 mL min−1 2 °C 230 °C 250 m 30 μm 250 μm 0.5 bar 1.1 μL 10 min 14.1

conducted in a stirred batch reactor (Figure 2). A 250 roundbottom flask was filled successively with three different amounts of [C4mim][AlCl4] (xAlCl3 = 0.64) catalyst (VIL = 5 mL, 10 mL, and 22 mL). Thereafter, a mixture of 80 mL i-hexane/1-hexene or i-pentane/1-pentane was slowly added on top of the catalyst. A small magnetic impeller (volume of 0.6 mL) with a rotation speed of around 0.3 s−1 provided a certain mixing of the ionic liquid catalyst without mixing both phases. To avoid concentration gradients of olefin and i-paraffin in the organic phase an overhead stirrer operating at 1 s−1 was installed. The volume of the IL phase as function of the filling height (hIL) is given by Bronstejn:25 1 2 VIL = π ·hIL ·(3rflask − hIL) (3) 3

clohexane, tert-butyl chloride, and AlCl3 (Fluka) were also used without further purification. All experiments were conducted under inert atmosphere (Argon) using standard Schlenk techniques and/or a nitrogen filled drybox. The purity of the chemicals is also shown in Table 1. 2.1. Synthesis of Ionic Liquid Catalyst. Ionic liquid catalysts were prepared by slow addition of the desired amount of anhydrous AlCl3 to liquid [C4mim][AlCl4] (xAlCl3 = 0.5). The resulting Lewis acidic mixture was stirred for 24 h. The completed reaction yielded a yellow to brown liquid, depending on the amount of AlCl3 added. In this work, a Lewis acidic IL catalyst containing a molar fraction xAlCl3 of 0.64 was used. For the solubility experiments with olefins, a neutral IL was used (xAlCl3 = 0.5) to enable the measurement of the solubility without falsification by reactions such as dimerization. The molar fraction x of AlCl3 in the ionic liquid is defined as n AlCl3 x AlCl3 = n AlCl3 + n[C4 mim]Cl (1)

The height and (interfacial) surface area of the IL phase are described by hIL = rflask −

2 2 rflask − rIL

(4)

2 AIL = π ·rIL

(5)

Combination of eq 5 with eq 4 and eq 3 yields the correlation between volume and surface area of the IL phase:

2.2. Determination of the Solubility and Partition Coefficient. The solubility of different i-paraffins, 1-olefins, and 2-olefins with C-numbers from 5 to 10 are derived by the reextraction method described by Eichmann.23 The partition coefficient, describing the solubility of the organic component in the ionic liquid, is defined as the mass fraction of the compound in the ionic liquid and the mass

VIL =

1 ⎛ π · ⎜rflask − 3 ⎝

2 rflask −

2 AIL ⎞ ⎛ ⎟ · ⎜2rflask − π ⎠ ⎝

2 rflask −

AIL ⎞ ⎟ π ⎠ (6)

The graphical solution of eq 6 is shown in Figure 1b for the 250 mL round-bottom flask. 16289

dx.doi.org/10.1021/ie302259j | Ind. Eng. Chem. Res. 2012, 51, 16288−16298


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In defined time steps small samples were taken from the organic phase and analyzed by gas chromatography (Table 2). 2.4. Setup for Kinetic Studies in a Nonstirred Batch Reactor. To determine the rate of mass transport from the organic into the IL phase, concentration profiles of the olefin in the organic phase were measured in an unstirred (static) cylindrical glass vessel with a diameter of 20.9 mm and a height of 46 mm (Figure 2). The vessel was filled successively with three different amounts of IL (1 mL, 2 mL, 3 mL). A syringe was placed at a fixed distance of 11 mm from the bottom. Due to the differences in IL-volume, the distance between the tip of the syringe and the IL-phase boundary varies (2.3 mm, 5.2 mm, 8.1 mm). A mixture of 5 mL i-hexane/1-hexene (13/1) was added very slowly on top of the ionic liquid phase to avoid mixing of both phases. Thereafter, a small amount of the organic phase (Vsample ≈ 0.1 ≪ Vorg = 5 mL) was sampled carefully by the syringe after 1 h, 2.5 h, 4 h, 5 h, and 22 h and analyzed by gas chromatography (Table 2). The change of volume of the organic phase by the sampling operation could be neglected because of the small sample volume.

