Thermal Diffusivity of 2-Ethoxy-2-methylpropane ... - ACS Publications

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Thermal Diffusivity of 2‑Ethoxy-2-methylpropane (ETBE) and 2‑Methoxy-2-methylbutane (TAME) at Temperatures from (293 to 523) K and Pressure up to 10 MPa Ying Zhang, Xiong Zheng, Yutian Chen, and Maogang He* Key Laboratory of Thermo-Fluid Science and Engineering, Ministry of Education, Xi’an Jiaotong University, Xi’an, Shaanxi Province 710049, P. R. China ABSTRACT: The thermal diffusivities of 2-ethoxy-2-methylpropane (ETBE) and 2-methoxy-2-methylbutane (TAME) (mass purity > 0.990, GC) were measured by the dynamic light scattering method. The investigated p−T regions are T = (293 to 523) K and p = (4 to 10) MPa, including saturated liquid, saturated vapor, and liquid. The expanded relative uncertainty in thermal diffusivity was estimated to be less than 2.4% over the whole investigated range. The influences of temperature and pressure on thermal diffusivity were presented. The empirical correlation of thermal diffusivities for both saturated liquid/vapor and liquid were also proposed with absolute average relative deviations (AARDs) of 0.22 and 0.26% for saturated-liquid ETBE and TAME, 0.13 and 0.20% for saturated-vapor ETBE and TAME, and 0.23 and 0.69% for liquid ETBE and TAME, respectively.

1. INTRODUCTION

TAME binary and ternary mixtures with a series of substances, such as water, alcohols, ethers, hydrocarbons, ionic liquids, and other organic fluids. However, reports on the thermophysical properties of pure ETBE and TAME are have been scarce until now, which are considered to be the foundation of multicomponent systems that include ETBE or TAME. Casanova27 measured the saturated heat capacities of ETBE and TAME at temperatures ranging from 277.15 K to their normal boiling temperatures by employing a micro DSC. Efimova28 used comparative ebulliometry to measure the boiling temperatures of ETBE at pressures ranging from (11 to 102) kPa. GonzalezOlmos29 measured the ultrasonic velocities and densities of ETBE and TAME with an Anton Paar DSA-5000 device at T = (278.15 to 323.15) K and normal pressure. Gmehling30 measured the density of ETBE in the temperature range from (273 to 473) K and at a pressure of up to 40 MPa by employing a hightemperature, high-pressure vibrating tube densimeter system. Gmehling31 measured the vapor pressures of ETBE and TAME by ebulliometry in the pressure range of (14 to 102) kPa. Thermal diffusivity is one of the most essential transport properties and is important for investigating the mechanism of conductive heat transfer in various chemical processes. However, there is no available experimental data of thermal diffusivities for ETBE and TAME that have been presented so far. In the present work, the dynamic light scattering (DLS) method was employed

A variety of ethers have been considered to use alone or with other ethers or alcohols as fuel additives, which can increase the octane number and reduce pollution effects.1 2-Methoxy-2methylpropane (MTBE), which is a tertiary ether, has been mostly employed until now because of its high octane number, low Reid vapor pressure, and excellent availability of ethanol feedstock. Nevertheless, there is an obvious drawback in that MTBE can be easily dissolved in water and can contaminate groundwater. The International Agency of Research on Cancer (IARC) and the U.S. Environmental Protection Agency (EPA) classified MTBE as a health risk threat in 2000.1 Because MTBE has negative effects on the environment, ETBE and TAME have been considered to be suitable and alternative candidates as fuel additives among ether compounds.2 It is necessary to obtain an exact knowledge of the thermodynamic properties and transport properties of ether compounds for their applications. In recent years, much research has been focused on vapor−liquid and liquid−liquid equilibria,3−13 thermodynamic excess properties,14−17 density,3,18−23 viscosity,20,24,25 the speed of sound,21 and the solubility26 of ETBE and Table 1. Specifications of the Sample Used in This Work chemical

source

CAS RN

mass purity

toluene 2-ethoxy-2-methylpropane (ETBE) 2-methoxy-2-methylbutane (TAME)

