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Energy & Fuels 2009, 23, 526–532
Continuous Production of Biodiesel via Supercritical Methanol Transesterification in a Tubular Reactor. Part 1: Thermophysical and Transitive Properties of Supercritical Methanol Wen Chen,†,‡ Cunwen Wang,‡ Weiyong Ying,*,† Weiguo Wang,‡ Yuanxin Wu,‡ and Junfeng Zhang‡ State Key Laboratory of Chemical Engineering, East China UniVersity of Science and Technology, Shanghai 200237, China, and Key Laboratory for Green Chemical Process of Ministry of Education, Wuhan Institute of Technology, Wuhan 430073, China ReceiVed July 2, 2008. ReVised Manuscript ReceiVed September 17, 2008
In the range of 520-600 K and 100-400 bar, the thermophysical properties of supercritical methanol, which includes density F, viscosity η, isobaric heat capacity CP, and coefficient of thermal conductivity λ, are calculated according to different methods and the effect of temperature and pressure is also discussed. On the basis of the thermophysical properties, the transitive properties of supercritical methanol flowing in a φ6 × 1.5 mm round tube, which includes the Reynolds number Re, the Prandtl number Pr, and the film coefficient of heat transfer R, are calculated and the change laws of them with temperature, pressure, and velocity are also illustrated. It is shown that all F, η, Cp, λ, Re, Pr, and R decrease with the increase of the temperature at constant pressure, but their changing trend is not consistent with the pressure increasing at a constant temperature. F, η, and λ always increase as the pressure increases. CP, Re, and Pr decrease consistently at 520-540 K and increase first and then decrease at 540-600 K. For R, with the increase of pressure, it almost remains stable at 520 K and first increases sharply and then decreases slowly at 530-570 K, but at 580-600 K, it always goes up from the beginning from 100 to 400 bar.
1. Introduction Biodiesel is a renewable and environmentally friendly energy. It is also an important substitute for petroleum diesel. Therefore, it has been studied widely in recent years. There are many methods to produce biodiesel: (a) dilution, (b) microemulsions, (c) pyrolysis, (d) catalytic cracking, (e) catalystic transesterification, and (f) noncatalytic transesterification in supercritical conditions.1-3 Among these methods, supercritical methanol transesterification is a better one and has drawn more attention because of its advantages: no catalyst is needed; the reaction rate and the conversion is high; the requirement for the content of water and free fatty acid in raw oil is not harsh; the process to separate the products is simple; and the continuous processing technique in large scale is easy to implement. However, many researches are focused on the intermittent method to produce biodiesel in supercritical methanol.4-7 In addition, the researches concerning the continuous method in a tubular reactor are few, in which more attention is paid to the optimization of the reaction conditions and the elementary dynamics.8 However, * To whom correspondence should be addressed. Telephone: +86-2164252192. E-mail:
[email protected]. † East China University of Science and Technology. ‡ Wuhan Institute of Technology. (1) Kazuhim, B.; Masaru, K.; Takeshi, M. Biochem. Eng. J. 2001, 8, 39–43. (2) Furuta, S.; Matsuhashi, H.; Arata, K. Catal. Coummun. 2004, 5, 721– 723. (3) Vicente, G.; Martinez, M.; Aracil, J. Energy Fuels 2006, 20, 394– 398. (4) Kusdiana, D.; Saka, S. J. Chem. Eng. J. 2001, 34, 383–387. (5) Saka, S.; Kusdiana, D. Fuel 2001, 80, 225–231. (6) Warabi, Y.; Kusdiana, D.; Saka, S. Bioresour. Technol. 2004, 91, 283–287. (7) Kusdiana, D.; Saka, S. Bioresour. Technol. 2004, 91, 289–295.
