Dev. Chem. Eng. Mineral Process. 12(1/2), pp. 189-198, 2004. Momentum Balance for Two-Phase Horizontal Pipe Flow Part 2: Testing of Models P.L. Spedding", J.S. Cole and G.F. Donnelly School of Aeronautical Engineering, The Queen 's University of Belfast, Stranmillis Road, Belfast BT9 SAG, Northern Ireland, UK Momentum balance models were tested against reliable data for both holdup and pressure drop. The best prediction performance was achieved using a model that considered the actual shape of the liquid phase in the pipe. In such circumstances the momentum balance calculation tended to under predict both the holdup and pressure drop for some of the annular and stratijied regimes. Suggestions are made for improvements in the momentum balance approach. Introduction The one-dimensional momentum balance model for the prediction of holdup and pressure drop in two-phase pipe flow requires the input of wall shear stresses for the two phases and for the interface in order to achieve closure of the derived equations. In this work an evaluation is conducted on the models, which employ the various methods proposed to predict these shear stresses. *Authorfor correspondence. 189 P.L. Spedding, J.S. Cole and G.F. Donnelly Momentum Balance Models Although all existing momentum balance models were tested against a wide spread of data ranging from 0.0259 m to 0.0953 m in diameter [l-81, only the outcome of the more successful models is be presented here. The general method of calculation is given by Spedding and Hand [9]. Kowalski Model Figure 1 tests the Kowalski [ 101 model against the data of Hand [5]. Along with other data, the results highlight that the Kowalski model tended to over predict liquid holdup, with deteriorating performance as the diameter was reduced and the gas rate increased into the annular-type flows. Generally the pressure loss was under predicted, with performance improving as the diameter rose and the calculated data being confined to a narrow range. This suggests that a modification of the method could be advantageous. Hand Model Figure 2 details the results for the Hand [5] model tested against the data of Donnelly [8]. The general result was that this model possessed an improvement in performance over that of the Kowalski [ 101 model, but still had a wide scatter in the prediction of liquid holdup that increased as the pipe diameter and gas rate were reduced. The inadequacies of the Hand [ 5 ] model were in some ways attributable to the formulation of T ~ but~ mainly , to zi,where modelling solely in terms of Ysc invariably gave poor scale-up characteristics. This was due primarily to initiation of two-dimensional surface waves at much higher superficial gas rates in larger diameter pipes. 190 Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models 0.0 1 0.1 1 ExperkntalHold up 10 100 lo00 Eprkntal phssure Loss (palm) Figure 1. Holdup and pressure gradient prediction using Kowalski [IOJ fi-iction factor expressions tested against 0.0935 m diameter data of Hand [5J. 191 P.L. Spedding, J.S. Cole and G.F. Donnelly 1 9 a z 0.1 - B 5 e c 0.01 0.01 0.1 1 EiJperinrcntalHoldup Figure 2. Holdup and pressure gradient prediction using Hand [S] friction factor expressions tested against 0.0259 m diameter data of Donnelly [8]. I92 Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models Baker-Jardine Model Of the commercial computer packages available only the Baker-Jardine [11J model will be reported as it gave very similar results to the best of the codes. The performance of the model was satisfactory for pressure drop in the mid diameter range of 0.0508 m at the low to medium gas rate range as shown in Figure 3. However, there was an observable deterioration in pressure gradient prediction at higher and lower diameters. The model had difficulty in prediction of the liquid holdup in the annular-type regimes as illustrated in Figure 3. Andritsos-Hanratty Model Application of the Andritsos and Hanratty [4, 121 model revealed that the method predicted the pressure gradient reasonably well when compared to other models, as shown in Figure 4. However, it showed a lack of rigour with the prediction of holdup. Modified Apparent Rough Surface ( M A R S )Model The MARS [7] model gave emphasis to the crescent shape of the gas liquid interface, and suggested new fnction factor calculation procedures for both the interface and liquid wall friction where the wetted wall fraction was involved. The model was reported to be applicable to small pipe inclinations although the level of accuracy was shown to be superior for slight downflow. Typical results presented in Figure 5 show the technique gave the best performance overall. The model was designed to be applicable within the range of vsG from 1.8 to 40 m s-' and liquid holdup not exceeding 0.42. However, results show the level of confidence to diminish for superficial gas velocities in excess of 22 m s-' and liquid holdup exceeding 0.38. A degree of deterioration was exhibited for stratified and annular flows which manifested as an over prediction for pipe diameters in excess of 0.05 m. The converse held for smaller diameters although sensitivity to scale-up was somewhat less pronounced. I93 P.L. Spedding, J.S. Cole and G.F. Donnelly 0.15 1p 0.12 U a 5.- 0.09 G ;3 -u P 0.06 3 6 0.03 0 0 0.03 0.06 0.09 0.12 0.15 Measund Liquid Hoki up Figure 3. Holdup and pressure gradient prediction using the Baker-Jardine model [I 1) tested against 0.0935 m diameter data of Hand [5J and the 0.0508 m diameter data of Ferguson [6] respectively. I94 Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models 1 L a 5? p 0.1 B AST+RW 0 mF+D 0.01 1 0.1 0.01 Epnimental Hold up .