BENCHMARK FLOW PROBLEMS - A ROUND-ROBIN EXERCISE. Joseph C. Leung Leung Inc. (Consultant to Fauske & Associates, LLC)

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1 BENCHMARK FLOW PROBLEMS - A ROUND-ROBIN EXERCISE Joseph C. Leung Leung Inc. (Consultant to Fauske & Associates, LLC) Presented at: DIERS Users Group Meeting San Antonio, Texas October 20-22,

2 Critical Discharge Round-Robin Exercise For benchmarking purpose. Thermodynamic equilibrium assumption. Homogeneous flow (no slip). Three inlet qualities (0.0001, 0.01, 0.1). Case I (Cyclohexane) at 10 bara. Case II (20% mole Ethane in n-heptane) at 10 bara. Case III (2.5 % mole N 2 in Cyclohexane) at 33 bara. -2-

3 Proposed choked flow problems Case Liquid Composition (mole) P o (bar) T o ( C) x o (vapor mass) Ia 100% c-c (bubble pt) Ib 100% c-c Ic 100% c-c IIa 20% C2/n-C (bubble pt) IIb 20% C2/n-C IIc 20% C2/n-C IIIa 2.5% N 2 /c-c (bubble pt) IIIb 2.5% N 2 /c-c IIIc 2.5% N 2 /c-c

4 Data Submission Invite EDUG. Two weeks before next US DIERS Users Group Mtg. all relevant results (outputs) together with a summary sheet listing the mass flux G and choking pressure (bar) or ratio. Post invitation and problem specification in DIERS website. -4-

5 Two-Phase Flow in Nozzle DIERS UG San Antonio Mtg./October From Thermodynamics: First Law (Energy Equation) ( Gv) 2 u2 h = h + = h + (1) o 2 2 Second Law (Adiabatic Reversible) Combining: dh = T ds + v dp (2) P v dp 2h ( o - h) Po G = = (3) v v -5-

6 Two-Phase Simple Fluid Expansion dp or ρ v dp v Po ρ o P 1 1, o =ω + =ω v P ρ P o Flashing flow (phase change) : Pov fgo C pf ToPo v fgo ω = α o h v h fgo o fgo 2 Non flashing flow (no phase change) : ω = α k o -6-

7 Alternate Method for Multicomponent System with wide boiling pt. range (Nazario-Leung 1992 paper) Use the original EOS as suggested by v P = ω o (36) v P o Re-defining ω to account for realistic flashing behavior by v 1 vo ω = (37) Po 1 P Do a multicomponent flash calculation at 90% of the inlet pressure P o. Calculate v and ω. Use generalized G* - ω correlation to obtain the flashing flow rate per unit area. -7-

8 Flashing and non-flashing choked flow through nozzles - a unified chart. Merging the two analytical solutions, Eqs. (10) and (12). Source: Leung, 1990a and 1990b. L. L. Simpson empirical fit for P c /P o given by [ Process Safety Progress 22(1),27(2003)] P c/ Po = 1 + ( ω ) ω ( ln ω) -8-

9 Participants Flash Routine Method of Calculation Joseph Leung (Leung Inc.) in-house H, vdp, omega Greg Hendrickson (Chevron Phillips) Aspen Plus H James Goom (Aspen Tech.) Aspen Dynamics H, vdp (Simpson) Nikita Podlevskikh (CISP) VENT (TSS) G = (dv/dp) 1/2 s Warren Greenfield (ISP) SimSci PRO/II H Bob D'Alessandro (Evonik-Degussa) Aspen Plus vdp Bob D'Alessandro (Evonik-Degussa) SuperChem vdp Harold Fisher (Fisher Inc.) Proprietary vdp (Simpson) Georges Melhem (Iomosaic) SuperChem vdp Enio Kumpinsky (Ashland) SuperChem vdp Dan Smith (Albermarle) in-house vdp (Simpson) in-house omega Chemcad unknown

10 Method (initials) DIERS UG San Antonio Mtg./October % c-c6, 10 bar, C Case Ia x o = Case Ib x o = 0.01 Case Ic x o = 0.1 ω o (JL) ω 0.9 (JL) vdp (JL) Aspen H (GH) Aspen H (JG) Aspen vdp (JG) Vent (NP) Simsci H (WG) Aspen vdp (RD) SuperChem vdp (RD) SuperChem vdp (GH) vdp (HF) Mean Value Std. Dev