3. RESULTS AND DISCUSSION 3.1. Solubility of n- and i-Paraffins, 1- and 2-Olefins in the Ionic Liquid. The paraffin to olefin (P/O) ratio in the organic phase and in the IL phase is an important parameter in the alkylation-reaction to achieve a good alkylate quality (high octane number, low production rate of unwanted high boiling compounds by oligomerization).1 Liu et al.26 showed that for i-butane-alkylation a (P/O) ratio of less than 10:1 should be avoided to suppress excessive formation of acid-soluble oil. Data on the solubility of paraffins and olefins in ionic liquids are rare and unknown for the investigated IL. The Nernst partition coefficient was therefore determined for different mixtures of paraffins and olefins. 3.1.1. Influence of Chain Length on the Solubility of Pure Aliphatic Hydrocarbons. The solubility of C4-aliphates is difficult to determine because of the high vapor pressure at room temperature (formation of gas phase). To overcome this problem, the solubility of pure aliphatic compounds with C-numbers higher than four was measured by a re-extraction technique, and the solubility of C4-aliphates was estimated by extrapolation to the C-number of four. Figure 3 shows the

Figure 1. Experimental setup and IL-surface as a function of the ILvolume in a 250 mL round-bottom flask.

Figure 2. Experimental setup to measure the mass transport from the organic phase into the ionic liquid (concentration profile in the organic phase) by glass vessels containing with different IL-volumes at a fixed volume of the organic phase (dimensions in mm). 16290



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Figure 3. Partition coefficient Kw,i for pure aliphatic compounds with different C-numbers at 25 °C (xAlCl3 = 0.5 mol mol‑1).

solubility (partition coefficient Kw,i, eq 2) of different pure olefins, n- and i-paraffins with C-numbers from 5 to 10. In Figure 3a the data are shown for i-paraffins and n-paraffins in [C4mim][AlCl4] at different temperatures (6 and 25 °C) and compared to values given by Chunming27 for a composite-IL (with unknown composition) used in the PetroChin plant. The solubility of the i-paraffins in the composite-IL is a magnitude higher than in [C4mim][AlCl4], but, in both cases, an exponential decrease in solubility with increasing C-numbers is observed (log Kw,i proportional to C-number, see Figure 3). This is in agreement with data from Domańska and Marciniak28 who also found an increase of solubility (in [C4mim][PF6]) from n-octane to n-pentane at different temperatures. The solubility of the n-paraffins is slightly lower compared to the corresponding i-paraffins (e.g., i-pentane vs n-pentane). A decrease of temperature from 25 to 6 °C has no significant effect on solubility (Figure 3a). This is confirmed by data given by Marciniak and Karczemna29 for the solubility of n-hexane and n-heptane in [C4mim][CF3SO3]. Figure 3b summarizes the solubility measurements with pure 1- and 2-olefins as well as those done by Eichmann23 for 1-olefins in [C4mim][PF6] and slightly acidic [C2mim][AlCl4]IL (xAlCl3= 0.55) buffered with methylpyrrol. The solubility of 2-olefins is slightly higher than of 1-olefins (factor of about 1.5). The influence of the chain length is similar. The values of Eichmann23 for 1-olefins in [C2mim][AlCl4] + methylpyrrol correlate well with our data in [C4mim][AlCl4]. Compared to paraffins (Figure 3a) olefins show a 2 to 3 times higher solubility, but the influence of the chain length (slope of log Kw,i vs C-number) is almost identical. 3.1.2. Influence of Paraffin-to-Olefin Ratio on the Partition Coefficient. The influence of the concentration on the solubility was studied using various i-hexane/2-hexene and i-pentane/ 2-pentene mixtures. Figure 4a shows the mass fraction of the hydrocarbons in the IL for a variation of the content (mass fraction) of i-paraffins and olefins, respectively, in both mixtures. For all four hydrocarbons, a linear slope from the origin (wi‑paraffin,org or w2‑olefin,org → 1) can be drawn. Hence, the increase

