Density, Viscosity, and Surface Tension of Liquid Phase Beckmann

Article pubs.acs.org/jced

Density, Viscosity, and Surface Tension of Liquid Phase Beckmann Rearrangement Mixtures Klaas T. Zuidhof,† Mart H. J. M. de Croon,† Jaap C. Schouten,*,† and Johan T. Tinge‡ †

Department of Chemical Engineering and Chemistry, Laboratory of Chemical Reactor Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands ‡ DSM Chemical Technology R&D BV, Industrial Chemicals, P.O. Box 18, 6160 MD, Geleen, The Netherlands ABSTRACT: We have determined the density, dynamic viscosity, and surface tension of liquid phase Beckmann rearrangement mixtures, consisting of ε-caprolactam and fuming oleum. These important properties have been measured in wide ranges of both temperature and molar ratios of acid and ε-caprolactam, covering conditions that are of relevance for industrial production of ε-caprolactam from cyclohexanone oxime, i.e., T = (293 to 393) K and ([H2SO4] + [SO3])/[ε-caprolactam] = (1.4 to 2.6). The results were correlated as functions of temperature and composition. The density of oleum/ ε-caprolactam mixtures shows a linear relationship with both temperature and composition. A modification of the traditional Reynolds model proved to be the most suitable way to represent the dynamic viscosity of these Beckmann rearrangement mixtures. The reduction of the surface tension with temperature is described with a power law expression, while the decrease of the surface tension with increasing molar ratios of acid over ε-caprolactam is described with a linear relationship. These results can be applied to design liquid phase Beckmann rearrangement processes on both large scale and microscale.

1. INTRODUCTION By the end of 2013, the global annual ε-caprolactam production capacity reached approximately 6.5 million tons. In addition for the next few years, especially in China, a number of new ε-caprolactam plants and expansion of existing ε-caprolactam plants will be put into operation. Almost all ε-caprolactam produced goes into the production of the polymer Nylon-6 (polyamide-6, PA6) that is applied in a broad range of (technical) products including carpets, clothing, tire cord, and many under-the-hood parts in the automotive industry. Virtually all ε-caprolactam is obtained by conversion of cyclohexanone oxime into ε-caprolactam in the presence of fuming sulfuric acid, also called oleum being sulfuric acid in which SO3 has been dissolved, whereby an ε-caprolactamsulfuric acid complex is formed. Then (aqueous) ammonia is added to neutralize the acid mixture and to detach the produced ε-caprolactam from the ε-caprolactam-sulfuric acid complex. As a result of the neutralization, ammonium sulfate is obtained as coproduct. Both reaction steps, the formation of ε-caprolactam and the subsequent neutralization, are strongly exothermic. These reactions are visualized in Figure 1. Nowadays, the conversion of an oxime into an amide is known as the Beckmann rearrangement reaction and reaction mixtures containing ε-caprolactam in oleum are often referred to as Beckmann rearrangement mixtures after a publication by Ernst Beckmann of almost 130 years ago.1 In 1951, Wichterle and Roček2,3 reported a kinetic model of the Beckmann rearrangement reaction of cyclohexanone oxime into ε-caprolactam. In the first paper they reported © 2015 American Chemical Society

Figure 1. Beckmann rearrangement reaction of cyclohexanone oxime to ε-caprolactam in fuming sulfuric acid (oleum) and the succeeding neutralization of sulfuric acid with (aqueous) ammonia whereby ammonium sulfate is formed.

rearrangement experiments of mixtures containing (30 to 80) % oleum (in all cases they used oleum with a sulfur trioxide mass fraction of 0.05). Because of the high reaction rates they performed their experiments at temperatures down to 283 K, which are far below industrial relevant process conditions that range from (363 to 403) K. Under these conditions they observed a first order kinetics with respect to the stoichiometric concentration of the cyclohexanone oxime and they presented the reaction rate constant and its temperature dependency. In Received: October 13, 2014 Accepted: March 3, 2015 Published: March 12, 2015 1056

