Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 325-332 Geibshtein, A. I.; Stroeva, S. S.; Parfenov, A. N.; Zinov’eva, T. V. Kinet. Katal. 1978. 77, 412. Germain, J. E. “Catalytic Oxidation of Hydrocarbons”, I n “Theoretical and Experimental Aspects of Catalyzed Oxidation”; Ecole de Printemps, Institut de Recherches sur la Cataiyse, Lyon, France, 1978. Germain, J. E.; Perez, R. Bull. SOC.Chlm. h . 1975, 739. Win, 0. W.; McCain, C. C.; Porter, E. A. Roc. 4th Int. Congr. Catal. 1968, Paper 20, 271. bber, J. “Contributions of Recent Physical Techniques to the Understanding of Oxidation Catalysts”, I n “Theoretical and Experimental Aspects of Catalyzed Oxidation”; Ecoie de Printemps, Institut de Recherches sur ia Cataiyse, Lyon, France, 1978. Keuiks. G. W. J . Catal. 1970, 79, 232. Krenzke. L. D.; Keulks. G. W.; Sklyarov, A. V.; Firsova, A. A,; Yu, M.; Kutirev, L.; Margoiis, Y.; Kryiov, 0. V. J . Catal. 1978, 5 2 , 418.
325
Lankuyzen, S. P.; Fiorack, P. M.; Van der Bann, H. S. J . Catal. 1976, 4 2 , 20. Moro-Oka, A.; Taklta, Y.; Ozaki, A. J . Catai. 1971, 2 3 , 183. Renken, A.; Mueiler, M.; Wandrey, C. 4th International Symposium on Chemical Reaction Reaction Engineering, Frankfurt. Germany, 1976; 11 1-07, Sala, F.; Trifiro, F. J . Catal. 1978, 47, 1. Sokoiovskii, V. D.; Buigakov, N. N. React. Kinet. Catal. Lett. 1977, 6.65. Trifiro, F.; Lambri, C.; Pasquon, I . Chim. Ind. 1971, 53(4),339. Unni, M. P.: Hudgins. R. R.; Siiveston, P. L. Can. J . Chem. Eng. 1973, 3 7 , 623.
Received for review September 18, 1981 Revised manuscript received May 21, 1984 Accepted June 1, 1984
Thermal Conductivity of Coal-Derived Liquids and Petroleum Fractionst Monlca E. Baltatu Fluor Engineers, Incorporated, Advanced Technology Division, Irvine, Califomia 92730
James F. Eiy and Howard J. M. Haniey* Chemical Engineering Science Dlvlsion. National Engineering Laboratory, National Bureau of Standards, Boulder, Colorado 80303
Mlchael S. Graboski, Richard A. Perkins, and E. Dendy Sioan Department of Chemical Engineering and Petroleum-Refining, Colorado School of Mines, Golden, Colorado 8040 7
Thermal conductivity coefficients of coal-derived liquids and petroleum fractions are calculated by an extended corresponding states, conformal solution technique. The method requires as input pseudocritical parameters, molecular weight and acentric factor, and a pseudddeal gas heat capacity for each pseudocomponent or fraction. These quantities are estimated here from the mean average boiling point and specific gravity of the fractions using the techniques proposed by Riazi-Daubert, Kesler-Lee, and Winn: the relationship between the estimated conductivity and the choice of the method is noted. Predicted thermal conductivities are compared with data for three coal liquid samples measured at the Colorado School of Mines and with literature data. Agreement between prediction and experiment is generally within 10%, depending on the method used to calculate the input parameters. Some literature petroleum fractions data are also compared with the model. Again, agreement is within 10%.
Introduction This paper follows the work reported by Baltatu (1981, 1982), who applied the extended corresponding states conformal solution transport property model (CST) proposed by Ely and Hanley (1981,1983) to the viscosity of petroleum fractions and coal liquids. Specifically, the object of this report is to complement the viscosity studies by applying the CST model to thermal conductivity. This task was not possible until recently: limited data were available for petroleum fractions (Mallan et al., 1972; Jamieson et al., 1975) but none for coal liquids. Recently, however, Gray (1981) presented results on SRC-I1 coal liquids, and independent experiments have been carried out at the Colorado School of Mines on three liquids: two distillation cuts boiling in the naphtha range produced by Work carried out in part a t the National Bureau of Standards. Because of the intended audience, this manuscript sometimes departs from the usual NBS policy to use only SI units. 0 196-4305/85/ 11 24-0325$01 .50/0
the SRC-I and SRC-I1 processes, and a distillate from a Utah coal via the COED processes. An attractive feature of the new data is that they were obtained for liquids which are well characterized so that one can make a quantitative comparison between theory and experiment. The CST procedure is very flexible. It predicts the transport properties-over the phase range from the dilute gas to the dense liquid-for pure species and for mixtures with, in principle, an unlimited number of components. Input parameters required are: the temperature (T), pressure (p), and (for a mixture) mole fractions (xi);the critical temperature, pressure, and volume, molecular weight (M), and acentric factor ( w ) for each species of interest. An estimate of the dilute gas heat capacity at constant pressure is required for each species for the thermal conductivity calculation. To be consistent with our previous work, we will obtain the input parameters from the mean average boiling point T b and specific gravity SpG, but we stress that this step introduces considerable uncertainty into the prediction 0 1985 American Chemical Society
326 Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
procedure as a whole: failure to represent data could well be because the pseudo-critical constants are unreasonable, not necessarily because the corresponding-statestechnique is inadequate. We will not develop this point in this paper ill obtain the constants from three common methods, but w due to Riazi and Daubert (1980), Kesler and Lee (1976), and Winn (1957). The outline of the paper is as follows: the CST model is reviewed first; we discuss the Colorado School of Mines thermal conductivity data and represent them via the CST procedure. Comparisons between the theory and data are carried out in three ways: (1)by treating the coal liquid in bulk as a pseudo-pure compound, (2) by treating the liquid as a pseudo-mixture of several subfractions, and (3) by regarding the liquid as a defined mixture, which can be done since a compound analysis is available (Sloan, 1983). We then examine the data reported by Gray (1981). Finally, the paper includes a brief comparison between theory and experiment for the thermal conductivity of petroleum fractions.