of the amount of each hydrocarbon solved in the ionic liquid is straight proportional to the rising mass fraction in the organic phase, i.e. the Nernst partition coefficient (eq 2) in neutral chloroaluminate melts (xAlCl3 = 0.5) is constant (Figure 4). Eichmann23 also found a constant partition coefficient for different mixtures of heptane/1-hexene in [C4mim][AlCl4] + methylpyrrol. In conclusion, the partition coefficients determined for other (pure) paraffins and olefins (Figure 3) can also be assumed to be constant over the entire concentration range. 3.1.3. Influence of the Ionic Liquid’s Acidity (Molar Fraction xAlCl3). For the solubility experiments with olefins, a value for xAlCl3 of 0.5 had to be adjusted to avoid experimental errors by a chemical reaction such as dimerization of the olefins. Hence, the solubility in the acidic IL system (xAlCl3 of 0.64) was only measured for paraffins. The results for n-pentane, n-hexane, and n-heptane indicate that the solubility increases by a factor of about 2.5 compared to the neutral IL with xAlCl3 = 0.5 (for details see ref 24). 3.1.4. Influence of Ionic Liquid (Length of Alkyl Chain) on the Solubility. To investigate the influence of the ionic liquid (length of alkyl chain of imidazolium cation) on the solubility, additional measurements were done with [i-C5mim][AlCl4] and [C6mim][AlCl4] (xAlCl3 of 0.5). The results are very similar to those presented here for [C4mim][AlCl4]; for details see ref 24. The partition coefficients are summarized for all investigated hydrocarbons in Table 3. The respective values of the partition coefficient, if the molar concentrations and not the mass fractions have to been used for the definition of the partition coefficient (Kc,i) are calculated to eq 21 accordingly. These values are relevant for the simulation of the effective kinetics of alkylation and the deduction of the intrinsic reaction rate (constant), as discussed below. The solubility measurements can be summarized as follows (see also Table 3): • strong (almost exponential) increase in solubility with decreasing chain length of olefin and paraffin, 16291



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Table 3. Mean Partition Coefficient Kw,i and Kc,i of Different Aliphatic Compounds in [C4mim][AlCl4] (xAlCl3 = 0.5)a Kw,i

compound i-pentane i-hexane 2,2,4-trimethylpentane 2,3,4-trimethylpentane 2,2-dimehtylhexane 2-pentene 2-hexene 2-octene 1-pentene 1-hexene 1-octene

2.1 1.1 1.0 1.2 1.0 5.4 3.1 2.2 3.9 3.4 2.4

× × × × × × × × × × ×

Kc,i according eq 21 −2

10 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2 10−2

4.4 × 10−2 2.2 × 10−2 1.8 × 10−2 2.2 × 10−2 1.8 × 10−2 10.7 × 10−2 5.9 × 10−2 4.0 × 10−2 8.0 × 10−2 6.2 × 10−2 4.3 × 10−2

a

Note that the values are by a factor of around 2.5 higher for an acidic IL (xAlCl3 = 0.64; see chapter 3.1.3).