DOI: 10.1021/je500836b J. Chem. Eng. Data 2015, 60, 1056−1062

Journal of Chemical & Engineering Data

Article

residence time of the produced ε-caprolactam under rearrangement conditions, which impacts the quality of the product. The second method is the addition of a solvent to the Beckmann rearrangement mixture. In general it is proposed to introduce the mixture of solvent and cyclohexanone oxime to the reaction zone. The purpose of the solvent is to absorb heat and in special cases even to evaporate partially or almost completely. Although this method has been described in several patents, any industrial application is not known to the authors.6−9 An important disadvantage of this method seems to be that none of the applied solvents is really inert and as a result new impurities are produced that might impact the quality of the produced ε-caprolactam. However, this method of dilution with an inert solvent has been applied in several research studies of Beckmann rearrangement of cyclohexanone oxime in micro reactors in order to prevent plugging of the micro channels.10−14 The third method is the addition of sufficient heat transfer area to remove the heat of reaction as soon as it is produced at a sufficient high heat transfer rate in order to prevent the appearance of high local temperatures. This requires a high surface to volume ratio of the reaction zone where the heat is produced. Micro reactors with their inherent large surface area over volume ratio might meet this requirement. However, up to now, to the knowledge of the authors, just one publication reported a successful Beckmann rearrangement of cyclohexanone oxime, without a solvent, in a micro reactor, despite rather high viscosities of the reaction mixture resulting in potential solidification or blockage of raw materials and reaction products in the feed lines, mixers, and reaction zones.15 Although equipment to perform Beckmann rearrangement reactions have already been designed and applied for a long period of time, physical data, especially density, dynamic viscosity, and surface tension, are not available in the open literature. The objective of this paper is to determine and describe density, dynamic viscosity, and surface tension of liquid phase Beckmann rearrangement mixtures of ε-caprolactam and fuming oleum over wide ranges of both temperatures and molar ratios. Based on the experimental results, correlations will be presented for these physical properties as functions of temperature and composition. These correlations might be useful for future design and optimization of equipment (both micro reactors and full-scale apparatus) for handling liquid phase Beckmann rearrangement mixtures.

the second paper they measured the influence of the SO3 mass fraction ranging from 0.00 to 0.28 at a temperature of 303 K. Again first order kinetics were observed. For low sulfur trioxide mass fractions (i.e., 0.00 to 0.05) the reaction rate increases strongly with the SO3 content, and then for sulfur trioxide mass fractions ranging from 0.05 to 0.12 the reaction rate is constant, while for higher SO3 contents increasing reaction rates were observed again. In 2008, Fábos et al.4 suggested that the ε-caprolactam− sulfuric acid complex is in fact the ionic liquid caprolactamium hydrogen sulfate. Based on the experimentally determined low values of vapor pressures of dissolved SO3 in Beckmann rearrangement mixtures they proposed a strong interaction between the ionic liquid and sulfur trioxide by formation of another anion such as [HS2O7]−. It is quite common to quantify the composition of Beckmann rearrangement mixtures by the so-called molar ratio M. The molar ratio M of a reaction mixture is defined as quantities of acids over the sum of quantities of ε-caprolactam and its precursors in that reaction mixture: M = (n H2SO4 + nSO3)/(ncap + noxime)

(1)

where nH2SO4, nSO3, ncap, and noxime are the quantities of sulfuric acid, sulfur trioxide, ε-caprolactam, and cyclohexanone oxime in the reaction mixture. In fact the M ratio is the molar ratio of sulfur atoms over nitrogen atoms in the reaction mixture. This molar ratio M is not to be confused with the molar ratio of the reaction mixture defined as quantities of acids over the sum of quantities of acids, ε-caprolactam and its precursors, so the ratio of sulfur atoms over the sum of sulfur and nitrogen atoms in the reaction mixture. In industrial practice high conversion of cyclohexanone oxime (i.e., almost 1) and high selectivity toward ε-caprolactam (i.e., > 0.99) are required because of both product quality and economic reasons. The combination of reaction times in the order of milliseconds to seconds and the strongly exothermic reaction would lead to an almost instantaneous release of the massive heat of reaction resulting in high local temperatures, due to insufficient removal of heat under industrial relevant conditions. Such high temperatures cause the formation of byproducts, hence reducing the quality of the produced ε-caprolactam and the yield and selectivity. In theory a molar ratio M of 1 should be sufficient to obtain full conversion of cyclohexanone oxime. However, reaction mixtures with equimolar amounts of caprolactam and sulfuric acid (M = 1) have, even at increased temperatures, very high viscosities,4 which makes mixing, required for mass and heat transfer, very difficult, resulting in poor selectivities and yields. Increasing the M ratio by addition of extra sulfuric acid and/or SO3 results in reaction mixtures with reduced viscosity and as a result mixing becomes less challenging. In industrial practice values of M ranging up to 1.7 are applied. These higher values of M are in general considered as undesirable because these also result in the formation of large quantities of the coproduct ammonium sulfate. To mitigate the problem of local high temperature, several scenarios can be followed. The first one, which is applied in industrial practice, is dilution: a large recycle loop (50 times) in comparison with the cyclohexanone oxime feed is used to limit the temperature rise and to maintain a high selectivity.5 A disadvantage of this method is that it results in a large reactor volume and a long

