Article pubs.acs.org/jced
Thermal and Mutual Diffusivity of Binary Mixtures of n‑Dodecane and n‑Tetracontane with Carbon Monoxide, Hydrogen, and Water from Dynamic Light Scattering (DLS) Andreas Heller,† Matthieu S. H. Fleys,‡ Jiaqi Chen,‡ Gerard P. van der Laan,‡ Michael H. Rausch,†,§ and Andreas P. Fröba*,†,§ †
Erlangen Graduate School in Advanced Optical Technologies (SAOT), University of Erlangen-Nuremberg, Paul-Gordan-Straße 6, D-91052 Erlangen, Germany ‡ Shell Global Solutions International B.V., Grasweg 31, 1031 HW Amsterdam, The Netherlands § Department of Chemical and Biological Engineering, Institute of Engineering Thermodynamics, University of Erlangen-Nuremberg, Am Weichselgarten 8, D-91058 Erlangen, Germany ABSTRACT: The present work represents a continuation of a former study where the simultaneous determination of thermal and mutual diffusivity for binary mixtures of n-octacosane (nC28H58) with dissolved carbon monoxide (CO), hydrogen (H2), or water (H2O) by using dynamic light scattering (DLS) was demonstrated. Here, the same properties are studied for binary mixtures of the n-alkanes n-dodecane (n-C 12 H 26 ) or ntetracontane (n-C40H82) with dissolved CO, H2, or H2O. In most cases, expanded relative uncertainties (k = 2) ranging from 2 to 12 % and 3 to 25 % for the thermal and mutual diffusivities could be obtained. The experimental mutual diffusivities for mixtures of n-C12H26 with CO, H2, or H2O measured at temperatures from 398 to 524 K and pressures from 0.2 to 4.2 MPa at saturation conditions agree well with molecular dynamics (MD) simulations using atomistic models and with experimental data from literature. Binary mixtures of n-C40H82 with dissolved CO, H2, or H2O were investigated in a temperature range from 447 to 498 K and pressures from 0.3 to 3.9 MPa. For mixtures with n-C40H82, the accessible temperature range was limited due to a change in the optical characteristics of the sample at elevated temperatures where DLS measurements suffered from absorption effects and particle scattering.
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INTRODUCTION Transport properties of liquids containing dissolved gases are of technological interest in different industrial fields of chemical and energy engineering.1−3 For example, the production of high valued petroleum products from synthesis gas by the Fischer− Tropsch synthesis has been for several decades and still is a frequently discussed topic in chemical engineering. Here, information on the mutual diffusivity of compounds typically found in such systems is required for a fundamental understanding and adequate modeling of the process.1 In a previous study, thermal and mutual diffusivities of binary mixtures of n-octacosane (n-C28H58) with dissolved hydrogen (H2), carbon monoxide (CO), or water (H2O) determined from dynamic light scattering (DLS) experiments were reported.4 In the present study, the same transport properties of homologous binary systems consisting of n-dodecane (nC12H26) or n-tetracontane (n-C40H82) and dissolved H2, CO, or H2O investigated by DLS are presented and compared with our previous results, literature data, and theoretical values from molecular dynamics (MD) simulations. Systems containing nC12H26 were investigated in a process-relevant temperature © 2016 American Chemical Society
range from 398 to 524 K at pressures between 0.2 and 4.2 MPa. In three cases, it could be observed that thermal and mutual diffusivity are identical. In this context, a possible coupling effect between the corresponding hydrodynamic modes will be discussed. The systems containing n-C40H82 could only be investigated in a limited temperature range from 447 to 498 K because of a change in the optical characteristics of the sample at elevated temperatures.
