Calculating Two-Phase Pressure Drop - River City Engineering

1 Chemical Processing, 2000 Fluid Flow 1 of 8 Calculating Two-Phase Pressure DropScott S. Haraburda, PE Engineer, GE Plastics, Mt. Vernon, INAndSteve Chafin Process Engineer, River City Engineering , Lawrence, KSFluid flow concerns are quite prevalent among systems that handle chemicals, either inthe liquid or the vapor state. An important parameter for characterizing the energy of thefluid flowing within a contained system, such as pipes, is Pressure . This pressurebecomes important for designing pipe sizes, determining pump requirements, andaddressing safety concerns. Often the fluid is flowing as both liquid and TypeThe flow type of Two-Phase liquid-gas flow can be characterized into one of seven typesshown in Figure 1. These types could be predicted using the following processparameters:Gas density ratio (gas ratio) = (gas) / (air)Liquid density ratio (liquid ratio) = (liquid) / (water)Viscosity ratio (ratio) = (liquid) / (water)Surface tension ratio (ratio) = (liquid) / (water)Mass FluxMF (liquid or gas) = F(liquid or gas) / (3600*AR)To determine which type of flow exists, use the following coefficients in Figure 1, whichis a flow-pattern (lb/sec ft2) = MF(gas) / [ (gas ratio) * (liquid ratio)] = MF(liquid) * [ (gas ratio) * (liquid ratio)] * (ratio) / [MF(gas) * (ratio) 3 * (liquid ratio) 2]5-Step Pressure drop CalculationThe following steps can be used.

2 Three examples will be provided, two oil - hydrogenmixtures and one ethanol - air mixture. The following steps have been replicated in thedownloadable MS Excel spreadsheet at Processing, 2000 Fluid Flow 2 of 8 Step 1: Select the pipe choosing the nominal pipe size, ensure that you have the appropriate insidediameter, based upon the pipe schedule. For the provided examples, a 4 inch standardpipe will be used for the oil - hydrogen mixtures and a 1 inch standard pipe will be usedfor the ethanol - air mixture. Both have an absolute roughness ( ) of AreaAR = ( * d2) / 576 Step 2: Obtain the process important properties are flow rate (F), safety factor (SF), density ( ), viscosity ( ),and surface tension ( ). The first example has a 5,000 lb/hr flow, a lb/ft3 density, a15 cP viscosity, and a 20 dynes / cm surface tension for the liquid (oil).

3 The gas(hydrogen) is flowing at 800 lb/hr, with a lb/ft3 density and a cP second example is the same as the first, with the exception that the liquid flow is140,000 lb/hr. The third example has a lb/hr flow, a lb/ft3 density, a cPviscosity, and a dynes/cm surface tension for the liquid (ethanol). The gas (air) isflowing at lb/hr, with a lb/ft3 density and a cP viscosity. For allthree examples, there is no safety factor (SF=1).Step 3: Calculate the single phase line sizing Pressure following equations are used to calculate this Pressure drop for both the liquid andthe gas phase = F * SF / (3600 * * AR)Reynolds NumberRe = * F * SF / ( * d * )Friction Factorf = 64 / Refor Re < 2100f = 8 * [(8/Re) 12 + 1/(A + B) ]1/12whereA = [ * ln(1 / ((7/Re) + * / d))]16B = (37,530/Re)16 Pressure drop P = * f * v2 * / (gc * d) (this is in per 100 ft)The first example has a ft/sec velocity, a 523 Reynolds Number, a friction factor and a Pressure drop of psi / 100 ft of pipe for the liquid.

4 The gas is flowing ft/sec, with a Reynolds Number of 105,000, a friction factor of and a pressuredrop of psi / 100 ft. The second example has the same gas properties as the firstexample. However, the liquid is flowing at ft/sec, with a Reynolds Number of14,600, a friction factor of and a Pressure drop of psi / 100 ft. The thirdexample has a ft/sec velocity, a 893 Reynolds Number, a friction factor of anda Pressure drop of psi / 100 ft. The gas is flowing at ft /sec, with a ReynoldsNumber of 66,000, a friction factor of and a Pressure drop of psi / 100 Processing, 2000 Fluid Flow 3 of 8 Step 4: Calculate the two phase line sizing properties. The density, velocity, and viscosity are averaged for a characteristic property of thecombined phases in the fluid flow. And, the resulting Two-Phase Reynolds Number iscalculated.

