458
Ind. Eng. Chem. Fundam. 1983,22, 458-463
Mlchels, A,; Sengers, J. V.; Van de Klundert J. M. fhysica 1963, 29, 149- 160. MISIC, D.; tho do^, G. AIChf J . 1965. 11, 650-656. Mlsic, D. Ph.D. dissertation, Northwestern University Evanston, IL, 1965. MISIC, D.; Thodos, G. t ' h y ~ i ~1966, a 32, 885-899. Reid, R. C.; Prausnltz, J. M.; Sherwood, T. K. "The Properties of Gases and Liquids", 3rd ed.; McGraw-Hill: New York, 1977; pp 629-665. Stlel, L. I.; Thodos. G. AIChE J . 1964, 10, 26-29. Tanaka, Y.; Noguchi, M.; Kubota, H.; Makita, T. J . Chem. fng. Jpn. 1979, 12, 171-176. Touloukian, Y. S.; Liley, P. E.; Saxena, S. C. "Thermal Conductivity, Non-
metallic Liquids and Gases, Thermophysicai Properties of Matter"; I F I , Plenum Press: New York, 1970; Voi. 3. Tsederberg, N. V. "Thermal Conductivity of Gases and Liquids"; The MIT Press: Cambridge, MA 1963. Tufeu, R.; Le Neindre, 8.; Bury, P. fhysica, 1969, 4 4 , 81-85.
Received for review December 2, 1981 Revised manuscript received February 7 , 1983 Accepted June 23, 1983
Thermal Conductivities of Binary Gas Mixtures at High Pressures: N2-02, N,-Ar, C0,-Ar, and COp-CH, Masahlro Yorlzane, Shoshln Yoshlmura, Hlrokatsu Masuoka, and Hldeto Yoshlda Department of Chemical Engineering, Hiroshima University, Higashihiroshlma 724, Japan
The thermal conductivities of blnary gases (N2-02, N,-Ar, C0,-Ar, C0,-CH,) have been measured at temperatures from 25 to 35 OC and under pressures up to 90 bar. The measurements were carried out with a vertical coaxial cylindrical cell. The uncertainty of the data is estimated to be within 3 % . The experimental results were compared with the values calculated by the Wassiljewa equation, in which the Mason-Saxena equation was used as a combination factor, and with values predicted by the Stlel-Thodos equation extended to binary gas mixtures. Both methods were found to represent the experimental results within a maximum deviation of 5 % .
Introduction Industrial heat exchangers are often operated under high pressures; therefore, thermal properties of fluids at high pressures must be known in order to design and operate the exchangers successfully. Among these properties, thermal conductivity is one of the most important. However, information on the thermal conductivity of gaseous mixtures at high pressures is often unavailable (Michels et al., 1962, 1963; Misic et al., 1966). Thus, the thermal conductivities of binary gas mixtures were measured for the N2-02, N2-Ar, C02-Ar, and C02-CH4systems at temperatures from 25 to 36 "C and at pressures up to 90 bar. It is also desirable to predict the thermal conductivities of gaseous mixtures from the values for pure gases. Thus, the experimental results are compared by two prediction methods. The first is the Wassiljewa equation with the Mason-Saxena equation as a combination factor. The other is the Stiel-Thodos equation extended to gaseous mixtures. Both predictions agreed fairly well with the experimental results, within the maximum deviation of
Experimental Results and Discussion Experimental results are shown in Tables I to IV. In these tables the experimental results are compared by two prediction methods: the first is the Wassiljewa equation (Wassiljewa, 1904) with the Mason-Saxena equation (Mason et al., 1958) as a combination factor and the other is the Stiel-Thodos equation (Stiel et al., 1964) extended to gaseous mixtures. The Wassiljewa Equation. The Wassiljewa equation (Wassiljewa, 1904) for binary gases is given by A,
XlXl
=
+ A12xz
+
A2x2
(1)
+ x2 where A, is a combinational factor. These factors are expressed by Mason and Saxena (Mason et al., 1958) as x1
XlA21
5%.
