2-Butene

Article pubs.acs.org/IECR

Effective and Intrinsic Kinetics of Liquid-Phase Isobutane/2-Butene Alkylation Catalyzed by Chloroaluminate Ionic Liquids L. Schilder,† S. Maaß,‡ and A. Jess*,† †

Department of Chemical Engineering, University Bayreuth, Universitätsstraße 30, 95440 Bayreuth, Germany SOPATec UG, Department of Chemical and Process Engineering, Technical University Berlin, Fraunhoferstraße 33-36, 10587 Berlin, Germany

‡

S Supporting Information *

ABSTRACT: The kinetics of the IL-catalyzed reaction of isobutane with 2-butene and the size distribution of the dispersed IL droplets were investigated in a stirred tank reactor. The results were used to calculate the intrinsic reaction rate constant with a model accounting for the interplay of external and internal mass transport and chemical reaction. The intrinsic reaction rate was found to be very high, leading to a low effectiveness factor of the IL catalyst. The used fraction of the IL droplets with a diameter of about 400 μm was very small, and the actual reaction took place only in a thin spherical shell with a thickness of about 5 μm.

1. INTRODUCTION The alkylation of isobutane with light olefins is an important process for the production of high-octane gasoline. Until now, sulfuric acid and (anhydrous) hydrofluoric acid have been the catalysts of choice in industry.1,2 Because both catalysts exhibit severe drawbacks, such as high toxicity and corrosivity, several alternative catalysts have been proposed and tested. Solid acid catalysts (e.g., zeolites) show a remarkable initial alkylation performance, but their rapid deactivation caused by carbonaceous deposits is still quite a problem.3 Ionic liquids (ILs), especially acidic ILs, are also considered as promising candidates for managing the handicaps of both the industrially employed homogeneous catalysts and the solid catalysts (zeolites).4 It has been shown that Lewis acidic chloroaluminate ionic liquids (CAILs) such as 1-butyl-3-methylimidazolium chloride/aluminium chloride melts (BMIMCl/AlCl3, xAlCl3 > 0.5) in combination with suitable promoters are able to compete with both H2SO4 and HF in terms of the yield of trimethylpentanes (TMPs) and research octane number (RON).5,6 In commercial alkylation, large amounts of H2SO4 or HF have to be used, typically about 60 vol %. Hence, acid forms the continuous phase in the alkylation unit, whereas the organic feed is dispersed in the catalyst phase as small hydrocarbon droplets.7 In contrast, less than 10 vol % of the IL catalyst is sufficient to catalyze alkylation because of the high activity of the IL.8 As a consequence, the phase behavior is reversed, meaning that the feed becomes the continuous phase in which the ionic liquid is dispersed. Intensive mixing of the biphasic system is required to generate a large interfacial area and to prevent phase separation because the density difference between the two phases is large (ρIL ≈ 1200 kg/m3, ρorg ≈ 600 kg/m3). As shown in this work, the intrinsic chemical reaction rate of alkylation with IL catalysts is extremely high. Hence, a low interfacial area leads to a low effective reaction rate and, in turn, to high residence times. The interfacial area, which is governed by the droplet size of the IL catalyst, is affected by the interplay of several © 2013 American Chemical Society

variables. Here, operating parameters such as temperature, stirrer speed, and dispersed phase fraction; physicochemical properties of the catalyst, reactants, and products such as viscosity, interfacial tension, and density; and the reactor configuration (e.g., stirrer type, reactor geometry) have to be taken into account.7,9 In the present work, we present the droplet size distribution of the IL catalyst BMIMCl/AlCl3 (xAlCl3 = 0.64) dispersed in C4 hydrocarbons. Using a photo-optical endoscope method, the size distribution was determined at technically applied alkylation reaction conditions (between −5 and 15 °C, 6 bar) in a laboratory-scale stirred tank reactor. In addition, kinetic studies of the IL-catalyzed isobutane/2-butene alkylation were performed. The results obtained were then used to simulate the interplay of the chemical reaction and mass transfer to and within an IL droplet based on the measured mean droplet diameter, ddroplet, and the measured effective reaction rate, keff. To the best of our knowledge, it was possible for the first time, in this way, to determine the true chemical intrinsic rate (constant) of ILcatalyzed alkylation, as well as the effectiveness of the utilization of the IL (i.e., thickness of the droplet shell where the actual reaction takes place).