5 The following equations are used:Avg. density (average) = (F(gas) + F(liquid))/(F(gas)/ (gas) + F(liquid)/ (liquid))Avg. velocity v(average) = (F(gas) + F(liquid)) / ( (average) * AR)Avg. viscosity (average) = (F(gas) + F(liquid))/(F(gas)/ (gas) + F(liquid)/ (liquid))Figure 2 depicts values for this step and the next step for the examples 5: There are three different types of Two-Phase Pressure drop are determined by the viscosity ratio and the mass flux. a. For viscosity ratios greater than 1000 and a mass flux greater than , use theChisholm-Baroczy (C-B) method [see example 1]. The C-B method is unique in that thepressure drops for each of the phases are calculated assuming that the total mixture flowsas either liquid or gas. Therefore:F(total) = F(liquid) +F(gas)MF = F(total) / (3600*AR)It should be noted that the Reynolds number and friction factor for each phase is alsocalculated assuming it is a function of total (liquid or gas) = [F(total), SF, d, (liquid or gas)]f (liquid or gas) = [Re(liquid or gas), / d] P(liquid or gas) = * f * MF2 / (gc * (liquid or gas) * d) (this is in per 100 ft)A Pressure ratio is calculated:PR = [ P(gas) / P (liquid)] this Pressure ratio, a C-B constant is calculated:CB = / MF PR < = / (PR * MF )for < PR < 28CB = / (PR2 * MF )for PR > 28 Chemical Processing, 2000 Fluid Flow 4 of 8 Now, the C-B Pressure correction factor and the associated Two-Phase Pressure drop iscalculated.

6 (C-B) = 1 + (PR2 - 1) * (CB * (xg((2-n)/2) ) * ((1-xg) ((2-n)/2) ) + xg (2-n) )Where xg = F(gas) / (F(gas) + F(liquid)) and n= P (C-B) = * (C-B) * f(liquid) * MF2 / (gc * (liquid) * d) (this is in per 100 ft)b. For viscosity ratios greater than 1000 and a mass flux less than , use the Lockhart- Martinelli (L-M) method [see example 2]. The Reynolds Number for both the liquidand the gas are used. Unlike the C-B method, the separate Pressure drops for both theliquid and the gas are used explicitly, along with the Pressure ratio. Using these, a uniqueL-M Pressure correction factor for each phase is calculated. This requires the use of adifferent Pressure factor than the C-B method:PR = ln [( P (liquid) / P (gas)) ]b1. For Re(liquid) > 2100 and Re(gas) > 2100: (liquid) = *PR+ * * *PR4 (gas) = + *PR+ * * *PR4b2. For Re(liquid) > 2100 and Re(gas) < 2100: (liquid) = *PR+ * * *PR4 (gas) = + *PR+ * * *PR4b3.

7 For Re(liquid) < 2100 and Re(gas) > 2100: (liquid) = *PR+ * * *PR4 (gas) = + *PR+ * * *PR4b4. For Re(liquid) < 2100 and Re(gas) < 2100: (liquid) = *PR+ * * *PR4 (gas) = + *PR+ * * *PR4 Now, a separate Pressure drop is calculated for each phase: P(liquid1) = [exp[ (liquid)]]2 * P (liquid) P(gas1) = [exp[ (gas)]]2 * P (gas)Then, the estimated Two-Phase Pressure drop is the maximum of these: P(L-M) = max { P(liquid1), P (gas1)}Chemical Processing, 2000 Fluid Flow 5 of 8c. Finally, for viscosity ratios less than 1000, use the Friedel method [see example 3]. Inaddition to the Reynolds number, the Froude number and Weber numbers are used. In thefollowing equations, be sure to use the mass flux of the total mass (liquid+gas) flowing inthe NumberFr = 12 * MF2 / (gc * (average)2 * d)Weber NumberWe = * d * MF2 / ( (average) * )A gas mass ratio and two Friedel coefficients are also used:Gas mass ratio xg = F(gas) / [F(liquid) + F(gas)]Calculate 1 for both phases using the Reynolds number calculated for each phase:Friedel coefficient 1 1 = 64 / Refor Re < 1055 1 = [ * ln(Re/( *ln(Re) - ))] -2 for Re > 1055 Friedel coefficient 2 2 = (1- xg)2 + (xg 2) * [ (liquid) * 1(gas) / { (gas) * 1(liquid)}]Two Pressure correction factors are used, one for horizontal flow (which includes verticalup) and another for vertical down flow.