Experimental Section Apparatus and Procedure. Thermal conductivity measurements for mixtures were made with a vertical coaxial cylindrical cell. The apparatus was calibrated with Ar, CH4, COz,and O2 as standard gases. The uncertainty of the data is estimated to be within 3%. The details were presented in a previous paper (Yorizane et al., 1983). Sample Gases and Analysis. The purities of the gases used in this measurements are the same as in our previous paper (Yorizane et al., 1983). The mixtures were analyzed by means of gas chromatography. 0196-4313/83/1022-0458$01.50/0
In eq 1, information on the thermal conductivities of pure components is needed in the calculations for binary gases. Usually eq 1 and 2 have been restricted to use for the estimation of thermal conductivity of binary gases at 1bar, but in this study these equations were tried for estimating the thermal conductivities at high pressures, less than critical pressure. The Stiel-Thodos Equations. The Stiel-Thodos 0 1983 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983 458 Table I. Comparison of Measured Values with Predicted Values for the N,-0, System expt, x lo2 Wassiljewa, XWZ) temp, "C press., bar W/(m K) x loz W/(m K) dev," %
0.149 0.149 0.149 0.444 0.444 0.444 0.444 0.527 0.527 0.527 0.527 0.881 0.881 0.881 0.881 0.881 0.320 0.320 0.320 0.320 0.320 0.320 0.620 0.620 0.620 0.620 0.864 0.864 0.864 0.864 0.864 0.864 0.917 0.917 0.917 0.917 0.917
29.3 29.3 29.3 28.9 28.8 29.1 29.2 29.3 29.3 29.2 29.1 29.1 29.0 28.8 29.1 29.0 36.1 36.1 36.2 36.1 36.1 36.0 36.3 36.2 36.2 36.0 35.7 35.8 35.6 35.2 36.4 36.3 36.3 36.3 36.3 36.3 36.2
97.5 29.8 1.0 70.0 50.0 29.8 1.0 70.4 50.0 29.0 1.0 97.3 72.1 50.0 30.4 1.8 88.7 70.0 50.0 30.2 10.0 1.0 50.9 30.1 10.2 2.0 86.0 69.6 50.3 30.3 12.3 1.0 70.0 50.1 30.4 10.2 1.0
3.21 2.83 2.69 3.14 2.88 2.79 2.75 3.09 2.89 2.83 2.71 3.12 3.09 2.93 2.89 2.68 3.16 3.15 2.97 2.84 2.76 2.70 2.96 2.85 2.72 2.68 3.14 3.00 2.82 2.86 2.78 2.70 3.01 2.90 2.75 2.69 2.71
3.192 2.843 2.693 3.057 2.965 2.797 2.655 3.050 2.958 2.795 2.655 3.146 3.079 2.989 2.844 2.706 3.104 2.996 2.924 2.827 2.768 2.720 2.900 2.818 2.758 2.709 3.112 2.991 2.930 2.854 2.796 2.746 3.003 2.942 2.873 2.809 2.760
-0.56 t 0.64 +0.15 -2.61 + 2.88 +0.43 -3.28 -1.23 + 2.53 -1.20 -2.10 + 0.80 -0.36 +2.12 -1.69 + 0.97 -1.77 -4.86 -1.55 -0.56 +0.15 + 0.74 -1.86 -1.09 +1.55 + 1.01 -1.02 -0.30 +3.83 -0.25 t0.72 +1.59 -0.30 +1.41 t4.43 t4.62 + 1.92
