# Prediction of Holdup in Pipe Two-phase Gas-Liquid Co-current Down Flow at 45d.

код для вставкиСкачатьPrediction of Holdup in Pipe Two-phase Gas-Liquid Co-current Down Flow at -45' P.L. Spedding* and W.J. McBride Department of Chemical Engineering The Queen's University of Belfast Belfast BT9 5AG, Northern Ireland, UK. Holdup was measured for air-water co-current two-phaseflow in a perspex tube (45.4 mm id) set at an angle of -45". The data were used to check the predictions of holdup given by various models (>120) using the input and geometrical conditions of the experiments. The prediction data were grouped according to the flow regimes that were observed for the system. Four models gave acceptable predictionsfor the annular-plus-wave condition, two of the models were also successful in predicting the annular-plus-dropletregime. Ten models were successful with dropletflow, and four models with the slug-plus-froth regime. No model could predict successfullyfor either the stratifed or slug-type flow regimes. In general, prediction performance deteriorated as the downward angle of inclination increased from the horizontal position. Introduction Hand and Spedding [l] have shown that of the many holdup prediction models that have been proposed, only a few were successful in prediction across the range of angles from the horizontal to upward vertical flow. In addition, successful prediction was often dependent on the particular flow regime present in the conduit. This was to be expected since the basic mechanisms that govern the formation of flow regimes vary from one regime to another. There is a lack of data on holdup measurement in downward inclined co-current pipe flow. Beggs [2] reported data at angles of -35" and -55" for air-water flow in both 1 and 1.5 inch pipes. RL was shown to reach a minimum value at -50" for all liquid flows used. Nguyen [3] reported air-water data for various angles between vertical upwards to vertical downwards flow in a 45.4 mm pipe. The minimum value of AL occurred at -67"with a dramatic change in the region of the horizontal. The lack of data for downward inclined flow is unfortunate since it is an important condition for offshore rigs where it would be advantageous to accurately predict multiphase flow phenomena. Experimental Details Holdup was measured using the quick closing valve technique for air-water twophase flow in a 45.4 mm id perspex pipe inclined at -45".The apparatus is shown schematically in Figure 1 in the downward vertical mode. Air was drawn from a Roots blower at 0.5 bar (8) and measured (up to 0.141 kg s-l) using either a suitable rotameter or a calibrated orifice meter. Water was recirculated from a reservoir by a *Authorfor correspondence. 14 Prediction of Holdup in Pipe Two-Phase Gas-Liquid Co-current Down Flow at -45' Llj 1-J reservoir TEST SECTION Figure 1. Schematic diagram of the test rig in vertical downwardflow. centrifugal pump metered by a suitable rotameter (up to 1.7 kg s-*).The air and water were mixed in an annular mixing section fitted with a bypass which operated when the holdup valves on the main test section were closed. In the annular mixing section, water was fed peripherally through perforations in the inner wall of a piezometer ring into the air stream emerging from a calming section. The intense mixing ensured that the two-phase flow was free of end effects from the end of the 2 m long inlet pipe to the test section. A cyclone (not shown in Figure 1) on the outlet pipe separated the air from the water (the latter was recirculated). The cyclone was designed to avoid back reflection of waves into the test section. The entire apparatus was held rigidly on a beam section. The experimental procedure used was to set the pipe angle at -45" and, for a chosen liquid flow rate, to vary the gas flow in appropriate steps from minimum to maximum rate. The holdup was measured by mechanically isolating the test section using two synchronously operated sliding gate valves, and subsequently measuring the volume of water held between the valves. A calibrated correction was added to the collected water volume to compensate for any liquid held in the test section after draining. An electrical circuit was used to ensure the holdup valves and bypass acted simultaneously. The data were checked in several ways to ensure the reliability of the holdup measurements obtained. Data were grouped according to the observed flow patterns in the pipe for various combinations of gas and liquid flows. These patterns are shown in Figure 2. The input data from each experimental determination of holdup were used as input to each predictive model. The predicted result was then compared to the actual measured value and the average error calculated by: % error = ( [prediction-experimental]/experimental } x 100 (1) 15 P. L. Spedding and W.J. McBride INCREASING LIQUID FLOW RATE SLUG t FROTH zzzrzz - - - - - == SLUG ~ z z z ? - - - - STRATIFIED ST ST ST z ST S ~ ~ Sl 45zm-- - +- - - - c w STRATIFIED K RIPPLE $.