Sizing of relief valves for supercritical fluids March 23 rd , 2011 Alexis Torreele
Sizing of relief valves for supercritical fluids
March 23rd, 2011
Alexis Torreele
Overview
� Jacobs – Introduction
�Relief Valve Study – An Engineering Approach
�Relief Calculation for Supercritical Fluids− Introduction− Theoretical Background− Example Case− Discussion & Evaluation
Jacobs
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Relief Valve Study
An Engineering Approach
Relief Valve Study – An Engineering Approach
� Gather info:− P&ID’s− Equipment data − Etc.
� Define relief scenario’s:− E.g.: External fire, Blocked outlet, etc.− Use list API 521 as guidance− Use tools as HAZOP, PLANOP , client specific methods
to determine applicable scenarios
Relief Valve Study – An Engineering Approach
� Calculate relief scenario’s− Relief load− Relief valve orifice size
� Determine governing case− General approach:
Scenario requiring the largest orifice size =
Governing case
Relief Valve Study – An Engineering Approach
� Verify inlet and outlet conditions− Pressure drop over inlet (< 3% of set pressure)− Pressure at outlet (backpressure):
� Superimposed backpressure : static pressure (if variable: NO conventional type valve)
� Built-up backpressure : pressure increase as result of relief flow (< 10% for conventional, < ca. 50% for balanced & > 50% for pilot operated type valves)
Relief Valve Study – An Engineering Approach
� Determine safety valve type:− Conventional spring-loaded− Balanced bellows − Pilot operated
� Mechanical stress analysis
� Flare network study
Relief Calculation for Supercritical Fluids
Introduction
� Objective:Calculate mass relief flow , volume relief flow and required orifice size of heat-input driven relief cases on systems with supercritical relief temperature and/or pressure.
� Examples:− Fire case for a Vessel− Blocked-in Heat Exchanger
� References: R. Ouderkirk , “Rigorously Size Relief Valves for Supercritical Fluids,” CEP magazine, pp. 34-43 (Aug. 2002). L. L. Simpson , “Estimate Two-Phase Flow in Safety Devices,” Chem. Eng., pp. 98-102, (Aug. 1991).
Theoretical Background
� Definition of enthalpy:H = U + pV (1)
dH = dU + Vdp + pdV (2)
dU = δQ – pdV (3)
Combining (2) & (3)
dH = δQ + Vdp (4)
p is constant during relief; hence,
∆H = Q (5)
And,
∆∆∆∆H/∆∆∆∆t = Q (6)
Theoretical Background
� Heat input = Enthalpy change
Hi (∆H)p Hi+1
∆t * Q
Vi ∆t Vi+1
∆∆∆∆V////∆∆∆∆tH: Specific enthalpyV: Specific volumeQ: Heat inputt: Time
Example Case – Information
� Fire case for a Vessel� Process Data (normal operation):
− Content: Methane� Crit. Temp. -82,7 °C� Crit. Press. 45,96 bara
− Level: 60% Liquid− Pressure: 10 barg− Temperature: -122 °C− Volume: 10 m³− Area: 25 m²
Qfire
SP
50barg
Example Case – Relief Process Overview
� 1 → 2 Heating before Relief: ‘Isochoric’ processNo volume or mass change (no relief)
� 2 → 3 Relief: Isentropic flashAdiabatic & frictionless flow through relief valve
� 2 → 2’ Relief Progression: Isobaric processSystem at constant pressure (i.e. relief pressure)
P-E Diagram of Methane
0.1
1
10
100
-100 100 300 500 700 900 1100 1300 1500
Enthalpy (kJ/kg)
Pressure (bar)
δ = 1kg/m3
δ = 0,1kg/m3
δ = 10kg/m3
δ = 100kg/m3
T = 10
0K
T = 20
0K
T = 15
0K
T = 30
0K
T = 40
0K
T = 50
0K
1
2 2'
3 3'
+ Qfire
+ Qfire
Density [kg/m³] - Temperature [K] - Entropy [kJ/(kgK)]
δ = 400kg/m3
Relief Press.
Example Case – Calculation Steps
� Step 1: Select Property Method� Step 2: Gather Relief Case Information� Step 3: Determine Heat Input� Step 4: Calculate Physical Properties� Step 5: Calculate Relief Flow Rate� Step 6: Determine Isentropic Choked Nozzle Flux� Step 7: Determine Required Orifice Size
Example Case – Step 1
Select Property Method
� Requirements:− Suitable for respective component(s)− Accurate for the relevant pressure and temperature range
(Pr > 1 // Tr > 1)− Accurate for both liquid and gas properties
� Important: Always verify property method with empirical property data!