Tianjin Baishi Aladdin Aladdin

108-88-3 637-92-3 994-05-8

>0.990 >0.990 >0.990

© 2017 American Chemical Society

Received: May 3, 2016 Accepted: January 19, 2017 Published: February 2, 2017 893

DOI: 10.1021/acs.jced.6b00365 J. Chem. Eng. Data 2017, 62, 893−901

Journal of Chemical & Engineering Data

Article

Figure 1. Typical photon correlation function for ETBE: ⧫, discrete points from the digital correlator; ---, fitted correlation function.

Table 2. Experimental Uncertainty in Temperature, Pressure, and Thermal Diffusivity temperature/K platinum resistance, u1 temperature stability, u2 resistance measurement circuits, u3 standard combined uncertainty, uc pressure/MPa pressure transmitter, u1 pressure measurement circuits, u2 pressure control system, u3 standard combined uncertainty, uc thermal diffusivity wavelength, ur(λ0) incident angle, ur(ΘEX) decay time, ur(τR) impurity, ur(i) relative standard combined uncertainty, ur(a)

Table 3. Comparison of the Thermal Diffusivity of SaturatedLiquid Toluene with Literature Dataa

0.005 0.008 0.002 0.01 0.001 (0−5.0 MPa) 0.007 (5.0−10 MPa) 0.001 0.015 (0−5.0 MPa) 0.030 (5.0−10 MPa) 0.015 (0−5.0 MPa) 0.030 (5.0−10 MPa) 3.76 × 10−5 0.001 0.01 0.006 0.012

to measure the thermal diffusivity over a wide temperature range, and new experimental data of ETBE and TAME are presented. Previously, our group has investigated the thermal diffusivity of MTBE at T = (303.15 to 493.15) K, p = (1.5 to 10) MPa and of di-isopropyl ether (DIPE) at T = (298 to 530) K, p = (1.5 to 10) MPa.32,33 Here an extension of the research program on the thermal diffusivity of ETBE and TAME is presented. The investigated temperature ranges are T = (293 to 496) K for saturatedliquid ETBE, T = (433 to 493) K for saturated-vapor ETBE, T = (291 to 493) K for saturated-liquid TAME, and T = (477 to 522) K for saturated-vapor TAME. Moreover, the isothermal thermal diffusivities at pressures p = (4, 7, and 10) MPa were also measured at T = (373 to 493) K for ETBE and T = (373 to 523) K for TAME. In addition, the temperature and pressure influences on the thermal diffusivities of ETBE and TAME were discussed, and the reference relations were given.

T/K

athis work/10−8 m2·s−1

aWill12/10−8 m2·s−1

Δ/%b

302.90 312.45 323.07 333.27 343.52 353.73 363.73 373.04 382.94 392.88 402.93 413.06 422.73 432.67 442.68 452.96 462.99 473.20 482.98 493.05 503.17 513.41 523.38

8.63 8.33 8.03 7.77 7.52 7.30 7.09 6.90 6.71 6.52 6.33 6.15 5.98 5.81 5.64 5.48 5.33 5.19 5.06 4.94 4.84 4.74 4.66

8.64 8.32 8.15 7.71 7.48 7.33 7.00 6.90 6.63 6.48 6.19 5.99 5.92 5.71 5.60 5.45 5.28 5.24 5.06 4.92 4.89 4.75 4.72

−0.13 0.18 −1.48 0.75 0.59 −0.47 1.27 −0.01 1.19 0.56 2.32 2.66 0.97 1.83 0.78 0.53 0.96 −1.02 −0.03 0.44 −1.09 −0.15 −1.18

a

The expanded uncertainties U are U(T) = 0.02 K, and the relative expanded uncertainty Ur is Ur(a) = 0.024. The level of confidence is 0.95 (k = 2). bΔ = 100 × (athis work − aWill)/aWill

