Calculaton of ODH classfcaton for Nevs LHe e-bubble Chamber Cryostat. Physcal parameters Thermal propertes of Helum and Ntrogen Yongln Ju Nevs Laboratores, Columba Unversty, NY 533 T 3 [K] Pa 76 [mmhg] ρhe.625 [kg/m 3 ] ρn2.56 [kg/m 3 ] T_he.2 [K] Pv.3. 5 [Pa] ρfv 2.8 [kg/m 3 ] ρgv 6.9 [kg/m 3 ] hfv 5.77. 3 [J/kg] hgv.98. 3 [J/kg] hfgv hgv hfv hfgv = 2.72. [J/kg] T_n2 77.3 ρfn 86.8 [kg/m 3 ] ρgn.623 [kg/m 3 ] hfn 2.877. 3 [J/kg] hgn 76.99. 3 [J/kg] hfgn hgn hfn hfgn =.989. 5 [J/kg] R 296.929 [J/kg.K] -------------------------------------------------------------------------------------------------------------------------------------------------------- A. LHe Dewar he 25 [L] tt.. he tt. [L/h] [LHe dewar normal bol-off rate, %] 2 --------------------------------------------------------------------------------------------------------------------------------------------------------- B. LN2 Dewar n2 25 [L] tt2.5. n2 tt2.56 [L/h] [LN2 dewar normal bol-off rate,.5%] 2 ------------------------------------------------------------------------------------------------------------------------------------------------------------ C. LHe essel Dr 2. 25.. 3 Dr.35 [m] Hr 2.5. 25.. 3 Hr.56 [m] Dz.2 [m] Dn 5. 25.. 3 Dn.27 [m] Hn 2. 25.. 3 Hn.58 [m] A A2 Dr2 Dn 2 A.6 [m 2 ] A3 Dn. Hn A3 3 [m 2 ] Dr2 Dz 2 A2.73 [m 2 ] A Dr. Hr A.523 [m 2 ] Ar_he A A3 A Ar_he.786 [m 2 ] [Cold surface of the LHe reservor] r r2 Dr2 Dz 2. Hr r. [m 3 ] r. = 39.675 [L] [olume of LHe n LHe reservor] Dn2 Dz 2. Hn r2 = 6.276. 3 [m 3 ] r2. = 6.276 [L] [olume of LHe n neck space] r_he ( r r2). r_he = 5.95 [L] [Total volume of LHe n LHe reservor] --------------------------------------------------------------------------------------------------------------------------------------------------------------- D. LN2 essel Dno. 25.. 3 Dno.356 [m] Dn 6. 25.. 3 Dn.52 [m] Hnz 2. 25.. 3 Hnz.58 [m] Hfn. 25.. 3 Hfn = 5 [m] Dn 3. 25.. 3 Dn.33 [m] Dn2. 25.. 3 Dn2 = 79 [m] Ar_n2 2. Dno 2 Dn 2 Dno. Hnz Dn. Hfn Ar_n2 = 5 [m 2 ] [Cold surface of LN2 reservor] π r_n2. Dno2 Dn 2. Hnz. r_n2 =.85 [L] [olume of lqud n the LN2 reservor] ----------------------------------------------------------------------------------------------------------------------------------------------------------
E. LHe e-bubble Chamber Dv.8 [m] Hv.7 [m] Hfv.5 [m] [Hght of LHe n e-bubble chamber] π Av. Dv2 Av = 9.6. 3 [m 2 ] Av2 Dv. Hv Av2.58 [m 2 ] Ae_he 2. Av Av2 Ae_he.76 [m 2 ] [Cold surface area of e-bubble chamber] π fv. Dv2. Hfv fv = 9.69. [m 3 ] e_he fv. e_he.962 [L] [olume of LHe n e-bubble chamber] 2. Mass 2. Thermal Load f vacuum s lost: We assume qt [W/m 2 ] Et_he Et_n2 Ee_he qt. Ar_he Et_he = 7.859. 3 [W] qt. Ar_n2 Et_n2 = 8.53. 3 [W] qt. Ae_he Ee_he = 76. [W] 2.2 Mass n LHe vessel: LHe vessel: p.3. 