Table 11. Comparison of Measured Values with Predicted Values for the N,-Ar System exptl value, M-S value, A X 10' A X 10' x(N2) temp, "C press., bar W/(m K) W/(m K) dev, % 2.158 +0.19 28.7 70.3 2.15 0.165 t 1.88 2.063 28.9 51.0 2.03 0.165 +0.33 1.817 28.6 1.4 1.81 0.165 -2.88 2.325 2.39 28.0 69.2 0.404 -3.17 2.230 2.30 28.1 51.0 0.404 -0.19 2.109 28.9 2.11 9.9 0.404 -4.21 1.981 28.9 2.07 1.2 0.404 -1.10 2.529 2.56 28.6 70.0 0.633 t0.62 2.432 2.42 28.6 50.3 0.633 -2.73 2.284 2.35 28.9 10.0 0.633 -0.94 2.845 2.87 28.5 70.5 0.909 -2.69 2.746 50.0 2.82 28.5 0.909 -0.08 2.557 2.56 28.4 9.9 0.909 -1.27 2.488 1.0 2.52 28.2 0.909 0.134 34.3 70.0 2.20 2.196 -0.36 0.134 2.16 34.8 51.0 2.138 -0.88 0.134 31.0 2.033 + 2.11 33.3 1.99 -0.11 0.134 36.0 10.0 1.86 1.861 0.446 35.7 70.0 2.42 2.408 -0.66 36.3 50.0 2.24 2.352 + 5.00 0.446 +1.03 29.7 0.446 36.3 2.23 2.250 2.14 9.6 -3.04 0.446 36.3 2.071 34.6 71.0 -1.26 0.730 2.71 2.671 50.0 35.7 +0.15 0.730 2.61 2.618 -3.01 35.7 29.8 0.730 2.59 2.516 70.0 +0.80 0.934 35.5 2.89 2.911 50.0 0.934 35.6 2.82 2.860 + 1.38 36.0 + 2.41 30.0 0.934 2.70 2.760 +1.67 10.0 0.934 36.0 2.52 2.563 1.0 +0.64 0.934 36.0 2.49 2.503
Stiel-Thodos, loz W/(m K)
X
dev," %
+ 0.40 + 0.85
3.223 2.849 2.708 3.03 2.916 2.808 2.664 3.028 2.915 2.807 2.661 3.226 3.076 2.960 2.854 2.706 3.170 3.075 2.971 2.865 2.769 2.724 2.962 2.854 2.758 2.712 3.200 3.11 3.00 2.891 2.793 2.747 3.13 3.02 2.91 2.81 2.77
+0.71 -3.47 +1.18 t0.83 -2.95 -1.94 + 1.03 -0.78 -1.88 + 3.36 -0.45 +1.13 -1.35 + 0.97 +0.32 -2.35 +0.03 +0.77 t0.18 t0.89 t0.24 +0.18 +1.55 +1.12 +1.78 + 3.67 + 3.83 +1.05 t 0.61 +1.63 t 3.92 t4.10 + 5.78 t4.66 +2.29
Stiel-Thodos, x 10, W/(m K) 2.142 2.043 1.825 2.324 2.222 2.034 1.995 2.535 2.430 2.24 2.860 2.75 2.540 2.498 2.203 2.107 2.022 1.94 2.397 2.40 2.211 2.123 2.640 2.539 2.44 2.878 2.772 2.660 2.56 2.52
dev, % -0.56 + 0.89 +0.77 -2.92 -3.52 -3.74 -3.53 -0.86 +0.54 -4.60 -0.42 -2.55 -0.74 -0.87 -0.05 -2.32 +1.56 +4.13 -1.11 +7.14 -0.72 -0.61 -2.40 -2.87 -5.94 -0.35 -1.74 -1.30 +1.55 +1.33
480
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
Table 111. Comparison of Measured Values with Predicted Values for the C0,-Ar System exptl MSW x 101, x 102, Stiel-Thodos, x(C0,) temp, "C press., bar W/(m K) W/(m K ) dev, % x 10zW/(mK) dev, % -a 0.061 25.0 71.0 2.10 2.084 -0.96 0.061 1.87 1.878 25.3 31.0 1.852 -1.02 +0.37 0.061 1.79 1.788 -0.33 25.2 11.0 1.778 -0.89 -a 0.150 2.16 2.214 t 2.64 25.3 91.0 -a 0.150 2.13 -1.69 25.2 71.0 2.089 0.150 25.0 1.975 1.96 