2. EXPERIMENTAL SECTION Feed gases trans-2-butene (purity grade 2.0) and isobutane (purity grade 3.5) were purchased from Rießner Gases. The ionic liquid 1-butyl-3-methylimidazolium tetrachloroaluminate ([BMIM][AlCl4], 95% purity) and cyclohexane (99.9% purity) were obtained from Sigma Aldrich. AlCl3 was obtained from Fluka (99.9% purity). All chemicals were used without further purification. All experimental manipulations were conducted Received: Revised: Accepted: Published: 1877

October 15, 2012 January 9, 2013 January 10, 2013 January 10, 2013 dx.doi.org/10.1021/ie3028087 | Ind. Eng. Chem. Res. 2013, 52, 1877−1885

Industrial & Engineering Chemistry Research

Article

Figure 1. Experimental setup for liquid-phase batch alkylation. S, stirrer (retreat curve impeller); SP, sampling point; TIR/PIR, temperature/ pressure indication registration; FV, feed vessel (T = 5.15 cm, H = 1.77 T, lB = 1.4T, sB = 0.1T, h = 0.17T, d = 0.66T, hSt = 0.1T, Ne = 1).

confirmed for strong coalescing systems at a ratio of the liquid level height to the tank diameter (H/T) of 1.0.11 A detailed study of volume streams created by a retreat curve impeller, such as the one used in this study, was published recently.12 The internal gas chromatography (GC) standard cyclohexane, the IL, and isobutane were consecutively charged into the reactor in accordance with the desired molar paraffin/olefin ratio (P/O ratio) and volumetric ratio of IL catalyst to organic phase (VIL/Vorg). After the system had been cooled to 5 °C with a cooling bath, the reaction was started when 2-butene was charged into the reactor through a connected tube. Before sampling, the stirrer was stopped, allowing rapid separation of the IL catalyst and hydrocarbon phase. This was required because contamination of the liquid sample with catalyst would lead to further alkylation reaction and inaccurate measurements. 2.3. GC Analysis and Calculations of 2-Butene Conversion. Analysis of the hydrocarbons was carried out using an HP 5889 Series I gas chromatograph. The detailed parameters are given in Table 1. Sampling was performed in such a way that the total hydrocarbon phase was kept liquid. The samples were collected in small containers joined with DESO (double-end shut-off) connectors to provide quick coupling and operation. Then, the liquid samples were

under inert atmosphere (argon) using standard Schlenk techniques or in a nitrogen-filled drybox. 2.1. Preparation of Ionic Liquid Catalyst. Ionic liquid catalysts were prepared by slow addition of the desired amount of anhydrous AlCl3 to liquid 1-methyl-4-butylimidazolium chloroaluminate ([BMIM][AlCl4], xAlCl3 = 0.5). The resulting Lewis-acidic mixture was stirred for 24 h. After completion of the reaction, a yellow to brown liquid was obtained depending on the amount of AlCl3 added. The mole fraction of AlCl3 in the ionic liquid, xAlCl3, is defined as n AlCl3 x AlCl3 = n AlCl3 + nBMIMCl (1) where ni represents the number of moles of compound i. 2.2. Experimental Setup and Procedure for LiquidPhase Batch Alkylation. Liquid-phase alkylation batch experiments were carried out in a 250 mL tank reactor pressurized to 6 bar to maintain the feed as a liquid (Figure 1). Reaction temperature was adjusted by a cryostat. The reactor was equipped with four equally spaced stainless steel baffles and a retreat curve impeller (RCI) operating at a constant agitation rate of n 1800 min−1 to guarantee effective dispersion of the two liquid phases. The power number Ne of the RCI, which is related to the power input P of the stirrer, is given by the equation P Ne = ρn3d5

Table 1. Parameter and Setup of Gas Chromatographic Analysis

(2)

carrier gas detector capillary column pressures gas flow rates

10

and can be estimated as unity according to Maaß et al. Ne also depends on the stirrer diameter d and the mean density of the dispersion ρ. A more specific interior view of the reactor, including baffles, stirrer, and measuring probe position, is pictured in the enlarged detail of Figure 1. Droplet size distribution can be assumed to be independent of local position because of the high-volume streams within the vessel, as has already been shown in other studies.10 The high-volume streams ensure the same droplet size distribution in every volume element inside the vessel, especially for laboratory-scale reactors. This was

temperatures column pressure temperature program

1878

He 4.6 FID CP Sil Pona CB (length, 50 m; inner diameter, 0.5 μm; outer diameter, 0.21 mm) oxygen, 2.41 bar; hydrogen, 1.24 bar; He, 4.13 bar purge gas, 8 mL min−1; split flow, 35 mL min−1; carrier gas, 30 mL min−1 injector, 250 °C; detector, 260 °C 1.41 bar isothermal at 40 °C (3 min), heat to 180 °C (10 K min−1), heat to 250 °C (15 K min−1), isothermal at 250 °C (10 min) dx.doi.org/10.1021/ie3028087 | Ind. Eng. Chem. Res. 2013, 52, 1877−1885


