Vessel depressurization modeling

• Flare system

– Most pressure vessels on topsides must be operated under the allowable

pressure. The overpressure would cause damage of vessels, leak of

hydrocarbons, fire or explosion.

– Depressurization: A process of rapidly removing the fluid in the pressure

vessel when an overpressure occurs in the pressure vessel.• ex) API: Decrease to 50% of maximum allowance working pressure(MAWP) or 690kPa

– The discharged gas is flared.

(New York Times,2007.10.13)

Problems

• One of the most big and long piping on an offshore platform.Big cost impact

• If it fails, the hydrocarbon is leakedBig safety impact, a conservative design is required.

• Therefore, if the initial design has problems, Critical for whole project

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Depressurization analysis

• Relief load Calculation

• Low temperature analysis

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Fire caseMaximum heat

influxMaximum discharge

rateValve sizing

Relief load calculation

As the valve size increases, the size of flare system also increases.

AdiabaticCase

Expansion with lack of heat

influx

Temperature drop to DBTT

Vessel material property

Low temperature

analysis

※ DBTT: Ductile to Brittle Transition Temperature

Requires stronger material for vessel and flare system.

Limitation of some commercial software

• Comparison with experimental results (Haque et al.,1990) and simulation results of Aspen HYSYS v8.8 Depressuring Utility

– Initial condition: 150bar, 290K, depressurization to atmospheric pressure

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Phenomena during blowdown

• The pressure inside the vessel rapidly drops, resulting in phase transition inside.

• Because it is too rapid, the equilibrium assumption inside the vessel is not valid. – Pressure drops due to discharge– Expansion of the fluid in the vessel– Temperature drop due to the expansion– Liquid droplet nucleation and condensation– Vaporization of liquid due to hotter wall temperature– Repeated liquid pooling and boiling– Continuous temperature drop of vessel wall

contacting liquid

Main Algorithm

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- The purpose of this model is to obtain the thermodynamic propertiesand conditions of the fluid and the wall which change with suddenpressure drop.

- The pressure decreasing at a fixed rated for each step, the properties andtime interval.

𝑷𝒊 = 𝟎. 𝟗𝟓𝑷𝒊−𝟏

- Coexisting in the pressure vessels, gas and liquid phases become non-equilibrium. → Temperature of phases is different → Material and energyexchange occur between two phases.

- Definite ‘evaporated liquid’ and ‘condensed vapor’ calculated by flashcalculation of each phase at any phase.

- Main Assumption

∙ Equilibrium inside liquid or gas

∙ Ignore vaporization and condensation time at each pressure stage

∙ Expansion with Polytropic path

Main Algorithm

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Calculate the pressure at current stage𝑷𝒊 = 𝟎. 𝟗𝟓𝑷𝒊−𝟏

Assume time interval (∆𝒕′),Entropies for each phases (𝒔𝒁𝟏

′, 𝒔𝒁𝟐′)

Calculate composition and amount of evaporated liquid according to Ps-flash

Calculate heat transfer of zone 2, the temperature of the wall contacted

with zone 2

Update Entropies of Zone 2 (𝒔𝒁𝟐)

𝑠𝑧2 =𝑇𝑧2𝑖 𝑠𝐿

𝑖−1𝑁𝐿𝑖−1 + 𝑠𝐶𝑉

𝑖−1𝑁𝐶𝑉𝑖−1 + 𝑄𝑖𝑛,𝑧2

𝑖

𝑇𝑧2𝑖 𝑁𝐿

𝑖−1 + 𝑁𝐶𝑉𝑖−1

Calculate composition and amount of Condensed vapor according to Ps-flash

Calculate discharged flow rate through the

valve

Calculate heat transfer of zone 1, the temperature of the wall

contacted with zone 1

Update Entropies of Zone 2 (𝒔𝒁𝟐)

𝑠𝑧1 =𝑇𝑧1𝑖 𝑠𝑉

𝑖−1𝑁𝑉𝑖−1 + 𝑠𝐸𝐿

𝑖 𝑁𝐸𝐿𝑖 +𝑄𝑖𝑛,𝑧1

𝑖

𝑇𝑧1𝑖 𝑁𝑉

𝑖−1 + 𝑁𝐸𝐿𝑖

Calculate time interval(∆𝒕)

∆𝒕 = ∆𝒕′ &𝒔𝒁𝟐 = 𝒔𝒁𝟐

′ & 𝒔𝒁𝟏 = 𝒔𝒁𝟏′ ?