1.973 + 0.46 51.0 t 0.56 0.150 25.0 1.865 1.85 1.842 31.O -0.33 t 0.92 1.75 1.756 0.150 11.0 24.9 1.765 t 0.23 t 0.74 -a 0.286 2.06 2.112 71.0 25.4 t 2.67 1.85 0.286 31.0 25.4 1.853 1.840 -0.54 t 0.16 0.286 25.4 1.69 1.689 1.0 1.685 -0.47 -0.24 0.301 31.0 25.4 1.85 1.853 1.839 -0.81 -0.05 1.75 0.301 11.0 25.4 1.740 1.725 -1.43 -0.57 1.69 0.301 25.4 1.0 1.686 1.683 -0.59 -0.41 -a 2.11 0.359 25.4 71.0 2.134 +1.28 0.359 25.4 51.0 1.98 1.984 +0.25 2.028 + 2.48 0.359 25.4 31.0 1.86 1.841 1.852 -0.75 -0.16 0.359 25.3 11.0 1.716 1.75 1.732 -2.05 -1.14 -a 0.500 25.2 2.15 71.0 2.189 +1.86 0.500 25.1 2.01 2.080 51.0 2.011 t 3.59 + 0.1 5 0.500 25.1 31.0 1.85 1.861 t 0.38 1.856 +0.11 0.500 25.2 1.72 11.0 1.722 1.704 -0.81 t 0.23 0.500 1.0 25.1 1.67 1.656 1.658 -0.54 -0.42 -a 0.503 91.0 25.2 2.37 2.401 +1.52 -a 0.503 25.2 2.19 71.0 2.190 t 0.09 0.503 24.8 2.04 51.0 2.083 2.012 t 2.11 -1.37 -a 0.744 25.1 2.37 71.0 2.390 +0.80 0.744 25.1 51.0 2.06 2.209 2.103 t7.13 + 1.99 0.744 24.9 31.0 1.92 1.912 1.892 -0.26 -1.30 0.744 24.7 1.66 1.0 1.647 1.650 -1.02 -0.84 0.787 27.2 2.16 51.0 2.270 2.128 -1.48 + 5.09 0.787 26.6 1.90 31.0 1.902 1.922 0.00 +1.05 0.787 26.3 11.0 1.74 1.706 1.725 -2.07 -0.98 0.787 26.2 1.65 1.649 1.0 1.651 + 0.06 +0.18 -a 0.162 35.3 91.0 2.21 2.252 + 2.04 -a 0.162 35.3 71.0 2.11 2.134 +1.19 0.162 1.99 35.3 51.0 2.024 2.023 +1.66 t 1.61 0.162 1.91 35.3 31.0 1.890 1.916 -1.20 ~0.16 0.162 35.3 11.0 1.83 -1.04 1.811 1.822 -0.44 0.162 35.3 1.0 1.78 1.773 -0.34 1.773 -0.34 -a 0.323 35.3 91.0 2.26 2.307 +2.12 -a 0.323 35.3 71.0 2.15 2.161 +0.37 0.323 35.3 51.0 2.03 2.057 +1.28 2.031 0.00 0.323 35.4 1.91 31.O 1.886 -1.21 1.904 -0.26 0.323 35.3 11.0 1.81 1.780 -1.87 1.798 -0.88 -a 0.431 35.4 91.0 2.35 2.363 +0.51 -a 0.431 35.2 2.20 71.0 2.194 -0.32 0.431 35.2 2.06 51.0 2.085 + 1.46 2.046 -0.44 0.431 31.0 35.1 1.90 1.891 1.906 -0.26 +0.53 0.431 35.4 11.0 1.81 1.767 -2.27 1.788 -1.11 0.431 35.9 1.74 1.0 1.728 1.732 -0.40 -0.17 -a 0.688 35.2 71.0 2.37 2.338 -1.14 0.688 35.1 51.0 2.09 2.188 +4.59 2.118 +1.24 0.688 35.0 31.0 1.90 1.922 1.939 +1.37 t 2.27 0.688 34.9 11.0 1.80 -2.34 1.756 1.787 -0.61 0.688 34.6 1.o 1.74 1.717 1.719 -1.27 -1.15 0.853 35.3 51.0 2.22 2.277 2.208 + 2.80 -0.32 0.853 35.2 31.0 2.00 1.965 -1.70 1.981 -0.90 0.853 35.1 11.0 1.83 1.740 1.804 -5.02 -1.53 0.853 34.8 1.o 1.75 1.723 -1.60 1.727 -1.37 a Estimation by Wassiljewa's equation cannot be determined because the pressure approaches to the critical pressure of
co,.