11 20% C2/n-C7 (Liq. Comp.), 10 bar, 51.9 C Method Case IIa x o = Case IIb x o = 0.01 Case IIc x o = 0.1 (initials) ω 0.9 (JL) vdp (JL) Aspen H (GH) Aspen H (JG) Aspen vdp (JG) Vent (NP) Simsci H (WG) Aspen vdp (RD) SuperChem vdp (RD) SuperChem vdp (GH) vdp (HG) Mean Value Std. Dev

12 2.5% N 2 /c-c6 (Liq. Comp.), 33 bar, 25 C Method Case IIIa x o = Case IIIb x o = 0.01 Case IIIc x o = 0.1 (initials) ω 0.9 (JL) vdp (JL) Aspen H (GH) Aspen H (JG) Aspen vdp (JG) Vent (NP) Simsci H (WG) Aspen vdp (RD) SuperChem (GM) SuperChem (GH) vdp (HF) Mean Std. Dev

13 20% C2/n-C7 (Liq. Comp.), 10 bar, 51.9 C Sensitivity to VLE model, H, vdp (Aspen) Method (initials) Case IIIa x o = Case IIIb x o = 0.01 Case IIIc x o = 0.1 Aspen H, kij = (JG) Aspen vdp, kij = (JG) Mean Value Std. Dev

14 2.5% N 2 /c-c6 (Liq. Comp.), 33 bar, 25 C Sensitivity to VLE model (Aspen) Method (initials) Case IIIa x o = Case IIIb x o = 0.01 Case IIIc x o = 0.1 Aspen H, NRTL (JG) Aspen vdp, NRTL (JG) Aspen H, kij=0.176 (JG) Aspen H, kij= (GH) Mean (ALL submitted) Std. Dev. (All submitted)

15 Sensitivity to liquid density for bubble pt mass flux evaluation Method Case Ia Case IIa Case IIIa (initials) x o = x o = x o = Cyclo-C6 C2-nC7 N2-cycloC6 Liquid density (kg/m 3 ) Liquid density (kg/m 3 ) Liquid density (kg/m 3 ) (kg/m 2 s ) ω 0.9 (JL) PR EOS liquid density Aspen H (JG) API liquid density (default) Aspen vdp (JG) API liquid density (default) -15-

16 Case I - Cyclohexane One-component P o = 10 bara (145 psia), T o (saturation) DIPPR (P-T, liquid density, latent heat, etc.) advantage : accurate P sat, ρl, HVL disadvantage : no data on H, H, S, S EOS (SRK, PR) - advantage: Z,Z,H,H,S,S disadvantage : Z (5% off ) L V L V L V L L V L V -16-

17 Case 1 cyclo-c6 constant S flash P T VL VV V/F mole V 2ph BAR C m3/kmol m3/kmol quality m3/kmol

18 -18-

19 Case I Cyclo-C6 Preliminary Solution (Long Form) PR EOS (P c = 40.8 bar, T c = 553.8K, acentric factor = 0.208) 10 bar, C, x o = 0.0 (0.0001) Constant S flash to 9 bar, 8 bar and so on Curve fit P-v data v P o = 1 vo P Numerical integration of 2 vdp /vt to seek max G P P t o 1/2-19-

20 -20-

21 Case II 20% mole Ethane / n-heptane Bubble-point prediction to match available literature VLE data on C2-C7 binary system - Kays, I&EC 30, 459 (1938) Gasem et. al., J Ch Eng Data, 34, 397 (1989) PR EOS for C2-C7 binary k 12 = 0.01 (best fit) (caution - different value for SRK) -21-

22 -22-

23 -23-

24 Case IIa C2 / n-c7 constant S flash P T X (C2) Y (C2) VL VV L/F mole BAR C mole fr mole fr m3/kmol m3/kmol liq/feed

25 -25-

26 Case II C2-C7 Preliminary Solution (Long Form) PR EOS (20% mole C2 in n-c7) 10 bara, 51.9 C, x o = 0.0 (0.0001) Constant S flash to lower pressures Curve fit P-v data v P o = 1 vo P Numerical integration of 2 vdp /vt to seek max G P P t o 1/2-26-

27 -27-

28 -28-

29 Case III - N 2 / Cyclo-C6 Bubble-point prediction using PR EOS to match available N 2 solubility data in cyclo-c6 : Hildebrand, JACS, 71, 3147 (1949) Hildebrand, I&EC Fund 6, 130 (1967) Wilhelm, Chem Rev, 1, 73 (1973) Wild, Ch E J, 15, 209 (1978) Sandler, J Ch E Data, 34, 419 (1989) Determine initial condition and k 12 (BIP) for this mixture. -29-

