put. S o t e that the ol~viouslyspurious result a t X has had no effect upon subsequent' calculat'ions. Figure 2 shows the results of part of an invei;t,igationinto the at,t:tinment of t8hesteady state of t,lie reactor. Data from the computer output are shown toget,her with some results obtained by a mai;s balance (by weighing) on the reactor discharge. Also shown is R predicted attainment of the steady state derived by w e of t'he process equations and updated kinetic parameters. ,In important feature of tlie technique is tlie ease with which such a n investigation can he carried out, as a matter of routinr. during normal production.
Efficient use has been made of computer time by retaining tlie existing control system of the chromatograph (which incidentally maintains the off-line capability) and by using additional hardware rather than software to monitor the state of the a n a l p i s and to determine the periods of data acquisition. Conclusions
The syst'em has funct,ioned satisfactorily for 18 months aiid has been extensively used. I n the event of a computer hardware failure, tlie chromatograph mill still perform all essential analytical and coiit'rol operations. However, in practice the Discussion The program has been written specifically for the ~ x ~ r t ~ i c i i l a r main failures have been in t'he unmodified aspects of the chromatograph, aiid this reinforces the philosophy that instrudescribed, but I)ec:iuh11/*in. acrylic pipe. The air-water system was chosen because it was used in the Russian study. The smooth acrylic pipe was used for two reasons: First, the pipe used by Gallpamov and Goldzberg was 1-in. glass, and the roughness coefficient for glass and acrylic pipes is similar; second, various data based on air-water flow in a ll/z-in. acrylic pipe were available t o this m t h o r (Greskovich, 1970), providing a n independent comparison of the two correlations. Various gas and liquid flow rates were chosen covering a range of input liquid volume fractions (1 - p) from approximately 0.03-0.75 for angles of -2', -6O, and -10' from the horizontal. The flow rates were judiciously selected based on the results of Guzhov e t al. (1967), such that only stratified downflow would exist. For a pipe inclination of -2' from the horizontal, values for the in situ liquid holdup predicted by open-channel flow were sizeably larger (up to approximately 30% larger) over the range 0 < q < 0.25 (Figure 3). However, a t q = 0.35, values predicted by Equation 6 became larger than those predicted by open-channel flow. Based on the slope of the curve at this point, the deviations were increasing sharply with increasing 7. Similar curves were found for inclinations of -6' and - 10' from the horizontal (Figure 3). For a pipe inclination of - 6 O , the in situ liquid holdups predicted by open-channel flow were up t o 35y0 larger than those predicted by Equation 6 for 0 < q < 0.19. hbove q = 0.19, the opposit,e was true-that is, Equation 6 predicted values of q u p to 30y0 larger than open-channel flow. For a n inclination of -lo', the differences between predicted values increased up to 60% for large values of 7. 84
Ind. Eng. Chern. Process Des. Develop., Vol. l l , No. l , 1972
0.1 7(
0.2
0.3
0.4
PREDICTED BY OPEN-CHANNEL FLOW
Figure 3. Comparison of liquid holdup predictions for various pipe inclinations
The general conclusion drawn from the comparison presented on Figure 3 is t h a t open-channel flow equations yield correct values for q during stratified downflow of gas-liquid mixtures over a narrow range of 7. This narrow range occurs where the curves intersect the bias line. On either side of this intersection deviations exist but are opposite in magnitude. If the predictions of Gallyamov and Goldzberg (1968) for air-water flow in relatively small, smooth pipes are assumed to be valid (as mentioned earlier, their prediction method agreed within 10% of their experimental data based on air-water flow in a 1-in. glass pipe), then open-channel flow equations are not applicable in determining liquid holdup during twophase flow. Additional Independent Data Used to Test Prediction Methods. ,4s a final test of t h e conclusion just drawn, d a t a collected by Greskovich (1970) were used to test the predicted values in Figure 3. The system used was air and water, and the pipe was ll/?-in. acrylic. Figure 4 shows the comparison with experimental data. The values predicted by Equation 6 sharply disagreed with the experimental holdup d a t a for inclinations of -2', -6', and -loo, whereas the openchannel flow approach, Equation 9, closely agreed with the experimental data. These values fell close to or on the bias line on Figure 4, and deviations only at upper values of 7 were noted. On the surface, it would seem that a dilemma exists-that is, based on the experimental data of Gallyamov and Goldzberg (1968), Equation 6 yielded predicted values within 10% of experimental and therefore should be more exact than the open-channel flow equations based on the differences noted in Figure 3. On the other hand, based on the data presented here, from Figure 4 open-channel flow yields the better predictions. hfter more careful scrutiny of the results of Gallyamov and Goldzberg, the comparisons between predicted and mea-
Even if Equation 2 were tested over a wider range of liquid holdups and inclinations and reformulated to permit better predictions through Equation 6, the remarkable agreement between the holdups predicted by open-channel flow and experimental d a t a is not to be discounted. More extensive testing of the open-channel flow approach should be carried out by using gas-liquid systems ot'lier than air-water and pipes of larger diameter and roughness. HOWever, based on this author's data, liquid holdup during stratified downflow of gas-liquid mixtures can be predicted with good accuracy by using open-channel flow equations.