equations (Stiel et al., 1964), extended in this work to mixtures, are (A, - Amo)~,zcm5= 14.0 X 10-8[exp(0.535pr,) - 11 (0.03 C prm C 0.5) (3) (Am - ~ m 0 ) ~ m ~ c = m 513.1 X
10-8[exp(0.67pr,) - 1.0691 (0.5C ,or, C 2.0) (4)
(A,
- x,0)5;,~c,5 = 2.976 X 2.0161 (2.0 C prm C 2.8) 10-s[exp(1.155p,,)
where
+
Crnand prmare expressed as
(5)
Ind. Eng. Chem. Fundam., Vol. 22, No. 4, 1983
Table IV. ComDarison of Measured Values with Predicted Values for the C0,-CH. System exptl MSW Stiel-Thodos, x 102, x 102, x(CH,) temp, "C press., bar W/(m K) W/(m K) dev, % x 10, W/(m K ) -a -a 4.10 0.902 25.2 90.0 -a 25.1 3.872 3.90 0.902 70.0 3.644 25.1 3.73 3.681 -1.39 0.902 50.1 25.1 0.902 3.440 3.48 +0.17 3.482 30.0 25.1 0.902 3.259 3.34 -2.43 10.0 3.258 -a -a 4.20 25.4 0.823 89.9 -a 25.4 0.823 3.696 70.0 3.79 25.4 0.823 3.48 3.550 3.460 50.0 + 2.07 0.823 +0.12 3.32 3.320 3.265 29.5 25.4 25.4 -2.04 3.14 3.079 3.078 10.0 0.823 3.336 25.1 0.763 3.33 3.452 + 3.60 50.0 3.133 25.2 0.763 3.11 3.197 + 2.86 30.0 -a 3.741 25.2 0.701 89.9 3.78 -a 3.462 3.54 0.701 25.2 70.0 3.214 25.2 3.26 0.701 3.306 + 1.54 50.0 3.002 25.2 0.701 3.025 3.03 30.0 -0.23 25.2 2.823 0.701 + 0.04 2.772 2.77 10.0 2.748 25.1 0.701 + 1.32 2.65 2.680 1.0 -a 3.252 25.2 0.575 70.0 3.31 2.979 25.1 3.154 + 2.67 50.0 0.575 3.07 2.766 0.575 25.1 2.83 2.840 +0.50 30.0 25.1 2.580 0.575 2.59 2.587 10.0 -0.23 2.502 0.575 25.1 2.44 2.491 + 2.05 1.0 2.884 0.518 25.2 2.94 3.070 +4.42 50.0 25.3 2.667 0.518 2.67 2.737 + 2.51 30.0 25.2 2.47 2.480 + 0.61 0.518 2.486 10.0 0.467 25.2 2.801 2.84 2.957 +4.01 50.0 0.467 25.3 2.579 2.603 +0.58 2.59 30.1 0.467 2.39 2.395 2.342 -2.17 25.4 10.1 2.316 25.5 0.467 2.37 2.255 -5.01 1.0 2.311 25.1 0.285 2.37 2.372 + 0.21 30.0 2.118 25.1 0.285 2.13 2.101 -1.55 10.2 2.033 25.1 0.285 2.00 2.032 +1.85 1.o 2.210 25.1 0.210 2.14 2.233 t 4.54 29.5 2.012 25.0 2.06 1.967 10.2 -4.42 0.210 1.932 25.0 0.210 1.91 1.908 -0.21 1.2 -a -a 0.925 35.3 4.10 70.0 3.844 -0.26 3.794 0.925 35.3 50.0 3.85 3.576 -1.65 3.607 0.925 30.0 35.3 3.64 3.433 10.0 3.428 -1.10 0.925 35.3 3.47 3.360 1.0 + 3.88 3.349 0.925 35.3 3.22 -a 3.722 90.0 0.675 3.80 35.2 -a 3.469 70.0 0.675 35.2 3.59 3.249 50.0 35.2 0.675 3.32 3.365 +1.26 3.060 3.08 30.0 35.3 0.675 3.059 -0.98 2.882 35.2 0.675 2.81 10.0 2.866 +2.10 1.0 2.805 0.675 35.2 2.73 2.801 + 2.49 -a 3.280 0.565 35.4 3.32 70.0 3.042 0.565 3.03 3.177 50.0 35.4 +4.82 2.849 0.565 35.3 +1.10 30.0 2.82 2.852 2.670 0.565 35.3 2.67 2.656 10.0 -0.64 35.2 2.595 2.64 0.565 1.0 2.587 -1.90 2.950 0.508 35.3 3.03 50.0 3.082 +1.78 2.751 0.508 35.3 30.0 2.749 2.70 + 1.66 35.3 2.58 -1.01 2.576 0.508 10.0 2.550 2.46 1.0 + 1.02 2.500 0.508 35.3 2.489 2.32 30.1 2.353 0.258 2.360 +1.94 35.3 2.18 2.132 10.0 -2.16 2.175 0.258 35.3 2.08 2.104 0.258 35.3 1.0 + 0.43 2.085 35.3 2.10 2.170 29.8 2.172 0.122 + 3.58 1.94 1.940 10.1 1.990 0.122 35.3 +0.21 1.0 0.122 35.2 1.90 -0.42 1.894 1.920 Estimation cannot be determined because the pressure approaches to the critical pressure of CO,.