-10, T , * . , , , , ,, 100 loo0 ...I loo00 FaperimcntalRessm Loss (Palm) Figure 4. Holdup and pressure gradient prediction using the Andritsos-Hanratty model [I21 tested against 0.0454 m diameter data of Nguyen [2]. 195 P.L. Spedding, J.S. Cole and G.F. Donnelly 0.01 0.1 Experimental Hold up 10 100 lo00 !3pnmxtalPressure Loss (Palm) Figure 5. Holdup and pressure gradient prediction using the MARS model [7/ tested against 0.0454 m diameter data of Nguyen [2]. I96 Momentum Balance for Two Phase Horizontal Pipe Flow: Testing of Models Discussion The momentum balance model shows promise in predicting two-phase parameters if consideration is given to the shape of the liquid interface in the pipe and the resulting wetted perimeter. Ignoring fluctuations, undoubtedly a balance of forces is established with the fluids in the pipe cross-section between the actual liquid shape within the pipe and the shear stresses due to fluid movement. Most models that assumed smooth stratified liquid geometry have developed interfacial friction relations that encompass not only the actual interfacial roughness but also inadvertently the associated turbulence and the wetted surface. There has been an observed dependence of the initiation of definite wave structure on diameter which complicates prediction scaleup. In addition, as evidenced in Figure 4, there exists a definite variation in the pressure loss prediction pattern as droplet and annular-type patterns of flow were initiated. Thus, a simple function used for prediction of, say, interfacial shear stress cannot possibly correctly handle both surface effects and size of the interface. The whole momentum balance would be made more reliable if some accurate method could be employed to predict the actual liquid holdup and its cross-sectional shape. This would allow a relatively simple correlation to be used in the closure of the balance equations to handle interfacial shear stress. Conclusions Detailed experimental data have demonstrated that prediction methods used to determine liquid phase and interfacial shear stresses in two-phase pipe flow often result in a very wide scatter [13]. Despite the possible error in the value obtained when the shear stresses were applied to the momentum balance calculation reasonable results were often obtained, more so for the pressure drop estimates. However, improved predictions were realised when consideration was given to the shape of the liquid phase as with the use of the MARS model. Improvements are still required as the MARS model tended to under predict both holdup and pressure loss for annular and stratified-type flows. Better performance may be achieved if an independent but 197 P.L. Spedding, J.S.Cole and G.F. Donnelly accurate method were used to predict liquid holdup, thus enabling the liquid interface geometry and shear stress to be determined in a more simplified balance closure calculation. It should be noted that the slughntennittent flow regime was not included in any of these calculations Nomenclature A Annular regime St BTS D F Blow through slug regime Droplet regime V Stratified regime Velocity ( m s-’ T Shear stress (kg m.’ IW LRW R- R RW SA Film regime Interfacial wave regime Long roll wave regime Ripple regime Holdup ) Subscripts G Gas i Interfacial L Liquid S Superficial W Wall Roll wave regime Semi annular regime References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 1 1. 12. 13. Andrews, D.E. 1996. The prediction of pressure loss during two phase horizontal flow in two-inch line pipe. MSc. Thesis, Univ. Texas. Nguyen, V.T.1975. Two phase gas-liquid co-current flow. An investigation of holdup, pressure drop and flow pattern in a pipe at various inclinations. Ph.D. Thesis, Univ. Auckland. Chen, J.J.J. 1979. Two phase gas liquid flow with particular emphasis on holdup measurements and predictions. Ph.D. Thesis, Univ. Auckland. Andritsos, N. 1986. Effects of pipe diameter and liquid viscosity on horizontal stratified flow. Ph.D. Thesis, Univ. Illinois Urabana. Hand, N.P. 1991. Gas liquid co-current flow in a horizontal pipeline. Ph.D. Thesis, The Queen’s Univ. of Belfast. Ferguson, M.E.G. 1993. An investigation of horizontal and inclined two phase pipe flow. Ph.D. Thesis, The Queen’s Univ. of Belfast. Grolrnan, E. 1994. Gas-liquid flow with low liquid landing in slightly inclined pipes. Ph.D. Thesis, Univ. Amsterdam. Donnelly, G.F. 1997. An analytical evaluation of horizontal multiphase flow. Ph.D. Thesis, The Queen’s-Univ. of Belfast. Spedding, P.L. and Hand, N.P. 1997. Prediction of stratified gas-liquid co-current flow in horizontal 1923-1935. pipelines. Int. J. Heat Mass Transfer, 9, Kowalski, J.E. 1987. Wall and interfacial shear stress in stratified flow in a horizontal pipe. AIChEJ, 21,274-28 I . Baker, A. and Gravestock, N. 1987. New correlations for predicting pressure loss and holdup in gascondensate pipelines. Int. Conf. Multiphase Flow, 2,417435. Andritsos, N. and Hanratty, T.J. 1987. Interfacial instabilities for horizontal gas-liquid flow in pipelines. Int. J. Multiphase Flow, 583-603. Spedding, P.L., Cole, J.S. and Donnelly, G.F. 2004. Momentum balance for two phase horizontal pipe flow: 1. Friction factors. Dev. Chem. Eng. Min. Process., in this issue. u, Received: 16 July 2002; Accepted ajler revision: 1 May 2003. 198

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