1. Overview
Compressor horsepower is the shaft power required to compress gas from suction pressure (P₁) to discharge pressure (P₂). Accurate calculations are essential for driver sizing, energy cost estimation, and system design.
Gas HP (GHP)
Thermodynamic Work
Ideal power; function of head and mass flow
Brake HP (BHP)
Shaft Power
BHP = GHP / η; includes losses
Head (H)
ft·lbf/lb
Energy per unit mass
Compression Ratio
r = P₂/P₁
Key driver of power requirement
Compressor Types
| Type | Flow Range | Ratio/Stage | η (typical) | Application |
|---|---|---|---|---|
| Centrifugal | 1–200 MMSCFD | 1.5–3.5 | 0.75–0.82 (poly) | Pipeline, process |
| Reciprocating | 0.1–50 MMSCFD | 2.0–6.0 | 0.80–0.88 (isen) | Gas lift, fuel gas |
| Screw | 0.5–15 MMSCFD | 2.0–5.0 | 0.70–0.80 (isen) | Field compression |
| Axial | 50–500+ MMSCFD | 1.1–1.3 | 0.82–0.88 (poly) | LNG, large pipelines |
Why accuracy matters: A 5% error means oversizing or undersizing the driver. Oversizing wastes capital ($100K–$1M); undersizing prevents achieving design capacity.
2. Calculation Methods
Two primary methods: isentropic (adiabatic) for reciprocating compressors and polytropic for centrifugal compressors per API 617.
Isentropic (Adiabatic) Method
Assumes reversible compression with no heat transfer. Preferred for reciprocating compressors.
Isentropic Head (GPSA Eq. 13-4):
H = (Z × R × T₁ / MW) × (k/(k-1)) × [(P₂/P₁)^((k-1)/k) - 1]
Where:
H = Head (ft·lbf/lb)
Z = Compressibility factor (0.85–1.0)
R = 1545.35 ft·lbf/(lbmol·°R)
T₁ = Suction temperature (°R = °F + 459.67)
MW = Molecular weight (lb/lbmol)
k = Specific heat ratio (Cp/Cv)
Brake Horsepower:
BHP = (ṁ × H) / (33,000 × η_isentropic)
Discharge Temperature (GPSA Eq. 13-18):
T₂_isentropic = T₁ × (P₂/P₁)^((k-1)/k)
T₂_actual = T₁ + (T₂_isentropic - T₁) / η
Keep T₂ < 300°F to avoid seal/material issues.
Polytropic Method
Accounts for non-ideal behavior. Preferred for centrifugal compressors per API 617.
Polytropic Exponent (GPSA Eq. 13-18):
η_p = [(k-1)/k] / [(n-1)/n]
Solving for n:
(n-1)/n = (k-1) / (k × η_p)
n = 1 / [1 - (k-1)/(k × η_p)]
Note: n > k always for real compression.
Polytropic Head:
H_p = (Z × R × T₁ / MW) × (n/(n-1)) × [(P₂/P₁)^((n-1)/n) - 1]
Gas Horsepower:
GHP = (ṁ × H_p) / 33,000
(Polytropic head already accounts for thermodynamic losses via n > k)
Discharge Temperature:
T₂ = T₁ × (P₂/P₁)^((n-1)/n)
Specific Heat Ratio (k) Values
| Gas | k @ 60°F | k @ 150°F | MW | Notes |
|---|---|---|---|---|
| Natural Gas (SG=0.65) | 1.27 | 1.24 | 18.9 | Typical pipeline |
| Methane (CH₄) | 1.31 | 1.28 | 16.04 | Primary NG component |
| Ethane (C₂H₆) | 1.19 | 1.16 | 30.07 | Lower k → less power |
| Propane (C₃H₈) | 1.13 | 1.10 | 44.10 | Watch for liquids |
| CO₂ | 1.29 | 1.26 | 44.01 | Z < 0.9 near critical |
| N₂ / Air | 1.40 | 1.40 | 28 | k ≈ constant |
| H₂ | 1.41 | 1.41 | 2.02 | Very light; high head |
3. Efficiency Factors
Efficiency accounts for irreversibilities that cause actual power to exceed ideal thermodynamic power.