the state of mixing and flowing of methanol and oil has an important effect on the biodiesel yield during biodiesel preparation by supercritical methanol transesterification in a continuous tubular reactor because the residence and reaction time of them is short in the tubular reactor (about 5-15 min). Thus, the study of the effect of mass and heat transfer on supercritical methanol transesterification in a tubular reactor is very significant. However, this study depends upon the thermophysical properties of different components in this reaction system. However, it is difficult to determine these properties under supercritical conditions. Therefore, experimental data about the thermophysical properties of supercritical methanol is absent in large quantity, and at the same time, there is no report on the calculation of thermophysical and transitive properties of supercritical methanol in the tubular reactor and their changing rules with the variation of the temperature and pressure. These properties and the laws of their changes in the tubular reactor are beneficial for understanding and establishing the macrodynamics model and the scale-up design of the tubular reactor. Therefore, the thermophysical properties of supercritical methanol: density, viscosity, isobaric heat capacity, and coefficient of thermal conductivity would be calculated here, and on the basis of these thermophysical properties, the transitive properties of supercritical methanol in the tubular reactor and their changing laws in the different conditions are also discussed. 2. Computational Method 2.1. Thermophysical Properties of Supercritical Methanol. 2.1.1. Density of Supercritical Methanol. The density of supercritical methanol can be calculated through equation of state (EoS). The Redlick-Kwong equation is a practical EoS with analytic
10.1021/ef8005299 CCC: $40.75 2009 American Chemical Society Published on Web 11/14/2008
Properties of Supercritical Methanol
Energy & Fuels, Vol. 23, 2009 527
solution, but its computation error is more than 5% when methanol is in the supercritical state. Therefore, its accuracy is not enough for the requirements of engineering calculation. The equations of state with multiparameters and numerical solution should be better choices for calculating the density of supercritical methanol because their average computation error is below 2%. However, they often need many model parameters, which depend upon experimental data, and moreover, the computational process according to this method is also complicated. Thus, the density of supercritical methanol would be calculated via cubic spline interpolation based on the experimental data, and its average computation error is below 2%, which is suitable for the engineering calculation. 2.1.2. Viscosity of Supercritical Methanol. The Stiel-Thodos, TRAPP, Chung, Reichenberg, and Lucas methods are feasible for calculating the viscosity of supercritical fluids. However, for the first three methods, state variables are temperature and density, and they are temperature and pressure for the last two. For the polar matter, Poling recommends that the Lucas method should be adopted and its average computation error is about 5%,9because methanol is a strongly polar material and temperature and pressure are easy to be determined accurately as state variables. Thus, the Lucas method is employed to calculate the viscosity of supercritical methanol in this paper. First, ξ and µr are defined as follows:
( )
ξ ) 0.176
Tc
Fp ) [1 + (Fp0 - 1)Y-3]/Fp0
(7)
FQ ) {1 + (FQ0 - 1)[Y-1 - 0.007(ln Y)4]}/FQ0
(8)
At last, the viscosity of methanol at low pressure is calculated as follows:
η0)Z1/ξ
In addition, the viscosity of supercritical methanol is calculated as follows:
η)Z2FPFQ/ξ
(1)
µr ) 52.46(µ2Pc/Tc2)
(2)
Then, calculate Z1 and Z2 according to the following:
FP0 ) 1 + 30.55(0.292 - Zc)1.72 (0.022 e µr < 0.075) FQ0 ) 1
(3)
Z1 ) η0ξ ) [0.807Tr0.618 - 0.357 exp(-0.449Tr) + 0.340 exp(-4.058Tr) + 0.018]FP0FQ0 (4) Z2 ) η0ξ[1 + aPre/(bPrf + (1 + cPrd)-1)]
(5)
(10)
where Tc is the critical temperature of methanol (512.64 K), Pc is the critical pressure of methanol (80.97 bar), Zc is the critical compressibility factor of methanol (0.224), µ is the dipole moment of methanol (1.7 D), M is molar mass of methanol (32.042 g/mol), and Tr and Pr are reduced temperature and pressure, respectively. 2.1.3. Isobaric Heat Capacity of Supercritical Methanol at Constant Pressure. Isobaric heat capacity of supercritical methanol at constant pressure is calculated according to the following equation:
