Prediction of Oil-Water Two Phase Flow Pressure Drop by Using Homogeneous Model

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Kenneth Harvey
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1 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008 Prediction of Oil-Water Two Pase Flow Pressure Drop by Using Nay Zar Aung a, Triyogi Yuwono b a Department of Mecanical Engineering, Institute Tecnology Sepulu Nopember b Department of Mecanical Engineering, Institute Tecnology Sepulu Nopember Abstract Pressure drop in oil-water two-pase flow in a 8 mm diameter steel pipe were predicted by using omogeneous model. Predictions of friction pressure drop and total pressure drop were made at upward inclinations +5, +0, downward inclinations -5. Te mixture velocity was varied from 0.7 m/s to.5 m/s and oil volumetric concentration was between 0% and 90%. Te data resulted form predictions were compared wit experimental data of Angeli (006). Te results sowed tat omogeneous model gives acceptable predictions for total pressure drop at low oil concentration (< 0.4). Homogeneous model gives overestimates for frictional pressure drop. Keyword: Pressure drop, Oil-water two pase flow, Homogeneous model. Introduction Two-pase liquid-liquid flows are very common in te oil and cemical process industries. In te oil industry, in particular, oil and water are often produced and transported togeter in pipelines tat ave various degrees of inclination from te orizontal or vertical. Te knowledge of pressure drop in a twopase flow system is very important for piping design. It enables te designer to size te pump required for te operation of te flow system. Many of empirical correlations ave been proposed for prediction for gas liquid flows some of wic ave been adapted to predict gas water flow or gas-oil flow. In te area of oil industries, liquid-liquid (oil-water) flows are also encountered and many of researc ave been done on oilwater flow and gas-oil-water tree pase flow. However, sometimes problems of test facilities difficulties are still encountered and it takes a long time to get te results. Moreover, modern CFD softwares are also comparatively as expensive as experiments. For two liquids flow wit nearly te same densities, te assumption of combined liquid pases as a single entity (omogeneous fluids) is very reasonable and te assumption makes teory become simple to predict te ydrodynamic penomena and gives acceptable prediction. Spedding (006) tried to use Lockart Martinelli correlation, Dukler Wicks Cleveland correlation, Beggs Brill correlation, etc., to predict te pressure drop in gas oil two-pase flow and gaswater-oil tree-pase flow. Te objective of tis present work is to predict te pressure drop in oil-water two pase by using omogeneous model and to validate wit experimental data of oil-water flow Angeli (006).. In te omogeneous model, te fluids are caracterized by an effective fluid tat as suitably averaged properties of te two pases in te pipe. It is also known as No-Slip Model. It is assumed tat tere is no velocity difference between te pases and te two fluids flow at te same velocity. By assuming no eat and mass transfer, for omogeneous model te pressure gradient can be written as te sum of tree pressure gradient components due to friction, gravity, and acceleration, dp dx total = f ρ U m d US USL + ρgsin( θ) + ρ + ρl D dx α α L () ρ = α ρ + α LρL () μ = α μ + α μ () L L

To simplify te teory in analytical predictions, momentum pressure drop in Equation () will be neglected.

2 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008 f 9.5 = 4log (k / D + ) (4) Re f Re Dρ U μ = m (5) U S α = β = (6) U m U m =U S +U SL (7) Normally, contribution of momentum pressure drop is very small. To simplify te teory in analytical predictions, momentum pressure drop in Equation () will be neglected.. Metodology of Prediction Prediction of pressure drop wit omogeneous model was implemented by using a MATLAB UI (called HOMO). Te UI (rapical User Interface) was created in MATLAB 7. based on te equations of omogeneous model mentioned above. It is sown in Figure. Tere are nine input data for prediction of pressure drop. Te results data will be produced in te results box and also simulated as a grapic. Te required input data are sown in Table. Table. Te required input data for prediction of pressure drop Input Data Pipe Diameter (m) 6 Density of water (kg/m ) Mixture velocity (m/s) 7 Density of oil (kg/m ) Oil concentration 8 Pipe inclination (Degree) 4 Absolute viscosity of water (N-s/m ) 9 Pipe surface rougness (m) 5 Absolute viscosity of oil (N-s/m ) rapic Result box Input data Figure. A MATLAB UI for predicting oil water flow pressure drop

3 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008. Properties of Liquids in Prediction of Pressure Drop In prediction of pressure drop, te liquids used are Oil Exxsol D40 (Exxon Cemicals) and water. Te properties of fluids used in Angeli s experiments are also used for prediction and summarized in Table. Pipe ydraulic surface rougness for steel pipe was mm. Table. Properties of liquids at 5 C Liquid Oil Exxsol D40 (Exxon Cemicals) Water Density (kg/m ) Viscosity (Ns/m ) Surface Tension (N/m) Results and Discussion Te predicted frictional and total pressure drops from omogeneous model are sown in te following tables by comparing wit Angeli s experimental data. Predicted total pressure gradient sowed a good agreement wit experimental data, owever frictional pressure gradients over estimation. At low oil concentration, omogeneous model gives nearly exact solution because at low concentration, oil bubble dispersed in te water as omogeneous flow. Figure. Example of UI for prediction of pressure gradient wit omogeneous model Inclination At +0 inclination, total pressure gradient from omogeneous model as a good agreement wit experimental data. At low mixture velocities (0.7 m/s, m/s,.5 m/s), omogeneous model sowed acceptable accuracy in prediction for total pressure drop. Frictional pressure drop from experiments sowed tat tere is flow pattern affect at medium range of oil concentration. At upward inclination frictional pressure drop are decreasing at medium range of oil concentration and increased again at iger oil concentration.

