Output Data
Total Piping Volume:
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Total Equipment Volume:
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LLL Volume in Vessel:
-
Total System Volume (Cold @ LLL):
-
HLL Volume in Vessel:
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Expansion Calculation
Volume Increase Factor:
-
Expansion Volume Required (Theoretical):
-
Expansion Volume (with Margin):
-
Vessel Capacity Check
Available Holdup Volume (LLL → HLL):
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Is Vessel Sized Adequately?
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Formulas Used
Vsys,cold = Vpiping + Vequipment +
Vvessel@LLL
Vexp = Vsys,cold × [(ρmin /
ρmax) − 1]
Vexp,design = Vexp × (1 + Margin%)
Technical Notes
Variable Definitions
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Vpiping: Total liquid volume inside piping included in the system (m³).
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Vequipment: Sum of liquid holdup volumes for connected equipment (m³).
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Vvessel@LLL: Liquid volume inside the expansion vessel at LLL (m³).
-
Vsys,cold: Total system liquid volume at cold condition,
V_piping + V_equipment + V_vessel@LLL (m³).
-
ρmin: Liquid density at minimum temperature (cold condition, highest
density) (kg/m³).
-
ρmax: Liquid density at maximum temperature (hot condition, lowest
density) (kg/m³).
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Vexp: Theoretical expansion volume required to accommodate heating from
Tmin → Tmax (m³).
-
Margin: Design margin (%) applied to the theoretical expansion
volume.
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Vexp,design: Expansion volume including margin (m³).
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Vholdup: Available vessel volume between LLL and HLL,
V(HLL) − V(LLL) (m³).
Formulas / Logic
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Mass conservation for incompressible liquid (screening
approach): as temperature increases, density decreases and the same
mass occupies more volume.
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Volume increase factor:
f = (ρ_min / ρ_max) − 1 (dimensionless)
-
Theoretical expansion volume:
V_exp = V_sys,cold × f
-
Design expansion volume:
V_exp,design = V_exp × (1 + Margin/100)
-
Adequacy check: vessel is adequate if
V_holdup ≥ V_exp,design
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Piping internal volume for each line item:
V = (π × ID² / 4) × Length, where
ID = OD − 2×WT.
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Vessel holdup geometry:
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Vertical: bottom head volume (full) + cylindrical volume up
to the entered level (levels measured from bottom tangent line).
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Horizontal: cylindrical segment area × length + approximate
head contribution (screening).
Assumptions / Notes
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This tool is intended for screening / preliminary sizing based
on liquid density change with temperature. For final design, confirm
with project specifications, detailed vessel geometry, operating
philosophy, and vendor review.
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Enter densities at Tmin and Tmax from reliable property data
(e.g., lab data, process simulator, supplier curves). Ensure
ρ_min > ρ_max.
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For vertical vessels, LLL/HLL are assumed measured from the
bottom tangent line; the top head is treated as vapour space in
this screening model.
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For horizontal vessels, head holdup is approximated; if high
accuracy is required, use 3D geometry/GA drawings or vendor-provided
level/volume tables.
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Typical margin selection is project-dependent; many designs use
10–25% depending on uncertainty and future tie-ins.
Reference Standards / Guidance (typical)
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ASME Boiler and Pressure Vessel Code (Section VIII) for
pressure vessel design and construction (mechanical integrity).
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API 521 for guidance on pressure-relieving and depressuring
systems (system philosophy context).
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Project/company engineering practices often define
expansion/accumulator sizing basis for closed-loop liquid systems
(levels, margins, allowable operating band).