&..&~~2.&.&& $ FILM+OROPLET STtR ST+R --&&A F t D FfO m - 3 ANNULAR t ROLL WAVE I r F t D mam AtW ...:4h a = ..... . ANNULAR + DROPLET At0 A+D .;>- iy. .I.+ , I DROPLET Figure 2. Flow regimes present in downward inclinedflow -45" The criteria used to determine if the prediction was acceptable were determined in the following manner. The apparatus was operated more than 20 times on a particular setting for each observed flow regime, enabling the standard deviation to be determined. The greatest value of the standard deviation was +7% for the intermittent flow regimes. Acceptable prediction performance was assumed when the average error for all data in a flow pattern given by equation (1) was within a range of &15% (i.e. twice the standard deviation of the experimental data) with all data being within a range of +30% (i.e. a 100% confidence limit of twice the maximum acceptable average range).Thus acceptable model performance was guaranteed to be within experimentally prescribed limits rather than with say a 95% confidence band that would vary from model to model and present the possiblity of some data prediction being outside the 95% confidence limit. Prediction performance showed a consistent pattern within any particular flow pattern so that grouping data according to the regime present had validity. When obtaining the results it was attempted to ensure data were evenly distributed between the flow regimes. Results Of the loo+ models tested, only those which achieved acceptable prediction with at least one flow regime are presented in any detail. (a) Armand Models The modification suggested by Chisholm [4] is: 16 Prediction of Holdup in Pipe Two-Phase Gas-LiquidCo-current Down Flow at -45" This model successfully predicted the A+W and D regimes as shown in Table 1. The results are shown in this table in full to illustrate the usual performance. For other models tested, only the successful data will be given as shown in Table 2. Table 1. Error in predicted holdup by the Chisholm-Annand relation of Equation ( 2 ) using data f o r -45" co-current downward flow. Flow Rcgiiiie Range % Av. error % ! Range % Av. error % ~ st -77 to 0 -30 +25 to +715 f 265 St+R -17 to 0 -5 +27 lo +IS0 +85 F+D -17 to 0 -3 +7 to +I40 +4s A+W -5 to 0 -2 +s to +30 + 15 A+D -2 10 0 -1 +5 to +ss -t 15 S -78 tc, -45 -68 +20 to +8S S +Fro -65 to -4s -SO +so + 12 D -1 10 +I +s to +20 -7 to 0 0 -3 (b) Lockhart-MartinelliModels The Butterworth [5] modification of the model was successful in prediction of the D regime, namely: RLKG= 0.28 [( 1 - x/x)]O.~~ [p&] 0.36 [pL/pG10.07 (3) The Chisholm and Laird [6] model is given by: EL =[0.8/(1 + C/X+ 1/X2)]1.75 (4) This predicted the A+W and S+Fro regimes for both horizontal (C=21) and vertical flow (C=26). The Chen and Spedding [7] model is: - R, = W(K + P I 3 ) It predicted the A+D, A+W, S+Fro and D regimes for K = 5. 17 P.L.Spedding and W.J. McBride Table 2. Error in predicted holdup using data for -45" co-current down jlow. Model Regime ~ Butterworth eq (3) Chisholm-Laird eq (4); C = 26 eq (4); c = 21 A+W S Fro A+W + I Chen-Spedding 'eq ( 5 ) S+Fro A+D A+W S+Fro D Turner-Wallis eq (6) D Nishino eq (7) D Taitel-Dukler TT VT D D St+Fro A+W A+D D Tandon Eaton D D S+Fro Levy 18 D Prediction of Holdup in Pipe Two-Phase Gas-Liquid Co-current Down Flow at -45" The Turner and Wallis [8] separate cylinders model: predicted the D regime. Other Models The Nishino and Yamazaki [9] relation is: It gave good prediction for the D regime. The Taitel and Dukler [ 101 model predicted the D regime for the turbulent-turbulent (T-T) and viscous-turbulent (V-T) gas-liquid conditions. The Spedding and Chen [ 111 relations are given by: &EL = 140.2 + K , QL/Q,] In K , = -0.931n vsL-0.44 (8) (9) These gave acceptable prediction for the S+Fro pattern, while the equations: vsL+ 0.66 In K3 = 0.88 In vsL-3.2 K2 = 0.072 In (1 1) (12) gave prediction for the A+D, A+W and D regimes. The Tandon [12] and Eaton [13] models both predicted the D regime, while the latter also predicted the S+Fro regime. The simple Levy [ 141 relation: EG = @L/ (l*L) (13) predicted the D regime whether the frictional or total two-phase pressure loss was employed. Discussion and Conclusions A summary of the results in Table 3 shows that the most successful model was that of Chen-Spedding [7]. However, half the flow regimes were not successfully predicted by any available model. I9 P.L. Spedding and W.J. McBride Table 3. Recommended models for prediction of holdupfrom flow regime in cocurrent -45', downward gas-liquidflow. ~~ Flow regime Model St St+R F+D A+W Chisholm-Armand, Chisholm-Laird, Chen-Spedding, Spedding-Chen I1 A+D Chen-Spedding, Spedding-Chen I1 S S +Fro Chisholm-Laird, Chen-Spedding, SpeddingChen I, Eaton D Chisholm-Armand, Butterworth, Chen-Spedding, Turner-Wallis, Nishino, Taitel-Dukler, Spedding-Chen 11, Tandon, Eaton, Levy As the angle of inclination was moved down from the horizontal it became more difficult to predict holdup. For example, in horizontal flow [15,16] over 30 models were successful in prediction of at least one flow regime, while the corresponding number for -6.17" [22] and -20" [23] were 17 and 13 models respectively. This increase in the difficulty of prediction is not inconsistent with the abnormal twophase pressure drop reported at these geometries 1241. Table 3 shows that annular and droplet-type flows were the easiest to predict where the gas rate was considerably greater than that of the liquid. Such flow would be similar to the equivalent case in the horizontal geometry because the effect of the high gas rate would be predominant regardless of the gravitational influence on the heavier phase. This would not be the case for stratified-type flows which became predominant at downward angles of flow [22,23] because of the stabilising effects of gravitational forces on the liquid. By contrast, in upward flow angles [17,21], slug and intermittent flows were predominant. In downward flow [22,23] the stratified regimes extended over a much wider range (typically two-thirds) of the flow rate ranges of the two phases, when compared to the horizontal case in which the stratified regimes extended over about a third of the range [15,16]. Figure 2 illustrates the predominance of the stratified regimes over the flow regime range at -45' geometry. The film-plus-droplet regime occurs between the stratified and annular type flows, and as such has proved to be more difficult to predict. For example, the annular-plus-droplet regime was predicted by only three models for horizontal [ 151 20 Prediction of Holdup in Pipe Two-phase Gas-Liquid Co-current Down Flow at -45" and -6.17' geometry [22]. Correspondingly the stratified-plus-roll wave regime was predicted by five [15] and seven [22] models, respectively. The prediction of the annular-plus-droplet regime is little affected by downward inclination since it is a gas predominant pattern and thus negligibly affected by gravity. The stratified-plus-roll wave regime is affected by gravity and became easier to predict at downward angles. The film-plus-droplet regime was predicted by two models for horizontal [15] and seven models for the -6.17' angle [22]. Therefore the film-plus-droplet regime shows an increasing similarity to the stratified-type flow regimes for prediction for down flow. The data in Table 1 also shows this effect. There also appears to be some consistent prediction performance patterns emerging for the annular-plus-droplet regime. The Chen-Spedding [7], and to some extent the Chisholm-Laird [6] models, are able to give reasonable prediction for the annular-plus-wave type regimes [ 15,16,22,23] regardless of the downward angle, while the Chen-Spedding [7] and Spedding-Chen I1 [ l l ] models are comparable for the annular-plus-droplet regime. This was in contrast to the prediction performance for annular flow in upward geometry [17-211. The implications of such observations for prediction are not immediately obvious, but they suggest that it may be possible to group together the observed flow regimes into three basic classes, namely annular, stratified and intermittent. The film-plus-droplet regime occurs at the boundary between the first two of these major classifications, and therefore its prediction performance characteristics are crucial to an understanding of their possible boundary. Certainly more work is required on measurement