CP ) CP0 + ∆CP
1/6
M3Pc4
(9)
(11)
where CP0 is the isobaric heat capacity of the ideal methanol gas at low pressure and ∆CP is the heat capacity difference between high and low pressure at the same temperature, which can be calculated according to the Perry-Chilton pressure calibration figure about molecular heat capacity.10 CP0 can be calculated according to the Benson or Constantinou-Gani (CG) method, in which average computation errors are all below 2%; thus, the two methods are all suitable for the engineering calculation. The CG method is adopted to calculate CP0 of methanol here. CP0 is calculated according to the following:
CP0 ) [∑Nk(CPA1K) + W∑Mj(CPA2j) - 19.7779] + [∑Nk(CPB1K) + W∑Mj(CPB2j) + 22.5981]θ + [∑Nk(CPC1K) + W∑Mj(CPC2j) - 10.7983]θ2 (12)
where
θ ) (T - 298)/700
a ) (a1/Tr)exp(a2Trγ) b ) a(b1Tr - b2) c ) (c1/Tr)exp(c2Trδ) d ) (d1/Tr)exp(d2Trη) e ) 1.3088 f ) f1 exp(f2Trφ) a1 ) 1.245 × 10-3,
a2 ) 5.1726,
b1 ) 1.6553,
γ ) -0.3286
b2 ) 1.2723
c1 ) 0.4489,
c2 ) 3.0578,
δ ) -37.7332
d1 ) 1.7368,
d2 ) 2.2310,
η ) -7.6351
f1 ) 0.9425,
f2 ) -0.1853,
λ - λ0 ) F1X1(λR - λR0)
(14)
λ0
φ ) 0.4489
After Z1 and Z2 are calculated, Y and the correction factors FP and FQ are given by
Y ) Z1/Z2
(13)
where Nk is the number of the first-order group, CPA1K, CPB1K, and CPC1K are contribution values of the first-order group, Mj is the number of the second-order group, CPA2j, CPB2j, and CPC2j are contribution values of the second-order group, and T is the temperature (K). The value of W is 0 for the first-order group and 1 for the second-order group. 2.1.4. Coefficient of Thermal ConductiVity of Supercritical Methanol. The TRAPP method is used to calculate the coefficient of thermal conductivity of supercritical methanol, which is a compared method for pure fluid or mixed fluids, and its average computation error is about 4-6%.9 The relationship of the excessive coefficient of thermal conductivity between methanol and propane (propane is the referenced fluid) is given by
(6)
(8) Bunyakiat, K.; Makmee, S.; Sawangkeaw, R.; Ngamprasertsith, S. Energy Fuels 2006, 20, 812–817. (9) Poling, B. E.; Prausnitz, J. M.; O’Connell, J. P. The Properties of Gases and Liquids, 5th ed.; Zhao, H. L., Wang, F. K., Chen, S. K., Eds.; Chemical Industry Press: Beijing, China, 2006; pp 346-357.
In eq 14, is the coefficient of thermal conductivity of the ideal methanol gas at low pressure and can be calculated according to the following:
λ0 ) (1.32CP0 + 3.741)(η0/M)
(15)
where CP0 is the isobaric heat capacity of the ideal methanol gas at low pressure, which is calculated by the CG method (J mol-1 K-1), (10) Chopey, N. P. Handbook of Chemical Engineering Calculations, 3rd ed.; Zhu, K. H., Ed.; China Petrochemical Press: Beijing, China, 2005; pp 16-18.
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Table 1. Experimental Data of the Density of Compressed Methanol (kg/m3)11 temperature (K) pressure (bar)
200
250
300
350
400
450
500
550
600
75 100 150 200 300 400 500
884.96 886.52 888.89 892.06 898.47 903.34 908.26
837.52 839.63 843.17 846.02 853.24 859.11 865.05
791.76 794.28 798.72 802.57 810.37 817.66 824.40
744.60 747.94 753.01 759.30 768.05 776.40 784.93
690.61 694.93 702.74 710.23 722.54 733.68 743.49
619.58 626.96 640.20 651.47 670.24 685.40 698.81
479.85 512.30 547.95 571.10 603.86 627.75 647.25
73.584 a a 432.15 510.99 526.87 582.75
57.471 84.175 153.54 244.44 384.62 458.30 505.05
a
There are no experimental data in the original table.
η0 is the viscosity of methanol at low pressure, which is calculated by the Lucas method (N S m-2), and M is the molar mass of methanol (kg/mol). λR is the coefficient of thermal conductivity of propane at the temperature of T0 and the density of F0. λR0 is the coefficient of thermal conductivity of propane at the temperature of T0 and low pressure. For propane, λR - λR0 is calculated as follows:
λR - λR0 ) C1FrR + C2(FrR)3 + (C3 + C4/TrR)(FrR)4 + C5 + C6/TrR)(FrR)5 where Tr ) T0/Tc and Fr ) F0/Fc The unit of m-1 K-1). R
R
C1 ) 15.2583985944, C4 ) 0.450477583739,
R
R.
