1. Sizing Principles
Liquid line sizing balances capital cost (pipe diameter) against operating cost (pumping energy) while meeting velocity and pressure drop constraints.
Key Design Criteria
- Velocity limits: Prevent erosion, noise, water hammer
- Pressure drop: Must not exceed available pump head
- NPSH: Suction lines must provide adequate NPSH
- Elevation: Account for static head changes
- Economics: Balance pipe cost vs. pump power cost
Basic Sizing Equation
Diameter from velocity:
d = √(0.4085 × Q / v)
Where:
d = Inside diameter (inches)
Q = Flow rate (gpm)
v = Velocity (ft/s)
Or from flow rate:
v = 0.4085 × Q / d²
2. Velocity Criteria
Velocity limits depend on service, economics, and potential for erosion or cavitation.
Recommended Velocities
| Service | Typical (ft/s) | Maximum (ft/s) |
|---|---|---|
| Pump suction (water) | 2-4 | 5 |
| Pump discharge (water) | 5-8 | 12 |
| Crude oil | 3-6 | 10 |
| NGL/LPG | 3-5 | 8 |
| Produced water | 3-6 | 8 |
| Glycol | 2-4 | 6 |
| Gravity drain | 1-3 | 4 |
Erosional Velocity
API RP 14E erosional velocity:
v_e = C / √ρ
Where:
v_e = Erosional velocity (ft/s)
C = Empirical constant (typically 100-150)
ρ = Fluid density (lb/ft³)
For clean liquids: C = 125-150
For liquids with solids: C = 100 or less
Example: Crude (ρ = 54 lb/ft³)
v_e = 125 / √54 = 17 ft/s maximum
Design practice: Size for 50-70% of erosional velocity under normal conditions, with margin for flow surges.
3. Pressure Drop Calculations
Pressure drop in liquid lines is calculated using the Darcy-Weisbach equation with friction factor from the Moody diagram.
Darcy-Weisbach Equation
Head loss:
h_f = f × (L/D) × (v²/2g)
Pressure drop (theoretical):
ΔP = f × (L/D) × (ρv²/2) / 144
Where:
h_f = Head loss (ft of fluid)
f = Darcy friction factor (dimensionless)
L = Length (ft)
D = Diameter (ft)
v = Velocity (ft/s)
g = 32.174 ft/s²
ρ = Density (lb/ft³)
ΔP = Pressure drop (psi)
Practical Pressure Drop Formula
Pressure drop per 100 ft (GPM units):
ΔP = 1.348 × f × SG × Q² / d⁵
Where:
ΔP = Pressure drop (psi per 100 ft)
f = Darcy friction factor (dimensionless)
SG = Specific gravity (dimensionless)
Q = Flow rate (GPM)
d = Inside diameter (inches)
Derivation:
Starting from h = f × (L/D) × (v²/2g)
v = 0.4085 × Q / d² (ft/s, with Q in GPM, d in inches)
Convert head to pressure: ΔP = SG × 62.4 × h / 144
For L = 100 ft, D in feet: 1.348 = 100 × 12 × 62.4 × 0.4085² / (2 × 32.174 × 144)
Reynolds Number
Reynolds number:
Re = ρvD/μ = 3,160 × Q × SG / (d × μ)
Where:
Q = Flow rate (GPM)
SG = Specific gravity (dimensionless)
d = Inside diameter (inches)
μ = Dynamic viscosity (cP)
Derivation of constant 3,160:
From Crane TP-410: Re = 6.31 × W / (d × μ)
where W = mass flow (lb/hr) = Q × 8.34 × SG × 60
Substituting: 6.31 × 8.34 × 60 ≈ 3,160
Flow regimes:
Re < 2,100: Laminar
Re > 4,000: Turbulent
2,100 < Re < 4,000: Transition
Friction Factor
Laminar flow (Re < 2,100):
f = 64 / Re
Turbulent flow (Colebrook):
1/√f = -2 log₁₀(ε/3.7D + 2.51/(Re√f))
Explicit approximation (Swamee-Jain):
f = 0.25 / [log₁₀(ε/3.7D + 5.74/Re^0.9)]²
Where ε = Pipe roughness (ft)
Steel pipe: ε ≈ 0.00015 ft
Hazen-Williams (Water Only)
For water systems:
h_f = 10.67 × L × Q^1.852 / (C^1.852 × d^4.87)
Where:
h_f = Head loss (ft/100 ft)
Q = Flow (gpm)
d = ID (inches)
C = Hazen-Williams coefficient
Typical C values:
New steel: 140
Aged steel: 100-120
Cast iron: 100-130
Plastic: 150
4. NPSH Considerations
Suction line sizing must ensure adequate Net Positive Suction Head (NPSH) to prevent cavitation.
NPSH Available
NPSH available:
NPSH_a = P_s/γ + z_s - h_f - P_vp/γ
Where:
P_s = Source pressure (psia)
γ = Specific weight (lb/ft³)
z_s = Static suction head (ft, + above pump)
h_f = Friction losses in suction line (ft)
P_vp = Vapor pressure at pumping temperature (psia)
Design requirement:
NPSH_a > NPSH_r + margin (typically 3-5 ft)
Suction Line Sizing
- Keep suction velocities low: 2-4 ft/s typical
- Minimize fittings: Each fitting adds friction loss
- Avoid air pockets: Continuous slope toward pump
- Eccentric reducers: Flat side up at pump
- 5-10 diameters straight: Before pump inlet
Vapor Pressure Effects
| Fluid | Temp (°F) | P_vp (psia) |
|---|---|---|
| Water | 100 | 0.95 |
| Water | 150 | 3.72 |
| Light crude | 100 | 2-5 |
| Propane | 100 | 190 |
| Butane | 100 | 52 |
5. Applications
Sizing Example
Given: 1,000 GPM crude (SG=0.85, μ=5 cP), size discharge line for 6 ft/s max
d_min = √(0.4085 × 1000 / 6) = √68.1 = 8.25"
Select 10" Sch 40 (ID = 10.02")
Actual v = 0.4085 × 1000 / 10.02² = 4.07 ft/s ✓
Re = 3160 × 1000 × 0.85 / (10.02 × 5) = 53,600 (turbulent)
Line Sizing Summary
| Line Type | Primary Constraint | Secondary Check |
|---|---|---|
| Pump suction | NPSH available | Low velocity |
| Pump discharge | Pressure drop/head | Erosional velocity |
| Transfer lines | Available pressure | Economics |
| Gravity flow | Elevation difference | Full pipe flow |
References
- Crane Technical Paper 410 – Flow of Fluids
- API RP 14E – Offshore Production Platform Piping
- ASME B31.3 – Process Piping
- Hydraulic Institute Standards
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