and predictive technique development for this geometry, particularly with the stratified and slug-type flow regimes. Nomenclature A C D F Fro K K, K2 K3 1 P Q R R S St V W W X Annular flow regime Constant in equation (4) Droplet flow regime Film flow regime Froth flow regime Constant in equation (5) Factor in equation (9) Factor in equation ( 1 1) Factor in equation (12) Length (m) Pressure (kg m-l s-*) Volume flow rate (m3 s-l) Ripple flow regime Average holdup Slug flow regime Stratified flow regime Average velocity (m s-I) Wave flow regime Mass flow rate (kg s-l) Dryness fraction = W p T 21 P.L. Spedding and W.J. McBride X B P P 0 Lockhart Martinelli factor, ((dP/dl)sL/(dP/dl)s,) Os Input gas volume rate (Q,/QT) Viscosity (kg m-l s-I) Density (kg m-3) Lockhart-Martinelli loss parameter, ((dP/dl)d(dP/dl),)o.5 Subscripts G L S T = Gas = Liquid = Superficial = Total References 1. Hand, N.P. and Spedding, P.L. 1990. Prediction of holdup in horizontal and upward cocurrent flow. Irish Res. Symp., 2.39-45. 2. Beggs, H.D. 1972. An experimental study of two-phase flow in inclined pipes. PhD thesis, University of Tulsa, USA. 3. Nguyen, V.T. 1976. Two phase flow. PhD thesis, Universiry of Auckland, New Zealand. 4. Chisholm, D. 1983. Two phase flow in pipelines and heat exchangers. p.45 Goodwin London. 5. Butterworth. D, 1975. A comparison of some void-friction relationships for co-current gasliquid flow. Int. J. Multiphase Flow, 1,845-850. 6. Chisholm, D. and Laird, A.D.K. 1958. Two phase flow in rough tubes. Trans. ASME, 276-286. 7. Chen, J.J.J. and Spedding, P.L. 1981. An extension of the Lockhart-Martinelli theory of two-phase pressure drop and holdup. Int. J. Multiphase Flow, 1,659-675. 8. Turner, J.R.S.and Wallis, G.B 1965. The separate-cylinder model of two-phase flow. Rep. NYO-3114-6Thayer School Eng., Dartmouth College. 9. Nishino, H. and Yamazaki, Y. 1963. Holdup correlations in two phase flow. J. SOC.Atom. Energy Japan, 5,39-45. 10. Taitel, Y and Dukler, A.E. 1976. A model for predicting flow regime transitions in horizontal and near horizontal gas-liquid flow. AIChE J., 22,47-55. 1 1 . Spedding, P.L. and Chen, J.J. 1984. Holdup in two-phase flow. Inf. J. Multiphase Flow, lo,307-341. 12. Tandon, T.N., Gupta, C.P.and Vanna, H.K. 1985. A void fraction model for annular twophase flow, Int. J. Heat Mass Transfer, 28,191-198. 13. Eaton, B.A., Andrew, D.E., Knowles, L.R., Silberberg, I.M. and Brown, K.F. 1967. The prediction of flow patterns, liquid holdup and pressure losses occurring during continuous two-phase flow in horizontal pipes. J. Pet. Tech., fi,815-820. 14. Levy, S. 1963. Prediction of two-phase pressure drop and density distribution from 137-152. mixing-length theory. Trans. ASME J. Heat Transfer, 15. Spedding, P.L. and Spence, D.R. 1988. Prediction of holdup in two-phase flow. Int. J. Eng. Fluid Mech., 1,67-82. 16. Spedding, P.L. and Spence, D.R. 1989. Prediction of holdup in two-phase flow. Inr. J. Eng. Fluid Mech., 2,109-118. 17. Spedding, P.L., Spence, D.R. and Hand, N.P. 1990. Prediction of holdup in two-phase gasliquid inclined flow. Chem. Eng. J., Q,55-74. a, a, 22 Prediction of Holdup in Pipe Two-phase Gas-Liquid Co-current Down Flow at -45" 18. Spedding, P.L., Spence, D.R. and Hand, N.P. 1990. Prediction of holdup in two-phase gasliquid upward inclined flow. Int. J. Eng. Fluid Mech., 1, 293-322. 19. Spedding, P.L., Spence, D.R. and Hand, N.P. 1991. Prediction of holdup in two-phase gasliquid upward inclined flow. Int. J. Eng. Fluid Mech., 4, 127-155. 20. Spedding, P.L., Spence, D.R. and Hand, N.P. 199 1. Prediction of holdup in two-phase gasliquid upward inclined flow. Int. J. Eng. Fluid Mech., 4,237-258. 21. Spedding, P.L. and Spence, D.R.1990. Prediction of holdup in vertical two-phase gasliquid flow. Handbook of Heat and Mass Transfer.4. Advances in Reactor Design and Combustion Science. Editor N.P. Cheremisinoff, Gulf, 57-92. 22. Spedding, P.L. and Hand, N.P. 1992. Prediction of holdup in two-phase gas-liquid downward inclined flow. Int. J. Eng. Fluid Mech., 5,55-76 (1992). 23. Donnelly, G., Ferguson, M.E.G. and Spedding, P.L. 1994. Holdup in gas liquid downward flow at -20.75". Irish Chem. Eng. Res. Symp., 4, 1-16. 24. Spedding, P.L., Chen, J.J.J. and Nguyen, V.T.1982. Pressure drop in two phase gas-liquid flow in inclined pipes. Int. J. Multiphase Flow, 8,407-431. Received 6 December 1994;Accepted after revision: 15 May 1995. 23

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