out both in a stirred and nonstirred batch reactor. In the static system, the concentration profile of the particular olefin in the organic phase was measured. 3.2.1. Kinetic Studies with Stirred Organic Phase and (Slightly Stirred) IL Phase. For the stirred batchwise operated reactor, we may assume that the concentration of the reactants (olefin and paraffin) is constant throughout the organic phase. We also assume that the reaction is first order with regard to both the olefin (here 1-hexene or 1-pentene) and i-paraffin (i-hexane or i-pentane). Simpson et al.30 and Langley and Pike31 showed that the alkylation of i-butane with olefins is first order or pseudo first order, thus confirming our assumptions. During the experiments, the molar ratio of the concentration of i-paraffin (cpara) to 1-olefin (cole) was 13. Hence the reaction is formally a simple first order reaction (high surplus of i-paraffin): −

dcole,org dt

= keff,2cpara,orgcole,org = keff cole,org (for c para ≫ cole)

(7)

Integration of eq 7 leads to

cole,org(t ) cole,org,0

= e−keff t (8)

Figure 5 shows the concentration decrease of 1-hexene (Figure 5a) and 1-pentene (Figure 5b) with reaction time. The first order reaction is clearly visible by the linear slope of log cole,org versus reaction time over a wide range of the residual concentration. The increase in reaction rate at a high degree of conversion (>90%) can probably be explained by the increased solubility of the olefin in the IL due to an increase of acid soluble oil which acts as a surfactant.32 The straight proportional rise of the effective reaction rate constant for 1-hexene and 1-pentene with increasing interfacial area (Figure 6a) (but not with increasing IL volume, Figure 6b) is a clear indication that the reaction takes place at the interphase and in a small film of the IL. On the basis of kole,eff versus AIL/Vorg (Figure 6a) the effective reaction rate constant related to the specific phase transition area (keff,A in m s−1) can be calculated:

Figure 4. Partition coefficient and mass fraction of olefins and paraffins for different mixtures of i-pentane/2-pentene- and i-hexane/2-hexene in [C4mim][AlCl4] (T = 25 °C; xAlCl3 = 0.5).

• olefins are about 2.5 times more soluble than corresponding n- or i-paraffins, i.e. the i-paraffin to olefin ratio in the IL also drops by this factor compared to the ratio in the organic phase, • almost constant partition coefficient over the entire concentration range (Nernst equation is valid), • small influence of the alkyl chain length of the imidazolium cation on solubility. 3.2. Effective Reaction Rate of Alkylation. After determining the solubility and the partition coefficient of the used substances, kinetic studies of the alkylation were carried

− 16292

dcole,org dt

= keff cole,org = keff, A

AIL cole,org Vorg

(9)



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interphase). This process can be mathematically described by Fick’s second law (and the proper choice of the respective boundary conditions): ∂c ∂ 2c = Dole/para 2 ∂t ∂y

(10)

The first boundary condition requires that at zero time the concentration of 1-hexene in the whole organic phase equals the initial (starting) concentration: c(0 < y < ymax )|t = 0 = cole,org,0

(11)

To solve eq 10, two other boundary conditions are needed: 1. At the (upper) surface of the organic phase, no concentration gradient exists for all time (ymax = 14.6 mm): dcole,org dy

=0 (12)

y = ymax

2. At the interphase between the organic phase and the ionic liquid (y = 0), the diffusional flux of the olefin into the IL phase equals the (effective) rate of consumption in the ionic liquid (cf. eq 9). Hereby we have to consider that the rate is determined by the concentration of olefins in the organic phase at the interphase (cole,org * ): keff, A

AIL A dcole,org * cole,org = −Dole,org IL Vorg Vorg dy

y=0

* → keff, Acole,org = −Dole,org

dcole,org dy

y=0

(13)