Article

connected to heating equipment and heated to 250 °C, which resulted in the complete vaporization of the product compounds and unconverted feedstock. When the pressure in the vaporizer reached a constant value of ca. 2 bar, the vessel was opened until a system pressure of 1.5 bar was obtained. Thereby, the sample loop was flushed with the gas mixture prior to switching of the sampling valve for GC analysis. The 2butene conversion was determined by GC analysis using cyclohexane as the internal standard. 2.4. Measurement of Ionic Liquid Droplet Size Distribution and Image Analysis. Droplet size analysis covers a wide range of techniques. An excellent review by Barth and Flippen13 includes all techniques that were available at the time it was written, and most of them are still in use. The difficulty in applying such methods to stirred vessels is related to turbulence. Turbulence is not very well characterized because it is not only inhomogeneous throughout the vessel but also highly anisotropic, consisting of high-shear regions on the surface of the impeller.14 Therefore, local analysis is needed. Photo-optical systems using image analysis are the standard in the literature for precise measurements.15−17 However, because the image analysis is carried out manually, this procedure is extremely time-consuming. An online measurement technique has been developed for droplet size distributions in multiphase reactors using an in situ microscope18 and a fully automated image analysis procedure.19 This approach was used in this work. With this endoscope technique, images were taken intrusively from inside the vessel by placing a 10-mm-thick endoscope in front of a CCD camera as a microscope lens. To avoid disturbances by droplets in front of the focal plane, a covering tube with a window was placed at the tip of the endoscope lens (see Figure 2). A strobe flash was guided by a

Ritter and Kraume11 suggested a minimum number of 200 droplets for building one sample for one droplet size distribution as a reliable number for statistical demands. This number was always exceeded by a factor of 4−7 (800−1400 droplets for each data point) for all cases investigated in this study. The droplet size distribution (DSD) of the dispersed IL droplets was measured in pure isobutane (unreactive DSD) and during alkylation of isobutane and 2-butene (reactive DSD).

3. RESULTS AND DISCUSSION 3.1. Ionic Liquid Droplet Size Distribution and Calculation of Mean Droplet Diameter. Experiments with a static reaction system consisting of chloroaluminate IL and C5 or C6 isoparaffins and olefins revealed that the thickness of the IL layer in which the alkylation reaction takes place is only a few micrometers.20,21 For C4 alkylation, an even smaller IL film thickness is expected, because the reactivity of protonated olefins derived from alkylation initiation reaction decreases in the order C4 > C5 > C6. Thus, the effective reaction volume in hydrocarbon-continuous dispersions is the spherical shell volumes of the ionic liquid droplets. The equivalent surfacerelated mean diameter, ddroplet, to reach the same active IL volume is, therefore, given by ddroplet =

∑ nidi 2 ∑ ni

(3)

Figure 3 shows representative photographs of dispersed IL droplets for the unreactive system (IL and isobutane only) and during the alkylation (i.e., IL droplets dispersed in isobutane and 2-butene). The distinct outlines of the IL droplets (Figure 3A) enable easy droplet detection with the image analysis software. In contrast, accurate detection of the sizes is a difficult task during alkylation because the fast alkylation reaction causes concentration differences in the continuous phase (Figure 3B). To avoid falsification of the mean droplet diameter by these concentration fields around droplets, the unreactive mean droplet diameter (measured in the IL/isobutane mixture) was used for the kinetic calculations in section 3.2. This simplification is also justified by the fact that 2-butene accounts for only 0.93 wt % of the organic phase and, thus, has only a small effect on its physical properties (viscosity, density). Measurement of the droplet size distribution in the unreactive system showed no transient behavior of dispersion because the DSD became constant after 30 s to 1 min (Figure 4A). This can be easily explained by the high coalescence efficiency of the IL. The droplet size increase was a result of the parallel starts of measurement and stirring. The ionic liquid was dispersed throughout the reactor. The measurements show that this process took around 30 s. The number and size of the droplets increased rapidly in this initial phase. After complete dispersion was reached, the coalescence and breakage processes reached equilibrium, and the droplet size remained constant. All measured DSDs could be described as approximately logarithmic-normal distributed. Figure 4B shows the number distribution, q0, of the unreactive isobutane/IL system after a dispersion time of 90 s. q0 is defined as the ratio of the number of droplets having diameters within a defined width Δd and the product of Δd with the sum of all measured droplet diameters

Figure 2. Detailed three-dimensional sketch of the photo-optical probe used in this work.

fiber-optic cable surrounding the endoscope to ensure sharp pictures even in the vicinity of the stirrer, where the speed of the droplets could reach up to 3 m/s. To ensure robust and accurate droplet detection, a series of images was first prefiltered and then analyzed. The results of the droplet recognition led to real-time size quantification of the system within a possible size range of 4−6000 μm. This fast data-acquisition approach allows for online process control. 1879

dx.doi.org/10.1021/ie3028087 | Ind. Eng. Chem. Res. 2013, 52, 1877−1885


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Figure 3. Representative images recorded by the endoscope technique: (A) IL dispersed in isobutane (nonreactive system) and (B) IL dispersed in isobutane and 2-butene during alkylation reaction.