The CST Method We refer to the paper of Ely and Hanley (1983) for a complete description of the method, the equations, and parameters of the equations. Here we only outline the procedure. The concept is that the transport properties of a mixture can be equated to those of a hypothetical pure fluid. The properties of this fluid can then be determined, via corresponding states, in terms of those of a reference fluid. Methane is the reference fluid for these calculations. The thermal conductivity of a pure substance or mixture is divided into two contributions-one arising from the transfer of energy from purely collisional or translational effects, A’, and the other from the transfer of energy via the internal degrees of freedom, A”. I t is then assumed that this latter contribution is independent of the density and may be calculated from the modified Eucken correlation for polyatomic gases (Hirschfelder et al., 1954)
-iff?
y)
- 1.32 (q,, -
9,
The equivalent temperature (To) and density ( p o ) for the reference fluid are defined by the relations Po = A
, o ; To = T/fx,o
(7)
The equivalent substance reducing ratios f x , o and hx,O are defined by the mixing rules fx,Ohx,O
=
(8)
CCxolx@fa@’hol,d
a B
and
CC%&&9
(9)
(faf@)’/’(1 - kq3)
(10)
hx,0 =
a B
where fa0 =
and 1 h,, = -(hall3 + hB1/3)3(l- la@) 8
(11)
Finally
f,
= e,T,c/T~c
ha = 4, VaC/VOC
(12)
(13)
where 0, and 4, are the shape factors of Leach and Leland, whose detailed functional forms are given in our previous work (Ely and Hanley, 1981). They are functions of o, Pitzer’s acentric factor. k,, and I,, are binary interaction constants. In this paper we set ha, and l,, equal to zero. The mixing rule for the mass was chosen to be analogous to that used for the viscosity
Mx-1/2fx,01/2hx,{4/3 = CC x , x u M , g - ’ ~ z f , u 1 ~ z h , ~ (14) ~~3 a B
where
where A”, is the internal contribution for component C Y , Ma is the molecular weight, T,* is the dilute gas viscosity of component CY, e:,,is the ideal gas heat capacity, and R is the gas constant. For a mixture, iffmix is calculated via the empirical mixing rule iffmix(T)
where the subscript “0” refers to the reference fluid and
= ccx,x&f,p
(2)
a B
where we use (3) We emphasize that in general the assumption that the internal contribution is independent of density must be incorrect although we cannot assess to what extent. Since, however, X” contributes only about 5-10% to the total conductivity of the liquid, the assumption is justified. The translational contribution A‘ is calculated via corresponding states. As remarked, therefore, it is assumed that the translational mixture thermal conductivity at a density, p, and T i s identical with that of a hypothetical pure fluid, denoted by a subscript x , viz. i f m i x ( P t T ) E i’x(p,T) (4) The corresponding-states principle is then invoked on the hypothetical pure fluid if,(P,n = i’o(Po,To)F,
(5)
1 Ma,-’ = -(Ma-’ 2
+ MK’)
(15)
It was found for the viscosity that a correction factor was needed to allow for the failure of the corresponding-states model to predict correctly variations in local composition. Based on studies of the Enskog theory (Ely, 1981), using results from computer simulation of a model fluid mixture (Hanley and Evans, 1981), a correction factor was introduced which depends only on PVT properties of the fluid mixture. For the thermal conductivity we have adopted a similar correction factor, viz.
x,=
([ (: $)“z]g)2 1-
(16)
where for a mixture Zxc= Cx,ZaC.This expression also has some justification from the Enskog theory in that the density dependence of the thermal conductivity is dependent on the derivative (dP/aT),. The correction factor eq 16 is applied to the entire collisional contribution to the thermal conductivity, i.e. if,(Px,Tx) = i’o(po,To)F~X~ (17) Using eq 2, 5, 16, and 17, we have then for our final working equation i m i x ( P , T ) = X’O(PO,TO)FAXA + iff,ix(T) (18)
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Table I. Some Physical Properties of Three Coal Liquids SRC-I Utah COED SRC-I1 naphtha distillate naphtha molecular weight 132 135 115 bromine no., g/100 g -16.3 35 refractive index, ng 1.438 1.499 1.539 specific gravity 0.781 0.879 0.820 (60' /60°) kinematic viscosity, cSt 0.280 2.120 0.870 100 O F 29.4 41.0 OAPI' 49.7 K Watsonb 11.2 10.8 10.9
" O A P I = (141.5/SpG) - 131.5. b K Watson = Tb1I3/SpG; Tb in O R
and SpG a t 60 OF.