(7)
To obtain the values of Tcm,P,, V,
z,, and wm,the van der Waals one-fluid model (Leland et al., 1968) was used. Mixing rules are
wm = c x i w i i
dev, %
-0.74 -2.38 -1.04 -2.40
-
-2.56 -0.52 -1.54 -2.07 +0.12 + 0.80 -1.06 -2.26 -1.26 -0.99 + 1.84 + 3.89 -1.84 -3.03 -2.12 -0.50 +2.50 -1.90 -0.11 +0.36 -1.48 -0.35 + 0.04 -2.24 -2.37 -0.75 + 1.90 + 3.46 -2.24 + 1.05
-
-1.56 -0.80 -0.95 +4.22 -2.06 -3.40 -2.23 -0.75 + 2.67 + 2.63 -1.18 t 0.36 + 0.99 -0.11 -1.59 -2.58 +1.74 0.00 +1.46 + 1.64 -0.14 +1.35 + 3.68 + 2.79 +0.79
461
462
Ind. Eng.
Chem. Fundam., Vol. 22, No. 4,
1983
0 31
0 30 bar elobar
bar
e I I bar
3.5
3 0-
i
Stiel-Thodos Eq. Wassilijewa Eq.
Stiei-Thcdos Eq Wassiti~ewaEq.
3
05 mole fraction ot methane(-)
0 10
Figure 1. Comparison of measured values with predicted values for the C02-CH4 system.
0.5 1.0 mole fraction of carDon dioxide(-)
Figure 2. Comparison of measured values with predicted values for the C02-Ar system.
Acknowledgment z,, = 0.291 - 0 . 0 8 ~ ~
This work was largely supported by a Grant-in-Aid for Scientific b e a r c h from the Ministry of Education, Japan. The authors wish to express their thanks to K. Hozumi, S. Masaki, and S. Yamamoto for their work in the experiments and to M. Koizumi at Hikari-Koatau-Kiki Co. Ltd. for the construction of the thermal conductivity cell.
Nomenclature
In eq 7 the compressibility factor of a mixture is calculated from the Lee-Kesler equation of state (Lee et al., 1975).
Figures 1and 2 show a comparison of experimental and predicted thermal conductivities for the C02-CH4 system at 25.2 O C and the C02-Ar system at 25.2 “C. The solid lines are the predicted results from the Stiel-Thodos equation and the dotted lines are from the Wassiljewa equation. In applying the Stiel-Thodos equation both correlational parameters, kij and sij,were negleded because fitting of kij and sij to the experimental data did not lead to significant modification. These figures show that in the lower pressure region the predicted results of the two methods agree fairly well with the experimental data, but as the pressure increases the deviation between experimental data and the calculated results by the Wassiljewa equation becomes larger. As the pressure approaches the critical pressure of COZ the thermal conductivity of pure C02 becomes anomalous. The prediction of the’thermal conductivity of the mixture by the Wassiljewa equation becomes difficult. On the other hand, the Stiel-Thodos equation can predict fairly well the values of thermal conductivity of gaseous mixtures at high pressure.
Ai; = combination factor for i and j molecules kij = interaction parameter for i and j molecules M = molecular weight, g/mol P = pressure, bar R = gas constant, (L bar)/(mol K) sij = interaction parameter for i and j molecules T = temperature, K V = molar volume, mol/L xi = mole fraction of component i z = p
compressibility factor
= molar density, mol/L
X = thermal conductivity, W/(m w
K)
= acentric factor
{=
parameter defined by eq 6
Superscripts and Subscripts 0 = property at 1 atm (r) = reference fluid (0)= simple fluid * = monatomic value of thermal conductivity c = critical property i, j = components in a mixture m = mixture property r = reduced property
Registry No. Nitrogen, 7727-37-9; oxygen, 7782-44-7; argon, 7440-37-1;carboh dioxide, 124-38-9; methane, 74-82-8.
Ind. Eng. Chem. Fundam. 1983, 22, 463-471
Literature Cited Lee, 6. I.; Kesler M. 0. AIChE J . 1975, 27, 510-525. Leland, T. w.; Rowlhmn, J. s.; Sather, G. A. T ~~~~~h~ ~ soc, ~ 1968, ~ 64, , 1447- 1460. Mason, E. A-Saxena, S. C. Phys. Fluids 1958, 1 , 361-369. Michels, A.; Sengers, J. V.; Van Der Gullk P. S. PhySlC8 1962, 2 8 , 12 16- 1220. Michela, A.; Sengers, J. V.; Van de Klunderl J. M. physlca 1983, 29, 149-1 60. Misic, D.; ThodOs, G. PhySiCe 1966, 32, 585-899.