(cp) and the olefin 2-butene (co) was kept high (>10, i.e., high surplus of isoparaffin). Hence, we assumed a pseudo-first-order reaction with regard to the paraffin isobutane. This assumption was confirmed by the works of Simpson et al.23 and Langley and Pike,24 who both showed that isobutane/butene alkylation is first-order or pseudo-first-order. Hence, for the assumption of a first-order reaction for the olefin 2-butene, the overall reaction should also formally be a simple first-order reaction, for which the effective reaction rate (including a possible influence of external or internal diffusion) is given by ro,org = −

dco,org dt

= keff,2cp,orgco,org = keff co,org

(for c p,org ≫ co,org)

(5)

Integration of eq 5 leads to ⎡ co,org(t ) ⎤ ⎥ = −keff t ln⎢ ⎢⎣ co,org(t = 0) ⎥⎦

Thus, a plot of ln{[co,org(t)]/[co,org(t = 0)]} versus reaction time t should yield a straight line if the alkylation reaction truly obeys a first-order dependence with respect to 2-butene. This is confirmed by Figure 5, which depicts the residual content of unconverted 2-butene on a logarithmic scale versus the reaction time for P/O ratios of 13 and 100, that is, for the two very different initial concentrations of 2-butene of 0.096 and 0.673 mol/L, respectively.

Figure 4. (A) Mean IL droplet diameter, ddroplet, as a function of stirring time. (B) Droplet size distribution, q0, of IL droplets dispersed in a continuous isobutane phase (nonreactive system) at a dispersion time of 90 s and a temperature of 5 °C.

q0(dn) =

nddroplet, Δd Δd∑ nddroplet, Δd

(6)

(4)

The two distinctive maxima of the number frequency q0 (Figure 4B), which are indicative of a bimodal distribution, suggest the existence of multiple breakage mechanisms and unusual breakage patterns, which is typical for dispersions of viscous phases.22 For the unreactive system, the mean droplet diameter calculated from eq 3 was 400 ± 10 μm at a temperature of 5 °C. A comparison of our data with the literature was not possible, because the effects of differences in the systems (type of ionic liquid, stirrer type, overall reactor configuration) on the measured droplet sizes cannot be explicitly taken into account. 3.2. Effective and Intrinsic Reaction Kinetics of Isobutane/2-Butene Alkylation. During the experiments, the molar ratio of the concentrations of the paraffin isobutane

Figure 5. 2-Butene concentration as a function of reaction time for different initial concentrations of 2-butene (5 °C, BMIMCl/AlCl3, xAlCl3 = 0.64, molar IL/O ratio = 0.2). 1880



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imidazolium-based ionic liquids, whereas Hou and Baltus30 determined values of up to 33 for a similar system. Even ϕ values less than 1 have been reported for diffusion of dissolved gases in imidazolium-based ionic liquids.31 Because of the disagreement in the literature regarding the value of the association factor in ILs, for simplicity reasons, we chose an association factor of ϕ = 1 for this work. Furthermore, use of ϕ = 1 facilitates the comparison of our kinetic model with a similar one derived by Aschauer and Jess, who also used a value of ϕ = 1.20 For a detailed discussion of the influence of the diffusion coefficient, Do,IL, on the calculated values, see the error discussion later in this section. The diffusion coefficients of 2butene in both isobutane and the ionic liquid at 5 °C and the respective parameter values for their calculation are reported in Table 2.

The slight increase of the reaction rate for a high P/O ratio of 100 and a conversion of >90% is probably explained by the increased solubility of 2-butene in the ionic liquid caused by an accumulation of conjunct polymers in the catalyst phase.25 The effective rate constant, keff, determined from the initial slope of the 2-butene concentration versus time (Figure 5) is 0.0042 ± 0.0001 s−1. The flux of 2-butene into the IL droplet equals the effective rate of 2-butene consumption in the ionic liquid, which is determined by the intrinsic rate constant, k chem ; the effectiveness factor for the IL droplet, ηIL; and the olefin concentration in the ionic liquid at the interphase, c*o,IL ro,IL = −

dco,IL dt

* = ηILkchemco,IL

(7)

ηIL is a function of the Thiele modulus ϕIL ηIL =

tanh(ϕIL) ϕIL

1 ≈ ϕIL

(for ϕIL > 2)

Table 2. Viscosity ηB of Isobutane and IL36 and Diffusion Coefficient of 2-Butene, D2‑butene,i, in Isobutane and IL at 5 °C Calculated from the Wilke−Chang Equation (Eq 11)a

(8)