Summary of the Calculation Procedure A summary of the calculation procedure to evaluate thermal conductivity is as follows. Input parameters are the critical temperature, volume, and pressure, the acentric factor, ideal gas heat capacity, and molecular weight of the pure fluid or of each component of the mixture, as the case may be. These parameters for the reference fluid are required with an equation of state and some functional form for the thermal conductivity for this reference fluid. Given, say, the pressure, temperature, and mixture composition, the density of the fluid or mixture is obtained by finding the equivalent pressure of the reference substance via the ratio p o = pxhx,o/fx,o from the corresponding pressure in the mixture, px. Initially, the shape factors in the eq 12 and 13 are set to unity. Given p o = p(po,To), density po follows. Thus, a first guess of the density is that obtained with classical two-parameter corresponding states. This first guess allows one to approximate the shape factors. Repeated iterations using eq 12 and 13 give the final density. Having, therefore, final values of p, f,,o and h,,o, one can evaluate FA,po, and To and hence X',(po,T0)and X"(T), thereby obtaining a value for X,(p,T). Clearly, if we treat the fluid as a pure substance in the first place, the mixing rules are not required. Corresponding-States Input Parameters Three procedures were used to obtain the parameters required of the CST procedure: (1)pseudocritical constants and molecular weights via Riazi-Daubert with acentric factors from the Edmister equation (1961); (2) the Kesler-Lee correlations; (3) Winn's nomograph for molecular weight and the pseudocritical pressure, a nomograph for the pseudocritical temperature, and Edmister's method for the acentric factor. The ideal gas heat capacity at constant pressure was estimated for all three procedures by the Kesler-Lee equations (1976). Equations for the above are given as an Appendix. Coal Liquid Data: Colorado School of Mines Thermal conductivity data were obtained at the Colorado School of Mines for three liquids: SRC-I naphtha, Utah COED distillate, and SRC-I1 naphtha. Some physical properties of the fluids are listed in Table I. Table I1 presents a saturate-olefin-aromatic analysis, and D-86 ASTM distillation curves are represented in Table 111. A thorough description of the hot wire apparatus is presented by Mohammadi (1980),by Perkins et al. (1981), and by Mohammadi et al. (1981). Only a brief summary is presented here. Basically, the method consists of measuring the temperature rise as a function of time in a fine, steadily heated, vertical wire immersed in the fluid. The.thermal conductivity of the fluid is then determined from the analytical solution of the partial differential equations which describe the heat transfer process.
327
Table 11. Saturate-Olefin-Aromatic Analysis (wt %) SRC-I Utah COED SRC-I1 naphtha distillate naphtha saturates 61.2 65 70 olefins aromatics asphaltenes"
1
4
6
37.8
31
24
0.1
3
1.2
a Asphaltene content reported by Hauser Laboratories, Colorado, using cyclohexane as solvent.
Table 111. ASTM Distillation % recovered
(by vol) IBP 5 10 20 30 40 50 60 70 80 90 95 EP
SRC-I naphthaa 332 348 355 363 369 375 383 392 403 415 436 450 463
temp, K Utah COED distillate* 344
__-
387 427 460 479 501 511 528 540 566
---
588
SRC-I1 naphthab 339 351 363 380 390 398 408 418 429 442 455 481 485
'Distillation performed by Pittsburg and Midway Coal Mining Co. Solvent Refined Coal Pilot Plant, DuPont, WA. bDistillation performed by Colorado School of Mines, Golden, CO; ambient pressure of 0.088 MPa; temperature as corrected to 0.101 MPa using API Data Book method. In the present apparatus a ramp power forcing function was used to heat the wire. The temperature response of the fluid in time resulted from the long time solution of the transient heat transfer equation
where AT = temperature rise, t = time, r = wire radius, D = Euler's constant, CY = thermal diffusivity, X = thermal conductivity, and q = slope of the ramp power input. Therefore, a plot of AT/t against In t gives the thermal conductivity as the slope of the straight part of the curve. The success of the hot wire technique depends largely on the accuracy and rate of the transient voltage generation and measurement. We therefore used a microprocessor to drive the power supply and measured the imbalance of a dynamic Wheatstone bridge curcuit. Microprocessor control allowed 1022 readings to be obtained in a period of 1s, as illustrated for a sample fluid toluene in Figure 1.
The measurement of thermal conductivity with a ramp power forcing function is a new technique. It is more common to employ a step power forcing function, but the ramp power forcing function has significant advantages with respect to prolonging the time for onset of convection. It is necessary, however, to verify the accuracy of the ramp forced thermal conductivity data. Figure 2 shows a scatter plot for ramp forced vs. step forced toluene data obtained with this instrument. The scatter is random and of the order of 1% , increasing to 2% at high temperatures as the fluid critical point is approached. Figure 3 shows the pressure-temperature plot of our toluene data compared with an isobar and the saturation curve drawn from the data of Mani and Venart (1973). Our data are consistent. A detailed analysis of the maximum uncertainty in pre-
328 Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
12-
A
4
I
10L
* B r
1
A
AT/t
A
A A~
S-
I
I
I
1
80
100
120
140
A
4-
A
A
-2
I
I
2c
STEP THERMAL CONDUCTIVITY, mW/m.K 1i > L-1- - _ 1 -
0 -6.0
-5.0
-3.0
-4.0
-2.0
0
-1.0
Lrt)
Figure 1. Raw data for toluene at 294.5 K and 3.1 MPa. Plot of temperature change vs. time. The thermal conductivity is proportional to the slope of the straight part of the line.