Since both boundary conditions (eq 12 and eq 13) are inhomogeneous boundary conditions, an analytical solution is not possible, and the differential eq 10 has to be solved numerically, which was done in this work with MATLAB. The parameter keff,A (eq 13) was thereby used as the only fitting parameter. Figure 7 shows the good agreement of the simulation with the experimentally determined concentration profiles in the organic phase. Similar measurements and calculations were done with tert-butyl chloride as promotor (Figure 8). As expected, the effective rate increases with increasing amount of promoter (0.5 mol-%; and 1 mol-%; Table 5). The good accuracy of the model is also indicated by the parity plot in Figure 9. The respective values of keff,A are listed in Table 5 for the experiments with and without promotor addition. For the unpromoted reaction (0 wt.-% tert-butyl chloride) the effective reaction constant (keff,A) deduced from the simulation is 4.7 × 10−6 m s−1, which is almost the same value (5.4 × 10−6 m s−1) derived from the experiments in the stirred reaction system with varied phase transition area (chapter 3.2.1). 3.2.3. Effectiveness Factor of IL Phase and Intrinsic Reaction Rate of Alkylation. Figures 7 and 8 clearly show a pronounced concentration gradient in the organic phase in case that both phases are stagnant (not stirred). The diffusion coefficient in the IL phase is by about 2 orders of magnitude slower compared to the organic phase (Table 4). Hence, an even more pronounced concentration gradient will be present in the IL phase, where the alkylation reaction takes place. This leads to a low effectiveness factor of the IL phase (ηIL), defined as the ratio of the effective reaction rate and the maximum rate

Figure 5. Concentration profile of 1-hexene and 1-pentene for different phase transition areas (T = 23 °C; IL = [C4mim][AlCl4]; xAlCl3 = 0.64, initial i-paraffin-to-1-olefin ratio = 13 mol/mol).

This yields a value of keff,A 5.4 × 10−6 m3 m−2 s−1 for 1-hexene and 13.5 × 10−6 m3 m−2 s−1 for 1-pentene, respectively. 3.2.2. Experiments with Unstirred Organic Phase and Ionic Liquid. In the biphasic alkylation system the reaction compounds in the organic phase have to be transported to the catalytic IL phase either by convection or diffusion. In a static (nonstirred) system, the mass transfer in both phases is solely controlled by diffusion, which simplifies the evaluation of the experimental data and modeling of the effective kinetics. In the experimental setup shown in Figure 2, the (static) organic phase is added on top of the (also static) IL catalyst phase. The reaction starts, the organic compounds react at the interphase, and a pronounced concentration gradient of the olefin (at almost constant paraffin concentration because of the high surplus) evolves in the static organic phase (Figure 7). This indicates that the rate of diffusion in the organic phase to the interface is not sufficiently fast relative to the effective rate of olefin consumption in the IL phase. The transient nature of the experiment leads to a concentration gradient in the organic phase that changes both with reaction time and local position (distance from the 16293



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Figure 6. Reaction rate constant for 1-hexene and 1-pentene versus the IL- interfacial area and the volume of ionic liquid in relation to organic volume of 80 mL (P/O = (13/1)(moli‑paraffin/mol2‑olefin)).

that could be achieved without any diffusional resistance in the IL phase. To elucidate this in more detail, the concentration gradient in the IL and the intrinsic reaction rate have to be inspected by further calculations. From the viewpoint of the organic phase, the rate of conversion of 1-hexene (mol m−3 s−1) is given by the flux of 1-hexene from the organic phase to the phase boundary: role,org = −

dcole,org dt

= −Dole,org

* ) AIL (cole,org − cole,org δy Vorg

= −Dole,org

⎛ AIL ⎜ dcole,org Vorg ⎜ dy ⎝

⎞ ⎟ ⎟ y=0 ⎠

(14)

The rate of consumption of 1-hexene in the ionic liquid is given by role,IL = −

dcole,IL dt

* = ηILkole,chemcole,IL

Figure 7. Concentration profiles for 1-hexene at different distances to the phase boundary and after different reaction times at a temperature of 23 °C (curves: numerical solution of eq 10; k1‑hexene,eff,A = 4.7 × 10−6 ms−1; AIL/Vorg = 68.6 m2org; D1‑hexene/i‑hexane = 4 × 10−5, cm2 s−1, cf. Table 4, ymax = 14.6 mm).