5 [Pa] T.2 K ρfv = 2.8 [kg/m 3 ] hfgv = 2.72. [J/kg] ρgv = 6.9 [kg/m 3 ] LHe mass at.2k n LHe vessel: Mhe ρfv. r_he Mhe = 5.735 [kg] Saturated gas helum mass at.2k n LHe vessel: Mghe ρgv. r_he Mghe.758 [kg] The total enthalpy ncrease of load LHe of 5 lters n phase change: Elg Mhe. hfgv Elg =.88. 5 [J] 2.3 Mass n e-bubble Chamber: LHe vessel: p.3. 6 [Pa] T.2 K ρfve 5.55 [kg/m 3 ] hfgv = 2.72. [J/kg] ρgve 5 [kg/m 3 ] LHe mass at.2k n LHe vessel: Mhee ρfve. e_he Mhee.6 [kg] Saturated gas helum mass at.2k n LHe vessel: Mghee ρgve. e_he Mghee.39 [kg] The total enthalpy ncrease of load LHe of 5 lters n phase change: Elge Mhee. hfgv Elge = 3.2. 3 [J] 2
2. Mass n LN2 vessel: LN2 vessel: p.3. 5 [Pa] T 77.3 K ρfn = 86.8 [kg/m 3 ] hfgn =.989. 5 [J/kg] ρgn =.623 [kg/m 3 ] LHe mass at.2k n LHe vessel: Mn2 ρfn. r_n2 Mn2 = 33.228 [kg] Saturated gas ntrogen mass at 77.3K n LN2 vessel: Mgn2 ρgn. r_n2 Mgn2.9 [kg] The total enthalpy ncrease of load LHe of lters n phase change: Elg Mn2. hfgn Elg = 6.68. 6 [J] 3. Mass flow rate and release tme 3. Tme and mass flow rate estmaton for LHe: Et_he = 7.859. 3 [W] m_he Et_he hfgv m_he.379 [kg/s] t_he Mhe m_he t_he = 5.2 [s] If: Pb.3. 5 [Pa] T [K] Γ.9 τ.659 Po 3. 5 [Pa] Mass flow rate estmaton for relef valve: d. [m] n 2 Ar moutr Γ. Ar. Po τ. R. T 3.2 Tme and mass flow rate estmaton for LHe: Ee_he = 76. [W] d2. n Ar =.57. [m 2 ] moutr [kg/s] > m_he.379 [kg/s] me_he Ee_he hfgv me_he.37 [kg/s] te_he Mhee me_he te_he = 3.975 [s] If: Pb.3. 5 [Pa] T [K] Γ.9 τ.659 Po. 5 [Pa] Mass flow rate estmaton for relef valve: d. [m] n Ar moutr Γ. Ar. Po τ. R. T 3.3 Tme and mass flow rate estmaton for LN2: Et_n2 = 8.53. 3 [W] m_n2 Et_n2 hfgn m_n2.3 [kg/s] t_n2 d2. n Ar = 7.85. 5 [m 2 ] moutr =.7 [kg/s] > me_he.37 [kg/s] Mn2 m_n2 t_n2 = 776.256 [s] If: Pb.3. 5 [Pa] T [K] Γ.9 τ.659 R 287.6 [J/kg.K] P 3. 5 [Pa] 3
Mass flow rate estmaton for open tube: d2.75..25 d2.9 [m] n2 3 Ar moutr Γ. Ar. P τ. R. T. ODH calculaton wth fan avalable Data of the confned volumn and fan vent rate: d22. n2 Ar = 8.55. [m 2 ] moutr.338 [kg/s] > m_n2.3 [kg/s] 25.. = 3. 3 [m 3 ] [The confned volumn] C.283 [m 3 /CF] CC.283 6 CC =.77. [m 3 /s] [Fan rate] 3 [SCFM]. CC [m 3 /s]. [m 3 /s] [The ventlaton rate of the fan] Case I. The normal operaton of 25L LHe and 25L LN2 Dewars The normal vaporzaton rate: % LHe /day and.5% LN2/day Rn tt. 36 [m 3 /s] Rn = 2.89. 8 [m 3 /s] Rn2 tt2. 36 [m 3 /s] Rn2 =.3. 8 [m 3 /s] R Rn. ρfv ρhe R = 2.222. 5 R2 Rn2. ρfn ρn2 R2 = 3.29. 5 R R R2 R = 5.25. 5 [m 3 /s] <. [m 3 /s] [The spll rate] t 25 25 tt tt2 t =.92. 3 [hr] t. 36 = 6.92. 6 [s] R CC... 3. R R < C. R. t. 36. e C 92 = After the spll perod (R=) Ce C. 92 e. t 92. 36 C C k.. 8 C k 92 Ce k 92 996 992 Oxygen concentraton C 988 98 98 976 972 968 96 96 2 6 8 2 6 8 2 Tme [hr]