Figure 2. Percent deviation between the thermal conductivity of toluene obtained via a ramp and step forcing function vs. the conductivity obtained from the step. The percent deviation is defined as 100 (ramp-step)/step.
Table IV. Sample Experimental Thermal Conductivity Coefficients of Three Coal Liquids pressure, thermal conductivity, T,K MPa mW/(m K) SRC-I Naphtha 302.91 3.45 111.7 302.91 6.89 113.3 10.30 116.0 302.91 302.91 13.79 115.5 375.03 375.03 375.03 375.03
3.45 6.89 10.30 13.79
96.8 99.4 101.1 101.4
494.23 494.23 494.23 494.23
3.45 6.89 10.30 13.79
83.0 84.5 86.0 89.0
h 1 3 . 8 MPa
5
398.30 398.30 398.30
3.45 6.89 10.30
112.3 113.2 115.0
493.65 493.65
3.45 6.89
101.4 103.8
298.81 298.81
SRC-I1 Naphtha 1.52 5.07
125.7 127.8
10.3 MPa 6.89 MPa
zc
0
3.44 MPa
80C
I
400
440
480
520
560
TEMPERATURE, K
Figure 3. The thermal conductivity of toluene as a function of pressure and temperature. The dashed lines were obtained from the data of Mani and Venart (1973). Each value of conductivity displayed is a composite of data obtained via the ramp and step method. The accuracy of our points is about 3%.
Utah COED Distillate 3.45 120.0 6.89 121.0 13.79 125.0
334.45 334.45 334.45
0
c
cision given by Mohammadi (1980) yields 1.0% for the instrument based on the significant errors. The coal liquids tend to be somewhat thermally unstable. Thus this
precision of our coal liquid measurements is somewhat worse than that for pure fluids. Due largely to the instability, it is estimated overall that the coal liquid data are accurate to within 3%. Sample data for the three liquids are given in Table IV. The data for each of the coal liquids were obtained for one sample of the liquid of interest. The results in Table IV are each from one selected run at the given temperature and pressure; however, at least one duplicate datum point was taken for each point and was within the stated accuracy of the value reported. Comparison between Theory and the Colorado School of Mines Data The coal liquids were treated first in bulk, i.e., as a pseudo-pure liquid. The pseudocritical properties and the other input parameters were calculated from the three
Table V. Pseudocritical Properties for Three Coal Liquids" method
petMPa
V', cm3/g-mol
T',K
w
M
M (exptl)
0.287 0.322 0.354
102.7 109.1 104.2
132.0
1 2 3
3.2 3.2 3.3
388.0 412.1 393.5
SRC-I Naphtha 580.9 575.1 573.1
1 2 3
2.6 2.8 2.8
516.1 563.4 545.6
Utah COED Distillate 682.0 678.2 672.1
0.375 0.427 0.467
141.2 154.1 149.3
135.0
1 2 3
3.4 3.4 3.5
379.0 407.2 384.4
SRC-I1 Naphtha 600.2 594.0 591.1
0.277 0.316 0.352
103.4 111.1 104.8
115.0
Values of the pseudocritical properties, acentric factor, and molecular weight for the three School of Mines liquids treated as bulk. Values calculated via three methods designated: 1, Riazi-Daubert; 2, Kesler-Lee; 3, Winn. The experimental molecular weight is included.
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Table VI. Comparisons between Predicted Thermal Conductivity and the Experimental Data of Table IV" method 1 method 2 method 3 T,K P, MPa A B A B A B SRC-I Naphtha 302.91 3.45 12.98 13.41 3.94 6.45 16.11 17.46 302.91 6.89 12.89 13.32 3.71 6.28 15.89 17.18 302.91 10.30 11.72 12.15 2.50 5.09 14.48 15.79 302.91 13.79 13.59 14.07 4.24 7.27 16.28 17.63
mixture 20.99 20.40 18.68 23.39
375.03 375.03 375.03 375.03
3.45 6.89 10.30 13.79
8.19 7.26 7.33 8.46
8.09 7.16 7.13 8.36
0.31 0.61 -0.69 0.0
1.97 1.00 0.89 1.87
10.58 9.48 9.32 10.33
11.20 10.09 9.97 10.99
17.62 16.14 15.73 16.56
494.23 494.23 494.23 494.23
3.45 6.89 10.30 13.79
0.48 2.01 3.26 2.36
1.03 1.80 0.51 -1.28
-4.46 -3.20 -2.21 -3.26
-5.23 -3.67 -2.56 -3.40
2.05 3.55 4.53 3.60
0.78 2.54 3.60 2.72
11.45 12.02 12.42 10.80
334.45 334.45 334.45
3.45 6.89 13.79
5.83 6.12 5.04
7.73 8.00 6.74
Utah COED Distillate -7.92 -4.79 -7.77 -4.72 -9.12 -6.14
2.25 2.40 0.88
3.98 4.02 2.42
18.52 18.72 17.17
398.30 398.30 398.30
3.45 6.89 10.30
-3.10 -1.90 -1.14
-1.50 -0.44 0.44
-14.45 -13.75 -13.34
-11.96 -11.19 -10.59
-6.11 -5.29 -4.64
-4.67 -3.88 -3.24
8.76 9.75 10.52
493.65 493.65
3.45 6.89
-9.57 -9.63
-8.86 -8.85
-16.27 -19.75
-16.47 -16.75
-11.74 -11.95
-11.01 -11.29
2.30 1.98
298.81 298.81
1.52 5.07
6.76 6.18
7.72 7.12
11.29 10.48
11.48 10.73
SRC-I1 Naphtha -3.50 -4.15
-1.19 -1.79
10.50 9.78
329
"Shown are percent deviations defined by [A (calcd) - X (exptl)/X (exptl)] X 100 for three methods used to obtain the pseudocritical constants. The three methods are: 1, Riazi-Daubert; 2, Kesler-Lee; 3, Winn. The liquids were treated as bulk (column A) and as a five-function mixture (column B). They were also regarded as a well defined mixture.