Example Case – Step 1
� Selected Method: Lee Kesler− Fit for light hydrocarbons− Application range
Pr : 0 to 10 (up to ca. 460 bara)
Tr : 0,3 to 4 (ca. -216 to 485 °C)
− One correlation for both liquid as well as vapor phase→ No distinguishable transition from supercritical ‘liquid’ to
supercritical ‘vapor’
− Integration of the thermal properties with the other physical properties→ Thermodynamic cohesiveness
Example Case – Step 2
Gather Relief Case Information
� Relief pressure:PSV set press.: 50 bargFire case relief press.: 121 % of set pressure
Relief press.: 61,5 bara (Pr = 1,3)
� Initial relief temperature:Considering an isochoric process:
(Tini(pini))ρini → (Trlf (prlf))ρini
(Tini(10barg))ρini → (Trlf(61,5barg))ρini
-122°C → -77°C
Example Case – Step 3
Determine Heat Input
� API 521 – external pool fire, heat absorption for liquids:
Qfire = 43.200 * f * αααα0,82
With f = 1 (no fireproof insulation / bare metal vessel)
α = 25 m²
Qfire = 605,05 kW= 2.178.196 kJ/h
αααα: Wetted surface [m²]f: Environment factor [-]Q: Heat input [W]
Example Case – Step 4
Calculate Physical Properties
� Determine the specific volume (V), specific enthalpy (H) & entropy (S) at initial relief conditions:− Applying property method correlations in Excel spreadsheets− Using property models in Simulation Tools (Pro/II, Aspen Plus, etc.)
� Reiterate at increasing temperatures:− At relief pressure− Step size: ca. 3°C− # iterations: see later
P-E Diagram Methane
0.1
1
10
100
-100 100 300 500 700 900 1100 1300 1500
Etnhalpy (kJ/kg)
Pressure (bar)
δ = 1kg/m3
δ = 0,1kg/m3
δ = 10kg/m3
δ = 100kg/m3
T =
100K
T =
200K
T =
150K
T =
300K
T =
400K
T =
500K
1
2 2'
3 3'
+ Qfire
+ Qfire
Density [kg/m³] - Temperature [K] - Entropy [kJ/(kgK)]
δ = 400kg/m3
Example Case – Step 4
0,01459-8,710,079-38
0,01414-18,710,036-41
0,01303-43,79,927-47
0,01259-53,79,882-50
0,01193-68,79,814-53
0,01127-83,79,746-56
0,01062-98,79,676-59
0,00978-118,79,582-62
0,00896-138,79,487-65
0,00781-168,79,341-68
0,00662-203,79,169-71
0,00527-253,78,920-74
0,00455-288,78,742-77
V, m3/kgH, kJ/kgS, kJ/(kg.K)T, °C
Example Case – Step 5
Calculate Relief Flow Rate
� Volumetric flow rate:
� Mass flow rate:
HV
QV∆∆= &&
VV
m&
& =
H: Specific enthalpy [kJ/kg]V: Specific volume [m³/kg]V: Volume flow [m³/s]m: Mass [kg]m: Mass flow [kg/s]Q: Heat input [kW]
Example Case – Step 5
-
1,899
2,061
2,124
2,232
2,340
2,448
2,588
2,714
2,849
2,891
2,710
2,389
m, kg/s
0,01459
0,01414
0,01303
0,01259
0,01193
0,01127
0,01062
0,00978
0,00896
0,00781
0,00662
0,00527
0,00455
V, m3/kg
-
0,02686
0,02687
0,02674
0,02662
0,02638
0,02602
0,02532
0,02432
0,02227
0,01916
0,01427
0,01088
V, m3/s
-8,710,079-38
-18,710,036-41
Max. volume flow-43,79,927-47
-53,79,882-50
-68,79,814-53
-83,79,746-56
-98,79,676-59
-118,79,582-62
-138,79,487-65
-168,79,341-68
Max. mass flow-203,79,169-71
-253,78,920-74
-288,78,742-77
H, kJ/kgS, kJ/(kg.K)T, °C
Example Case – Step 6
Determine Isentropic Choked Nozzle Flux
� For ‘each’ relief temperature calculate the chokednozzle flux:− Iteratively, at decreasing
outlet pressure:
− And, along isentropic path:
− Max. flux = Choked flux
( )b
b0
V
HH2G
−=
b0 SS =H: Specific enthalpy [J/kg]V: Specific volume [m³/kg]G: Mass flux [kg/(m².s)]S: Entropy [kJ/(kg.K)]
0: Inlet condition
b: Outlet condition
P-E Diagram Methane
0.1
1
10
100
-100 100 300 500 700 900 1100 1300 1500
Etnhalpy (kJ/kg)
Pressure (bar)
δ = 1kg/m3
δ = 0,1kg/m3
δ = 10kg/m3
δ = 100kg/m3
T = 1
00K
T = 2
00K
T = 1
50K
T = 3
00K
T = 4
00K
T = 5
00K
1
2 2'
3 3'
+ Qfire
+ Qfire
Density [kg/m³] - Temperature [K] - Entropy [kJ/(kgK)]
δ = 400kg/m3
Example Case – Step 6
� Relief temperature: -68 °C
17479
17931
18058
16496
14009
10248
-
G, kg/(m².s)T0, p0:
-185,00,0130934,5-92
-179,50,0113439,0-88: GChoked
-174,70,0098843,5-85
-170,40,0092448,0-80
-166,40,0087852,5-76
-162,50,0084057,0-72
-158,80,0080861,5-68
Hb, kJ/kgVb, m³/kgpb, baraTb, °C
Example Case – Step 6
� Iteration = time consuming process!!
