1. Overview & Energy Units
Energy is the capacity to do work. In midstream operations, energy calculations are essential for equipment sizing, fuel consumption analysis, cost estimation, and efficiency optimization.
Compressor power
HP, kW calculations
Convert brake horsepower to kilowatts for motor selection and electrical sizing.
Fuel consumption
BTU/hr to scf/hr
Calculate gas consumption from heat input requirements for engines and heaters.
Heat duty
MMBtu/hr to kW
Size heat exchangers, heaters, and cooling systems using energy balance.
Economic analysis
Cost per unit energy
Compare operating costs for gas vs. electric vs. diesel equipment.
Fundamental Energy Units
| Unit | Symbol | Definition | Typical Use |
|---|---|---|---|
| British Thermal Unit | BTU | Heat to raise 1 lb water by 1°F | US gas industry standard |
| Kilowatt-hour | kWh | 1000 watts for 1 hour | Electrical energy billing |
| Horsepower | HP | 550 ft-lb/s (mechanical power) | Compressor and pump sizing |
| Kilojoule | kJ | 1000 joules (SI unit) | International standards |
| Therm | thm | 100,000 BTU | Natural gas billing |
| Calorie | cal | Heat to raise 1 g water by 1°C | Laboratory, scientific |
Energy vs. Power
- Energy: Total quantity of work or heat (BTU, kWh, kJ) - cumulative over time
- Power: Rate of energy transfer (BTU/hr, kW, HP) - instantaneous rate
- Relationship: Energy = Power × Time (e.g., 1 kW × 1 hr = 1 kWh)
- Example: A 100 HP compressor running 10 hours consumes 1000 HP-hr of energy
Why conversions matter: Equipment specifications mix units - compressor brake horsepower, electrical kW demand, gas fuel consumption in MMBtu/hr, and billing in therms or kWh. Accurate conversions ensure proper sizing, cost estimation, and fuel supply planning.
2. Energy Unit Conversions
Energy unit conversions are essential for comparing equipment specifications, fuel options, and operating costs across different measurement systems.
Primary Conversion Factors
Fundamental Energy Conversions:
1 BTU = 1055.06 joules (J)
1 BTU = 1.0551 kilojoules (kJ)
1 BTU = 0.000293 kWh
1 BTU = 0.0003931 HP-hr
1 kWh = 3412.14 BTU
1 kWh = 3600 kJ
1 kWh = 1.341 HP-hr
1 HP-hr = 2545 BTU
1 HP-hr = 2684.5 kJ
1 HP-hr = 0.746 kWh
1 therm = 100,000 BTU
1 therm = 29.3 kWh
1 therm = 105.5 MJ
Power Conversions
Power Unit Conversions:
1 HP = 0.746 kW
1 HP = 2545 BTU/hr
1 HP = 0.707 Boiler HP
1 HP = 550 ft-lb/s
1 HP = 745.7 watts
1 kW = 1.341 HP
1 kW = 3412.14 BTU/hr
1 kW = 1000 joules/s
1 kW = 737.6 ft-lb/s
1 BTU/hr = 0.000393 HP
1 BTU/hr = 0.293 watts
1 BTU/hr = 0.0002931 kW
1 Boiler HP = 33,475 BTU/hr
1 Boiler HP = 9.81 kW
1 Boiler HP = 13.15 mechanical HP
Comprehensive Conversion Table
| From/To | BTU | kWh | HP-hr | kJ |
|---|---|---|---|---|
| 1 BTU | 1.0 | 0.000293 | 0.000393 | 1.055 |
| 1 kWh | 3412.14 | 1.0 | 1.341 | 3600 |
| 1 HP-hr | 2545 | 0.746 | 1.0 | 2684.5 |
| 1 kJ | 0.9478 | 0.000278 | 0.000373 | 1.0 |
| 1 MJ | 947.8 | 0.278 | 0.373 | 1000 |
| 1 therm | 100,000 | 29.3 | 39.3 | 105,506 |
Natural Gas Energy Content
Natural gas heating value varies with composition. Pipeline quality gas typically ranges from 950-1050 BTU/scf.
Gas Heating Values:
HHV (Higher Heating Value) - includes water condensation heat
LHV (Lower Heating Value) - excludes water condensation heat
Typical pipeline natural gas:
HHV = 1000-1050 BTU/scf (dry basis)
LHV = 900-950 BTU/scf (dry basis)
Relationship:
LHV ≈ HHV × 0.90 (for natural gas)
Standard conditions: 14.73 psia, 60°F
Conversion to other units:
1000 BTU/scf = 37.26 MJ/m³
1000 BTU/scf = 10.35 kWh/m³
Fuel Heating Values (EIA/GPSA Standards)
| Fuel Type | HHV (BTU/unit) | LHV (BTU/unit) | Unit |
|---|---|---|---|
| Natural gas (pipeline) | 1,000 | 900 | scf |
| Methane (pure) | 1,012 | 911 | scf |
| Propane (gas) | 2,516 | 2,316 | scf |
| Propane (liquid) | 91,500 | 84,250 | gallon |
| Diesel fuel #2 | 137,380 | 128,700 | gallon |
| Gasoline (regular) | 120,286 | 109,000 | gallon |
| Kerosene / Jet fuel | 135,000 | 127,000 | gallon |
| Crude oil (average) | 5,800,000 | 5,400,000 | barrel |
Source: EIA Monthly Energy Review, GPSA. HHV includes latent heat of water vapor; LHV excludes it.