methods mentioned with the results shown in Table V. Since these critical properties are artificial, we cannot check them with respect to experiment. The molecular weights were, however, measured by a freezing point depression and are listed in the last column in Table V. The thermal conductivity was then estimated using eq 18 for each set qf pseudoparameten. Percent deviations are given in Table VI under the columns denoted by A. The liquids were then considered to be a mixture of five subfractions and the bulk fluid was split according to the procedure of Erbar and Maddox (1982). Pseudoparameters were estimated for each subfraction and the conductivity was calculated by eq 18. The deviations are reported in Table VI under columns B. As a matter of interest we include, under the last column, deviations for the coal liquids treated as a well-defined mixture, given the component analysis and literature values of the input parameters. Of course, the component analysis is not necessarily complete since the liquids contain a high number of compounds and only the major ones have been identified (Sloan, 1983).
Comparison for Coal Liquid Data: Gray (1981) We also examined the data reported by Gray on measurements performed on eight coal liquid fractions at temperatures to approximately 500 K. Based on our experience with eq 18 and the Colorado School of Mines results, however, we decided to treat the fluids only in bulk. We also considered only the procedures of Riazi-Daubert and of Kesler-Lee since the Winn method appeared consistently less successful. Results are given in Table VII. Comparison for Petroleum Fractions To round out our study and to be consistent with the paper of Baltatu (1982), we also examined how well our procedure predicts the thermal conductivity of petroleum fractions. We report here results-elected to cover a wide
range of Tb and SpG-from two major literature sources, Mallan et al. (1972), and Jamieson et al. (1975). The liquids were treated in bulk with the pseudocritical constants obtained from Riazi-Daubert and Kesler-Lee, Respectively. Results are listed in Table VIII. Agreement is good using the latter. Discussion and Conclusion This work reports some new data on the thermal conductivity of coal liquids together with an extensive characterization of the liquids. We feel that it is essential to give the latter if the conductivity results-or any thermophysical properties-are to be really useful. The data were compared with predictions from an extended corresponding states procedure (CST) which has been shown to be satisfactory for the viscosity of coal liquids, and also of petroleum fractions. Comparisons between the procedure and literature thermal conductivity data for coal liquids and petroleum fractions are included in this work. There are several comments. (1)The deviations shown in Tables VI and VI1 for coal liquids, and in Table VI11 for petroleum fractions, indicate that the theoretical procedure is satisfactory. Depending on the method used to estimate pseudocritical constants and the other necessary input parameters, the deviations are generally substantially less than 10%. (2) Following the comment (l),the prediction procedure as a whole is somewhat clouded because the input parameters do have to be estimated. Hence it is not possible to say unambiguously that the deviations between theory and experiment result from defects in the basic CST method or from the input parameters (or from the data). One should note, however, that the CST method has been tested successfully against those pure species that are typical components of coal liquids and petroleum fractions (Baltatu, 1981, 1982) for which the problem of estimating the input parameters is minimized. Clearly, further work
330
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985
Table VII. Thermal Conductivity of Coal Liquid Fractions (Gray, 1981). Deviations between Theory and Data Reported by Gray, Treating the Liquids in Bulk. Methods as in Table VI exptl thermal cond, % dev Tb.K SDG temD.K m W / ( m K ) method 1 method 2 372.6 0.7701 302.09 116.72 5.89 -1.41 1.78 -4.2 395.54 94.68 -4.2 438.93 87.28 0.93 -2.75 510.43 77.09 0.99 410.4
0.8125
301.98 395.48 481.65 510.54
119.85 100.31 85.44 83.01
7.66 0.77 0.38 -1.32
-2.90 -7.78 -6.21 -6.61
524.8
0.9761