463
Stiel, L. I.; Thodos, G. AIChE J. 1964, IO, 26-29, Wasslljewa, A. Phys. 2.1904. 5 , 737-742. YoriWW, M.; Yoshimura, S.; Masuoka, H.; Yoshkla, H. Ind. Eng. C2mm. Fundarn. 1983, preceding paper In this issue.
Received for review December 2, 1981 Revised manuscript received February 7 , 1983 Accepted June-23, 1983
Flow Distribution in Piping Manifolds Robert L. Pigford,’ Muhammad Ashraf,t and Yvon D. Mlron’ Depadmnt of Chemical Englneerlng, University of Delaware, Newark, Delaware 1971 1
The uniformity of flow rates among the parallel tubes of a piping manifold is governed by the variations in fluid pressure inside the entrance and discharge headers. These result from fluid friction and from loss or gain of fluid momentum at exit and entrance ports. Using hydraulic flow coefficients derived from experiments, a theory for the distribution of velocities is developed for turbulent flow In manifolds having cylindrical headers of equal diameter. The results are confirmed by experiment and are used in two design examples.
Introduction There are many times in the design of process flow equipment when it is necessary to subdivide a large fluid stream into several parallel streams, to process these streams separately, and then to recombine them into one discharge stream before sending the fluid to another step in a process. The entering feed stream is subdivided by a header to which the parallel small tubes are connected at right angles. After treatment, the parallel streams are combined through ports leading into an output header. Aa an example, reactions which are accompanied by evolution or absorption of heat can be carried out in small tubes in order to provide surface for heat transfer. This occurs in furnaces used for heating fluids in petroleum refineries and in some fixed-bed catalytic reactors. A key question which arises in the design of such units is the uniformity of the flow distribution which will be obtained. The greater the pressure drop across the parallel tubes and the smaller the pressure changes inside the two headers to which the tubes are connected the more uniform the flow distribution will be. Headers can have various shapes. This paper assumes cylindrical piping headers. Given the number of tubes to be placed in parallel and the fluid friction coefficient, the length, and the diameter €or each tube, how large must the inlet and exit headers be to provide a flow distribution among the tubes as uniform as may be required? The detailed flow patterns among all the paths of a complex piping system can be computed from straightforward use of the one-dimensional equations of fluid motion if enough information is available on the pressure changes that occur near the points at which streams divide or recombine. For turbulent flow, at least, the computations are expected to be simple because all pressure changes will be nearly proportional to squares of velocities and the percentage variation of flow will be independent ‘Stanford Research Institute,
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of velocity. Nevertheless, the numerical work required may be long and tedious when there are many tubes in parallel. A general solution of the flow equations leading to tables or graphs which are generally applicable should save much effort when a design is needed. Such a solution is presented here, along with some recommended values of empirical coefficients representing wall friction and momentum recovery in headers of uniform diameter. Turbulent flow and essentially constant fluid density are assumed. Vaporization of the fluid is not included. The entrance and discharge headers are assumed to have constant and equal diameters. Distributions in Piping Manifolds Two arrangemenh of two headers and parallel tubes are considered, as illustrated in Figure 1. The one at the top can be called “reverse-flow” because the fluid in the exit header leaves in the direction opposite to its path in the entrance header. It is referred to here as a “U-manifold.” Alternatively, the two flow directions may be the same, as in the parallel-flow “Z-manifold,” also shown in the figure. Among other things, we want to know which design is better, i.e., which gives the more nearly uniform flow distribution among the connecting tubes or requires the smaller total pressure drop when the input flow rates are the same. The flow streamlines in the headers are not simple near side ports but we assume nevertheless that the one-dimensional flow approximation, often called the “hydraulic approximation,” is valid. Thus the fluid pressure in an entrance header will change for two reason: (a) because of wall friction in the straight sections between adjacent side outlets, the fluid pressure will fall in the flow direction; (b) near each exit port in the entrance header the pressure will rise because an opposing force (a fluid pressure difference) is needed to cause the exit fluid to lose some of its forward momentum as it leaves. Similar changes occur in the exit header as entering fluid acquires momentum. The net result is that the pressure in each header both rises and falls, as illustrated in Figure 2. In the exit header, @ 1983 American Chemical Society