λR
-
λR0
(16) is (mW
C2 ) 5.29917319127, C3 ) -3.05330414748 C5 ) 1.03144050679, C6 ) -0.1854840417707
2.2.2. Prandtl Number of Supercritical Methanol. The Prandtl number of supercritical methanol is calculated according to the following:
Pr ) (CPη)/λ
where CP, η, and λ are isobaric heat capacity of supercritical methanol (J kg-1 K-1), the viscosity of supercritical methanol (Pa s), and the coefficient of thermal conductivity of supercritical methanol (W m-1 K-1), respectively. 2.2.3. Film Coefficient of the Heat Transfer of Supercritical Methanol in a Round Tube. The film coefficient of heat transfer of supercritical methanol in a round tube is calculated as follows: If Re > 10 000, R is calculated according to the following:
R ) 0.023(λ/d)Re0.8Pr0.4
(25)
If 10 000 > Re > 2000, R is calculated according to the following:
R ) 0.023(λ/d)Re0.8Pr0.4f
(26)
f ) 1.0 - (6 × 10 /Re )
(27)
5
T0, F0, F1, and X1 are given by
(24)
1.8
T0 ) T/f
(17)
F0 ) Fh
(18)
where λ and d are the coefficient of thermal conductivity of supercritical methanol and the diameter of the round tube, respectively.
F1 ) (0.044094f/M)1/2h-2/3
(19)
3. Results and Discussion
X1 ) {1 + 2.1866(ω - ωR) ⁄ [1 - 0.505(ω - ωR)]}1/2 (20) where f and h are the correlative value between methanol and propane and can be calculated as follows:
f ) (Tc/TcR)[1 + (ω - ωR)(0.05203 - 0.7498 ln Tr)] (21) h ) (FcR/Fc)(ZcR/Zc)[1 - ω - ωR)(0.1436 - 0.2822 ln Tr)] (22) where Tc is the critical temperature of methanol (512.64 K), Fc is the critical density of methanol (0.008474 mol/cm3), Zc is the critical compressibility factor of methanol (0.224), ω is the eccentric factor of methanol (0.565), F is the density of supercritical methanol at the temperature of T and pressure of P, TcR is the critical temperature of propane (369.83 K), FcR is the critical density of propane (0.005000 mol/cm3), ZcR is the critical compressibility factor of propane (0.276), ωR is the eccentric factor of propane (0.152), T is the absolute temperature (K), and Tr is the reduced temperature. 2.2. Transitive Properties of Supercritical Methanol. 2.2.1. Reynolds Number of Supercritical Methanol in a Round Tube. The Reynolds number of supercritical methanol in a round tube is calculated as follows:
Re ) (Fdu)/η
(23)
where F, η, d, and u are the density of supercritical methanol (kg/ m3), the viscosity of supercritical methanol (Pa s), the diameter of the round tube (m), and the velocity of supercritical methanol in the round tube (m/s), respectively.
3.1. Change Rules of Thermophysical Properties of Supercritical Methanol. 3.1.1. Density of Supercritical Methanol. Table 1 shows the experimental data of Speight.11 On the basis of these data, the density of sub-/supercritical methanol can be calculated via cubic spline interpolation on MATLAB in the range of 200-600 K and 100-500 bar. It is found that when the density of compressed methanol is higher than 300 kg/m3, the result of the method is accurate and reliable because of its average error of 1.2% and the maximum error of 4%. However, when the density of compressed methanol is lower than 300 kg/m3, the reliability of the data by the method is not good, with the average error of 6.5% and the maximum error of 12.4%, because the experimental data involving the density below 300 kg/m3 in Table 1 are fewer. Therefore, when the density of supercritical methanol is lower than 300 kg/m3, it is calculated via cubic spline interpolation based on the experimental data of Bazaev12 (see Table 2), and thus, the average and maximum errors can be reduced to 1 and 3%, respectively. Table 3 shows the residuals between the calculated value and experimental data. Figure 1 shows the density of supercritical methanol through interpolation based on the experimental data of Tables 1 and 2. From Figure 1, the density of supercritical methanol increases (11) Speight, J. G. Perry’s Standard Tables and Formulas for Chemical Engineers; Chen, X. C., Sun, W., Eds.; Chemical Industry Press: Beijing, China, 2006; pp 409-412. (12) Bazaev, A. R.; Abdulagatov, I. M.; Bazaev, E. A.; Abdurashidova, A. A.; Ramazanova, A. E. J. Supercrit. Fluids 2007, 41, 217–226.