(15)

The effectiveness factor of the unstirred IL phase ηIL =

tanh(ϕIL) ϕIL

≈

1 (for ϕIL > 2) ϕIL

(16)

stagnant liquid/liquid system. In a stirred biphasic system, mass transfer caused by convection has to be considered, e.g. by a mass transfer coefficient and a boundary layer thickness, respectively. The olefin diffusion coefficients in the respective paraffin and in the IL are calculated with the Wilke-Chang equation33 (eq 18; values in Table 4):

can be calculated by the Thiele-modulus (L = height of IL phase = VIL/AIL): ϕIL = L

kole,chem Dole,IL

(17)

Note that eqs 15 to 17 are analogous to those used for porous catalysts to account for the influence of pore diffusion on the effective reaction rate (porous plate with thickness 2 L surrounded by a fluid). They are therefore only valid for a

Di / j = 7.4·10−8 16294

ΦMj T ηjVĩ

0.6

(18)



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Figure 8. Concentration profiles of 1-hexene at different distances to the phase boundary, different times and different amounts of promoter at 23 °C (curves: numerical solution of eq 10; k1‑hexene,eff,A from Table 5; AIL/Vorg = 68.6 m2/m3org; D1‑hexene/i‑hexane = 4 × 10−5 cm2 s−1 (Table 4); ymax = 14.6 mm).

system and values below 1 could also be found.36 For the curse of simplification, the associative factor is then also set to 1 as in the organic phase. Both reaction rates are related by the ratio of the volume of both phases: role,org = role,IL

VIL Vorg

(19)

The concentrations at the interphase in the organic phase and in the ionic liquid are linked by the Nernst partition coefficient based on molar concentrations (mol m−3): * = Kc,olecole,org * cole,IL

(20)

with Kc ,ole = K w ,ole

Table 4. Diffusion Coefficient of Different Olefins in i-Paraffins (i.e. i-Cx with x = 4 for i-Butane) and Acidic [C4mim][AlCl4] (xAlCl3 = 0.64) at 23 °C in cm2 s−1a

a

i/j

x

i-Cx

[C4mim][AlCl4]

4 5 6

7.7 × 10−5 5.5 × 10−5 4.0 × 10−5

1.2 × 10−6 1.1 × 10−6 9.7 × 10−7

ρorg

(21)

For simulation of the effective kinetics of alkylation, the values given in Table 3 for Kc,i were multiplied by a factor of 2.5 to account for the increase of the solubility in the acidic IL (xAlCl3 = 0.64) compared to the neutral IL (see chapter 3.1.3). In case of a strong influence of diffusion in the IL on the effective reaction rate (ϕIL > 2, eq 16), eqs 14 to 21 lead to the equation to determine the intrinsic rate constant (kole,chem in s−1):

Figure 9. Parity plot of the 1-hexene concentration profile versus the numerical solution by eq 10.

1-butene 1-pentene 1-hexene

ρIL

kole,chem =

Calculated by the Wilke and Chang eq 18; η[C4mim][AlCl4] = 21 mPas.

Dole,org Kc ,ole Dole,IL

⎛ dcole,org ⎞ ⎜− ⎟ ⎝ dy y = 0 ⎠ * cole,org

(22)

For the ratio (dcole,org/dy)|y=0/cole,org * the measured value (Figures 7 and 8, c*ole,org by extrapolation to y = 0) was used (see also values exemplarily given in Table 5 for t = 4 h). For the experiment without addition of tert-butyl chloride, eq 22 leads to a value for k1‑hexene,chem of 14 (Kc,1‑hexene = 0.16 for xAlCl3 = 0.64; for Di/j see Table 4). The effectiveness factor of