� Alternative method: use simplified correlations to determine isentropic choked flux− J.C. Leung , “A Generalized Correlation for One-component
Homogeneous Equilibrium Flashing Choked Flow,” AIChE Journal, pp. 1743-1746 (Oct. 1986).
−0
0choked V
pG
⋅=
ωη
ATTENTION: 2-phase flow
� Relief of supercritical fluids can lead to 2-phase flow!
� Homogenous Equilibrium Model (HEM)Assumptions1. Velocities of phases are equal2. Phases are at thermodynamic equilibrium
� Formula applies:
And H = xL.HL + (1-xL).HG
V = xL.VL + (1-xL).VG
( )b
b0
V
HH2G
−=
H: Specific enthalpy [J/kg]V: Specific volume [m³/kg]G: Mass flux [kg/(m².s)]
0: Inlet condition
b: Outlet condition
L: Liquid phase
G: Gas phase
Example Case – Step 7
Determine Required Orifice Size
• API 521:
With backpressure correction, Kb = 1 (backpressure << 10%)
combination correction, Kc = 1 (no rupture disk)
discharge coefficient, Kd = 0,975 (assuming vapor)
viscosity correction, Kv = 1
vdcbchoked KKKKGm
A&
=
A: Effective orifice area [m²]m: Mass flow [kg/s]Gchoked : Choked mass flux [kg/(m².s)]
Example Case – Step 7
-
1,899
2,061
2,124
2,232
2,340
2,448
2,588
2,714
2,849
2,891
2,710
2,389
m, kg/s
-
-
-
141
-
-
-
-
152
155
153
-
96
A, mm²
0,01459
0,01414
0,01303
0,01259
0,01193
0,01127
0,01062
0,00978
0,00896
0,00781
0,00662
0,00527
0,00455
V, m3/kg
-
0,02686
0,02687
0,02674
0,02662
0,02638
0,02602
0,02532
0,02432
0,02227
0,01916
0,01427
0,01088
V, m3/s
-8,710,079-38
-18,710,036-41
-43,79,927-47
-53,79,882-50
-68,79,814-53
-83,79,746-56
-98,79,676-59
-118,79,582-62
-138,79,487-65
Req. Nozzle Size-168,79,341-68
-203,79,169-71
-253,78,920-74
-288,78,742-77
H, kJ/kgS, kJ/(kg.K)T, °C
Calculation Results
40%
50%
60%
70%
80%
90%
100%
200 210 220 230 240 250
Temperature (K)
Orifice Area
Volume Relief Rate
Mass Relief Rate
Example Case – Results
� When all values (relief volume flow, mass flow and nozzle size) decrease with increasing relief temperature: stop iterations.
� Determine selected effective orifice (API 526) based on maximum calculated nozzle size value:− Max. nozzle size value: 155 mm²− Selected standard orifice: 198 mm² (‘F’ - orifice)
� Calculate pressure drop over inlet and discharge
� Determine safety valve type (conventional, balanced bellows, pilot operated…)
� …
Example Case – Conclusions
� Specific calculation method is required:
− Fluids that are below critical conditions in normal operation can have super critical relief
− Max. mass flow ≠ Max. volume flow ≠ Min. required nozzle size
− Required nozzle size determined using a simplified method (API 521 §5.15.2.2.2): 254 mm² vs. 155 mm²
Extra Slides
Safety Valve Types
Bellows
Pilot
Conventional BalancedBellows
Pilot Operated
General flux equation
( )( )
( )
−+⋅
−+
−+−=
∫
t
2
2
fg
P
Pfg
2
x1xSv)x1(S
xv
dpv)x1xv2
G
t
r