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

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Thermal Diffusivity of 2‑Methoxy-2-methylpropane at Temperatures from (303.15 to 493.15) K and Pressures from (1.5 to 10) MPa Libin Chen,† Ying Zhang,† Sheng Wang,† Xiong Zheng,† 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-methoxy-2-methylpropane (MTBE, mass purity, > 0.990, GC) were measured by using the dynamic light scattering method at T = (303.15 to 493.15) K and p = (1.5 to 10) MPa, including saturated liquid, saturated vapor, and compressed liquid. The expanded relative uncertainty in thermal diffusivity was estimated to be less than 2.0 % over the entire investigated range. The polynomial representation for thermal diffusivity of MTBE was proposed by employing the experimental results. Comparing the calculated results with the experimental data, the average absolute deviations are 0.59 % for saturated liquid, 0.38 % for saturated vapor, and 0.43 % for compressed liquid.

1. INTRODUCTION Oxygenated compounds are increasingly added to gasolines to increase their octane number. It can also improve engine efficiencies and decrease NOx, carbon monoxide, and unburned hydrocarbons emission. Commonly used oxygenates include aliphatic alcohols and methyl ethers, which have excellent antiknock properties and are environmentally acceptable substances. 2-Methoxy-2-methylpropane (MTBE) is used as the most common gasoline additive,1 because its octane number is as high as 109 and its Reid vapor pressure is as low as 55 kPa. Moreover, MTBE is also increasingly used as a solvent and as a chemical intermediate. The thermophysical properties of MTBE are necessary for its application and study further. And thermal diffusivity is the most important property related to the energy transfer. The temperature distribution of the fuel in the combustion chamber can be calculated with the thermal diffusivity, which is significant for the design of an engine. Recently, most researches are focused on vapor−liquid or liquid−liquid equilibria,2−5 density,6,7 excess molar volumes, etc.8−11 in MTBE binary or ternary mixtures with water, alcohols, ethers, and so on. However, the experimental data of thermophysical properties about pure MTBE are very scarce. Gmehling et al.12 measured the vapor pressures of MTBE by the static method in the pressure ranges 3 kPa to 835 kPa. Wang et al.13 measured the surface tension of MTBE at temperatures from 243 K to 393 K with a differential capillary rise method. Ihmels et al.14 measured the densities of MTBE with a vibrating tube densimeter in the liquid state at temperatures from 273 K to 473 K. However, there are few data available for the thermal diffusivity of MTBE in the present literature. In this work, we measured thermal diffusivity of MTBE in a wide p−T region using the dynamic light scattering method. © 2014 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Materials. The MTBE sample was provided by Aladdin Reagent Inc. with specified mass purity higher than 0.990 (GC). The samples were not further purified in order to prevent sample alterations. The specifications of the sample are listed in Table 1. To fill the sample cell, the samples were filtered through membrane filters with 0.22 μm pore size to prevent dust and particles from entering the cell. Table 1. Specifications of the Sample Used in This Paper material MTBE

supplier Aladdin Reagent Inc.

mass purity

purification method

> 0.990

filtered through the membrane filters

2.2. Measurement Method and Apparatus. The dynamic light scattering method (DLS) was used to measure thermal diffusivity in this work. A complete and more detailed description of the measurement principle can be found in various fundamental studies.15−17 The experimental setup is the same with that in our previous paper18 and similar to that employed by Kraft et al.19,20 Here only the working equations are depicted briefly. The temperature relaxation is governed by the temperature diffusion equation, which is related to the thermal diffusivity. The photon correlation spectroscopy can be used to investigate the temperature relaxation process. The temperature disturbance relaxes back to equilibrium exponentially, which indicates that the photon correlation function of Received: September 10, 2014 Accepted: October 23, 2014 Published: November 4, 2014 3927

dx.doi.org/10.1021/je5008394 | J. Chem. Eng. Data 2014, 59, 3927−3931

Journal of Chemical & Engineering Data

Article

the dynamic light scattering is an exponential decay function as follows: G(τ ) = A + B exp( −τ /τR )

Table 2. Experimental Uncertainty in Temperature, Pressure, and Thermal Diffusion