2. EXPERIMENTAL SECTION 2.1. Materials. The synthetic oleum/ε-caprolactam mixtures that were used for the various measurements were produced by mixing accurately weighted quantities of oleum, ε-caprolactam and sulfuric acid of known composition, see Table 1. The Table 1. Used Chemicals chemical name

source

initial puritya (mass fraction)

analysis method

sulfuric acid oleum ε-caprolactam

Merck Sigma-Aldrich DSM

0.95−0.97 0.20−0.30 0.9995

titration titration NMR

a

Final concentrations in mixtures determined by NMR, HPLC, and titration.

resulting synthetic reaction mixtures were measured by NMR, HPLC and titration for verification of the chosen composition. The compositions of the obtained Beckmann rearrangement 1057



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3. RESULTS AND DISCUSSION 3.1. Density. In Figure 2 and Table 2, the experimental results of the density measurements for five oleum/ ε-caprolactam mixtures with molar ratio M values ranging from 1.4 to 2.6 in the temperature range of (293 to 383) K are shown. The error on the measured density is approximately 1.2 kg·m−3. From this figure a linear reduction in density with an increase of temperature can be observed for all five oleum/ ε-caprolactam mixtures; in addition the density of these mixtures is decreasing with an almost similar rate. Another observation is that, at the same temperature, the oleum/ ε-caprolactam mixture with the lowest molar ratio M value has the lowest density and that the density of the oleum/ ε-caprolactam mixtures increases almost linear with the molar ratio M. There is a difference of more than 100 kg·m−3 between the densities of an oleum/ε-caprolactam mixture with molar ratio M of 2.6 and a mixture with molar ratio M of 1.4. The (volumetric mass) density, ρ, of liquids and liquid mixtures is frequently expressed as a quadratic polynomial expression with temperature. However, in case of a rather limited temperature range an equation that is reduced to a linear relationship with temperature is in general satisfactory:

mixtures are expressed in the molar ratio M of acid over ε-caprolactam and its precursors as defined in eq 1. 2.2. Measurements. The temperature of the liquids during the measurements of density, dynamic viscosity, and surface tension was maintained by a Lauda ecoline thermostatic bath. The density was determined by means of a calibrated Blaubrand pycnometer (Borosilicate glass 3.3; DIN ISO 3507; Gay-Lussac type; with 10/19 capillary stopper; actual volume given to 1·10−9 m3 accuracy, based on calibration with distilled mercury, ρHg = 13545.892 kg·m−3, at 293.15 K).16 The dynamic viscosity of the oleum/ε-caprolactam mixtures was measured using a viscometer with rotating spindle at various speeds (Brookfield Viscometer DV-I Prime; spindle 61). Calibration was performed using mineral oil viscosity standard fluids B29 (η = 29 mPa·s) and B200 (η = 200 mPa·s; Brookfield Engineering Laboratories) at 298.15 K. The surface tension of the mixtures was quantified by a SensaDyna 6000 surface tensiometer by the maximum bubble pressure method and was calibrated by demineralized water (7.275·10−2 N·m−1 at T = 293.15 K)17 and ethanol (2.231·10−2 N·m−1 at T = 293.15 K).17 Absolute/relative standard uncertainties in densities, dynamic viscosities and surface tensions of the mixtures as given in Tables 2, 3, and 4 (u(ρ), ur(η), and ur(σ), respectively) are based on repeated experiments for each quantity, starting with fresh mixtures.