/
Acknowledgment
The author expresses appreciation to the Esso Research and Engineering Co. for releasing data contained in this paper. Nomenclature
A A, D, Ej,
0
0.I
0.2
0.3
7
0.4
0.5
EXPERIMENTAL
Figure 4. Comparison of prediction methods with experimental data for air-water flow in 1 '/2-in. acrylic pipe
9 Equation 6,
-2'
0
Equation 6,
-6"
Equation 6,
- 10'
.k Equation 9,
A
4
-2' Equation 9 , - 6 " Equation 9, - 10'
sured values were made only for inclinations of -15" and -25' from the horizontal. Furthermore, the range of 7 was for most cases between 0 and 0.20. If it is approximated that inclinations greater than - 10" essentially converge a t the curve for - 10' iii Figure 4,then Equation 6 yields values bet'iveen 0 < 7 < 0.20 which closely agree m-ith experimental data. Therefore, the accuracy of Equation 6 for small inclinations and!or large values for 7 is questionable. I n addition, the colorimetric met'hod used for measuring liquid holdup may be questionable. Conclusions
The equations developed by Gallyamov and Goldzberg (1968) for predicting liquid holdup during stratified downflow of gas-liquid mixtures represent the first effort in this area. Although their final equation yielded predicted values within 10% of their experimental values, the range of data used to test the equation was not great enough and did not provide a sufficient test. For most' practical applications, pipe inclinations between 0 and 10" are most' common, and within this range the equations are lacking. .In alternate approach to predicting liquid holdup, openchannel flow, deviate harply with Equation 6 for small inclinations and, based on new data, agreed more closely with measured values. Gallyamov and Goldzberg (1967) suggested that the role of tjhe interfaaceshould be included in their equations-that is. interfacial shear assumed t,o be negligible in their equations for simplicity has a finite value. Also the effect of surface roughness of the value of the wetted perimeter should be taken into account. Perhaps these modifications of Equat'ion 6 would yield a better agreement with experimental data on Figure 4.
area occupied by liquid, f t 2 cross-sectional area of the pipe, ft2 pipe diameter, ft = factor used in Equation 6 g = acceleration of gravity, 32.2 ft/sec2 J,, = fact'or used in Equation 9 n = roughness coefficient, dimeiisioiiless NFrL= Froude number for liquid, V L ~gRx, / ~dimensionless NF,,,= Froude number for mixture, vm2/DPg,dimellsionless YReL= Reynolds number for liquid, 4 R H V L / V L , dimensionless X R , , = Reynolds number for mixt'ure, D,V,/Y,, dimensionless Q L , &G = volumet'ric flow rates of liquid and gas, respectively, it3/sec R H = hydraulic radius for liquid, ft V L = actual liquid velocity, ft/sec V , = mixture velocity, Q L Qc/Ap,ft>;'sec y = depth of liquid in pipe, ft GREEKLETTERS (Y = angle of inclination of the pipe, degrees @ = volume fraction gas a t pipe iiilet, dimensiodess p = central half angle, degrees 7 = volume fractioii iii situ liquid, diniensiodess e = volume fraction liquid a t pipe inlet', dimelisionless X = hydraulic drag coefficient (Equation 1) ?r = dimelisionless constant vr, = kinematic viscosity of liquid, cm? Y , = mixture kinematic viscositj-, cm2 4 = volume fractioii in situ gas, dime1 = = =
+
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Bonnecaze, I{., Erpkine, W . j Greskovich, E. J., AIChE 62nd Annual Meeting, Washington, I).C., Paper 58b, 1969. Brigham, R. E., Holstein, E. I)., Hulltington, 11. L., Oii Gas J . , Nov. 11, 1957. Chon-, Y. T., "Opeii-Channel Hydraulics,!' lIcGraw-IIill, Yew York, S . Y . ,p 99, 1959. I)eGance, A . E., Athertoil, 11. IT.> Chern. Eng., 77 (21), 87 (1970). Flannigan, O., Oil Gas J . , 132, March 10, 1958. Chllyamov, A. K., Goldzberg, Y.I,., -\-f.ft Gaz, ( I ) , 70 (1967). Gallyamov, A. K., Goldzberg, V. L., ibid., (11), 67 (1968). Gouse, 8.W., Jr., NIT Ileport 1)SR 8734-1, N a y 1963. Gouse, 8. W., Jr., ibid., 8734-4, September 1964. Gouse, P.R.> Jr., i b i d . , 8734-6, Janiiary 1966. Greskovich, E . J., private commuiiication with Esso 1lesearc.h arid Engineering Co.,Florham Park, X.J,>1970.
Greskovich, E. J., Shrier, A. L., Bonnecaze, I?. H., Ind. Eng. C h ~ mFuntlam., . 8, .i91 (1969). Guzhov, il. I., Mamayev, V. A , Odishari national Gas Conferelice, Hamburg, Ger lramayev, V. A . , s c j t Gaz, 1 A , , In,t. Chcm. Eng., 5 ( 2 ) )318 (196,i). . E,>I'rnnsp. Khranrnie AYcfti,\-Eft. h'hoz., (9),54 (1966). Oi(Gas J . , 68 (9), 34 (1970). 111ximxr) for review January 21, 1971 ACCF:PTJ.:I) September 3, 1971 Ind. Eng. Chern. Process Des. Develop., Vol. 1 1, No. 1 , 1972
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