301.71 302.43 347.65 348.98 394.76 430.65 409.59 436.21 471.59 473.98 511.09
129.30 128.33 124.02 121.91 116.34 110.65 117.43 110.22 103.89 105.34 102.04
-8.06 -7.50 -13.15 -11.90 -15.92 -17.18 -18.99 -17.63 -17.25 -18.66 -19.92
14.75 15.42 8.67 2.37 -0.34 -1.85 -1.09 -1.98 -1.98 -3.76 -6.77
650.4
1.0793
298.37 299.93 344.71 348.87 394.76 398.37 428.65 430.76 464.87 473.43 511.09 512.15
128.68 125.56 125.41 123.26 118.11 119.75 118.59 114.18 115.37 112.21 110.25 110.56
-11.77 -9.65 -13.56 -12.53 -14.74 -16.38 -19.44 -16.60 -21.50 -20.26 -22.70 -23.02
19.11 21.89 14.66 15.83 11.11 8.85 3.74 7.32 -0.33 0.90 -3.78 -4.22
749.8
1.1733
356.87 363.21 391.15 404.26 433.26 466.37 492.98 510.82
131.41 130.30 132.02 128.23 124.65 115.22 116.76 113.68
-14.60 -14.20 -17.57 -16.42 -17.21 -14.54 -18.85 -18.75
11.34 11.57 6.30 7.33 5.42 7.76 1.51 1.06
on estimating pseudoconstants for poorly characterized fluids is in order. (3) It was not our intention to discuss the problem of pseudoconstants. We merely worked with the simplest
procedures which are accepted in the coal liquid and, especially, the petroleum literature. One should point out that we could have used, for example, the new revised methods recommended by the API Technical Data Book-Petroleum Refining (1982). They included a revised Riazi-Daubert equation for molecular weight and an acentric factor from the Maxwell-Bonnel equation. It does appear from Table IV that the Riazi-Daubert and Kesler-Lee methods are slightly better than that of Winn, but taking Tables VI, VII, and VI11 together, we cannot recommend at this time which of the two former methods is to be preferred. (4) It appears, at least in this context, that there is no real advantage in treating coal liquids or petroleum fractions as a set of subfractions or treating them in bulk as is demonstrated in Table VI. Furthermore, it does not seem very productive to analyze the fluids as multicomponent mixtures given a component analysis. Two possible explanations why the deviations (in the last column of Table VI, for instance) are large are: (a) the component analysis is not sufficient; we know from experience that even a very small addition of a species to a mixture can affect substantially the mixture’s properties; (b) the literature input constants for some of the less-studied components are not correct. This could certainly be true for the high-boiling point species. (5) There are still very few experimental results for the thermal conductivity (and other properties) of coal liquids and petroleum fractions. Well-documented results from proven apparatuses are very scarce. It is thus often difficult to arrive at an acceptable error estimate on the data that are available. We feel the Colorado School of Mines results are indeed accurate to within the stated tolerance of about 3%, but they are limited and the claimed accuracy should be tested via measurements on similar defined fluids. Obviously, more data over a wide range of compounds and experimental conditions are needed before one can properly assess any theoretical procedure. (6) The CST procedure used here is general: it applies to the class of nonpolar fluids and mixtures (including simple inorganic compounds) over the phase range from the dilute gas to the dense liquid. When assessing the procedure, therefore, it is fair to stress that it has neither been optimized to handle coal liquids or petroleum fractions, nor has it been optimized to cover the limited temperature and pressure range of the available data. The latter optimization is straightforward. Extending the method to cover properly coal liquids or fractions, which
Table VIII. Thermal Conductivity of Petroleum Fractions. Deviations between Theory and Data for Petroleum Fractions Treated as Bulk. Methods as Before % dev exptl thermal crude oil Tb, K SPG T,K cond, mW/(m K) method 1 method 2 A. Data of Jamieson et al. (1975) 0.731 333.3 104.8 3.2 -0.3 Petrol 3 Star 347.6 13.4 -7.3 303.3 129.0 oil no. 11 498.2 0.955 295.3 122.2 6.5 0.9 oil no. 6 506.8 0.807 0.838 443.3 96.0 4.0 -1.2 diesel fuel 572.1 oil no. 22 603.2 0.857 305.3 120.1 13.1 3.9 oil no. 8 616.1 0.877 341.1 122.7 5.6 -4.6 oil no. 3 631.5 0.924 295.0 117.0 21.4 2.4 398.3 110.0 16.4 -4.7 684.7 1.001 lubrication oilo oil no. 2 oil no. 6 oil no. 11 oil no. 23 oil no. 8 Nigerian extract.