ρ = ρM + A T1T

where ρ and ρM are the density and the reference density, respectively, T is the absolute temperature, and AT1 is a correlation parameter. Density experimental data obtained for each of the five investigated Beckmann rearrangement mixtures were correlated by linear relationships as described by eq 2. In order to incorporate the effect of the molar ratio M on the density, the following modified mathematical relationship, in which the reference density is extended with a linear dependency on the molar ratio M, is proposed:

Table 2. Experimental Data for Density of Synthetic Beckmann Rearrangement Mixtures (i.e., Mixtures of ε-Caprolactam with H2SO4 and SO3) as a Function of Temperature and M Value, whereby M Is Defined as the Molar Ratio of Acid over ε-Caprolactam and Its Precursorsa M ratio

ε-cap fraction

H2SO4 fraction

SO3 fraction

T

density (ρ)

mol·mol−1

mass fraction

mass fraction

mass fraction

K

kg·m−3

2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.3 2.3 2.3 2.0 2.0 2.0 2.0 1.7 1.7 1.7 1.7 1.4 1.4 1.4 1.4 1.4

0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.34 0.34 0.34 0.37 0.37 0.37 0.37 0.42 0.42 0.42 0.42 0.47 0.47 0.47 0.47 0.47

0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.55 0.55 0.55 0.52 0.52 0.52 0.52 0.47 0.47 0.47 0.47 0.42 0.42 0.42 0.42 0.42

0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11

293.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 293.15 343.15 373.15 293.15 346.15 373.15 383.15 293.15 343.15 373.15 383.15 293.15 323.15 343.15 373.15 383.15

1543.3 1523.2 1515.3 1509.0 1501.3 1492.8 1487.3 1478.6 1521.0 1487.5 1473.7 1501.2 1462.1 1444.0 1436.3 1473.8 1438.1 1417.5 1410.1 1439.6 1420.1 1406.0 1386.0 1379.1

(2)

ρ = ρM = 0 + AM M − A T2 T

(3)

where ρ is the density, ρM=0 is the reference density at M = 0, M is the molar ratio, T is the absolute temperature, and AM and AT2 are positive correlation parameters. The best fitted values for the parameters ρM=0, AM, and AT2 that were obtained by multiple linear regression with constant absolute error are listed in Table 5. The lines in Figure 2 are plotted from the correlation results based on eq 3. From the results it follows that the coefficients of the linear thermal expansion and the volumetric thermal expansion of Beckmann rearrangement mixtures are in the order of (2.3·10−4 and 6.9·10−4) K−1, respectively. It should be noticed that the thermal expansion coefficients of Beckmann rearrangement mixtures are comparable to those reported for various ionic liquids.18 3.2. Dynamic Viscosity. Dynamic viscosity experimental data obtained for the five oleum/ε-caprolactam mixtures under atmospheric conditions are presented as a function of absolute temperature in Figure 3 and Table 3. The decrease in viscosity with increasing temperature is expected and corresponds with observations reported in literature of other liquids and liquid mixtures.19 It is observed that the dependency of viscosity on temperature is exponential. By increasing the temperature by 50 K the dynamic viscosity of an oleum/ε-caprolactam mixture with a M value of 1.4 drops with a factor of more than 10. The dependency of viscosity on temperature is more marked in the case of Beckmann rearrangement mixtures with low M ratios compared to those with higher values. Dynamic viscosities for

a

p = 0.1 MPa. Standard uncertainties u are u(T) = 0.05 K, ur(M) = 0.02, and u(ρ) = 1.2 kg·m−3. 1058



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Table 3. Experimental Data for Dynamic Viscosity of Synthetic Beckmann Rearrangement Mixtures (i.e., Mixtures of ε-Caprolactam with H2SO4 and SO3) as a Function of Temperature and M Value, whereby M Is Defined as the Molar Ratio of Acid over ε-Caprolactam and Its Precursorsa M ratio

ε-cap fraction

H2SO4 fraction

SO3 fraction

T

viscosity (η)

M ratio

ε-cap fraction

H2SO4 fraction

SO3 fraction

mol·mol−1

mass fraction

mass fraction

mass fraction

K

mPa·s

mol·mol−1

mass fraction

mass fraction

2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0

0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37

0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52 0.52

0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11

319.15 323.15 327.15 330.15 337.15 338.15 344.15 345.15 350.15 350.15 358.15 364.15 318.15 322.15 326.15 330.15 336.15 338.15 341.15 346.15 350.15 354.15 357.15 360.15 361.15 368.15 370.15 318.15 325.15 326.15 332.15 336.15 343.15 343.15 348.15 351.15

59 44 43 34 33 26 26 21 21 17 17 14 85 65 62 49 47 39 37 30 28 24 22 19 19 16 14 142 120 102 87 65 56 50 39 43

