Expansion Vessel Sizing Calculator

Technical Notes

Variable Definitions

• V_piping: Total liquid volume inside piping included in the system (m³).
• V_equipment: Sum of liquid holdup volumes for connected equipment (m³).
• V_vessel@LLL: Liquid volume inside the expansion vessel at LLL (m³).
• V_sys,cold: Total system liquid volume at cold condition, V_piping + V_equipment + V_vessel@LLL (m³).
• ρ_min: Liquid density at minimum temperature (cold condition, highest density) (kg/m³).
• ρ_max: Liquid density at maximum temperature (hot condition, lowest density) (kg/m³).
• V_exp: Theoretical expansion volume required to accommodate heating from Tmin → Tmax (m³).
• Margin: Design margin (%) applied to the theoretical expansion volume.
• V_exp,design: Expansion volume including margin (m³).
• V_holdup: Available vessel volume between LLL and HLL, V(HLL) − V(LLL) (m³).

Formulas / Logic

• Mass conservation for incompressible liquid (screening approach): as temperature increases, density decreases and the same mass occupies more volume.
• 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
• Piping internal volume for each line item: V = (π × ID² / 4) × Length, where ID = OD − 2×WT.
• Vessel holdup geometry:
  • Vertical: bottom head volume (full) + cylindrical volume up to the entered level (levels measured from bottom tangent line).
  • Horizontal: cylindrical segment area × length + approximate head contribution (screening).

Assumptions / Notes

• 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.
• Enter densities at Tmin and Tmax from reliable property data (e.g., lab data, process simulator, supplier curves). Ensure ρ_min > ρ_max.
• 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.
• For horizontal vessels, head holdup is approximated; if high accuracy is required, use 3D geometry/GA drawings or vendor-provided level/volume tables.
• Typical margin selection is project-dependent; many designs use 10–25% depending on uncertainty and future tie-ins.

Reference Standards / Guidance (typical)

• ASME Boiler and Pressure Vessel Code (Section VIII) for pressure vessel design and construction (mechanical integrity).
• API 521 for guidance on pressure-relieving and depressuring systems (system philosophy context).
• Project/company engineering practices often define expansion/accumulator sizing basis for closed-loop liquid systems (levels, margins, allowable operating band).