Properties of Supercritical Methanol
Energy & Fuels, Vol. 23, 2009 529
Table 2. P-V-T Experimental Data of Supercritical Methanol at the Low Density (kg/m3)12 density (kg m-3) T (K)
113.5
138.6
177.6
252.4
305.2
360.5
368.2
513.15 523.15 533.15 543.15 553.15 563.15 573.15 583.15 593.15 603.15 613.15 623.15 633.15 643.15 653.15
7.3410 8.0890 8.6930 9.3110 9.9430 10.5880 11.2480 11.9210 12.6090 13.3100 14.0260 14.7550 15.4980 16.2550 17.0260
7.8590 8.6190 9.3900 10.1740 10.9690 11.7760 12.5950 13.4260 14.2690 15.1230 15.9900 16.8680 17.7580 18.6610 19.5750
8.1340 9.1140 10.1050 11.1050 12.1150 13.1350 14.1640 15.2040 16.2530 17.3120 18.3810 19.4600 20.5490 21.6470 22.7550
8.1990 9.5670 10.9440 12.3290 13.7220 15.1240 16.5330 17.9500 19.3750 20.8080 22.2500 23.6990 25.1570 26.6220 28.0960
8.1950 9.8790 11.5710 13.2690 14.9750 16.6880 18.4080 20.1350 21.8690 23.6100 25.3590 27.1140 28.8770 30.6470 32.4240
8.1960 10.1900 12.3340 14.4890 16.6540 18.8280 21.0130 23.2070 25.4120 27.6260 29.8510 32.0850 34.3290 36.5840 38.8480
8.2210 10.2740 12.4440 14.6090 16.8500 19.0470 21.5800 23.8290 26.0930 28.3740 30.6710 32.9830 35.3110 37.6550 40.0160
Figure 1. Density of supercritical methanol.
Table 3. Calculated Values and the Experimental Data of the Density of Supercritical Methanol density (kg/m3) pressure (bar)
temperature (K)
calculated values
experimental data
residuals (%)
151.2 238.3 400.0
563.2 583.2 550.0
255.2 371.1 525.3
252.4 368.2 526.9
1.1 0.8 -0.3
obviously with the pressure and is faster in the range of 100-300 bar than 300-500 bar. At the same time, Figure 1 also illustrates that the density fluctuates more greatly at high temperature than low temperature, with the pressure from 100 to 500 bar. For example, at 600 K, the density of supercritical methanol changes from 84.2 to 505.0 kg/m3 and increases 500% with the pressure from 100 to 500 bar, whereas it changes from 395.0 to 623.1 kg/m3 and increases 57.7% at 520 K. The density of methanol has an important influence on biodiesel preparation through the supercritical transesterification. The increase of the density can make supercritical methanol similar to liquid, which is beneficial for mixing and dissolving between methanol and oil, and thus, can promote the transesterification reaction. Therefore, to keep supercritical methanol “pseudo-liquid”, higher pressure should be adopted when the reaction temperature is higher. For example, to keep its density of 400 kg/m3, the operating pressure is about 14 MPa at 540 K but it is about 25 MPa at 580 K. 3.1.2. Viscosity of Supercritical Methanol. Table 4 displays the residual between the calculated value by the Lucas method and the experimental data of the viscosity of methanol at 484.9 K and 50 bar. Figure 2 shows the effect of pressure on the viscosity of supercritical methanol. It can be seen that the viscosity of supercritical methanol goes up with the pressure at a constant temperature. In addition, it increases quicker in the range of 100-200 bar than 200-400 bar. Figure 3 illustrates the influence of temperature on the viscosity of supercritical methanol at certain pressures. It shows that the viscosity of supercritical methanol decreases linearly with the increase of temperature when the pressure is above 200 bar. However, when the pressure is below 200 bar, it decreases sharply at low temperature and slowly at high temperature. Although the viscosity of supercritical methanol changes greatly with temperature and pressure, it is just about 10% of saturated liquid methanol of normal temperature. This reduction of the viscosity can improve the mixing and flowing state and strengthen the mass and heat transfer of the reaction system in a tubular reactor and, thus, promote the supercritical methanol transesterification and improve the biodiesel yield.
Figure 2. Relationship between the viscosity of supercritical methanol and the pressure at different temperatures.