2.0 2.0 2.0 2.0 2.0 2.0 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4

0.37 0.37 0.37 0.37 0.37 0.37 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47

0.52 0.52 0.52 0.52 0.52 0.52 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.42

a

T

viscosity (η)

mass fraction

K

mPa·s

0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11

353.15 358.15 363.15 366.15 371.15 378.15 320.15 321.15 327.15 327.15 333.15 336.15 340.15 343.15 347.15 349.15 353.15 357.15 359.15 367.15 368.15 377.15 318.15 330.15 331.15 338.15 340.15 344.15 347.15 353.15 353.15 358.15 362.15 368.15 369.15 377.15

31 34 25 27 22 20 320 320 218 220 220 151 164 106 111 79 81 60 42 43 34 33 970 549 695 350 405 203 271 182 158 112 130 84 94 71

p = 0.1 MPa. Standard uncertainties u are u(T) = 0.05, ur(M) = 0.02, and ur(η) = 0.08.

Later, in 1913, de Guzman21 proposed another simple empirical equation, again with just two adjustable parameters, for the dependency of liquid viscosity with temperature at a fixed pressure.

the various oleum/ε-caprolactam mixture fractions were found to be independent of rotation speed of the spindle. Liquid phase dynamic viscosity is formally defined as a measure of the resistance to gradual deformation by shear stress or tensile stress, but it is more known by its informal notion of “thickness”. In contrast to gas phase viscosity there is no widely accepted simple theoretical method for describing liquid viscosity. A theoretical description of a liquid is difficult due to long-range (attraction) effects, wide-range (electrostatic) effects, and intermolecular forces, which consist of short-range repulsion and hydrogen bonding. In 1886, Reynolds20 proposed a simple exponential model with just two parameters for the temperature dependency of viscosity:

η = η0R exp( −C R T )

η = η0G exp(CG/T )

(5)

where η is the dynamic viscosity, T is the absolute temperature, and η0G and CG are positive correlation parameters. Notwithstanding, that later many more multiparameter equations were developed, including the famous Vogel equation,22 which is in fact a modification of the Guzman equation with three adjustable parameters, in this paper we will limit us to (modifications of) the aforementioned two basic equations for viscosity-temperature relationship for Beckmann rearrangement mixtures. The dynamic viscosity data were fitted to both a Reynolds equation and a de Guzman equation as described by eqs 4 and 5,

(4)

where η is the dynamic viscosity, T is the absolute temperature, and η0R and CR are positive correlation parameters. 1059



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Table 4. Experimental Data for Surface Tension of Synthetic Beckmann Rearrangement Mixtures (i.e., Mixtures of ε-Caprolactam with H2SO4 and SO3) as a Function of Temperature and M Value, whereby M Is Defined as the Molar Ratio of Acid over ε-Caprolactam and Its Precursorsa M ratio

ε-cap fraction

H2SO4 fraction

SO3 fraction

T

surface tension (σ)

mol·mol−1

mass fraction

mass fraction

mass fraction

K

mN·m−1

2.6 2.6 2.6 2.6 2.6 2.6 2.6 2.3 2.3 2.3 2.3 2.3 2.3 2.3 2.0 2.0 2.0 2.0 2.0 1.7 1.7 1.7 1.7 1.7 1.7 1.7 1.4 1.4 1.4 1.4 1.4 1.4 1.4

0.31 0.31 0.31 0.31 0.31 0.31 0.31 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.37 0.37 0.37 0.37 0.37 0.42 0.42 0.42 0.42 0.42 0.42 0.42 0.47 0.47 0.47 0.47 0.47 0.47 0.47

0.58 0.58 0.58 0.58 0.58 0.58 0.58 0.55 0.55 0.55 0.55 0.55 0.55 0.55 0.52 0.52 0.52 0.52 0.52 0.47 0.47 0.47 0.47 0.47 0.47 0.47 0.42 0.42 0.42 0.42 0.42 0.42 0.42

0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11

293.15 313.15 323.15 343.15 363.15 383.15 393.15 293.15 313.15 323.15 343.15 363.15 383.15 393.15 293.15 333.15 343.15 363.15 383.15 293.15 313.15 323.15 343.15 363.15 383.15 393.15 293.15 323.15 333.15 343.15 363.15 383.15 393.15

68 61 58 55 52 51 50 81 68 63 59 56 54 53 92 65 62 57 55 119 88 79 67 61 57 55 135 103 93 80 68 62 58