30 -30-

31 PR EOS for N 2 / cyclo-c6 binary P o = 33 bar T o = 25 C Henry's Law constant for N2 / cyclo-c6 pair x 10-4 mole frac/atm (solubility form: x = H P) 1320 bar/mole frac (volatility form: P = H* x ) N 2 mole frac = 7.68 x 10-4 (33 x atm) = 0.025, 2.5% Best estimate k 12 = (PR EOS) (caution - different value for SRK) -31-

32 Case III N2 cyclo-c6 const S flash P T X (N2) Y (N2) VL VV L/F mole bar C mole fr mole fr m3/kmol m3/kmol liq/feed E

33 -33-

34 Case III N2 / Cyclo-C6 Preliminary Solution (Long Form) PR EOS (2.5% mole N 2 in cyclo C6) 33 bara, 25 C, x o = 0.0 (0.0001) Constant S flash to lower pressures Temperature stays relatively unchanged (expected) Curve fit P-v data v P o = 1 vo P Numerical integration of 2 vdp /vt to seek max G P P t o 1/2-34-

35 -35-

36 -36-

37 100% c-c6, 10 bar, C (selected data) Method Case Ia x o = Case Ib x o = 0.01 Case Ic x o = 0.1 (initials) ω o (JL - stagnation) ω 0.9 (JL 0.9) ω 0.9 (DS 0.9) vdp (JL - numerical) vdp (DS - numerical) vdp (DS - Simpson) Aspen H (GH) VENT (NP) SIMSCI H (WG) SUPERCHEM vdp (EK) vdp (HF) Mean Value Std. Dev

38 20% C2/n-C7 (Liq. Comp.), 10 bar, 51.9 C (selected data) Method (initials) Case IIa x o = Case IIb x o = 0.01 Case IIc x o = 0.1 ω 0.9 (JL) ω 0.9 (DS) vdp (JL numerical) vdp (DS numerical) vdp (DS - Simpson) CHEMCAD (DS) ASPEN H (GH) VENT (NP) SIMSCI H (WG) SUPERCHEM vdp (EK) vdp (HG) Mean Value Std. Dev

39 2.5% N 2 /c-c6 (Liq. Comp.), 33 bar, 25 C (selected data) Method (initials) Case IIIa x o = Case IIIb x o = 0.01 Case IIIc x o = 0.1 ω 0.9 (JL) ω 0.9 (DS) vdp (JL - numerical) vdp (DS - numerical) vdp (DS - Simpson) CHEMCAD(DS) ASPEN H (GH) VENT (NP) SIMSCI H (WG) SUPERCHEM (EK) Mean Std. Dev

40 Uncertainties in various models Case II bubble point calculation 61.7 C (RD) vs 51.9 C(EK), perhaps due to different k ij value, however G not much affected. NIST, DIPPR, PR-EOS would yield close agreement in P-T saturation, but not always in liquid density, however G not much affected. Chemcad uncertainty in its calculation method (DS will follow up). -40-

41 FINDINGS Good agreement so far for all cases. Flash results are quite consistent. G based on H from const S flash and integral vdp should yield consistent result, even for multicomponent system. Integral vdp method much more forgiving, even const H flash would yield close enough solution (not true approaching high quality flow). N 2 -chex case PR k ij = and NRTL model yield quite similar solutions. -41-

42 Next DIERS UG Round-Robin Non-equilibrium (or frozen ) nozzle flow? Slip-equilibrium nozzle flow? Extend to pipe flow of various length? Supercritical discharge? -42-

43 Next Benchmark Pipe discharge mass flux calculations HEM (homogeneous-equilibrium model) assumption. Same 3 systems, 3 inlet qualities x o = , 0.01, pipe configurations - N = K en + 4f F L/D = 1.5 (L/D = 50) N = K en + 4f F L/D = 5 (L/D = 225) fully turbulent two-phase, f F = (Fanning) sharp-edge entrance, K en =

PETE 310 Lectures # 36 to 37

PETE 310 Lectures # 36 to 37 Cubic Equations of State Last Lectures Instructional Objectives Know the data needed in the EOS to evaluate fluid properties Know how to use the EOS for single and for multicomponent