In heterogeneous catalysis, the Thiele modulus ϕ accounts for the influence of internal diffusion on the effective rate,26 and for spherical catalyst particles, such as IL droplets, it can be expressed as ϕIL =

ddroplet 6

kchem Deff

D2‑butene,i (m2/s)

ddroplet 6

kchem Do,IL

The reaction rates in the organic and IL phases (eqs 5 and 7) are related to each other by the ratio of the volumes of the two phases ro,org = ro,IL

V2‐butene

(12)

* = Kc,oco,org * co,IL

(13)

Kc,o is easily derived from the mass-related partition coefficient Kw,o ρ Kc,o = K w,o IL ρorg (14) For 2-butene, Kw,o at 5 °C was extrapolated from solubility data of longer-chain analogues of isoparaffins and 2-olefins in a neutral ionic liquid at 25 °C reported by Aschauer and Jess.20,21 According to Aschauer and Jess,20,21 the temperature dependency of Kw,o can be neglected. The obtained Kc,o value of 0.15 was multiplied by a factor of 2.5 to account for the increase in hydrocarbon solubility when passing from the neutral (xAlCl3 = 0.5) to the Lewis-acidic (xAlCl3 = 0.64) regime of the ionic liquid.20,21 The combination of eqs 7, 12, and 13 yields

(10)

ϕMi T ηB

VIL Vorg

The concentrations at the phase boundary in the organic phase (c*o,org) and in the IL (c*o,IL) are linked by the Nernst partition coefficient, Kc,o, based on molar concentrations (mol m−3)

− 0.6

1.9 × 10−4 40 × 10−2

Note that the values needed for calculation of D2‑butene,i with eq 11 are not in SI units.28

The diffusion coefficient of 2-butene in a solvent i, D2‑butene,i, where i is isobutane or ionic liquid, can be calculated from the well-known Wilke−Chang equation28 D2‐butene, i = 7.4 × 10−8

ηB (kg m−1 s−1)

a

(9)

ddroplet kchem = 9Do,IL 18

5.6 × 10 7.1 × 10−11

isobutane IL (BMIMCl/AlCl3, xAlCl3 = 0.64)

where Deff is the effective diffusion coefficient in the IL droplet. Ionic liquid droplets can also be considered as “spherical particles”, but the molecular diffusion coefficient of 2-butene in the IL (Do,IL) can be used in place of Deff in eq 9 only for a static droplet without any motion taking place inside the droplet and, thus, no enhancement of mass transport by convection. This is valid only in the case of two immiscible phases with similar densities, because the droplets are then almost motionless (aside from Brownian motion) within the continuous phase. For the given system (IL/C4 hydrocarbons), there is a great difference in density (IL, 1254 kg m−3; isobutane, 576 kg m−3), and gravity will give rise to motion of the droplets relative to the hydrocarbon phase. The viscous forces between the two fluids cause circulation currents in the droplet interior, accelerating the mass transport.27 In the case of laminar circulation inside the droplet, Kronig and Brink27 found that the mass transport (formally the effective diffusion coefficient of 2-butene inside the IL droplet) was enhanced 9-fold compared to that in a static IL droplet without convection. Thus, for IL droplets, eq 9 leads to ϕIL =

−9

(11)

dco,org dt

* = ηILkchemKcco,org

VIL Vorg

(15)

In addition to the internal mass-transfer resistance in the IL droplets, an external mass-transfer resistance (from the organic phase to the external surface of the droplets) might exist

The association factor ϕ in eq 11 is unity for nonassociated solvents such as aliphatic or aromatic hydrocarbons.28 There has been much discussion about the value of the association factor ϕ with respect to diffusion in ionic liquids: Ropel29 measured a value of ϕ = 1.5 for the diffusion of CO2 in different

reff = − 1881

dco,org dt

* ) = βorg (co,bulk − co,org

AIL Vorg

(16)



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The mass-transfer coefficient βorg can be calculated from the Sherwood number Shorg, which equals the ratio of the droplet diameter ddroplet to the boundary layer thickness δorg βorg ddroplet

Shorg =

Do,org

The overall effectiveness factor, ηoverall, accounting for both external and internal mass transfer is ηoverall = ηext ηIL = ηext

ddroplet

=

δorg

1 1 = ϕIL ϕIL +

(for ϕIL > 2)

3ϕIL 2 Bi

(17)

(25)

For small droplets, Shorg is given by a correlation from Zlokarnik32,33

The maximum (initial) reaction rate without any masstransport influence is given by

Shorg = 2 + 0.31(Ar Sc)1/3

(18)

rchem = −

with the following definitions for the Archimedes number, Ar, and the Schmidt number, Scorg ρorg ddroplet (ρIL − ρorg )g ηorg 2

(19)