Isentropic Efficiency:
η_isen = (Isentropic Work) / (Actual Shaft Work)
Typical: 0.70–0.88 depending on compressor type
Polytropic Efficiency:
η_poly = (Polytropic Work) / (Actual Work)
Typical: 0.75–0.85 for centrifugal
Key relationship:
For same machine: η_poly > η_isen (by 2-5%)
| Operating Point | % Design Flow | Efficiency | Notes |
|---|---|---|---|
| Surge limit | 50–70% | 60–70% | Unstable; recycle required |
| BEP (design) | 100% | 78–85% | Maximum efficiency |
| Choke | 115–125% | 60–70% | Sonic velocity limit |
Overall efficiency: η_overall = η_thermo × η_mech. For centrifugal with η_poly = 0.78 and η_mech = 0.97, overall = 0.76 (24% becomes heat).
4. Multi-Stage Compression
When compression ratio exceeds 3.0–4.0, multi-stage with intercooling is more efficient.
| Overall Ratio | Stages | Rationale |
|---|---|---|
| r ≤ 3.0 | 1 | Optimal single-stage |
| 3.0 < r ≤ 4.0 | 1 or 2 | 2-stage improves efficiency |
| 4.0 < r ≤ 12 | 2 | Two-stage + intercooling |
| 12 < r ≤ 36 | 3 | Three-stage + intercoolers |
| r > 36 | 4+ | Four or more stages |
Equal-Work Distribution:
For N stages with overall ratio R:
r_per_stage = R^(1/N)
Example: Two-Stage
P₁ = 100 psia, P₃ = 900 psia, R = 9.0
r = 9.0^(1/2) = 3.0 per stage
Interstage: P₂ = √(100 × 900) = 300 psia
Stage 1: 100 → 300 psia
Intercooler: cool to ~T₁
Stage 2: 300 → 900 psia
| Configuration | Relative Power | Savings |
|---|---|---|
| Single-stage | 100% | — |
| Two-stage + IC | 85–92% | 8–15% |
| Three-stage + IC | 80–88% | 12–20% |
5. Worked Examples
Example 1: Single-Stage Reciprocating
Given:
10 MMSCFD, P₁ = 200 psia, P₂ = 500 psia, T₁ = 80°F
k = 1.27, MW = 18.9, Z = 0.95, η = 0.82
Step 1: r = 500/200 = 2.5 ✓ (single-stage OK)
Step 2: T₁ = 80 + 459.67 = 539.67°R
Step 3: Head calculation
(k-1)/k = 0.2126
k/(k-1) = 4.704
r^0.2126 - 1 = 0.2151
H = (0.95 × 1545.35 × 539.67 / 18.9) × 4.704 × 0.2151
H = 41,920 × 4.704 × 0.2151 = 42,407 ft·lbf/lb
Step 4: Mass flow
ṁ = (10 × 10⁶ / 1440 / 379.5) × 18.9 = 345.8 lb/min
Step 5: BHP
BHP = (345.8 × 42,407) / (33,000 × 0.82) = 542 HP
Step 6: Discharge temp
T₂_isen = 539.67 × 2.5^0.2126 = 655.7°R
T₂_actual = 539.67 + (655.7 - 539.67)/0.82 = 681.2°R = 222°F ✓
Quick Estimation (GPSA)
BHP ≈ (MMSCFD) × (BHP/MMSCFD factor)
Typical factors for natural gas (k ≈ 1.27):
• r = 2.0: ~35 BHP/MMSCFD
• r = 2.5: ~50 BHP/MMSCFD
• r = 3.0: ~65 BHP/MMSCFD
Example: 100 MMSCFD at r = 2.5
BHP ≈ 100 × 50 = 5,000 HP (planning estimate)
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