1. Volume Calculation
Pipe internal volume is calculated from the inside diameter and length. Various unit conversions are needed for practical applications.
Basic Formulas
Volume per foot of pipe:
V = π × d² / 4 × (1 ft)
Practical formulas:
V (gal/ft) = 0.0408 × d²
V (bbl/ft) = 0.000971 × d²
V (ft³/ft) = 0.00545 × d²
V (liters/m) = 0.7854 × d² [d in cm]
Where d = inside diameter (inches)
Inside Diameter
d = D - 2t
Where:
d = Inside diameter (inches)
D = Outside diameter (inches)
t = Wall thickness (inches)
Unit Conversions
| From | To | Multiply by | Source |
|---|---|---|---|
| ft³ | US gallons | 7.480519 | API MPMS |
| ft³ | barrels (42 gal) | 0.178108 | API |
| gallons | barrels | 0.023810 | API |
| ft³ | liters | 28.31685 | NIST |
| gallons | liters | 3.785412 | NIST |
| barrels | liters | 158.987 | API |
2. Volume Reference Tables
Standard Pipe Volumes
| NPS | OD (in) | Wall (Std) | ID (in) | gal/ft | bbl/mile |
|---|---|---|---|---|---|
| 2" | 2.375 | 0.154 | 2.067 | 0.174 | 21.9 |
| 4" | 4.500 | 0.237 | 4.026 | 0.661 | 83.4 |
| 6" | 6.625 | 0.280 | 6.065 | 1.501 | 189.4 |
| 8" | 8.625 | 0.322 | 7.981 | 2.599 | 327.9 |
| 10" | 10.750 | 0.365 | 10.020 | 4.098 | 517.0 |
| 12" | 12.750 | 0.375 | 12.000 | 5.875 | 741.2 |
| 16" | 16.000 | 0.375 | 15.250 | 9.489 | 1,197 |
| 20" | 20.000 | 0.375 | 19.250 | 15.12 | 1,907 |
| 24" | 24.000 | 0.375 | 23.250 | 22.05 | 2,782 |
| 30" | 30.000 | 0.375 | 29.250 | 34.90 | 4,403 |
| 36" | 36.000 | 0.375 | 35.250 | 50.71 | 6,398 |
| 42" | 42.000 | 0.500 | 41.000 | 68.60 | 8,655 |
Quick Reference: Volume per Mile
Volume per mile:
V (gal/mile) = 0.0408 × d² × 5,280 = 215.4 × d²
V (bbl/mile) = 5.129 × d²
Example: 24" × 0.500" wall (ID = 23")
V = 5.129 × 23² = 2,715 bbl/mile
3. Gas Volume at Pressure
For gas pipelines, volume must account for compressibility. The actual gas quantity depends on pressure, temperature, and gas composition.
Gas Inventory Calculation
Standard cubic feet in pipeline:
SCF = V_pipe × (P / P_std) × (T_std / T) × (Z_std / Z)
Where:
V_pipe = Physical pipe volume (ft³)
P = Operating pressure (psia)
P_std = Standard pressure (14.7 psia)
T = Operating temperature (°R)
T_std = Standard temperature (519.67°R = 60°F)
Z = Compressibility factor at operating conditions
Z_std = 1.0 (ideal gas at standard conditions)
Simplified (per AGA conventions):
SCF = V_pipe × P × 35.34 / (T × Z)
Z-Factor Estimation
The compressibility factor Z accounts for real gas behavior. For natural gas:
Sutton (1985) pseudo-critical correlations:
T_pc = 169.2 + 349.5×SG - 74.0×SG² [°R]
P_pc = 756.8 - 131.0×SG - 3.6×SG² [psia]
Reduced properties:
T_pr = T / T_pc
P_pr = P / P_pc
Typical Z values (SG = 0.60):
• 500 psia, 60°F: Z ≈ 0.92
• 1000 psia, 60°F: Z ≈ 0.84
• 1500 psia, 60°F: Z ≈ 0.78
Line Pack Formula
Line pack (MMSCF):
LP = 28.31 × d² × L × P_avg / (1,000,000 × T × Z)
Where:
d = Inside diameter (inches)
L = Length (miles)
P_avg = Average pressure (psia)
T = Average temperature (°R)
Z = Average compressibility factor