ηorg

Scorg =

ρorg Do,org

Table 3. Shorg, Ar, Scorg, and Bi as Calculated from Eqs 18−20 and 24a Ar Scorg Shorg Bi

6857 60 25 302

Parameters used for calculations: The density of IL at 5 °C was taken as ρIL = 1254 kg m−3.36 For the density of the organic phase at 5 °C, the density of isobutane (ρorg = 576 kg m−3) was used, because its mass fraction in the organic phase was more than 98 wt %. The same holds for the dynamic viscosity of the organic phase, ηorg = 1.9 × 10−4 Pa s.

kchem

dt

=

Shorg Do,org ddroplet

* ) (co,bulk − co,org

AIL Vorg

(21)

Shorg Do,org VIL A * ) IL = (co,bulk − co,org Vorg ddroplet Vorg (22)

For a strong influence of internal mass transfer on the effective rate (ϕIL > 2), insertion of eq 8 into eq 22 and rearrangement yields the effectiveness factor, ηext, with regard to external mass transfer only ηext =

* co,org co,bulk

=

1 1+

3ϕIL

(for ϕIL > 2) (23)

Bi

Using the Biot number, Bi, as a measure for the ratio of external to internal mass transfer, one can write Bi =

Do,org

Do,org

δorg

ddroplet / Shorg

K cDo,IL δ IL

=

K cDo,IL ddroplet / 18

=

Shorg Do,org 18KcDo,IL

(29)

Insertion of VIL/Vorg = 0.0047, keff = 0.0042 s , and the values given in Tables 2 and 3 yields an intrinsic rate constant of 54 s−1. The influence of the measured, error-prone values of keff and ddroplet on the overall error of kchem is negligible, because their standard deviations are rather small (see sections 3.2 and 3.1, respectively). Even an (unrealistically high) increase in ddroplet from the determined value of 400 μm to a value of 450 μm changes kchem by only 30%. The greatest uncertainty influencing the value of the calculated intrinsic rate constant, kchem, is thus the value of the diffusion coefficient of 2-butene in the IL phase, Do,IL. In fact, application of Wilke−Chang equation (eq 11) for ILs is controversial in the literature. Using the temperature-modified correlation of Morgan et al. for the calculation of diffusivity in ILs increases the value of D2‑butene,IL by a factor of 1.8 (2.0 × 10−10 m2 s−1) compared to that obtained using the Wilke−Chang equation.31,34 Substituting the diffusion coefficient calculated by the equation of Morgan et al. into eq 29 results in a decrease of kchem to a value of 21 s−1. A similar result can be obtained from the kchem values reported by Aschauer and Jess,20,21 who measured the effective kinetics in a static IL/isoalkane/alkene system at a temperature of 25 °C. We next calculate the intrinsic rate constant, kchem, at a temperature of 5 °C from the respective value of Aschauer and Jess at 25 °C. The intrinsic rate constant for isobutane/2butene alkylation at 25 °C was extrapolated (linear, 52 s−1; exponential, 72 s−1) from their measured kchem values for the analogue isopentane/pentene and isohexane/hexene pairs. Because linear extrapolation would lead to a kchem value of

and combination of eqs 15 and 21 yields * ηILkchemKcco,org

⎛ 18 D K VIL ⎞−2 o,IL c V d ⎜ droplet ⎟ org =⎜ − 6Bi Do,IL ⎟⎟ ⎜ ddropletkeff ⎝ ⎠ −1

Insertion of eq 17 into eq 16 leads to dco,org

(27)

Inserting eqs 5 and 10 into eq 28 and solving the resulting equation for kchem leads to an expression for the calculation of the intrinsic reaction rate constant, kchem, as a function of the measured droplet diameter, ddroplet, and the measured (initial) reaction rate constant, keff

a

−

(26)

Equating the two expressions for ηoverall in eqs 25 and 27 yields reff 1 (for ϕIL > 2) = VIL 3ϕIL 2 kchemKcco,bulk V ϕ + (28) IL org Bi

The values of Shorg, Ar, Scorg, and Bi are listed in Table 3.

value

VIL Vorg

Vorg

(20)

parameter

dt

= kchemKcco,bulk

The overall effectiveness factor, ηoverall, as defined in eq 25 is also given by the ratio of the measured (initial) rate, reff, at 5 °C (0.0004 mol L−1 s−1) and the maximum rate without any influence of mass transfer, rchem, which leads to r reff ηoverall = eff = V rchem kchemKcco,bulk IL

3

Ar =

dco,org

(24) 1882



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about 0 s−1 for a C8 isoalkane/alkene system, we used the exponentially derived value for our calculations. Assuming a negligible influence of external mass transfer, the effective rate constant, keff, is given by (see eqs 8 and 10) keff = ηoverall kchem =

18 ddroplet

kchem Do,IL

(30)

The intrinsic activation energy, EA,chem, can be determined from the expression EA,eff =

EA,chem

+

EA,diff

(31) 2 2 The effective activation energy, EA,eff, and the activation energy of diffusion, EA,diff, were obtained from the respective Arrhenius plots (data not shown, details in Schilder;35 see the Supporting Information). Inserting EA,eff = 25 kJ/mol and EA,diff = 27 kJ/ mol into eq 31 yields an EA,chem value of 23 kJ/mol. The kchem value at 5 °C is now easily obtained from kchem at 25 °C by

Figure 6. Concentration profile of 2-butene in the ionic liquid phase (eq 33) and organic phase (schematically) for a Shorg number (= ddroplet/δorg with ddroplet = 0.4 mm) of 25.