421.1 492.6 498.4 535.7 616.4
0.806 0.807 0.955 0.803 0.877
B. Data of Mallan et al. (1972) 295.6 118.2 295.6 117.9 303.3 128.8 133.3 305.6 298.9 121.5
10.6 10.5 19.2 -4.2 14.1
-0.1 3.5 -7.2 -7.1 2.2
Ind. Eng. Chem. Process Des. Dev., Vol. 24, No. 2, 1985 331
Table IX. Correlation Constants X a p c , atm 2.12494 X lo* 'P, R 24.21~ M 4.5673 X
K = Watson characterization factor b -2.3125 0.58848 2.1962
C
2.3201 0.3596 -1.0164
would include polar molecules and associated molecules, is more difficult and is under study. The program used to generate the theoretical results is a minor modification of the program TRAPP distributed by the Gas Processors Association, 1812 First Place, Tulsa, OK 74101. Acknowledgment M. E. Baltatu is grateful to the management of Fluor Engineers, Incorporated, for permission to publish this paper and for the help of W. E. Parente, Jr. H. Hanley and J. F. Ely acknowledge support from the Gas Research Institute and the Development of Energy, Office of Basic Energy Sciences, respectively. The work at the Colorado School of Mines was supported by the Department of Energy. Appendix Basic Parameters for the Generalized Boiling Point-Specific Gravity Correlations for the Corresponding States Input Parameters. 1. Riazi and Daubert (1980). X = aTbb SpGc where X = a physical property to be predicted, Tb = appropriate average normal boiling point, O R , and SpG = specific gravity at 60/60 O F . (See Table IX for correlation constants.) 2. Kesler and Lee (1976). M = -12272.6 + 9486.4SpG + (4.6523 3.3287SpG)Tb + (1 - 0.77084SpG - 0.02058SpG2) X (1.3437 - 720.79/Tb) X 107/Tb (1- 0.80882SpG 0.0226SpG2) X (1.8828 - 181.98/Tb) X 1012/Tb3
+
+
T" = 341.7 + 8llSpG
+
+
(0.4244 0.1174SpG)Tb +(0.4669 - 3.2623SpG) X 106/Tb
In pc = 8.3634 - O.O566/SpG (0.24244 + 2.2898/SpG + 0.11857/SpG2) X 10-3Tb (1.4685 + 3.648/SpG 0.47227/SpG2) X 10-7Tb2(0.42019 + l.6977/SpG2) X 10-1°Tb3 w = (In Pbr - 5.92714 6.09648/Tbr 1.28862 In Tbr- 0.169347Tbr6)/(15.2518 15.6875/Tbr - 13.4721 In Tbr 0.43577Tbl.6)
+
+
+
+
+
or w =
-7.904
+ 0.1352K - 0.007465p + 8.359Tbr + (1.408 + 0.01063K)Tbr
if Tbr > 0.8, in which T" and Tb are in OR and pcis in psia. Tbr and Pbr are the reduced normal boiling point temperature and pressure, respectively. C,O = -0.32646 0.02678K (1.3892 - 1.2122K + 0.03803h") X - 1.5393 X 10-7T2- CF[(0.084773 - 0.080809SpG) - (2.1773 2.0826SpG) X 10-4T + (0.78649 - 0.704235) x 10-7T2]
+
where
CF = [(12.8/K - 1) X (10/K- 1) X 1o12 CPo = ideal gas heat capacity, Btu/lb
OF
3. Winn's Method. The Winn nomograph for molecular weight and pseudocritical pressure and the Mobil nomograph for pseudocritical temperature were reduced to equation form for computer usage In M = -11.985 + 2.4966 In Tb - 1.174 In SpG In T" = 3.9935Tb0.08e16SpGo04614 In pc = 21.971 - 2.3177 In Tb
+ 2.4853 In SpG
where
T" = pseudocritical temperature, OR pc = pseudocritical pressure, psia
Tb = mean average boiling point, OR
SpG = specific gravity 60/60
O F
The Edmister equation suggested by the API Technical Data Book-Petroleum Refining (1977) has been used for prediction of the pseudoacentric factor of petroleum fractions with the Riazi and Winn methods. w =
(;)[
2 1 1 - Tbr
1npC- 1.0
Nomenclature C,O = ideal gas heat capacity FA = dimensional scaling factor for thermal conductivity M = molecular weight R = universal gas constant SpG = specific gravity T = temperature Tb = mean average boiling point V = volume X h = thermal conductivity correction factor 2 = compressibility factor f = equivalent substance temperature reducing ratio h = equivalent substance volume reducing ratio k, 1,b = binary interaction parameter p = pressure q = power r = wire radius t = time x = mole fraction Greek Letters a = thermal diffusivity 7 = viscosity 8, 9 = energy and size shape factors, respectively X = thermal conductivity p = density (J = Pitzer's acentric factor Subscripts c = critical point value 0 = reference fluid x = fluid of interest, mixture or pure a@ = binary pair in the mixture a,@= component in mixture Superscripts ' = translational conductivity " = internal conductivity * = dilute gas value Literature Cited American Petroleum Instltute, "Technical Data Book-Petroleum Refining"; rev ed.;Washington, DC, 1982. Baitatu, M. E. Ind. Eng. Chem. ProcessDes. D e v . 1982. 21, 192. Baitatu, M. E. "International Conference on Coal Sclence. DusseMorf"; Verlag Ghxkauf: GmbH, Essen, 1981; p 482. Edmister. W. C. "Applied Hydrocarbons Thermodynamics"; Gulf Publishing Co.: Houston, TX. 1961; p 27. Ely, J. F. J . Res. Natl. Bur. Stand. (US.)1981, 86, 597.
332
Ind. Eng. Chem. Process Des. Dev. 1985, 2 4 , 332-338
Ely, J. F.; Hanley, H. J. M. Ind. Eng. chem. Fundsm. 1981, 2 0 , 323. Ely, J. F.; Hanley, H. J. M. Ind. Eng. Chem. Fundam. 1983, 22, 90. Erbar, J. H.; Maddox, R. N. “GESConditioning and Processing”; Campbell Petroleum Series, Norman, OK, 1982. Gray, J. A. Interim Report for March 1980-Feb 1981, under DOE Contract No. AC05-76ET10104, 1981, 129; Ind. Eng. Chem. Process Des. D e v . 1983, 22, 410. Hanley, H. J. M.; Evans, D. J. Int. J. Thermophys. 1981. 2 , 1. Hirschfekler, J. 0.;Curtiss, C. F.; Bird, R . B. “Molecular Theory of Gases and Liquids”; Wlley: New York, 1954. Jamleson, D. T.; Irving, J. B.; Tudhope, J. S. “Liquid Thermal Conductivity: A Data Survey to 1973”; National Engineerlng Laboratory Report No. 601, Her Majesty’s Stationary Office, Edinburgh, 1975. Kesier, M. G.; Lee, B. I . Hydrocarbon Frocess. 1976, 55(3). 153. Mallan, G. M.; Michaellan, M. S.:Lockhart, F. J. J. Chem. Eng. Data 1972, 1 7 , 412.