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METHOD The main advantage of the DLS technique is its capability of determining thermophysical properties in macroscopic thermodynamic equilibrium. The method allows for an absolute determination of thermophysical properties with high accuracy over a wide range of thermodynamic states.5,6 In the following, a brief introduction to the underlying theory of DLS from bulk fluids is given. For a more detailed description of the Received: November 20, 2015 Accepted: January 27, 2016 Published: February 15, 2016 1333
DOI: 10.1021/acs.jced.5b00986 J. Chem. Eng. Data 2016, 61, 1333−1340
Journal of Chemical & Engineering Data
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EXPERIMENT AND DATA EVALUATION The experimental setup, the sample cell, and the temperature control system employed for the determination of thermal and mutual diffusivity are described in detail in our previous study.4 In the following, only the experimental conditions as well as the sample preparation procedure within the present investigations are summarized. Materials and Sample Preparation. According to the specifications of the manufacturer, the purchased n-alkanes nC12H26 (Merck KGaA) and n-C40H82 (Alfa Aesar GmbH & Co. KG) had purities of >99% and >97% by mass. CO and H2 were provided by Linde AG with purities of 99.997 vol % and 99.9999 vol %. Deionized water generated by an ion-exchanger was utilized for the aqueous mixtures. All other materials except for n-C40H82 were used without further purification. The nC40H82 sample delivered by the manufacturer contained particles, see Figure 1a. Thus, the sample was heated in a
fundamentals and methodological principles, the reader is referred to specialized literature.7−9 When coherent light irradiates a translucent fluid sample in macroscopic thermodynamic equilibrium, light scattered from the sample can be observed in all directions. The underlying scattering process is governed by microscopic fluctuations in temperature, pressure, and in species concentration in fluid mixtures. The relaxations of these statistical fluctuations follow the same laws valid for relaxations in macroscopic systems. The decay of temperature fluctuations is governed by the thermal diffusivity a. Pressure fluctuations in fluids are moving with sound speed cS, and their decay is governed by the sound attenuation DS. In a fluid mixture, the decay of concentration fluctuations is related to mass diffusivities. In the simplest case of a binary fluid mixture, this is represented by the binary diffusion coefficient or mutual diffusivity D12. In light scattering experiments, the above-mentioned equilibration processes result in a temporal modulation of the scattered light intensity. From the calculated time-dependent intensity correlation function (CF), the mutual and thermal diffusivity can be evaluated for binary mixtures.7−9 Realizing heterodyne DLS experiments, where much stronger reference light is superimposed on the scattered light, the CF takes the form of a superposition of two exponentially decaying functions according to g(2)(τ ) = b0 + bt exp( −τ /τC,t) + bc exp(−τ /τC,c)
(1)
Here, b0, bt, and bc are experimental constants. In eq 1, the decay times τC,t and τC,c can be interpreted as mean life times or relaxation times of temperature and concentration fluctuations. From the two relaxation times evaluated from the experiment at a defined scattering geometry, the mutual diffusivity D12 and thermal diffusivity a can be calculated according to a=
1 τC,tq2
and
D12 =
1 τC,cq2
Article
Figure 1. (a) Original n-C40H82 sample. (b) n-C40H82 sample after three filtering steps at about 360 K.
glass syringe to a temperature slightly above the melting temperature of 355 K and filtered by a syringe filter with a pore size of 200 nm 2 to 3 times. By this procedure, the sample could be purified, and a transparent colorless liquid could be obtained; see Figure 1b. A summary of the used chemicals is given in Table 1.
(2)
In eq 2, q is the modulus of the scattering vector which can be approximated by q ≅ 2πλ−1 0 sin Θi for small angles. Here, λ0 is the laser wavelength in vacuo, and Θi is the incident angle defined as the angle between the directions of detection of scattered light and of the incident light irradiating the sample. Investigations on binary systems consisting of n-C28H58 and dissolved gases as well as studies on a methane−ethane mixture in the near-critical region showed that a simultaneous determination of mutual and thermal diffusivity from only one CF is possible in case both transport properties expose similar values.4,10 The feasibility of resolving both signals from experimental CFs is mainly restricted by the ratio of scattering intensities resulting from fluctuations in temperature and concentration. This ratio strongly depends on the relative difference of the refractive indices of the two components and their concentration. In general, the simultaneous determination of both signals in binary mixtures is possible if the refractive indices of the two components are comparable, which holds for all mixtures studied here. In case of a large difference between the refractive indices, the scattered light intensity arising from concentration fluctuations dominates the CF. The separation of the exponential functions related to the relaxation of temperature and concentration from a single CF is possible if the corresponding decay times differ by a factor of more than 2. With increasing difference in the decay times, their uncertainties resulting from the regression decrease.
Table 1. Used Chemicals chemical name
source
initial purity
purification method
n-dodecane n-tetracontane hydrogen carbon monoxide water
Merck KGaA Alfa Aesar Linde AG Linde AG tap
>0.99a >0.97a 0.999999b 0.99997b
none filtration none none ion exchangec
a
Mass fraction. bVolume fraction. cSG Wasseraufbereitung, Germany, Model SG-2000, final conductivity