TAME are higher than 0.990 (GC) as stated by the supplier. No further purification was carried out for the samples, which was considered to prevent sample alterations. The specifications of the sample are listed in Table 1. When filling the sample cell, membrane filters with 0.22 μm pore size were used to filter the samples in order to prevent dust and particles from accessing the sample cell. 2.2. Measurement Method and Apparatus. The dynamic light scattering (DLS) method was applied to investigate the thermal diffusivity in this work. DLS is considered to be an effective experimental approach to measuring a fluid’s thermal diffusivity. The distinct advantage of the DLS technique is that it

2. EXPERIMENTAL SECTION 2.1. Materials. The ETBE and TAME samples were supplied by Aladdin. The specified mass fractions both for ETBE and 894



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Table 4. Experimental Thermal Diffusivity of ETBE and TAME along the Saturation Linea T/K

a/10−8 m2·s−1

T/K

a/10−8 m2·s−1

T/K

a/10−8 m2·s−1

ETBE saturated liquid 293.13 303.09 313.21 323.18 333.18 338.25 343.17 348.15 353.08 358.19 363.10 368.12 373.11 378.18 saturated vapor 433.07 443.25 453.13 463.05

5.67 5.45 5.16 4.96 4.79 4.70 4.64 4.55 4.49 4.43 4.38 4.33 4.30 4.26

383.14 388.07 393.06 398.17 403.22 408.16 413.10 418.18 423.09 428.08 433.18 438.17 443.06 448.18

4.20 4.17 4.15 4.10 4.08 4.02 4.00 3.97 3.95 3.90 3.85 3.82 3.77 3.74

453.18 458.10 463.19 466.12 469.18 472.09 475.06 478.15 481.24 484.23 487.17 490.09 493.14 496.24

3.68 3.61 3.53 3.50 3.45 3.39 3.33 3.25 3.16 3.05 2.95 2.77 2.63 2.27

30.29 25.73 21.40 17.01

468.16 473.25 478.20

14.98 12.81 10.80

483.18 488.25 493.22

8.76 6.52 3.68

TAME saturated liquid 291.50 302.19 312.11 323.00 332.51 342.71 352.32 363.24 373.18 382.92 388.10 392.60 398.45 402.91 saturated vapor 477.88 483.74 487.65 493.04 a

6.65 6.36 6.17 5.95 5.75 5.50 5.33 5.18 5.00 4.84 4.75 4.68 4.61 4.55

418.23 423.00 428.55 432.78 438.24 442.67 448.19 453.53 458.62 463.30 468.10 472.00 478.34 482.92

4.36 4.30 4.24 4.20 4.14 4.10 4.04 3.98 3.95 3.90 3.87 3.83 3.81 3.78

488.23 492.26 498.77 501.90 504.05 506.94 508.48 511.05 514.02 517.73 519.01 522.19

3.75 3.71 3.63 3.60 3.58 3.52 3.51 3.42 3.36 3.20 3.15 2.98

25.44 22.96 21.31 18.98

499.05 502.72 508.18 511.38

16.26 14.52 12.06 10.52

517.41 522.45

7.83 4.20

The expanded uncertainties U are U(T) = 0.02 K, and the relative expanded uncertainty Ur is Ur(a) = 0.024. The level of confidence is 0.95 (k = 2).

can be used to determine the thermophysical properties of a fluid within the macroscopic thermodynamic equilibrium. DLS allows for an absolute measurement over a wide range of thermodynamic states.34−36 In the following text, a brief introduction of the DLS measuring principle and working equations is given. Complete and more detailed descriptions of the DLS principles can be found in specialized literature.37−41 Temperature relaxation is governed by the temperature diffusion equation, which has a close relationship with thermal diffusivity. For the pure fluid, the scattered light arises from the microscopic temperature (or entropy) fluctuation at constant pressure. The decay time in the time correlation function of the photocurrent is related to the sample’s thermal diffusivity. Therefore, the photon correlation technique was employed in the work, and the photon autocorrelation function, which is expressed as an exponential decay function, is shown as

