Two-Phase Gas/Liquid Pipe Flow - AIChE

1 Two-Phase Gas/Liquid pipe Flow Ron Darby PhD, PE Professor Emeritus, Chemical Engineering Texas A&M University Types of Two-Phase Flow Solid-Gas Solid-Liquid Gas-Liquid Liquid-Liquid Gas-Liquid Flow Regimes Homogeneous Highly Mixed Pseudo Single-Phase High Reynolds Number Dispersed Many Possibilities Horizontal pipe Flow Vertical pipe Flow Horizontal Dispersed Flow Regimes Vertical pipe Flow Regimes Horizontal pipe Flow Regime Map 1 / 2 GLAW 1 / 22 WLWLWLV ertical pipe Flow Regime Map DEFINITIONS Mass Flow Rate , Volume Flow Rate (Q) Mass Flux (G): LGLLGGmmmQQ m GLLGmmmGGGAAA Volume Flux (J): Volume Fraction Gas: Vol. Fraction Liquid: 1- Phase Velocity: GLLGmLGLGmGGGJJJQQVA GLLGJJV,V1 Slip Ratio (S): Mass Fraction Gas (Quality x): Mass Flow Ratio Gas/Liquid : GGLLmxSm1 - x1 - GLVSV GGLmxmmDensity of Two-Phase Mixture: where is the volume fraction of gas in the mixture mGL1 GLx x S 1 x / Holdup (Volume Fraction Liquid): GLGLS 1 x / 1 x S 1 x / Slip (S) Occurs because the gas expands and speeds up relative to the liquid.

2 It depends upon fluid properties and flow conditions. There are many models for slip (or holdup) in the literature. Hughmark (1962) slip correlation Either horizontal or vertical flow: where GLGL1 K1 x / x / SK1 x / x / / Z 1 / 41 / 61 / 8 ReFrZNN/ 1 HOMOGENEOUS GAS-LIQUID pipe FLOW Energy Balance (Eng q Bernoulli Eqn) where 22mGLmm2G2 f GdxdzG g DdLdLdPd dL1 xGdP GLGLGL1 /1 / For frozen flow (no phase change): If flow is choked. For ideal gas: dx0dL 2Gd xG1dP 1 / kGG11 k / kTs1 P1,P PP kP For frozen ideal Gas/Liquid choked flow: For flashing flow (Clausius-Clapeyron eqn): 2GL pG2 GLTcTP mm kPGc Homogeneous Horizontal Flow Flashing Flow - Determine x from (adiabatic) energy balance (or thermo properties database).

3 2mGLmm2G2fGdL dx dz DdP1 xG d / dP posGLc TTx Finite Difference Solution solve for L 2fit2mD2 L - P G g Z / K4f G Dimensionless where *2mfito o*24f L2 K- G g Z / P D G o P / P *o oooGG / P G / P oo / / iiL= L Using , where is the pipe inclination angle with the vertical for horizontal = 0 for vertical up flow = 1 for vertical down flow = -1 cos cos ZLcos cos *2*2fitmoo2 G / G K4f L-D1 gD cos / 4 fP Procedure: Find G, Given Select desired and determine at each pressure step from to Assume a value for Calculate at each pressure step. At choke point, Adjust until L 0 P oPeP*G L L L oeL, P and PEx: Flashing Water in pipe Given: Calculate: Pressure Drop over L a value for ; (Moody, Churchill, ~ ) 3.

4 , 4. 5. Choked if dL L ooooGoLoG , P ,T , x , s . , mmffn DG / 21mm PG 2 f L / D 1111o11s 1G 1L11 GLsGL11PP Px ,T , , x , mLG fn , , x , S 212PP P 2 P P Separated pipe Flows Each Phase Occupies a Specific Fraction of the Flow Area Two-Phase Multiplier for friction loss: 2 RfmfRPP LL Reference Single-Phase Flow: R = L Total flow is liquid: R = G Total flow is gas: R = Total flow is liquid in mixture: R = Total flow is gas in the mixture LmGm / AG GmGm / AG GmL LmG1 x G GmGGmGxG Lockhart-Martinelli (1949) or: 2 LmffLmPP LL 2 GmffGmPP LL L-M Two-Phase Multipliers 2Lm2C1 1 22Gm 1 C State Liquid Gas C tt turbulent turbulent 20 vt laminar turbulent 12 tv turbulent laminar 10 vv laminar laminar 5 L-M Correlating Parameter LmGm2ffPP LL 22 LmfLmL2 f1 x GPL D 22 GmfGmG2 fx GPL D Friction Factors is based on liquid only Reynolds No.

5 Is based on gas-only Reynolds No. Lmf LmReL1 x GDN GmfGmReGxGDN=mDuckler et al. (1964) and where are no slip values 2 LLm 2 GGm 1 , and 234ln ln ln 22 GLmm1 1 The Reynolds Number is based on mixture properties: mRemDGN sizing Relief Valves for Two-Phase Flow valvemAG valvedidea l nozzzleGK G Assume Homogeneous Gas-Liquid Mixture in an Isentropic Nozzle no1 / 2 PdnPdPGK 2 Discharge Coefficient ( ) Values given by manufacturer, or in the Red Book If flow is choked (critical) use : If flow is not choked (sub-critical) use : d ,liquidKdKd ,gasKTWO-PHASE DENSITY Where is the volume fraction of gas: x = mass fraction of gas phase (quality).