The associative factor Φ is set to 1 for 1-hexene in the organic phase (nonassociative fluids).33 The associative factor in ionic liquid is difficult to set: Ropel34 found a value of 1.5 for diffusion of CO2 in different imidazolium-based ILs, while Hou and Baltus35 used up to 33 different values for a comparable 16295



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the alkylation reaction takes place. For the given reaction system, the layer thickness is only in the order of magnitude of μm, which justifies this assumption even if the viscous IL was very slightly mixed by a small magnetic impeller. According to eq 24, the reaction rate and the effective rate constant (keff) should increase linearly with increasing ratio of the phase transition area and the volume of the (well-stirred) organic phase (AIL/VIL), as confirmed by the experiments (Figure 6b). Rewriting of eq 24 yields the equation to calculate the intrinsic rate constant (kole,chem) based on the measured effective rate constant of the experiments in the well-stirred reactor:

Table 5. 1-Hexene Concentration at the Phase Boundary, Concentration Gradient, Effective and Intrinsic Reaction Rate for Different Promoter Amounts at 4 h tert-butyl chloride in wt.-%

c*1‑hexeneorg (mol L−1)

(Δc/Δy)|y = 0 (mol L−1 mm−1)

k1‑hexene,eff,A (eq 13) (ms−1)

k1‑hexene,chem (eq 22) (s−1)

0 0.5 1

2.8 × 10−2 1.2 × 10−2 9.6 × 10−3

4.6 × 10−2 4.5 × 10−2 4.1 × 10−2

4.7 × 10−6 1.5 × 10−5 1.7 × 10−5

14 133 184

the unstirred IL phase (eqs 16 and 17) is then only 1 × 10‑2 % for a filling height L of 2.9 mm (VIL = 1 mL; cf Figure 2a) and just 3 × 10−3 % for a height of 8.7 mm (VIL = 3 mL; cf Figure 2c). Hence, the corresponding thickness of the reaction phase (≈2ηIL L) is only about 5 μm. If the promotor tert-butyl chloride is added to the IL (e.g., 1 wt.-%), the layer thickness would be even only about 1 μm (eqs 16 and 17 with k1‑hexene,chem from Table 5). We are now also able to reevaluate the experiments conducted with the stirred organic phase: The measured reaction rate, i.e. the change of 1-hexene concentration in the organic phase with time, equals the effective rate in the ionic liquid (see eqs 15 and 19): −

dcole,org dt

* = ηILkole,chemcole,IL

VIL Vorg

kole,chem = keff

dcole,org dt

= ( kole,chem Dole,IL Kc ,ole) · = keff cole,org

AIL

1 Dole,IL Kc ,ole

(25)

For 1-hexene, k1‑hexene,chem equals 18 s−1, which agrees quite well with the value obtained based on the unstirred experiments (cf. eq 22 k1‑hexene,chem = 14 s−1). Calculating the intrinsic reaction rate for 1-pentene in the same way (applying diffusion- and Nernst-coefficient for 1-pentene) leads to a k1‑pentene,chem of 34 s−1. Hence, the respective value for butene alkylation should be in a range of 52 s−1 (linear extrapolation) to 72 s−1 (in case of extrapolation assuming an exponential increase with rising C-number). In contrast to Joni et al.15 who observed a slow, intrinsic rate limited reaction for the Friedel−Crafts-Alkylation of propene with cumene in chloroaluminate ionic liquid, the chemical reaction in i-paraffin alkylation is extremly fast, e.g. 99% conversion of hexene would be achieved after only 2 s without any mass transfer resistance and for an equal volume of IL and organic phase (c/c0 = 0.01 = exp(−kchemKc t) with Kc = 0.16 and kchem = 16 s−1). Figure 10 shows the simulation of the transient experiment of 1-hexene alkylation in the static biphasic system. The reaction takes place in the ionic liquid in an extremely thin layer with a thickness of about 5 μm. For propene and butene, the thickness is even slightly lower (about 3 μm and 2 μm).