G(τ ) = A + B exp( −τ /τR )

(1)

where τR is the decay constant or decay time and A and B are the fitted constants. As shown in Figure 1, the discrete experimental data points, which were collected by the correlator, were employed to determine the photon correlation function G(τ) by nonlinear least-squares fitting (NLSF), and the decay constant τR can be determined. The thermal diffusivity as a function of the decay constant is shown as

a = 1/(q2τR )

(2)

where a is the thermal diffusivity and q is the scattering vector modulus. The scattering vector is related to the laser wavelength in vacuum (λ0) and the incident angle (ΘEX) as shown by eq 3. q = 2π sin ΘEX /λ 0 895

(3) DOI: 10.1021/acs.jced.6b00365 J. Chem. Eng. Data 2017, 62, 893−901


Article

Figure 2. Experimental thermal diffusivities of saturated ETBE and TAME: ■, saturated-liquid ETBE; □, saturated-vapor ETBE; ⧫, saturated-liquid TAME; ◊, saturated-vapor TAME; and ---, fitted line.

Table 5. Fitted Coefficients in Equations 6 and 9a ETBE A B C D E F

AARD/% MD/% bias/% TAME A B C D E F

AARD/% MD/% bias/% a

saturated liquid

saturated vapor

1.1829 × 10−3 1.4584 × 10−1 5.9751 × 10−1 −1.2702 × 100 −3.2377 × 100 9.3449 × 100

7.1877 × 10−4 −7.8774 × 10−1 3.3875 × 10−1 −4.2147 × 100 2.0904 × 101 −4.1230 × 100

0.22 0.83 0.0062 4.0697 × 10−2 −1.1524 × 10−1 9.9833 × 100 −1.1781 × 101 2.3900 × 100 −2.0865 × 100

0.26 0.94 0.0051

0.13 0.41 0.0003 3.8807 × 10−3 5.2633 × 10−3 −7.4027 × 10−2 4.4610 × 10−1 −1.7468 × 107 7.6071 × 102

0.20 0.51 0.0001

liquid c00 c01 c02 c10 c11 c12 c20 c21 c22 AARD/% MD/% bias/%

−1.7541 × 101 6.3526 × 100 −3.8121 × 10−1 1.1228 × 10−1 −3.0789 × 10−2 1.8363 × 10−3 −1.4512 × 10−4 3.7407 × 10−5 −2.2090 × 10−6 0.23 1.55 −0.0003

c00 c01 c02 c10 c11 c12 c20 c21 c22 AARD/% MD/% bias/%

8.5615 × 101 1.1217 × 101 −4.0087 × 10−2 −9.1459 × 10−3 −4.9827 × 10−3 1.8353 × 10−4 −2.0568 × 10−6 5.8806 × 10−6 −2.1816 × 10−7 0.69 1.57 0.0006

The coefficients cij are in units of 10−8 m2·s−1, whereas A−F is dimensionless. 896



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Figure 3. Deviations of experimental thermal diffusivities and calculation results from the fit according to eq 6: ■, saturated-liquid ETBE; □, saturatedvapor ETBE; ⧫, saturated-liquid TAME; and ◊, saturated-vapor TAME.

and 2.4% over the whole examined p−T region with a coverage factor of k = 2, respectively.

By coupling eqs 2 and 3, the thermal diffusivity of the sample can be obtained. The experimental setup is the same as that in our previous paper33 and similar to that employed by Leipertz et al.42,43 Here only the main equipment is listed briefly. A laser (Cobolt Samba, 532 nm, 300 mW) with a single longitudinal mode is adopted as the light source. The photon-counting heads (Hamamatsu H8259-01) and a digital correlator (Brookhavern BI-9000AT) are used to process the scattered light signal. The sample is heated by the electric heater that is controlled by the intelligent temperature controller (Shimaden, FP23). A platinum resistance thermometer (Fluke 5608-12) was employed to measure the temperature. A piston pump (HIP 87-6-5) was used to control the pressure that was measured by the pressure transmitter (Rosemount 3051s). 2.3. Experimental Uncertainty Evaluation. The experimental uncertainties in temperature and pressure can be determined as follows U = kuc = k

