PIPE DISCHARGE FLOW CALCULATIONS (A DIERS Users Group ...

1 DIERS Users Group Orlando 23-25, 2009-1-PIPE DISCHARGE FLOW CALCULATIONS (A DIERS Users Group Round-Robin Exercise)Presented by:Joseph C. LeungLeung Inc.(Consultant to Fauske & Associates, LLC)Presented at: DIERS Users Group MeetingOrlando, FloridaMarch 23-25, 2009 DIERS Users Group Orlando 23-25, 2009-2-Review and Update Completed nozzle DISCHARGE flow CALCULATIONS for three compositions:(I) Cyclohexane (10 bar)(II) 20% mole Ethane in Heptane (10 bar)(III) mole N2in Cyclohexane (33 bar) Methods used:omega methodPR-EOS flashASPEN Plus & DynamicsSIMSCI PRO IISuperChemVENT (CISP) DIERS Users Group Orlando 23-25, 2009-3-Data SubmittalInclude a summary sheet listing methods. Recommend using either fTP= or Re no. dependent fTP. Use homogeneous-equilibrium model (HEM). Provide, P, T, x (quality) along the pipe (if available), pipe exit pressure Pex, mass flux G, and DISCHARGE rate W (kg/s) corr.

2 To flow area Apof in2(2165 mm2). E-mail to Joseph Leung ( DIERS UG Design/Testing Committee Chair) at or Users Group Orlando 23-25, 2009-4-Proposed Inlet ConditionsDIERS Users Group Orlando 23-25, 2009-5-Horizontal Pipe DISCHARGE ProblemSame identical inlet (two-phase) conditions as the nozzle case. Two different piping (frictional) resistanceNote -N = Ken+ 4fTPL/D, with fTP= , and Ken = IPipe in inL/D Users Group Orlando 23-25, 2009-6-Horizontal Pipe DISCHARGE Problem- (Cont'd)TPTPTPenTPTP1 TPgfgfAlternate use of Reynolds no. dependent fGDffunctionLNK 4fDwhere f average two phase friction factorx(1x)accordingto McAdam,vapor and liquid viscosity = =+ = + = DIERS Users Group Orlando 23-25, 2009-7-Pipe Flow Formulation221112 22222 Constant diameter pipe (continuity)GuconstantEnergy balance (adiabatic flow) -11 HGvH Gvconstant22 Momentum balance (turbulent flow) -4fvdP + G vdvG v dZ 02D = = +=+= += DIERS Users Group Orlando 23-25, 2009-8-Expansion Law (Eq.)

3 Of State) Need P-v (pressure - sp. volume) relation. Normal practice is to use constant H (enthalpy) flash calculation. From adiabatic flow starting from stagnation -a constant H flash assumes to be Gv2=+ DIERS Users Group Orlando 23-25, 2009-9-Example Illustration Vapor cyclohexane DISCHARGE through pipe. Classical ideal-gas (IG) method:Shapiro text (1953)Bird Stewart Lightfoot text (1960)Levenspiel AIChE J (1977) Lappel correctionChurchill text (1980)Coulson & Richardson text (1996) Omega method. Constant H analytical integration Users Group Orlando 23-25, 2009-10-Classical IG Methodpv221111121112221C / Ck gas specific heat values from DIPPRP v relation (exact)Pvk1Gv v11Pv2k P vMomentum equationLk1 vvk1 P4fln1Dk vv2 KGv == = + =+ + DIERS Users Group Orlando 23-25, 2009-11- DIERS Users Group Orlando 23-25, 2009-12-Results from Classical IG ModelIG3go3gooIG kg/ m(10 bar, 455K)DIPPR kg/ m( ) = ==Pipe IPipe Density2130 kg/m2s 1560 kg/m2sDIPPR Density 2370 kg/m2s 1740 kg/m2sDIERS Users Group Orlando 23-25, 2009-13-Omega Method()o2fgofgoogopoofgofgo*oo122*22121 12parameter at isgiven byvv1 2 PC T equation GG / PL2(1)4flnDG 1(1 ) (1 )(1)2ln(1)

4 E = = + = = + =+ + + + *2ccxit choking criterionG = DIERS Users Group Orlando 23-25, 2009-14-Omega MethodNote:Po= 10 bar, go= kg/m3(DIPPR) 2c is exit choking pressure ratioPipe IPipe * kg/m2s1630 kg/m2s Users Group Orlando 23-25, 2009-15-Constant H Integration Method122oooPP2 Obtain P v data from constant H FLASH P v with best polynomialPPv1a1 b1vP Pwhere a , b or numerical integration of differential momentum = + == = 21v2lnv + DIERS Users Group Orlando 23-25, 2009-16- DIERS Users Group Orlando 23-25, 2009-17-Analytical Integration MethodNote:Po= 10 bar, go= kg/m3(DIPPR)Pipe IPipe * kg/m2s1610 kg/m2s Users Group Orlando 23-25, 2009-18-Summary of c-C6 Vapor DISCHARGE RatePipe I(N = )Pipe II(N = 5)IG (k = ) kg/sIG w/ real kg/s kg/sConst H analytical kg/sStd.

5 Kg/s5% Users Group Orlando 23-25, 2009-19-Pipe-Segment Numerical Integration222vP GvvL2fGvDwhereP is pressure incrementv is incremental specific volume over Pv is average specific volume in P + = DIERS Users Group Orlando 23-25, 2009-20-Numerical Integration is known or of pressure are taken from the initial to the final v are obtained for each increment for a constant-enthalpy L for each P taken is computed from Eq. in previous length of pipe L is L is negative, then P is too critical flow condition corresponds to L = 0, and the final pressure corresponds to choked L > L, then G was guessed too small and Steps 1-7 are repeated with a larger G. If L < L, then G was guessed too large; Steps 1-7 are repeated with a smaller converged solution is obtained when L = L to within a given :Perry's ChE Hdb, Fluid Dynamics section,7th ed.

6 , also Leung, CEP article, 1996.