Gas Rate Time
Engineering fundamentals for gas inventory and timing calculations
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 Engineering Data Book, Section 17
- ASME B31.8 – Gas Transmission Piping