∑ ui 2

3. RESULTS AND DISCUSSION First, the thermal diffusivities of saturated-liquid toluene were measured at T = (303 to 523) K in order to test the experimental apparatus reliability. The toluene sample was purchased from Tianjin Baishi Chemical Industry Co. Ltd., and the mass fraction is more than 0.990 as stated by the supplier. Compared to the experimental thermal diffusivities of saturated-liquid toluene presented by Will et al. from the DLS method,45 the absolute average relative deviation (AARD) is 0.90% and the maximum deviation (MD) is 2.66%, which is shown in Table 3. The experimental data are in good agreement with the literature data. 3.1. Saturated Liquid and Vapor. Measurements of ETBE and TAME thermal diffusivities were carried out along the saturation line. In the measurement process, the sample vessel was evacuated first and the pressure in the sample vessel was maintained at below 5 Pa for more than an hour. Then the sample was injected into the sample vessel and maintained in the vapor−liquid coexisting state to meet the saturation requirement. Six absolutely independent measurements have been carried out for each experimental point. The repeatability of the experimental results was required to fall in the range of ±1.5%, and the mean value was proposed. The investigated temperature ranges are T = (293 to 496) K for saturated-liquid ETBE, T = (433 to 493) K for saturated-vapor ETBE, T = (291 to 493) K for saturated-liquid TAME, and T = (477 to 522) K for saturated-vapor TAME. Here, the upper-limit temperatures of measurement are close to the critical temperature of ETBE or TAME. The experimental data are presented in Table 4 and shown in Figure 2. For both saturated ETBE and TAME, the thermal diffusivities decrease with the temperature increase and the influence of temperature on the thermal diffusivity of saturated vapor is obviously greater. As shown in Figure 2, about a 60 K rise in temperature gives an approximately 90% reduction in the thermal diffusivity of saturated vapor ETBE. When the temperature increases to the vicinity of the critical point of ETBE or TAME (T > 0.9TC), the thermal diffusivities decrease more with the temperature increase, especially for the saturated liquid. As shown in Figure 2, about a 10 K temperature rise in the vicinity of

(4)

in which ui is the ith effect factor uncertainty, uc is the combined standard uncertainty, and k is the coverage factor, which is usually considered to be 2 or 3 in correspondence with a 95 or 99% degree of confidence, respectively. The relative combined standard uncertainty in thermal diffusivity can be expressed by eq 5 ur (a) =

4ur 2(λ 0) + 4ur 2(ΘEX ) + ur 2(τR ) + ur 2(i)

(5)

in which ur(λ0), ur(ΘEX), ur(τR), and ur(i) are the relative standard uncertainties related to the wavelength of incident light, the incident angle of the laser, the decay time, and the impurity, respectively. According to ref 44, with a purity of 0.99, the standard uncertainty according to the purity is ur(i) = 0.01/ 3 ≈ 0.006

(6)

Reference 33 presented a complete description of the measurement uncertainties of thermal diffusivity. Table 2 lists the combined standard uncertainty in temperature, pressure, and thermal diffusivity. The experimental expanded uncertainties in temperature, pressure, and thermal diffusivity are estimated to be less than 0.02 K, 0.03 MPa (0−5 MPa) and 0.06 MPa (5−10 MPa), 897



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Table 6. Experimental Thermal Diffusivity of ETBE and TAME in Liquida 4 MPa

7 MPa

T/K

a/10−8 m2·s−1

T/K

372.96 383.37 393.00 402.94 413.35 421.78 431.42 442.12 452.09 462.41 472.45 478.20 482.44 488.65 493.13

4.40 4.34 4.27 4.20 4.12 4.07 4.00 3.92 3.85 3.75 3.65 3.60 3.52 3.44 3.34

373.15 383.35 392.97 402.99 413.34 421.86 431.52 442.19 452.26 462.47 472.63 478.14 483.15 488.15 493.16