EA,chem ⎛ 1 1 ⎞ ⎜ ⎟ − R ⎝ 298 K 278 K ⎠

ln(kchem,5 ° C) =

+ ln(kchem,25 ° C)

(32) −1

The extrapolated value of kchem (36 s ) is lower than the measured one (54 s−1), but the agreement between the measured and extrapolated values is still satisfying because accurate values are not known for all parameters, such as the diffusion coefficients calculated using the Wilke−Chang equation. If we use the calculated value of kchem (36 s−1), we obtain perfect agreement between measurement and calculation for a mean droplet size of 320 μm (355 μm without considering external diffusion). The overall effectiveness factor, ηoverall, given by eq 25 is 4%, and the effectiveness, ηIL, with regard to internal diffusion as defined by eqs 8 and 10 is 5%. Finally, the ηext value (eq 23) reflecting the external mass-transfer resistance is 82%. As discussed previously, the diffusion coefficient Do,IL, which is not known exactly, has the main impact on the accuracy of the three effectiveness factors. Whereas the value of the external mass-transfer resistance, ηext, remains approximately constant, the values of ηIL and ηoverall increase by a factor of 2.7 when using Do,IL derived from the Morgan et al. equation instead of the Wilke−Chang equation. Despite this uncertainty in the exact values of the effectiveness factors, the main message remains the same: The main resistance, by far, is within the droplet, where the olefin concentration drops rapidly in a very thin layer with a thickness of about 5 μm (co,IL/co,IL,surface = 1/e; Figure 6). The thickness of the external boundary layer is around 15 μm (= ddroplet/Shorg). In Figure 6, the entire concentration profile for 2-butene on the organic and ionic liquid sides is illustrated. The concentration decrease of 2butene in the IL droplet is given by solution of the differential equation describing simultaneous mass transport and reaction in a spherical catalyst (of radius r) for a first-order reaction26 co,IL(r ) co,IL(r = rdroplet)

=

Figure 7. Effectiveness factor, ηIL, and time for 95% 2-butene conversion, tX2‑butene=0.95, for two different volumetric ratios of IL phase and organic phase as a function of the droplet diameter ddroplet.

small IL droplets cannot be produced with conventional emulsion techniques, that is, by a simple one-stage stirrer as used in this work. Luo et al.8 found that a dramatic reduction in the mean IL droplet diameter to 30 μm is possible if a special nozzle from the company BETE (Greenfield, MA) is used. This nozzle, which was installed on top of a tubular reactor, comprised two inlets for hydrocarbon feed and ionic liquid catalyst, an internal mixing chamber, and one outlet. The nozzle generated a considerable amount of droplets less than 10 μm in size without any significant influence of internal diffusion. Thus, for better utilization of the catalyst amount in the reactor, more sophisticated emulsifying techniques should be developed and tested with adequate measurement techniques. In addition, Figure 7 includes the reaction time required for 95% 2-butene conversion, tX2‑butene=0.95, as a function of the droplet diameter for two different volumetric ratios of catalyst and feed phase. As expected, tX2‑butene=0.95 decreased with decreasing droplet diameter and increasing catalyst volume relative to the organic feed phase. In Figure 8A, the percentage of unconverted 2-butene is shown as a function of reaction time for three different catalyst concentrations defined in terms of the volumetric ratio, VIL/ Vorg. The effective rate constant calculated from the slopes of Figure 8A give a straight line when plotted against their respective VIL/Vorg ratios (compare Figure 8B). For the investigated range of catalyst concentrations, the conclusion is that the IL droplet size remained approximately constant.