8 The correlation for horizontal flow is: (F) = 2+ * xg *(1- xg) *( (liquid)/ (gas)) *( (gas)/ (liquid)) *(1- (gas)/ (liquid)) *Fr *We correlation for vertical down flow is: (F) = 2+ * xg *(1- xg) *( (liquid)/ (gas)) *( (gas)/ (liquid)) *(1- (gas)/ (liquid)) *Fr *We , the Two-Phase Pressure drop is then calculated using the following: P(F) = * (F) * 1(liquid) * MF2 / (gc * (liquid) * d) (this is in per 100 ft)Chemical Processing, 2000 Fluid Flow 6 of 8 Symbol ListSymbolDefinitionUnitsAFriction Factor numbernoneARPipe Areaft2 BFriction Factor numbernoneCBChisholm-Baroczy constantdimensionlessdPipe DiameterinchfFriction FactornoneFrFroude numbernonegcDimensional lb ft / lbf sec2 FMass flowlb / hourMFMass fluxlb/ft2-secnChisholm-Baroczy constantDimensionlessPPressurePsiPRPress ure ratiodimensionlessReReynolds numbernoneSFSafety factor (none = 1)dimensionlessvVelocityfeet / secondWeWeber numbernonexlLiquid Mass RationonexgGas Mass RationoneXDimensionless Flow Pattern Region coefficientnoneYFlow Pattern Region coefficientpounds / sec ft2 Surface Roughnessinches Friedel coefficientnone Pressure Correction factornone Densitylb / ft3 Surface Tensiondynes / centimeter ViscosityCentipoiseChemical Processing, 2000 Fluid Flow 7 of 8 Figure 1: Flow TypesTypeDescriptionSketchBubble (froth)Liquid with dispersed bubbles of plugs of gas and liquid inupper section of on the lower and gas on the uppersection pipe separated by a as stratified, except separated by awavy interface traveling in the samedirection of to stratified, except the gasperiodically picks up a wave and forms abubbly plug.

9 This flow can cause severeand dangerous vibrations because of theimpact of the high-velocity slugs againstthe in the center and liquid on the outerportion of the (dispersed)Liquid droplets in the Processing, 2000 Fluid Flow 8 of 8 Figure 2: Example ResultsExampleProperty123 Average Number105,000119,00066,900 Viscosity Ratio1250125059 Mass Flux1844217 Correlation TypeL-MC-BFriedelPressure , O., Oil & Gas J., Vol. 53, No. (12), 1954, pp. 185-190, 192, , and Martinelli, Chemical Engineering Progress, 1949, D., Int. J. Heat Mass Transfer, Vol. 16, pp. , L., "Improved Friction Pressure drop Correlations for Horizontal andVertical Two Phase Pipe Flow," European Two Phase Flow Group Meeting,Ispra, Italy, paper E2, , , Liquid-Gas Systems, Handbook of Multiphase Systems, Chapter 2, , , Chemical Process Equipment, Selection and Design, Butterworths,Massachusetts, , C., and J. Meyers, Momentum, Heat and Mass Transfer, 3rd Edition,McGraw-Hill, New York, , R.

10 And D. Green, Perry's Chemical Engineers' Handbook, 6th Edition,McGraw-Hill, New York, 1984.