Figure 2. Measured density vs absolute temperature for oleum/ ε-caprolactam mixtures with molar ratio acid over ε-caprolactam, M, ranging from 1.4 to 2.6. Yellow dot, M = 2.6; blue square, M = 2.3; red dot, M = 2.0; green triangle, M = 1.7; purple diamond, M = 1.4. The depicted solid lines are best fit linear trend lines, according to eq 3

Table 5. Coefficients ρM=0, AM, and AT2 of the Optimized Density eq 3 for Densities of Beckmann Rearrangement Mixturesa ρM=0 −3

kg·m

1530 (±21)

AM kg·m

−3

83.6 ± 3.8

AT2 kg·m−3·K−1

R2

0.689 (±0.054)

0.993

a

95 % confidence intervals are given in parentheses. Temperature range: from (293 to 383) K. M-value range: 1.4 to 2.6

a

p = 0.1 MPa. Standard uncertainties u are u(T) = 0.05, ur(M) = 0.02, and ur(σ) = 0.04.

respectively. Both equations were modified to account for the effect of molar ratio M on dynamic viscosity. In the following modified version of the Reynolds equation the correlation parameter η0R is replaced by a power law equation and the correlation parameter CR by a linear equation: η /η0 = M −BR exp(AR + (DR M − E R ) ·T

Figure 3. Experimental dynamic viscosity data of various Beckmann rearrangement mixtures with molar ratio acid over ε-caprolactam, M, ranging from 1.4 to 2.6, as a function of temperature at atmospheric pressure. Yellow dot, M = 2.6; blue square, M = 2.3; red dot, M = 2.0; green triangle, M = 1.7; purple diamond, M = 1.4. The depicted solid curves are best fit nonlinear trend lines, according to eq 6

(6)

where η is the dynamic viscosity, η0 is equal to 1 Pa·s, T is the absolute temperature, and AR, BR, DR, and ER are positive correlation parameters. The best fitted values for the parameters AR, BR, DR, and ER that were obtained by nonlinear regression with constant relative error are listed in Table 6. Lines in Figure 3 are plotted from the correlation results based on eq 6. In order to incorporate the effect of molar ratio M in the Guzman correlation, eq 5, several fitting simulations were performed. However, for the entire range of temperatures and

M values, no proper agreement with experimental dynamic viscosity results could be obtained; even for the best case the average deviation between experimental and calculated data was over 30 %. 3.3. Surface Tension. Figure 4 and Table 4 present the dependency of the measured surface tensions of oleum/ ε-caprolactam mixtures with molar ratios ranging from 1.4 to 2.6 as a function of temperature. The measured surface tension for these Beckmann rearrangement mixtures ranges from 50 mN·m−1 (at T = 393 K and M = 2.6) to 135 mN·m−1 (at 1060



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Table 6. Coefficients AR, BR, DR, and ER of the Optimized Reynolds Viscosity eq 6 for Dynamic Viscosities of Beckmann Rearrangement Mixturesa DR AR

BR

16.8 (±1.1)

9.5 (±1.6)

K

−1

0.0084 (±0.0024)

the presence of sulfur trioxide. Their reported surface tension value for various oleum concentrations was about 51 mN·m−1 at 303.15 K, which is just somewhat lower than our value for the Beckmann rearrangement mixture with the highest molar ratio (i.e., M = 2.6). The best fit of the experimental surface tension data points for the mixture with molar ratio M = 2.6 is obtained by a power law dependence on temperature with an exponent of about −1.0. While for the mixture with molar ratio M = 1.4 a power law dependence on temperature with an exponent of about −2.9 is found. This shows that the effect of the molar ratio M should be incorporated in the relationship as described by eq 7. In fact both correlation factors in eq 7 were modified in order to incorporate the effect of the molar ratio M on the surface tension:

ER K−1

R2

0.055 (±0.005)

0.982

a

95 % confidence intervals are given in parentheses. Temperature range: from 318 to 378 K. M-value range: 1.4 to 2.6

σ /σ0 = exp(A s − Bs M )(T /T0)(DsM − Es)