(23)

In the stirred reactor, the concentration of 1-hexene at the phase boundary equals the measured value in the organic bulk phase (cole,org = c*ole,org). For a strong influence of diffusion in the IL on the effective rate (ϕIL > 2), insertion of eqs 16, 17, and 20 into eq 23 yields −

Vorg

AIL cole,org Vorg (24)

Note that eq 24 is only valid for the assumption of a static IL phase, at least for the small layer at the phase boundary where

Figure 10. Result of the simulation of the transient experiment of 1-hexene alkylation in the nonstirred reactor without promotor (numerical solution of eq 10; diffusion coefficient from Table 4; Kc,1‑hexene = 0.16; k1‑hexene,eff,A = 4.7 × 10−6 cm s−1; AIL/Vorg = 68.6 m2/m3org). 16296



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4. CONCLUSIONS The presented kinetic studies carried out both in a stirred and nonstirred reactor show that the biphasic alkylation of light olefins with i-paraffins with chloroaluminate ionic liquids as catalyst is an extremely fast reaction. Hence in a technical process, the mass transfer resistance in the ionic liquid leads to a low effectiveness factor of the IL (compared to a complete utilization of the IL phase and the maximum intrinsic rate, respectively). The thickness of the IL layer, where the actual reaction takes place is only about 5 μm for 1-hexene alkylation and even slightly lower for pentene and butene (about 3 μm). In a well-mixed reactor (with negligible concentration gradient in the organic phase) the effective reaction rate is determined by the size of the interphase and of the characteristic length of diffusion in the IL phase, e.g. the thickness of an IL film or the diameter of the IL droplets dispersed in the organic phase.

■

■

xi = molar fraction of compound i, − xAlCl3 = molar fraction of aluminum chloride in the ionic liquid, − y = length dimension in simulation, mm ymax = maximum ionic liquid height in unstirred experiments, mm Φ = associative factor (Wilke Chang), − ϕIL = Thiele-modulus, − ηIL = effectiveness factor of ionic liquid, − ηj = dynamic viscosity of compound j, Pas

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AUTHOR INFORMATION

Corresponding Author

*Phone: +49 (0)921-557430. Fax: +49 (0)921-557435. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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LIST OF SYMBOLS AIL = phase transition area between the ionic and organic phase, m2 cpara,org = i-paraffin concentration in the organic phase, mol L−1 cole,org = olefin concentration in the organic phase, mol L−1 cole,IL = olefin concentration in the ionic liquid phase, mol L−1 c*ole,org = olefin concentration at the phase boundary from the organic side, mol L−1 c*ole,IL = olefin concentration at the phase boundary from the ionic liquid side, mol L−1 Dole,IL = olefin diffusion coefficient in the ionic liquid phase, cm2 s−1 Dole,org = olefin diffusion coefficient in the organic phase, cm2 s−1 hIL = height of ionic liquid in round-bottom flask, m Kc,i = Nernst partition coefficient based on concentration for compound i, − Kw,i = Nernst partition coefficient based on mass fraction for compound i, − keff = effective reaction rate constant, s−1 keff,A = area specific effective reaction rate constant, m s−1 kchem = chemical, intrinsic reaction rate constant, s−1 Mj = molar mass of component, g mol−1 nAlCl3 = molar amount of aluminum chloride, mol n[C4mim]Cl = molar amount of 1-butyl-3-methylimidazolium chloride, mol rflask = radius of the round-bottom flask, m role,org = rate of olefin consumption in the organic phase, mol m−3 s−1 role,IL = rate of olefin consumption in the ionic liquid phase, mol m−3 s−1 t = reaction time, s Vorg = volume of the organic phase, m3 VIL = volume of the ionic liquid phase, m3 Ṽ i = molar volume of compound i at boiling point, m3 mol−1 wi = mass fraction of compound i, − 16297



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