(1)

temp/K platinum resistance, u1 temperature stability, u2 resistance measurement circuits, u3 combined uncertainty, uc

where τR is the decay constant or decay time and A and B are the fitted constants. The correlator can measure the discrete photon correlation function as shown in Figure 1, and we get

0.005 0.008 0.002 0.01

pressure transmitter, u1 pressure measurement circuits, u2 pressure control system, u3 combined uncertainty, uc wavelength, ur(λ0) incident angle, ur(ΘEX) decay time, ur(τR) combined uncertainty, ur(a)

3. RESULTS AND DISCUSSION The thermal diffusivity of MTBE was measured along the saturation line and in a compressed liquid. During the measurements along the saturation line, the sample fluid was maintained in the two-phase region to satisfy the saturated conditions. Each experimental point was independently measured six times at three different scattering angles. The repeatability of the results was better than 0.5 % and the average value was adopted in the measurements. The experimental data of the thermal diffusivity along the saturation line and in the compressed liquid region have been also correlated as the function of temperature and pressure, respectively. The absolute average of the deviations (AAD), maximum deviation (MD), and average deviation (bias) are introduced to assess the performances of the polynomial expressions, which are defined as follows.

Figure 1. A typical photon correlation function: ○, discrete points from digital correlator; , fitted autocorrelation function.

the decay constant after fitting the discrete photon correlation function according to eq 1. The decay constant is connected with the thermal diffusivity as eq 2.

a = 1/(q2τR )

(2)

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

(3)

2.3. Assessment of Experimental Uncertainties. The experimental uncertainties in temperature and pressure can be determined by using the following equation,

U = kuc = k

∑ ui2

AAD/% =

4ur2(λ 0) + 4ur2(ΘEX ) + ur2(τR )

100 N

N

∑ i

aexp, i −1 acal, i

⎛ aexp, i ⎞ MD/% = 100 max⎜ cal, i − 1 ⎟ ⎝ a ⎠

(4)

in which ui is the uncertainty in each influencing factor, uc is the combined standard uncertainty which is composed of uncertainties of all influencing factors, and k is the coverage factor, it is usually considered to be 2 or 3 when the degree of confidence is 95 % or 99 %, respectively. Experimental uncertainty in thermal diffusivity is associated with uncertainties in the measured quantities as u r (a) =

pressure/MPa 0.001 (p < 5.0 MPa)/ 0.007 (p > 5.0 MPa) 0.001 0.015 (p < 5.0 MPa)/0.03 (p > 5.0 MPa) 0.015 (p < 5.0 MPa)/0.03 (p > 5.0 MPa) thermal diffusivity 3.76·10−5 0.001 0.01 0.01

bias/% =

100 N

N

⎛ aexp, i

∑⎜ i

⎝a

cal, i

⎞ − 1⎟ ⎠

(6)

(7)

(8)

exp,i

where a is the ith experimental datum of thermal diffusivity, acal,i is the ith thermal diffusivity calculated from the polynomial expression. 3.1. Saturated Liquid and Vapor. The experimental thermal diffusivities of MTBE measured along the saturation line are presented in Table 3. The temperature ranges are T = (303.15 to 493.15) K for saturated liquid and T = (377.15 to 493.15) K for saturated vapor. The thermal diffusivities of saturated MTBE are represented by the polynomial of eq 9.

(5)

in which ur(λ0), ur(ΘEX), and ur(τR) are the relative standard uncertainties due to the wavelength of the incident light, the out incident angle of laser, and the decay time, respectively. A complete and more detailed description of the measurement uncertainties of thermal diffusivity has been proposed in ref 18. The results listed in Table 2 show that the experimental uncertainties in temperature, pressure, and thermal diffusivity are estimated to be less than 0.02 K, 0.03 MPa for p = (0 to 5.0) MPa, 0.06 MPa for p = (5.0 to 20) MPa, and 2.0 % over the whole examined p−T region with a coverage factor of k = 2, respectively.