The partal pressure: PO2 C. Pa The fatalty factor: 6.5 G PO2 F f G,, f G <. 7,, G F 92 ODH fatalty rate: φ 3. 6 6. F φ 92 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH 6 2 8 2 3 6 2 8 2 3 Tme [hr] Tme [hr] Case 2. The normal operaton of 5L LHe and L LN2 vessel The normal vaporzaton rate: 3 days Rn Rn2 5. 72. 36. 72. 36 [m 3 /s] Rn =.736. 7 [m 3 /s] [m 3 /s] Rn2 =.53. 7 [m 3 /s] R Rn. ρfv ρhe R =.333. R2 Rn2. ρfn ρn2 R2 =.77. R2 R R2 R2 = 2.. [m 3 /s] <. [m 3 /s] t 3. 2 t = 72 [hr] t. 36 = 2.592. 5 [s] R2 CC.5... R2 R2 < C2. R2. t. 36. e C2 72 = After the spll perod (R=). t 72. 36 Ce C2. 72 e C C2 k.. 28 C k 72 Ce k 72 5
Oxygen concentraton C 99 98 97 96 95 9 93 92 9 9 2 3 5 6 7 8 9 Tme [hr] The partal pressure: PO2 C. Pa The fatalty factor: 6.5 G PO2 F f G,, f G <. 7,, G F 72 ODH fatalty rate: φ 3. 6 6. F φ 72 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH 2 6 8 2 6 8 Tme [hr] Tme [hr] Case 3. LHe vessel n EBC Cryostat broken, and the vacuum s lost m_he.379 [kg/s] t Mhe m_he t = 5.2 [s] R3 m_he ρhe [m 3 /s] R3 = 2.33 [m 3 /s] >. [m 3 /s] R3 = CC.98. 3 6
.. 6 R3 > C3 R3.. e C3 5 8 After the spll perod (R=). t 5. 36 Ce C3. 5 e C C3 k.. 5 C k 5 Ce k 5 95 9 Oxygen concentraton C 85 8 75 7 65 6 55 5 6 2 8 2 3 36 2 8 5 6 Tme [sec-hr] The partal pressure: PO2 C. Pa The fatalty factor: G 6.5 PO2 F f G,, f G <. 7,, G F 5 ODH fatalty rate: φ 3. 6 6. F φ 5 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme 7
Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH 2 2 36 8 6 2 2 36 8 6 Tme [s] Tme [s] Case. LN2 vessel n EBC Cryostat broken, and the vacuum s lost m_n2.3 [kg/s] t Mn2 m_n2 t = 776.256 [sec] R m_n2 ρn2 [m 3 /s] R.37 [m 3 /s] <. [m 3 /s] R CC = 78.57.. R < C. R. R. e C 776 8. The oxygen concentraton after the spll perod (R=, =const). t 776. 36 Ce C. 776 e C C k.. 22 C k 776 Ce k 776 95 9 Oxygen concentraton C 85 8 75 7 65 6 55 5 2 3 5 6 7 8 9 Tme [sec-hr] 8
The partal pressure: PO2 C. Pa The fatalty factor: G 6.5 PO2 F f G,, f G <. 7,, G F 776 ODH fatalty rate: φ 3. 6 6. F φ 776 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH 2 6 8 2 6 8 Tme [s] Tme [s] Case 5. LHe e_bubble Chamber broken, and the vacuum s lost me_he.37 [kg/s] t Mhee me_he t = 3.975 [s] R5 me_he ρhe [m 3 /s] R5 = 26 [m 3 /s] >. [m 3 /s] R5 CC = 78.528.. 3 R5 > C5 R5.. e C5 = After the spll perod (R=). t. 36 Ce C5. e C C5 k.. 26 C k Ce k 9
Oxygen concentraton C 997 99 99 988 985 982 979 976 973 97 3 6 9 2 5 8 2 2 27 3 Tme [sec-hr] The partal pressure: PO2 C. Pa The fatalty factor: 6.5 G PO2 F f G,, f G <. 7,, G F 5 ODH fatalty rate: φ 3. 6 6. F φ 5 ODH Classfcaton: ODH <. 7,, <. 5,, <. 3, 2, <., 3, tme Fatalty rate va tme ODH class va tme Fatalty rate [/hr] φ ODH class ODH 6 2 8 2 3 6 2 8 2 3 Tme [s] Tme [s]
Concluson Fatalty factor = 3*-6 Fatalty rate < -9 ODH class Under the worst case condton, fatalty rate s lower than -9 for Nevs e-bubble Chamber Cryostat at Atlas Buldng. Therefore, ODH s unclassfed accordng to "BNL ODH Rsk Assessment".