Mani, N.; Venart, J. E. S. “The Thermal Conductivity of Some Organic Fluids: HB-40, Toluene, Dimethylphthalate”; Proceedings Sixth Symposium on Thermophyslcai Properties, ASME: New York, 1973. Mohammadl, S. S. Ph.D. Thesis, Colorado School of Mines, 1980. Mohammadl, S. S.: Craboski, M. S.; Sloan, E. D. Int. J . Heat Mass Transfer 1981, 2 4 , 671. Perklns, R. A.; Mohammadi, S. S.; McAllister, R.; Graboski, M. S.; Sloan, E. D. J. Phys. E. Sci. Inshum. 1981, 14, 1279. Riazl, M. R.; Daubert, T. E. Hydrocarbon Process. 1980, 59(3), 115. Sloan, E. D., unpublished data, 1983, Colorado School of Mlnes; results available on request. Winn, F. W. Pet. Refining 1957, 3 6 , 157.
Received for review October 3, 1983 Accepted May 4, 1984
Optimization of In-Line Mixing at a 90’ Tee Claudia D. O’Leary and Larry J. Forney’ School of Chemical ,Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0 100
The use of in-line mixing techniques is common in the chemical industry to promote chemical reactions, heat transfer, mixing, and combustion processes. I n many cases, however, simple correlations are not available to optimize mixing for specific design requirements. I n the present study, optimal conditions for pipeline mixing downstream from a 90’ tee are determined for a variety of experimental conditions. The effects of the following dimensionless parameters are examined: pipe Reynolds number, jet Reynolds number, normalized distance downstream from the tee, density ratio, densimetric Froude number, velocity ratio, and the diameter ratio. By use of experimental results, empirical correlations are developed showing the relationship between the dimensionless groups that result in optimal mixing downstream from the tee and the limitations associated with these correlations are identified.
Introduction Direct injection of a secondary flow into a pipeline at a mixing tee has received considerable attention recently (Ger and Holley, 1976; Forney and Kwon, 1979; Forney and Lee;1982; Maruyama et al., 1981,1982; Fitzgerald and Holley, 1981; Forney, 1983,1985). Turbulence within the pipe and injected jet causes the fluids to mix rapidly as they travel downstream. Moreover, the mixing tees are simple to construct and do not create large pressure drops. Simple correlations to size the mixing tee for specific design requirements are not available in the literature. In addition, it may be critical that the concentration of a substance introduced by the secondary flow not exceed a maximum value before entering a downstream process, and simple correlations are necessary to eliminate that possibility. Other current problems which the present study attempts to address are the effects of pipe and jet Reynolds number, buoyancy, and the longitudinal distance downstream from the tee on optimum mixing conditions. An important assumption used in the present study is the mixing criteria. In particular, we have assumed that mixing efficiency is optimized when the injected jet is geometrically centered along the pipe axis at some distance between 2 and 10 diameters downstream from the injection point which is similar to the pioneering work of Chilton and Genereaux (1930). Tracer concentrations, measured along the vertical centerline of the pipe, were used to evaluate whether the jet was centered. While this approach cannot completely account for the three-dimensional nature of the jet, it significantly reduces the amount of data required to identify optimal mixing conditions. The same assumption was used by Forney and Kwon 0196-4305/85/1124-0332%01.50/0
(1979) and Forney and Lee (1982),whose results compared favorably with the majority of the data of other investigators. In the present study, the optimal conditions for pipeline mixing at a 90° tee were determined by injecting air containing a methane tracer into a turbulent airstream. The concentration of methane was monitored at specific distances downstream from the tee. Experimental data were obtained for jet-to-pipe diameter ratios ranging between 0.00612 and 0.0556, pipe Reynolds numbers between 1.8 X lo4and 1.8 X lo5, jet Reynolds numbers between 3.0 X lo3 and 1.5 X lo4,and distances downstream from the tee between 0.25 and 10 pipe diameters. In addition, a hotwire anemometer was used to determine the gas velocities. For small jet and pipe Reynolds numbers, the present technique represents a significant improvement compared with the earlier pitot tube measurements of Forney and Kwon (1979) and Forney and Lee (1982). Dimensional Analysis Following the work of Forney (1968), Wright (1977),and Holley (Ger and Holley, 1976; Fitzgerald and Holley, 1981), the penetration z of the buoyant jet into a pipe perpendicular to the pipe axis as shown in Figure 1can be written as
where 1, is the momentum length, lb is the bouyancy length, Re, is the pipe Reynolds number, and Rej is the jet Reynolds number. Assuming that we wish to cdnter the jet at some fixed distance downstream from the tee 0 1985 Amerlcan Chemical Society