i ⎛ Tc − T ⎞c5 ⎛T ⎞ ⎜ ⎟ c + c ⎟ ∑ i⎝ ⎠ 4⎜ K ⎝ Tc ⎠ i=0 3

a=

(9)

The coefficients are listed in Table 4. The critical temperature of MTBE is taken as Tc = 496.4 K.21 A comparison of the experimental thermal diffusivity data with the correlation in the 3928



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Table 3. Experimental Thermal Diffusivity of MTBE along the Saturation Linea T/K

a/10−8 m2·s−1

T/K

a/10−8 m2·s−1

303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15

6.40 6.17 5.87 5.70 5.42 5.26 5.05 4.83

383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

4.72 4.64 4.55 4.48 4.38 4.31 4.18 4.05

453.15 455.15 457.15 459.15 461.15 463.15 a

23.6 20.6 18.7 17.2 16.2 15.4

465.15 467.15 469.15 471.15 473.15 475.15

14.7 13.8 13.1 12.2 11.4 10.5

T/K

Saturated Liquid 458.15 463.15 468.15 473.15 475.15 477.15 479.15 481.15 Saturated Vapor 477.15 479.15 481.15 483.15 485.15 487.15

a/10−8 m2·s−1

T/K

a/10−8 m2·s−1

3.91 3.86 3.66 3.55 3.47 3.36 3.36 3.30

483.15 485.15 487.15 489.15 491.15 493.15

3.22 3.07 3.02 2.95 2.81 2.73

9.7 8.8 7.8 7.0 6.2 5.6

489.15 491.15 493.15

5.0 4.3 3.1

Standard uncertainties u are u(T) = 0.01 K and ur(a) = 0.01.

Table 4. Fitted Coefficients in Equations 9 and 10a saturated liquid

saturated vapor

c0 c1 c2 c3 c4 c5

1.7811·102 −1.2371·10° 2.9579·10−3 −2.3734·10−6 −1.6994·101 4.2902·10°

−3.6205·106 2.1523·104 −4.2633·101 2.8138·10−2 1.1028·106 2.4415·10°

AAD/% DM/% bias/%

0.59 1.36 −0.05

0.38 0.85 0.02

compressed liquid c00 c01 c02 c10 c11 c12 c20 c21 c22 AAD/% DM/% bias/% −8

1.9019·101 8.6771·10−1 −1.0569·10−1 −5.7470·10−2 −4.2411·10−3 5.3462·10−4 5.4359·10−5 5.0984·10−6 −6.4343·10−7 0.43 1.52 0.01

Figure 2. Thermal diffusivity of saturated MTBE: ■, saturated liquid; □, saturated vapor; , fitted line.

2 −1

The coefficients c0−c4 and cij are in unit of 10 m ·s , while c5 is dimensionless.

a

measured range shows that the AAD, MD, and bias are 0.59 %, 1.36 %, and −0.05 % for the saturated liquid, and 0.38 %, 0.85 %, and 0.02 % for the saturated vapor, respectively. The thermal diffusivities of saturated MTBE are shown in Figure 2. The deviations between the experimental results and the calculated results according to the correlations are shown in Figure 3. 3.2. Compressed Liquid. The experimental thermal diffusivities of MTBE, measured along seven isobaric lines p = (1.5 to 10) MPa and in the temperature range T = (303.15 to 493.15) K, are presented in Table 5. The thermal diffusivity of compressed liquid is represented by the polynomial expression of eq 10 with the fitted coefficients in Table 4. 2

a=

2

⎛T ⎞ ⎛ p ⎞ ⎜ ⎟⎜ ⎟ K ⎠ ⎝ MPa ⎠

∑ ∑ cij⎝ i=0 j=0

i

Figure 3. Deviations of thermal diffusivity from DLS and from the fit according to eq 8: ■, saturated liquid; □, saturated vapor.

j

(10)

and decreases obviously with a temperature increase over the whole examined p−T region.