373.11 382.80 392.61 402.72 412.73 423.00 432.66 442.61 453.47 463.14 472.15 478.39 483.31 488.54 492.58 499.00 503.16 508.25 512.28 517.79 523.25

5.20 5.08 4.90 4.77 4.66 4.52 4.42 4.31 4.20 4.14 4.08 4.06 4.02 3.98 3.96 3.90 3.85 3.80 3.72 3.63 3.53

373.10 382.83 392.63 402.77 412.76 423.06 432.76 442.70 453.58 463.21 472.25 478.14 483.16 488.17 493.13 498.25 503.20 508.09 512.29 517.85 523.25

10 MPa a/10−8 m2·s−1

T/K

a/10−8 m2·s−1

4.47 4.41 4.35 4.28 4.21 4.16 4.10 4.04 3.98 3.92 3.87 3.84 3.82 3.79 3.77

373.16 383.18 393.05 403.09 413.25 422.25 432.83 442.53 452.40 462.95 472.63 478.13 483.20 488.83 493.30

4.50 4.45 4.40 4.35 4.30 4.24 4.18 4.13 4.08 4.03 3.99 3.97 3.95 3.93 3.92

5.35 5.23 5.09 4.93 4.81 4.69 4.59 4.47 4.37 4.31 4.26 4.22 4.19 4.16 4.13 4.08 4.04 3.99 3.94 3.90 3.84

373.12 382.94 392.73 402.81 412.86 422.87 432.80 442.73 453.25 463.25 472.35 478.13 483.16 488.18 493.14 498.16 503.15 508.14 512.53 518.05 523.25

5.47 5.36 5.23 5.07 4.94 4.82 4.72 4.60 4.51 4.44 4.39 4.36 4.32 4.29 4.26 4.22 4.18 4.15 4.12 4.08 4.05

ETBE

TAME

a The expanded uncertainties U are U(T) = 0.02 K, U(p) = 0.015 MPa (0−5.0 MPa), and 0.03 MPa (5.0−10 MPa), and the relative expanded uncertainty Ur is Ur(a) = 0.024. The level of confidence is 0.95 (k = 2).

The absolute average relative deviations (AARDs), maximum deviation (MD), and average deviation (bias) of the correlation are introduced as shown in

the critical temperature gives more than 25 and 13% increments in the thermal diffusivity of saturated-liquid ETBE and TAME, respectively. Considering the specificity of thermal diffusivity in the vicinity of the critical region, the measured thermal diffusivities of saturated ETBE and TAME as functions of temperature were respectively represented by the empirical correlation suggested by Kraft and Leipertz ⎡ ⎤ Tr a = 10−8 × ⎢ + E exp(− FTr)⎥ (m 2·s−1) 2 3 ⎣ A + BTr + CTr + DTr ⎦ TC − T with Tr = TC

N ⎧ cal, i ⎪ AARD/% = 100 ∑ a −1 N i aexp, i ⎪ ⎪ ⎛ acal, i ⎞ ⎪ ⎪ ⎨ MD/% = 100 max⎜⎜ exp, i − 1 ⎟⎟ ⎪ ⎝ a ⎠ ⎪ N ⎛ acal, i ⎞ ⎪ 100 bias/% = ⎜ exp, i − 1⎟ ⎪ ∑ ⎪ N i ⎝a ⎠ ⎩

(7)

(8)

in which aexp,i is the ith experimental data point of thermal diffusivity and acal,i is the ith calculation result. Comparing the experimental thermal diffusivity data with the correlation in the measured range, the AARDs are 0.22% for

in which the critical temperature of ETBE is taken as TC = 509.40 K46 and the critical temperature of TAME is taken as TC = 537.00 K, which was suggested by Steele.47 A−F are the fitted coefficients that are listed in Table 5. 898