Go to the next pressure stageYes No

Zone 1

𝑉𝑖−1 𝐶𝑉𝑖−1

𝐿𝑖−1

𝑉𝑖−1

𝐿𝑖−1 𝐶𝑉𝑖−1

𝑉𝑖−1

𝐿𝑖 𝐸𝐿𝑖

𝑉𝑖−1

𝐿𝑖

𝐸𝐿𝑖

Zone 2

𝑉𝑖

𝐿𝑖

𝐶𝑉𝑖

𝐷𝑖

𝐿𝑖

𝑉𝑖 𝐶𝑉𝑖

𝐷𝑖

Equilibrium

Equilibrium𝑃𝑖−1∗ → 𝑃𝑖∗

𝑃𝑖𝑠𝑧2𝑖 Flash

Heat & mass

transfer 𝑃𝑖𝑠𝑧1𝑖 Flash Discharge

Heat transfer between air and wall

• Heat transfer between external air and outer wall– Consider natural convection only

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𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟖𝟐𝟓 +𝟎. 𝟑𝟖𝟕𝑹𝒂𝟏/𝟔

𝟏 + 𝟎. 𝟓𝟗𝟐/𝑷𝒓 𝟗/𝟏𝟔 𝟖/𝟐𝟕

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟐𝟕𝑹𝒂𝟏/𝟒 𝟏𝟎𝟓 ≤ 𝑹𝒂 ≤ 𝟏𝟎𝟏𝟎

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟓𝟒𝑹𝒂𝟏/𝟒 𝟏𝟎𝟒 ≤ 𝑹𝒂 ≤ 𝟏𝟎𝟕

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟏𝟓𝑹𝒂𝟏/𝟒 𝟏𝟎𝟕 ≤ 𝑹𝒂 ≤ 𝟏𝟎𝟏𝟏

(Churchill & Chu, 1975)

(Cengel & Ghajar, 2011)

(Cengel & Ghajar, 2011)

Heat transfer between gas and wall

• Heat transfer between the internal vapor and the wall contacting vapor – Consider combined convection of natural convection

and forced convection

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Nusselt numberfor natural convection

Side of the wall(Churchill & Chu’s Correlation)

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟖𝟐𝟓 +𝟎. 𝟑𝟖𝟕𝑹𝒂𝟏/𝟔

𝟏 + 𝟎. 𝟓𝟗𝟐/𝑷𝒓 𝟗/𝟏𝟔𝟖/𝟐𝟕

Top/bottom of the wall(McAdams’ Correlation)

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟐𝟕𝑹𝒂𝟏/𝟒 𝟏𝟎𝟓 ≤ 𝑹𝒂 ≤ 𝟏𝟎𝟏𝟎

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟓𝟒𝑹𝒂𝟏/𝟒 𝟏𝟎𝟒 ≤ 𝑹𝒂 ≤ 𝟏𝟎𝟕

𝑵𝒖𝒏𝒂𝒕 = 𝟎. 𝟏𝟓𝑹𝒂𝟏/𝟒 𝟏𝟎𝟕 ≤ 𝑹𝒂 ≤ 𝟏𝟎𝟏𝟏

Nusselt numberfor forced convection

Side of the vessel(Gnielinski’s Correlation)

𝑵𝒖𝒇𝒐𝒓 =𝒇/𝟖 𝑹𝒆 − 𝟏𝟎𝟎𝟎 𝑷𝒓

𝟏. 𝟎𝟕 + 𝟏𝟐. 𝟕 𝒇/𝟖 𝟎.𝟓 𝑷𝒓𝟎.𝟔𝟕 − 𝟏

Top/bottom of the vessel(Churchill & Ozoe’s Correlation)

𝑵𝒖𝒇𝒐𝒓 =𝟏. 𝟏𝟐𝟖𝑷𝒓𝟎.𝟓𝑹𝒆𝟎.𝟓

𝟏 + 𝟎. 𝟎𝟒𝟔𝟖/𝑷𝒓 𝟎.𝟔𝟕 𝟎.𝟐𝟓

𝑵𝒖𝒄𝒐𝒎𝒃 = 𝑵𝒖𝒏𝒂𝒕 𝟑 + 𝑵𝒖𝒇𝒐𝒓𝟑

𝟏/𝟑

Heat transfer between liquid and wall

• Pool boiling phenomenon– The boiling phenomenon that the temperature of the inner wall

contacted with liquid is higher than the boiling point of the

internal liquid.

– Nucleate boiling is considered in this model.

10Shiro Nukiyama. (1934). The Maximum and Minimum Values of the Heat Q Transmittedfrom Metal to Boiling Water under Atmospheric Pressure

Nucleate boiling

Critical heat flux

Transition boiling

Film boiling

Wolverine tube, Inc. Engineering Data BookⅢ

Simulation results verification

• The result was compared with the previous studies and commercial software for verification.

– Previous studies: BLOWDOWN (Haque, Richardson et al., 1992),

BLOWSIM (Mahgerefteh and Wong, 1999), BLOW (Speranza and Terezi,

2005), VBsim (D’Aleesandro and Valero et al., 2015)

– Commercial softwares: HYSYS v.9, VessFire1.2

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<Pressure changes in the pressure vessel over time during depressurization>

Case 1 Case 2 Case 3

Simulation results verification

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Internal vapor temperature

Case 1 Case 2 Case 3

Internal liquid temperature

Simulation results verification

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Wall contacted with vapor

Wall contacted with liquid

<Temperature changes of the wall in the pressure vessel over time during depressurization>

Future works

• Extension of these works to tail piping, flare header, and flare system.

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