The AAD, MD, and bias of the experimental thermal diffusivity data compared with the correlation in the measured range are 0.43 %, 1.52 %, and 0.01 %, respectively. The thermal diffusivities in the compressed liquid region are shown in Figure 4. It is shown that the polynomial describes the experimental data very well, and it can be seen that the thermal diffusivity of MTBE increases slightly with a pressure increase

4. CONCLUSIONS New experimental data on thermal diffusivity of 2-methoxy-2methylpropane (MTBE) are presented, which are measured by the dynamic light scattering method (DSL). The investigated p−T regions are T = (303.15 to 493.15) K for saturated liquid, 3929



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Table 5. Experimental Thermal Diffusivity of MTBE in Compressed Liquida p/MPa T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0

a/10−8m2·s−1 = 303.15 K 6.66 6.70 6.75 6.79 6.81 6.83 6.85 = 318.15 K 6.29 6.32 6.37 6.40 6.44 6.47 6.49 = 333.15 K 5.94 5.97 6.00 6.05 6.09 6.15 6.21 = 348.15 K 5.62 5.63 5.68 5.72 5.78 5.85 5.92 = 363.15 K 5.33 5.34 5.38 5.43 5.50 5.57 5.68 = 378.15 K 5.06 5.07 5.10 5.15 5.23 5.32 5.44

p/MPa T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 1.5 2.5 4.0 5.5 7.0 8.5 10.0 T 2.5 4.0 5.5 7.0 8.5 10.0

a/10−8m2·s−1 = 393.15 K 4.83 4.83 4.86 4.92 4.99 5.09 5.21 = 403.15 K 4.68 4.69 4.71 4.77 4.85 4.95 5.08 = 413.15 K 4.54 4.55 4.58 4.64 4.72 4.82 4.95 = 423.15 K 4.42 4.43 4.46 4.51 4.59 4.70 4.83 = 433.15 K 4.32 4.32 4.36 4.41 4.49 4.59 4.72 = 443.15 K 4.23 4.26 4.31 4.39 4.49 4.61

p/MPa T 2.5 4.0 5.5 7.0 8.5 10.0 T 2.5 4.0 5.5 7.0 8.5 10.0 T 2.5 4.0 5.5 7.0 8.5 10.0 T 2.5 4.0 5.5 7.0 8.5 10.0 T 2.5 4.0 5.5 7.0 8.5 10.0 T 4.0 5.5 7.0 8.5 10.0 T 4.0 5.5 7.0 8.5 10.0

a/10−8m2·s−1 = 453.15 K 4.15 4.18 4.23 4.30 4.40 4.51 = 458.15 K 4.11 4.15 4.20 4.27 4.36 4.47 = 463.15 K 4.08 4.11 4.16 4.23 4.32 4.43 = 468.15 K 4.05 4.09 4.14 4.20 4.28 4.38 = 473.15 K 4.02 4.06 4.11 4.18 4.25 4.34 = 483.15 K 4.02 4.07 4.12 4.19 4.27 = 493.15 K 3.99 4.03 4.08 4.14 4.21

Figure 4. Thermal diffusivity of MTBE in compressed liquid state.

calculated results from the correlations, the AAD, MD, and bias are 0.59 %, 1.36 % and −0.05 % for the saturated liquid, 0.38 %, 0.85 %, and 0.02 % for the saturated vapor and 0.43 %, 1.52 %, and 0.01 % for the compressed liquid, respectively.

■

AUTHOR INFORMATION

Corresponding Author

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

This work was supported by the National Nature Science Foundation of China (NSFC No. 51106129), and the Fundamental Research Funds for the Central University (No. XJTU- HRT-002). Notes

The authors declare no competing financial interest.

■

REFERENCES

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a Standard uncertainties u are u(T) = 0.01 K; u(p) = 0.015 MPa for p < 5.0 MPa, u(p) = 0.03 MPa for p > 5.0 MPa ; ur(a) = 0.01.

T = (377.15 to 493.15) K for saturated vapor and T = (303.15 to 493.15) K for compressed liquid along seven isobaric lines with p = (1.5 to 10) MPa. For the compressed MTBE liquid, the thermal diffusivity of MTBE increases slightly with pressure increase and decreases obviously with temperature increase over the whole examined p−T region. The polynomial representations suitable for the thermal diffusivity of MTBE are proposed, comparing the experimental data with the 3930



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

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