3.1.3. Isobaric Heat Capacity of Supercritical Methanol at Constant Pressure. Equation 11 is used to calculate the isobaric heat capacity of supercritical methanol. According to the CG method, CP0 of methanol is calculated using eqs 12 and 13. The first-order groups of methanol are -CH3 and -OH, and the second-order group does not exist. Table 5 shows the contribution value of the groups, and Table 6 shows CP0 of methanol in the range of 520-600 K. ∆CP of eq 11 can be calculated according to the Perry-Chilton pressure calibration figure, and the results are shown in Table 7. The computation deviation by this method is listed in Table 4. Figure 4 displays the effect of the temperature and pressure on the heat capacity of supercritical methanol. It can be seen that CP of supercritical methanol decreases sharply in the range of 100-160 bar and then slowly above 160 bar with the increase of pressure when the temperature is 520-540 K. However, when the temperature is 540-600 K, CP increases first and then decreases and the maximal value exists in 120-160 bar. Figure 4 also illustrates that CP of supercritical methanol decreases with the increase of the temperature at certain pressures. At the same time, in comparison to CP of liquid methanol at normal temperature and pressure, CP of supercritical methanol is 2 or 3 times that, which means huge amounts of heat energy is necessary for methanol to be heated from normal temperature to the supercritical state. Thus, energy consumption is large by using supercritical methanol transesterification to produce biodiesel. Therefore, it is valuable to employ a catalyst or other methods to lower the reaction temperature without decreasing its reaction rate. 3.1.4. Coefficient of Thermal ConductiVity of Supercritical Methanol. λ0 is the coefficient of thermal conductivity of the ideal methanol gas at low pressure and can be calculated by eq 15, in which CP0 is the isobaric heat capacity of the ideal methanol gas at low pressure and can be calculated by the CG method (see Table 6) and η0 is the viscosity of methanol at low pressure and can be calculated by the Lucas method (see Table 8). After λ0 is calculated, the coefficient of thermal conductivity of supercritical methanol λ is computed according to eq 14, and the result is shown in Figure 5. Figure 5 displays the relationship between pressure and the coefficient of thermal conductivity of supercritical methanol at different temperatures.
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Table 4. Calculated Values and the Experimental Data of the Viscosity, Coefficient of Thermal Conductivity, and Isobaric Heat Capacity of Methanol η (10-6 Pa s) P (bar)
T (K)
ηcal
ηexp
50.0
484.9
61
63
a
a
λ (W m-1 K-1)
residuals
(%)b
-3.2
a
λcal
λexp
0.150
0.154
CP (J mol-1 K-1)
residuals (%)
CP cal
CP expa
residuals (%)
-2.6
185.8
177.8
4.5
The experimental data are the properties of saturated liquid methanol. Residuals ) (calculated value - experimental data)/experimental data. b
Figure 3. Relationship between the viscosity of supercritical methanol and the temperature at different pressures.
Figure 4. Isobaric heat capacity CP of supercritical methanol.
Table 5. Contribution Value of the Groups of Methanol groups
Nk
Nk (CPA1K)
Nk (CPB1K)
Nk (CPC1K)
sCH3 sOH ∑NKFK
1 1
35.1152 27.2107 62.3259
39.5923 2.7609 42.3532
-9.9232 1.3060 -8.6172
Table 6. Heat Capacity CP0 of Methanol at Low Pressure (J mol-1 K-1) pressure (bar) 1
520
530
540
temperature (K) 550 560 570
580
590
600
61.19 61.94 62.68 63.41 64.14 64.85 65.56 66.26 66.96 -1
Table 7. ∆CP of Supercritical Methanol (J mol
Figure 5. Coefficient of thermal conductivity of supercritical methanol.