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saturated-liquid ETBE, 0.13% for saturated-vapor ETBE, 0.26% for saturated-liquid TAME, and 0.20% for saturated-vapor TAME, respectively. The deviations between the experimental data and calculated values are shown in Figure 3, which indicates that the relative deviations increase very close to the critical point. We considered the main reason to be that the variation in thermal diffusivity depending on temperature follows a simple power law in the vicinity of the critical point, which may result in a very large deviation in thermal diffusivity with a small deviation in temperature. Furthermore, the multiple scattering potentially arises when the sample thermodynamic state is very close to the critical point. 3.2. Liquid. The experimental thermal diffusivities of ETBE and TAME, measured along three isobaric lines p = (4, 7, and 10) MPa and at T = (373 to 493) K for ETBE and T = (373 to 523) K for TAME are presented in Table 6. The thermal diffusivity of liquid ETBE and TAME was correlated by the polynomial expression of eq 9 with the fitted coefficients listed in Table 5. 2

a=

2

⎛ T ⎞i ⎛ p ⎞ j ⎜ ⎟⎜ ⎟ K ⎠ ⎝ MPa ⎠

∑ ∑ cij⎝ i=0 j=0

Figure 5. Contour of the thermal diffusivity for TAME in the liquid state from eq 9.

4. CONCLUSIONS The present work aims to investigate the thermal diffusivity of ETBE and TAME, in which the DLS experimental apparatus was employed. First, the thermal diffusivities of saturated-liquid toluene were measured at T = (303 to 523) K to test the reliability of the experimental setup. AARD is 0.90% between our experimental results and the literature data. Then the thermal diffusivities of ETBE and TAME were measured over a wide temperature range, which includes saturated liquid, saturated vapor, and subcooled liquid. New experimental data and the correlations with good calculation accuracy were presented. The temperature and pressure influences on the thermal diffusivity were also discussed. It is observed that for both saturated ETBE and TAME the thermal diffusivities decrease with increasing temperature but decrease more significantly with increasing temperature when the temperature increases in the vicinity of the critical temperature (about T > 0.9TC). For liquid ETBE and TAME, the thermal diffusivities increase slightly with the pressure increase and decrease obviously with the temperature increase over the whole examined p−T region. When the temperature approached the critical temperature (about T > 0.85TC for both ETBE and TAME), the thermal diffusivities decrease more obviously with increasing temperature.

(9)

The AARD, MD, and bias of the experimental results compared to the correlation in the measured range are 0.23, 1.55, and −0.0003% for ETBE and 0.69, 1.57, and 0.0006% for TAME, respectively. Obviously, the polynomials describe the experimental data very well. Figures 4 and 5 show the contours of thermal diffusivities for ETBE and TAME in the subcooled-liquid state, respectively. It

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86-29-8266-3863. Fax: +86-29-8266-8789. E-mail: [email protected].

Figure 4. Contour of the thermal diffusivity for ETBE in the liquid state from eq 9.

ORCID

Maogang He: 0000-0002-2364-2140 can be seen that the thermal diffusivities increase slightly with the pressure increase and decreases obviously with the temperature increase over the whole examined p−T region. When the temperature is far away from the critical temperature (about T < 0.85TC for both ETBE and TAME), the temperature has a slight influence on the variation rate of thermal diffusivity along isobaric lines. Similarly, the pressure has a slight influence on the variation rate of thermal diffusivity along isothermal lines. As the temperature increases and approaches the critical temperature (about T > 0.85TC for both ETBE and TAME), the thermal diffusivities decrease more obviously with increasing temperature.

Funding

This work was supported by the National Natural Science Foundation of China (NSFC no. 51576161). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Yee, K. F.; Mohamed, A. R.; Tan, S. H. A review on the evolution of ethyl tert-butyl ether (ETBE) and its future prospects. Renewable Sustainable Energy Rev. 2013, 22, 604−620. (2) Marsh, K. N.; Niamskul, P.; Gmehling, J.; Bölts, R. Review of thermophysical property measurements on mixtures containing MTBE,

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