Quick estimate (ideal gas):
LP ≈ d² × L × P_avg / 1,000,000 [MMSCF]
Example: Gas Pipeline Inventory
Given: 24" × 0.500" wall, 100 miles, P_avg = 800 psia, T = 70°F, SG = 0.60
Step 1: Physical volume
ID = 24 - 2(0.500) = 23 in
V = 0.00545 × 23² × 5,280 × 100 = 15.23 MM ft³
Step 2: Z-factor (from DAK correlation)
T_pc = 169.2 + 349.5(0.60) - 74.0(0.36) = 352.5°R
P_pc = 756.8 - 131.0(0.60) - 3.6(0.36) = 676.8 psia
T_pr = 530/352.5 = 1.50; P_pr = 800/676.8 = 1.18
Z ≈ 0.87
Step 3: Line pack
SCF = 15.23×10⁶ × 800 × 35.34 / (530 × 0.87)
SCF = 934 MMSCF
Operating significance: Line pack represents stored gas that can be withdrawn by lowering pressure. A 100 psi pressure swing in this example releases/absorbs approximately 115-120 MMSCF—critical for balancing supply and demand.
4. Applications
Common Uses
| Application | Purpose |
|---|---|
| Hydrotesting | Calculate water volume needed for test |
| Purging/inerting | Determine nitrogen volume for displacement |
| Pigging | Estimate pig travel time at given flow rate |
| Batch tracking | Calculate batch interface location |
| Line pack | Gas storage capacity in pipeline |
| Blowdown | Gas release volume for depressuring |
| Chemical treatment | Inhibitor/biocide dosing volume |
Hydrotest Water Requirements
Water volume:
V_water = V_pipe × (1 + compression factor)
Compression factor ≈ 0.03 per 1000 psi test pressure
(Water compresses ~3% at 1000 psi)
Fill time estimate:
t (hours) = V_pipe (gal) / Q_fill (gal/hr)
Pig Travel Time
Travel time:
t = V_pipe / Q
For liquids:
t (hours) = V (bbl) / Q (bbl/hr)
t (hours) = L (miles) × 5.129 × d² / Q (bbl/hr)
For gas (at flow velocity):
t (hours) = L (miles) × 5,280 / (v × 3,600)
Where v = gas velocity (ft/s)
5. System Volume
Total system volume includes pipe plus vessels, headers, and fittings.
Vessel Volumes
Horizontal cylinder:
V = π × D² × L / 4
Sphere:
V = π × D³ / 6
2:1 Elliptical head:
V_head = 0.1309 × D³ (each head)
Hemispherical head:
V_head = π × D³ / 12 (each head)
Fitting Equivalent Volumes
| Fitting | Equivalent Pipe Length |
|---|---|
| 90° elbow (LR) | 1.5 × D |
| 90° elbow (SR) | 1.0 × D |
| 45° elbow | 0.7 × D |
| Tee (through) | 1.0 × D |
| Tee (branch) | 1.5 × D |
| Gate valve (open) | 0.5 × D |
| Ball valve (open) | 0.1 × D |
Partially Filled Horizontal Pipe
Cross-sectional area at depth h:
A = r² × arccos((r-h)/r) - (r-h) × √(2rh - h²)
Volume: V = A × L
Quick reference (% of full):
h/D = 0.25 → V = 14.7% of full
h/D = 0.50 → V = 50.0% of full
h/D = 0.75 → V = 85.3% of full
Where: r = D/2 (radius), h = liquid depth from bottom
References
- ASME B36.10M – Welded and Seamless Wrought Steel Pipe
- API MPMS Chapter 11.1 – Temperature and Pressure Volume Correction
- AGA Report No. 8 – Compressibility and Supercompressibility Factors
- GPSA, Section 17 – Fluid Properties
- Dranchuk & Abou-Kassem (1975) – Z-Factor Calculation Methods
- Sutton (1985) – Pseudo-Critical Property Correlations
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