⎛ r ⎞ ⎜ ⎟ rdroplet sinh⎝ rdroplet 3ϕIL⎠ r

sinh(3ϕIL)

(33)

The dependence of the effectiveness factor in the IL droplet as a function of the droplet diameter ddroplet is depicted in Figure 7. It can be seen that ηIL values of greater than 90% were achieved only with droplet diameters of less than 10 μm. Such 1883



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4. CONCLUSIONS The kinetics of isobutane/2-butene alkylation catalyzed by the Lewis-acidic ionic liquid BMIMCl/AlCl3 (xAlCl3 = 0.64) was studied focusing on the influence of external and internal mass transfer (i.e., from the organic bulk phase into IL droplets) on the effective rate. The size of the droplets was measured using the endoscope technique. Based on the mean droplet size of 400 μm and the measured effective rate constant, keff, the intrinsic chemical rate constant, kchem, was deduced. The overall effectiveness factor for the utilization of the IL droplets turned out to be very low (ηoverall = 4%). Internal mass transfer was, by far, the dominating factor, and resistance by external mass transfer was rather small (ηext = 82%). For the application of acidic ionic liquids in commercial alkylation plants, the effective rate, which is nearly proportional to 1/ddroplet, can be strongly increased by applying better dispersion techniques. ASSOCIATED CONTENT

S Supporting Information *

Arrhenius plot of IL-catalyzed isobutane/2-butene alkylation and Arrhenius plot of the diffusion coefficient of 2-butene in the IL phase, D2‑butene,IL. This material is available free of charge via the Internet at http://pubs.acs.org.

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LIST OF SYMBOLS AND ABBREVATIONS AIL = area of IL phase, m2 Ar = dimensionless Archimedes number Bi = dimensionless Biot number BMIMCl = 1-butyl-3-methylimidazolium chloride CAIL = chloroaluminate ionic liquid cp,org = i-paraffin concentration in the organic phase, mol m−3 co,org = olefin concentration in the organic phase, mol m−3 co,IL = olefin concentration in the ionic liquid phase, mol m−3 c*o,org = olefin concentration at the phase boundary in the organic phase, mol m−3 c*o,IL = olefin concentration at the phase boundary in the IL phase, mol m−3 D2‑butene,IL = olefin diffusion coefficient in the ionic liquid phase, m2 s−1 D2‑butene,org = olefin diffusion coefficient in the organic phase, m2 s−1 Deff = effective olefin diffusion coefficient in a porous particle, m2 s−1 d = stirrer diameter, m ddroplet = mean droplet diameter, m di = diameter of droplet i, m EA,eff = effective activation energy, J mol−1 EA,chem = intrinsic activation energy, J mol−1 g = gravitational acceleration, m s−2 GC = gas chromatography h = bottom clearance of the stirrer, m hSt = stirrer height, m H = liquid level height, m IL = ionic liquid Kc,o = Nernst partition coefficient for 2-butene based on concentration kchem = intrinsic reaction rate constant for pseudo-first-order reaction, s−1 keff = effective reaction rate constant for pseudo-first-order reaction, s−1 keff,2 = effective reaction rate constant for second-order reaction, m3 mol−1 s−1 Kw,o = Nernst partition coefficient for 2-butene based on mass fraction lB = baffle length, m Mi = molecular weight of compound i, kg mol−1 n = agitation rate, min−1 ni = amount of substance i, mol Ne = power number of stirrer P = power input of stirrer, W q0 = number frequency, m−1 rchem = intrinsic reaction rate, mol m−3 s−1 rdroplet = radius of ionic liquid droplet, m reff = effective reaction rate, mol m−3 s−1 ro,IL = rate of olefin consumption in the ionic liquid phase, mol m−3 s−1 ro,org = rate of olefin consumption in the organic phase, mol m−3 s−1 RON = research octane number sB = baffle width, m Scorg = dimensionless Schmidt number Shorg = dimensionless Sherwood number t = reaction time, s T = temperature, K T = tank diameter, m

Figure 8. (A) 2-Butene concentration as a function of reaction time for different volumetric ratios, VIL/Vorg, and (B) measured effective rate constant, keff, for three different portions of ionic liquid phase volume (5 °C, BMIMCl/AlCl3, xAlCl3 = 0.64).

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Article

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the German Research Foundation for supporting this project (JE257/14-1). 1884



Article

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tX2‑butene=0.95 = reaction time required for 95% 2-butene conversion, s TMP = trimethylpentane V2‐butene = molar volume of 2-butene at its normal boiling point, m3 mol−1 VIL = volume of the ionic liquid phase, m3 Vorg = volume of the organic phase, m3 X2‑butene = conversion of 2-butene, wt % xAlCl3 = mole fraction of AlCl3 in the ionic liquid βorg = mass-transfer coefficient in the organic phase, m s−1 δIL = boundary layer thickness of the IL side, m δorg = boundary layer thickness of the organic side, m Δd = width of the droplet diameter interval, m ηB = viscosity, kg m−1 s−1 ηext = effectiveness factor with regard to external mass transfer ηIL = effectiveness factor for the IL droplet ηoverall = overall effectiveness factor accounting for both external and internal mass transfer ρi = density of compound i, kg m−3 ϕ = association factor ϕIL = dimensionless Thiele modulus

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2-Butene

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