6 S = slip ratio = vG / vL = (fn(x, L/ G, ..etc) GL 1 GLx x S 1 x / Flashing Flow Non-Equilibrium If L 10 cm Flashing is not complete if In this case, use L = nozzle length (cm) = initial quality entering nozzle = local quality assuming equilibrium If xo > , x = xe L 10 cm oeoLxxxx10 oxexDetermine Quality, The quality is determined as a function of pressure by an energy balance on the fluid along the flow path. The path is usually assumed to be isentropic. exfn( P ) HDI Homogeneous Direct Integration Exact Solution Based on Numerical Finite Difference Equivalent of Nozzle Equation no1 / 21 / 2Pj n-1j 1jnndndjoj 1jPP- PdPG K -2 K -4 Required Information: vs P at constant s from Po to Pn in increments of Pj to Pj+1.)

7 Can be generated from an EOS or from a database ( steam tables). (If choked, Gn Gmax at Pn=Pc) TABLE I VALVE SPECIFICATIONS (Lenzing, et al, 1997, 1998) Valve KdG KdL Orifice Dia. (mm) Orifice Area B&R DN25/40 (Bopp & Reuther Si63) 20 ARI DN25/40 (Albert Richter 901/902) 1 x 2 E (Crosby JLT/JBS) Leser DN25/40 (441) 23 Experimental Data TABLE II FLOW CONDITIONS (Lenzing, et al, 1997, 1998) Fluid Nom. Pressure (bar) (psia) (psia) Air/Water 5 Air/Water 8 Air/Water 10 Steam/Water Steam/Water Steam/Water 8 Steam/Water oPbPAir-Water (Frozen) Flow Four Different Valves Three Different Pressures (kg/s m2)xoARI DN25/40, Air/WaterCalc 5 barData 5 barCalc 8 barData 8 (kg/s m2)xoLESER DN25/40, Air/WaterCalc 5 barData 5 barCalc 8 barData 8 barCalc 10 barData 10 (kg/s m2)xoB&R DN25/40, Air/WaterCalc 5 barData 5 barCalc 8 barData 8 barCalc 10 barData 10 (kg/s m2)xoCrosby 1x2 E, Air/WaterCalc 5 barData 5 barHNDI Homogeneous Non-Equilibrium Direct Integration For flashing flows, equilibrium is not reached until flow path length reaches 10 cm or more.

8 For L<10 cm, quality (x = gas mass fraction) is lower than it would be at equilibrium (xe). For L < 10 cm, quality is estimated from where xo is the initial (L = 0) quality (L in cm) If xo > , x = xe oeox = x + x - x L / 10 Steam-Water Flashing (non-Equilibrium) Flow One Valve - Leser 25/40 Four Different Pressures (kg/sm2)xoLeser DN25/40 Valve, Steam/Water, barDataHDIHNDI L= (kg/sm2)xoLeser Valve DN25/40, Steam/Water, barDataHDIHNDI L=40mm0 1000 2000 3000 4000 5000 6000 7000 8000 1 KdG (kg/sm2) xo Leser Valve DN25/40, Steam/Water, 8 bar Data HDI HNDI L=40mm (kg/sm2)xoLeser Valve DN25/40, Steam/Water, barDataHDIHNDI L=40mmSUMMARY/MORAL Two-Phase Flow is much more complex than single phase flow, because of the wide variety of possible flow regimes, phase distributions, thermo/mechanical equilibrium/non-equilibrium, etc.

9 Correlations are complex and limited in scope. Analysis requires good understanding of flow mechanism. References Baker, O., Simultaneous Flow of Oil and Gas , Oil & Gas J., 53:185-195, 1954 Darby, R., Fluid Mechanics for Chemical Engineers , 2nd Ed., Ch. 15, Marcel Dekker, 2001 Darby, R., Self and Edwards, Properly Size Pressure Relief Valves for Two-Phase Gas/Liquid Flow , Chemical Engineering, 109, no. 6, pp 68-74, June, (2002) Darby, R., On Two-Phase Frozen and Flashing Flows in Safety Relief Valves , Journal of Loss Prevention in the Process Industries, v. 17, pp 255-259, (2004) Refs (cont d) Darby,R, Self and Edwards, Methodology for sizing Relief Valves for Two-Phase Gas/Liquid Flow , Proceedings of the Process Plant Safety Symposium, 2001, AIChE National Meeting, Houston, TX, April 2001 Duckler, , M.

10 Wicks III and Cleveland, Frictional Pressure Drop in Two-Phase Flow: A Comparison of Existing Correlations for Pressure Loss and Holdup, AIChE J., 10:38-43, 1964 Govier, and K. Aziz, The Flow of Complex Mixtures in Pipes , Van Nostrand Reinhold Co., 1972 Hughmark, , Holdup in Gas-Liquid Flow , CEP, 58(4), 62-65, l962 Lockhart, , and Martinelli, Proposed Correlation of Data for Isothermal Two-Phase , Two-Component Flow in Pipes , CEP, 45(1), 39-48, 1949 Questions??