-1
K )
temperature (K)
pressure (bar)
520
530
540
550
560
100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400
385.2 251.2 192.6 163.3 154.9 150.7 142.4 138.2 129.8 125.6 117.2 108.8 106.8 104.7 102.6 100.5
355.9 221.9 175.8 159.1 150.7 146.5 140.2 134.0 125.6 121.4 113.0 100.5 98.4 96.3 90.0 83.7
213.5 217.7 167.5 142.4 136.1 129.8 117.2 108.8 104.7 100.5 94.2 87.9 85.0 82.1 78.7 75.4
96.3 146.5 142.4 138.2 129.8 121.4 108.8 100.5 92.1 83.7 79.5 75.4 73.3 71.2 69.1 67.0
83.7 129.8 138.2 129.8 117.2 108.8 100.5 92.1 87.9 83.7 78.7 73.3 70.8 68.2 65.3 62.8
570
580
590
600
58.6 41.9 33.5 29.3 117.2 71.2 58.6 41.9 121.4 100.5 83.7 79.5 117.2 104.7 92.1 75.4 108.8 98.4 87.9 73.3 100.5 92.1 83.7 71.2 90.0 83.7 77.4 69.1 79.5 75.4 71.2 67.0 76.6 72.4 68.2 62.8 73.7 69.1 64.9 58.6 70.3 65.7 61.5 54.4 67.0 62.8 58.6 50.2 64.0 60.7 56.9 49.0 62.0 58.6 55.3 48.1 60.3 56.5 53.6 47.3 58.6 54.4 52.3 46.0
It can be seen that both pressure and temperature have an obvious influence on the coefficient of thermal conductivity of supercritical methanol. λ of supercritical methanol increases obviously with the increase of the pressure at a constant temperature. On the contrary, it decreases greatly with the increase of the temperature at certain pressures. 3.2. Change Rules of Transitive Properties of Supercritical Methanol. 3.2.1. Reynolds Number of Supercritical Methanol in a Round Tube. Equation 23 is used to calculate the Reynolds number of supercritical methanol flowing in a φ6 × 1.5 mm
Figure 6. Reynolds number of supercritical methanol flowing in a φ6 × 1.5 mm round tube at different pressure and temperature (velocity u ) 0.5 m/s).
round tube. Figures 6-8 show the effect of temperature, pressure, and velocity on the Reynolds number. Figure 6 illustrates that the Reynolds number increases in the range of 100-250 bar and then decreases slowly in the range of 250-400 bar with the increase of the pressure at any temperature, except 520 K. This should be due to the difference of changing the degree of the density and the viscosity of supercritical methanol with the change of pressure or temperature. The density increases faster than the viscosity at low pressure, and it does conversely at high pressure. Figure 6 also displays the influence of the temperature on the Reynolds
Table 8. Viscosity of Methanol at Low Pressure (η0) (×10
-7
N s m-2)
temperature (K) pressure (bar)
520
530
540
550
560
570
580
590
600
1
169.07
172.17
175.25
178.31
181.36
184.40
187.42
190.42
193.41
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Energy & Fuels, Vol. 23, 2009 531
Figure 9. Prandtl number of supercritical methanol. Figure 7. Reynolds number of supercritical methanol flowing in a φ6 × 1.5 mm round tube at different temperature and velocity (P ) 160 bar).
Figure 10. Film coefficient of the heat transfer of supercritical methanol flowing in a φ6 × 1.5 mm round tube at different pressure and temperature (velocity u ) 0.5 m/s).
Figure 8. Reynolds number of supercritical methanol flowing in a φ6 × 1.5 mm round tube at different pressure and velocity (T ) 550 K).
number, and the influence is more obvious in the range of 100-250 bar than 250-400 bar. Figure 7 shows the influence of temperature and velocity on the Reynolds number at 160 bar. It can be seen that the Reynolds number decreases with the increase of the temperature at a certain velocity and the changing degree is larger at high velocity than low velocity. For example, the Reynolds number changes from 12 480 to 8330 with the temperature varying from 520 to 600 K and decreases to 4150 at the velocity of 0.5 m/s, but at the velocity of 0.1 m/s, it goes from 2495 to 1666 and decreases only to 829. Therfore, it can be concluded that high temperature is unfavorable for the increase of the Reynolds number at constant pressure, especially at high velocity. Figure 8 shows the influence of pressure and velocity on the Reynolds number at 550 K. From Figure 8, it can be seen that the Reynolds number increases obviously at first and then decreases slowly with the increase of the pressure and the maximum Reynolds number exists at 160 bar; moreover, this tendency stays the same at any velocity, although it becomes weak as the velocity reduces. 3.2.2. Prandtl Number of Supercritical Methanol. The Prandtl number of supercritical methanol at different temperature and pressure is computed according to eq 24, and the result is shown in Figure 9. From Figure 9, it can be seen that the Prandtl number of supercritical methanol decreases sharply at first and then slowly with the increase of pressure at 520 or 530 K. However, when the temperature is in the range of 540-600 K, the Prandtl number increases first and then decreases with the increase of the pressure and the maximum Prandtl number appears in the range of 120-160 bar. In addition, Figure 9 also displays the effect of temperature on the Prandtl number. It decreases obviously with the increase of the temperature at low