4 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008 Table.Total and frictional pressure gradient at +0 pipe inclination [Prediction Data] Oil Mixture Velocity (m/s) volume Input (%) Total and frictional pressure gradient (kpa/m) ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f Table 4.Total and frictional pressure gradient at +0 pipe inclination [] Inclination Results at -5 inclination are sown in Table 5 and 6 for frictional and total pressure gradient. From experimental data, it can be seen tat downward and upward as te same trend in frictional pressure drop. For downward inclination omogeneous model give overestimations. At mixture velocity.5 m/s, omogenous models started to give positive values for total pressure drop at oil concentration 0.6. But experimental data sowed negative values of total pressure drop at all te range of oil concentration. 4

5 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008 Table 5. Total and frictional pressure gradient at -5 pipe inclination [Prediction Data] Oil Mixture Velocity (m/s) volume Input (%) Total and frictional pressure gradient (kpa/m) ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f Table 6. Total and frictional pressure gradient at -5 pipe inclination [] 5

6 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November Inclination For +5 inclination comparison of predicted frictional pressure drop and experimental data at mixture velocities of m/s and m/s are sown in Figure and 4. At m/s te predicted frictional pressure drop approaced to experimental data. But for m/s te experimental frictional pressure drop is decreasing wit oil concentration and predicted frictional pressure drop is sligtly increasing wit oil concentration. Table 7. Total and frictional pressure gradient at +5 pipe inclination [Prediction Data] Oil Mixture Velocity (m/s) volume Input (%) Total and frictional pressure gradient (kpa/m) ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f ΔP t ΔP f Frictional Pressure Drop (kpa/m) Oil Volume Fraction Figure. Comparison of predicted frictional pressure gradient and experimental data, U mix = m/s, + 5 6

7 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November Frictional Pressure Drop (kpa/m) Oil Volume Fraction Figure 4. Comparison of predicted frictional pressure gradient and experimental data, U mix = m/s, Comparison of Pressure Drop at Low Oil Concentration At +0 pipe inclination, total pressure gradient from omogenous model and experimental data were compared for low oil concentration range of 0.~0.4. It can be seen tat omogeneous give an accurate predictions at low mixture velocity (0.7 m/s and m/s). It is obvious pressure drop start to be affected by flow pattern at iger mixture velocities. However predictions wit omogeneous model are still acceptable for low concentration (< 40 %) as sown in following Figures.5~9..5 Total Pressure radient Vs Total Pressure radient kpa/m Figure 5. Comparison of predicted total pressure gradient wit experimental data ( U mix =0.7 m/s), +0 inclination 7

8 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November Total Pressure radient Vs.5 Total Pressure radient Vs Total Pressure radient kpa/m.5 Total Pressure radient kpa/m Figure 6. Comparison of predicted total pressure gradient wit experimental data ( U mix = m/s) Figure 7. Comparison of predicted total pressure gradient wit experimental data ( U mix =.5 m/s) 4.5 Total Pressure radient Vs Total Pressure radient Vs Total Pressure radient kpa/m.5 Total Pressure radient kpa/m Figure 8. Comparison of predicted total pressure gradient wit experimental data ( U mix = m/s) 5. Conclusion Figure 9. Comparison of predicted total pressure gradient wit experimental data ( U mix =.5 m/s) Frictional and total pressure drop in oil-water flow were predicted by using omogeneous model at upward and downward inclination. At bot upward and downward inclination, omogeneous model gives acceptable prediction for total pressure drop for low oil concentration (<0.4). For frictional pressure drop, omogeneous model gives overestimated values. However omogeneous model is recommend for bubbly flow or dispersed pase fraction < 0.4.Homogeneous model will gives a good prediction if density ρ ratio, L < 0 or total mass flux () > 000 kg/m s. ρ 8

9 FUNDAMENTAL DAN APLIKASI TEKNIK KIMIA 008 Surabaya, 5 November 008 Nomenclature D Pipe Diameter (m) f Fanning friction factor k Hydraulic pipe rougness (m) P Pressure (N/m ) Mass flux (kg/m s) U Velocity (m/s) reek letters Subscripts α Pase oldup β Liquid content ρ Density (kg/m ) σ Surface Tension (N/m) μ Viscosity (Ns/m) θ Inclination angle (degree) f L S t friction gas omogeneous liquid superficial total 6. References. Angeli. P, 006, Upward and downward inclination oil water flows, International Journal of Multipase Flow (006) Crowe C.T, 006, Hand Book of Multipase flow, Wasington State University. Jassim. E.W, 005, Prediction of two-pase pressure drop and void fraction in microcannels using probabilistic flow regime mapping, International Journal of Heat and Mass Transfer 49 (006) , Multipase Flow Production Model (Teory and User s Manual), Maurer Engineering Inc, 96 West T.C. Jester Houston, Texas 5. Rodriguez. O.M.H., 005, Experimental study on oil water flow in orizontal a. and sligtly inclined pipes, International Journal of Multipase Flow (006) 4 6. Spedding, P.L., 006, Prediction of pressure drop in multipase orizontal pipe flow, International Communications in Heat and Mass Transfer (006) 05 06, 9

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