(8)

where σ is the surface tension, σ0 is a surface tension step of 1 N·m−1, T is the absolute temperature, T0 is a temperature step of 1 K, and As, Bs, Ds, and Es are dimensionless positive correlation parameters. The best values for the fitted parameters As, Bs, Ds, and Es that were obtained by nonlinear regression with constant relative error are listed in Table 7. Lines in Figure 4 are drawn from the correlation results based on eq 8. Table 7. Coefficients As, Bs, Ds, and Es of the Optimized Surface Tension eq 8 for Surface Tensions of Beckmann Rearrangement Mixturesa

Figure 4. Surface tension data of oleum/ε-caprolactam mixtures with molar ratio acid over ε-caprolactam, M, ranging from 1.4 to 2.6. Yellow dot, M = 2.6; blue square, M = 2.3; red dot, M = 2.0; green triangle, M = 1.7; purple diamond, M = 1.4. The depicted curves are best fit nonlinear trend lines, according to eq 8

As

Bs

Ds

Es

R2

28.6 (±5.2)

10.0 (±2.5)

1.65 (±0.43)

5.2 (±0.9)

0.961

a

95 % confidence intervals are given in parentheses. Temperature range: from 293 to 393 K. M-value range: 1.4 to 2.6

T = 293 K and M = 1.4). As can be seen from Figure 4, the surface tension increases with decreasing molar ratios of acid over ε-caprolactam. For all mixtures the surface tension is decreasing with increasing temperature. This dependency of surface tension on temperature is more marked in case the molar ratio of the oleum/ε-caprolactam mixture is reduced. For the mixture with the highest molar ratio (i.e., M = 2.6) a temperature increase from (293 to 393) K results in a drop of the surface tension of about 26 %, while for the mixture with the lowest molar ratio (i.e., M = 1.4) such a temperature increase leads to a decrease of about 57 %. Surface tension of a liquid is defined as the force that is required to close a cut of unit length in the surface of that liquid. So, the physical property surface tension is, in contrast to properties like density and viscosity, very much related to the structure and molecular distribution at the surface rather than those in the bulk of the liquid. Beckmann rearrangement mixtures with their ionic liquid characteristics are expected to own some degree of both structural and charge anisotropy. Although, often, the effect of temperature on the surface tension of a liquid is described with a linear relationship, we propose the following power law type of description: σ = σ0s(T /T0)−Cs

4. CONCLUSION Density, dynamic viscosity, and surface tension of liquid phase Beckmann rearrangement mixtures, consisting of ε-caprolactam and fuming oleum, have been determined in the temperature range (293 to 393) K. For each mixture of ε-caprolactam and fuming oleum, the measured values of density, dynamic viscosity, and surface tension reduced with increasing temperature. All these physical properties are severely impacted by the molar ratio of acid over ε-caprolactam M. The density increases linearly with molar ratio M, while both dynamic viscosity and surface tension have a decreasing trend with increasing molar ratio M. All experimental data are visualized in the figures; the results have been modeled and evaluated using several empirical equations. These equations, which include the dependency of both temperature and molar ratio M describe the experimental data quite well. The proposed equations for the physical properties can be applied to the simulation of operating conditions and to optimize design under various conditions.

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(7)

where σ is the surface tension, T is the absolute temperature, T0 is equal to 1 K, and σ0s and Cs are positive correlation parameters. The data points obtained for the various Beckmann rearrangement mixtures can be described with power law equations (see Figure 4). In 1969 Gillespie et al.23 determined the surface tension for both 100 % sulfuric acid and oleum with various SO3 contents. They concluded that the surface tension is hardly affected by

AUTHOR INFORMATION

Corresponding Author

*Tel: 31-40-2473088. Fax: 31-40-2446653. E-mail: j.c.schouten@ tue.nl. Funding

This work was supported by NWO ASPECT under Project No. 053.62.010. We thank Wessel Hengeveld and Digpalsinh Raulji for measuring the various physical properties of Beckmann rearrangement mixtures. 1061



Article

Notes

(21) de Guzman, J. Relation between fluidity and heat of fusion. An. Soc. Esp. Fis. Quim. 1913, 11, 353−362. (22) Vogel, H. D. Temperaturabhängigkeitsgesetz der Viskosität von Flüssigkeiten. Physics 1921, 22, 645−646. (23) Gillespie, B. E.; Smith, M. J.; Wyatt, P. A. H. Surface tension measurement in solvent sulphuric acid. J. Chem. Soc. A 1969, 304−306.

The authors declare no competing financial interest.

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REFERENCES

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Density, Viscosity, and Surface Tension of Liquid Phase Beckmann

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