pressure, but when the pressure exceeds 200 bar, the effect of temperature is weak. 3.2.3. Film Coefficient of the Heat Transfer of Supercritical Methanol in the Round Tube. Equation 25 or 26 is used to calculate the film coefficient of the heat transfer of supercritical methanol flowing in a φ6 × 1.5 mm round tube, and the result is shown in Figure 10. Figure 10 presents the effect of the pressure and temperature on the heat-transfer coefficient. With the increase of pressure, the heat-transfer coefficient almost remains stable at 520 K and first increases sharply and then decreases slowly for 530-570 K, but for 580-600 K, it always goes up from the beginning from 100 to 400 bar. 4. Conclusion 4.1. Temperature and pressure have an important influence on the thermophysical properties of supercritical methanol, and moreover, the influence is different for the different thermophysical property and this causes the transitive properties of supercritical methanol to change accordingly with the temperature and pressure. In addition, velocity also has a significant effect on the transitive properties of supercritical methanol flowing in a round tube. 4.2. The Reynolds number of supercritical methanol flowing in a round tube decreases as the temperature increases at certain pressures but increases first and then decreases with the increase of pressure at a constant temperature. The maximum Reynolds number exists in the range of 140-240 bar. Therefore, in the process of continuously producing biodiesel with supercritical methanol transesterification in the tubular reactor, the lower temperature is beneficial for better mixing of the reaction system; similarly, keeping the pressure in the range of 140-240 bar is also a good selection for the improvement of transfer properties of the supercritical reaction system. 4.3. At constant pressure, the film coefficient of the heat transfer of supercritical methanol flowing in a round tube decreases with the increase of the temperature, but at different temperatures, the influence of the pressure on the film coefficient
532 Energy & Fuels, Vol. 23, 2009
of heat transfer is different. Therefore, in the process of continuously preparing biodiesel with supercritical methanol transesterification in a tubular reactor, keeping a lower working temperature is favorable for better heat transfer, but for the selection of pressure, it depends upon the temperature. If the operating temperature is 550-600 K, keeping pressure in the range of 200-300 bar is beneficial for the heat transfer of the tubular reactor. Acknowledgment. We are grateful for the financial support from the National Natural Science Foundation of China (20576105) and Key Project of Hubei Provincial Department of Education (2004Z001).
Nomenclature T ) absolute temperature, K P ) absolute pressure, bar Tc ) critical temperature, K Pc ) critical pressure, bar Zc ) critical compressibility factor ω ) eccentric factor Fc ) critical density, mol/cm3 F ) density of supercritical fluid, kg/m3 µ ) dipole moment, debye µr ) contrastive dipole moment ξ ) contrastive reciprocality of viscosity, µ-1 P-1 M ) molar mass, g/mol Tr ) reduced temperature Pr ) reduced pressure FP0 ) modifying factor of the polarity effect at low pressure
Chen et al. FQ0 ) modifying factor of the quantum effect at low pressure FP ) modifying factor of the polarity effect at high pressure FQ ) modifying factor of the quantum effect at high pressure Nk ) number of the first-order group CPA1K ) contribution value of the first-order group Mj ) number of the second-order group CPA2j ) contribution value of the second-order group CP0 ) isobaric heat capacity of ideal gas at low pressure, J mol-1 K-1 CP ) isobaric heat capacity of supercritical fluid, J mol-1 K-1 η0 ) viscosity of ideal gas at low pressure, Pa s η ) viscosity of supercritical fluid, Pa s λ0 ) coefficient of thermal conductivity of ideal gas at low pressure, W m-1 K-1 λ ) coefficient of thermal conductivity of supercritical fluid, W m-1 K-1 λR ) coefficient of thermal conductivity of the referred fluid, W m-1 K-1 λR0 ) coefficient of thermal conductivity of the referred fluid at low pressure, W m-1 K-1 TcR ) critical temperature of the referred fluid, K FcR ) critical density of the referred fluid, mol/cm3 ZcR ) critical compressibility factor of the referred fluid ωR ) eccentric factor of the referred fluid d ) diameter of round tube, m u ) velocity of supercritical fluid in round tube, m/s Re ) Reynolds number Pr ) Prandtl number R ) film coefficient of heat transfer, W m-2 K-1 EF8005299
