Pipeline Operations

Gas Rate Time Calculations

Calculate gas inventory, fill time, blowdown timing, and line pack operations for pipeline pressurization, purging, and depressurization activities using real gas equations.

Launch Calculator Gas inventory

Line pack

5-15% capacity

Gas inventory in pipelines provides operational flexibility: 5-15% of daily throughput stored as line pack.

Fill time

Hours to days

Pressurization time depends on compressor capacity, pipeline volume, and target pressure differential.

Blowdown rate

10-50 MMscfd

Typical emergency blowdown rates: 10-50 MMscfd through flare or vent headers depending on size.

Contents

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1. Basic Relationships

Gas inventory, flow rate, and time are connected through the fundamental relationship: Volume = Rate × Time. For compressible gas, pressure and temperature must be considered.

Basic Equations

Fundamental relationship: Volume = Rate × Time V = Q × t Rearranged: t = V / Q (time to fill or empty) Q = V / t (rate needed for given time) For gas at pressure: V_scf = V_actual × (P/P_std) × (T_std/T) × (1/Z)

Unit Conversions

Rate Unit To SCFH To SCFM
MMSCFD × 41,667 × 694.4
MSCFH × 1,000 × 16.67
SCFM × 60 × 1
ACFM (at P, T) × 60 × P/14.7 × 520/T / Z × P/14.7 × 520/T / Z

2. Gas Inventory Calculations

Gas inventory in a vessel or pipeline depends on physical volume, pressure, temperature, and compressibility.

Inventory Formula

Standard cubic feet in a volume: SCF = V × (P / 14.73) × (520 / T) × (1 / Z) Where: V = Physical volume (ft³) P = Pressure (psia) T = Temperature (°R = °F + 460) Z = Compressibility factor 14.73 = Standard pressure (psia) 520 = Standard temperature (°R) Simplified (Z ≈ 1, T = 60°F): SCF ≈ V × P / 14.73

Pipeline Line Pack

Line pack for pipeline: LP (SCF) = 0.0283 × d² × L × 5,280 × P_avg / (T × Z) Where: d = Inside diameter (inches) L = Length (miles) P_avg = Average pressure (psia) Rule of thumb: For typical conditions (T ≈ 520°R, Z ≈ 0.9): LP (MSCF) ≈ 0.167 × d² × L × P_avg / 1,000

Vessel Inventory

Horizontal cylinder: V (ft³) = π × D² × L / 4 / 144 [D, L in inches] Sphere: V (ft³) = π × D³ / 6 / 1,728 [D in inches] Then apply gas law: SCF = V × P × 35.37 / (T × Z)

Example: Pipeline Inventory

Given: 20" × 0.500" pipeline, 50 miles, 800 psia average, 60°F, Z = 0.88

d = 20 - 1.0 = 19 inches
V = 0.00545 × 19² × 5,280 × 50 = 5.20 MM ft³

SCF = 5.20×10⁶ × 800 × 35.37 / (520 × 0.88)
SCF = 322 MMSCF line pack

3. Fill Time

Time to pressurize a system depends on volume, target pressure, and available flow rate.

Constant Rate Fill

Fill time at constant standard rate: t = (V₂ - V₁) / Q Where: V₂ = Final inventory (SCF) V₁ = Initial inventory (SCF) Q = Flow rate (SCF/time) t = Time (same units as Q) Pressure increase: ΔP = P₂ - P₁ = (Q × t × T × Z) / (V × 35.37)

Vessel Pressurization

Time to pressurize vessel: t (min) = V × (P₂ - P₁) × 35.37 / (Q_scfm × T × Z) Simplified (standard T, Z ≈ 0.9): t (min) ≈ V × ΔP / (Q_scfm × 16.4) Where: V = Vessel volume (ft³) ΔP = Pressure increase (psi) Q_scfm = Fill rate (SCFM)

Example: Vessel Fill Time

Given: 1,000 gallon vessel (134 ft³), fill from 0 to 500 psig at 50 SCFM

Final SCF = 134 × 514.7 × 35.37 / (520 × 0.95)
Final SCF = 4,940 SCF

t = 4,940 / 50 = 99 minutes

4. Blowdown Time

Blowdown (depressurization) is not constant-rate—flow decreases as pressure drops through a restriction.

Choked Flow Blowdown

Blowdown through orifice (critical flow): t = (V / (C × A × k)) × [(P₁/P₂)^((k-1)/k) - 1] × √(MW × T / (Z × R)) Simplified API 521 approach: t (minutes) ≈ V × ln(P₁/P₂) × 13.5 × √(MW × T × Z) / (A × P₁ × C_d) Where: C_d = Discharge coefficient (≈ 0.62–0.85) A = Orifice area (in²) k = Specific heat ratio (Cp/Cv)

Approximate Blowdown Time

Quick estimate (natural gas): t (sec) ≈ 1.5 × V × ln(P₁/P₂) / (A × C_d × √P₁) Where: V = Volume (ft³) P₁ = Initial pressure (psia) P₂ = Final pressure (psia) A = Orifice area (in²) For depressuring to 50% of initial: ln(P₁/P₂) = ln(2) = 0.693

API 521 Depressuring Rate

Target depressuring rate: Reduce to 50% of initial or 100 psig (whichever is lower) in 15 minutes Required orifice sizing: Size restriction to achieve required rate based on vessel volume and initial pressure.

Example: Blowdown Time

Given: 500 ft³ vessel at 1,000 psig, blowdown through 1" orifice (0.785 in²), C_d = 0.7

Blowdown from 1015 psia to 115 psia (100 psig):
ln(1015/115) = ln(8.83) = 2.18

t ≈ 1.5 × 500 × 2.18 / (0.785 × 0.7 × √1015)
t ≈ 1,635 / (0.55 × 31.9)
t ≈ 93 seconds

Temperature effect: Rapid blowdown causes significant cooling (Joule-Thomson effect). Final gas temperature can drop below -100°F, potentially causing brittle fracture concerns with carbon steel.

5. Applications

Common Uses

Application Calculation Purpose
Pipeline operations Line pack changes, pack/draft times
Compressor startup Suction header pressurization time
Emergency depressuring BDV sizing, blowdown time verification
Purging operations Nitrogen volume and time requirements
Leak testing Pressure decay rate analysis
Storage operations Injection/withdrawal scheduling

Line Pack Management

Pack/Draft calculation: ΔLP = LP₂ - LP₁ = f(ΔP_avg) Time for pressure change: t = ΔLP / (Q_in - Q_out) Delivery flexibility: At constant inlet flow, can temporarily increase deliveries by reducing line pack (drafting).

Nitrogen Purge Calculations

Displacement purge (3 volume changes): N₂ required ≈ 3 × V_system × (P/14.7) × (520/T) Dilution purge to target O₂ concentration: N₂ volumes = ln(C_initial/C_final) Example: Reduce O₂ from 21% to 1% Volumes = ln(21/1) = 3.04 volume changes

References

  • API 521 – Pressure-Relieving and Depressuring Systems
  • GPSA, Section 17
  • ASME B31.8 – Gas Transmission Piping

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