Example Calculation 1: HP to kW
Convert 1500 HP compressor brake horsepower to kilowatts for electrical motor sizing:
Given: Compressor requires 1500 brake HP
kW = HP × 0.746
kW = 1500 × 0.746
kW = 1119 kW
Add motor efficiency (assume 95%):
kW_input = 1119 / 0.95
kW_input = 1178 kW
Round up for motor selection: 1200 kW motor required
Example Calculation 2: Gas Energy to Volume
Calculate gas volume required for 10 MMBtu/hr heat duty:
Given:
Heat duty = 10 MMBtu/hr
Gas HHV = 1000 BTU/scf
Burner efficiency = 85%
Fuel input = Heat duty / Efficiency
Fuel input = 10,000,000 BTU/hr / 0.85
Fuel input = 11,765,000 BTU/hr
Gas flow = Fuel input / HHV
Gas flow = 11,765,000 / 1000
Gas flow = 11,765 scf/hr
Gas flow = 196 scfm
Convert to standard cubic meters:
11,765 scf/hr × 0.0283 m³/scf = 333 Sm³/hr
3. Power Calculations & Efficiency
Power calculations determine instantaneous energy transfer rates for equipment sizing, electrical demand, and fuel consumption rates.
Compressor Power
Adiabatic Compression Power:
BHP = (Q × P₁ × k / (k-1) × 229) × [(r^((k-1)/k) - 1)] / η
Where:
BHP = Brake horsepower (HP)
Q = Inlet flow rate (ACFM - actual cubic feet per minute)
P₁ = Inlet pressure (psia)
k = Specific heat ratio (Cp/Cv) ≈ 1.27 for natural gas
r = Compression ratio (P₂/P₁)
η = Compressor mechanical efficiency (0.80-0.85 typical)
229 = Conversion constant (33,000 ft-lb/min per HP ÷ 144 in²/ft²)
For multi-stage compression:
r_stage = r_overall^(1/n)
Where n = number of stages
Power per stage: BHP_stage = BHP_total / n
Pump Power
Liquid Pumping Power:
BHP = (Q × H × SG) / (3960 × η)
Where:
BHP = Brake horsepower (HP)
Q = Flow rate (GPM - gallons per minute)
H = Total head (feet)
SG = Specific gravity (relative to water)
η = Pump efficiency (0.70-0.85 typical)
3960 = Conversion constant
Total head:
H = H_static + H_friction + H_velocity + P_discharge/(2.31 × SG)
Alternatively in SI units:
kW = (Q × H × ρ × g) / (1000 × η)
Where:
Q = Flow rate (m³/s)
H = Total head (m)
ρ = Liquid density (kg/m³)
g = 9.81 m/s²
Heat Transfer Power
Heat Exchanger Duty:
Q = ṁ × Cp × ΔT
Where:
Q = Heat duty (BTU/hr or kW)
ṁ = Mass flow rate (lb/hr or kg/s)
Cp = Specific heat (BTU/lb·°F or kJ/kg·K)
ΔT = Temperature change (°F or K)
For phase change:
Q = ṁ × λ
Where λ = Latent heat (BTU/lb or kJ/kg)
Unit conversions:
1 MMBtu/hr = 293 kW
1 ton refrigeration = 12,000 BTU/hr = 3.517 kW
Electrical Power
Three-Phase Electrical Power:
kW = (√3 × V × I × PF) / 1000
Where:
kW = Real power (kilowatts)
V = Line voltage (volts)
I = Line current (amps)
PF = Power factor (0.80-0.95 typical)
√3 = 1.732
Apparent power:
kVA = (√3 × V × I) / 1000
Reactive power:
kVAR = kVA × sin(arccos(PF))
Relationship:
kVA² = kW² + kVAR²
Equipment Efficiency
| Equipment Type | Typical Efficiency | Range | Notes |
|---|---|---|---|
| Electric motor (induction) | 93% | 90-96% | Higher for larger motors |
| Gas engine (4-stroke) | 35% | 30-40% | Shaft power / fuel energy |
| Gas turbine | 32% | 25-40% | Higher for combined cycle |
| Centrifugal compressor | 80% | 75-85% | Isentropic efficiency |
| Reciprocating compressor | 83% | 80-88% | Isentropic efficiency |
| Centrifugal pump | 75% | 70-85% | Hydraulic efficiency |
| Fired heater (gas) | 85% | 80-90% | Thermal efficiency |
| Shell-tube heat exchanger | 92% | 85-95% | Effectiveness |
| VFD (variable frequency drive) | 97% | 95-98% | Power electronics efficiency |
Efficiency cascade: A gas-engine-driven compressor has overall efficiency = engine efficiency × compressor efficiency = 0.35 × 0.80 = 0.28 (28%). This means 72% of fuel energy is rejected as heat. Electric motor driven: 0.93 × 0.80 = 0.74 (74% wire-to-air efficiency).
Example Calculation 3: Compressor Power
Calculate brake horsepower for a natural gas compressor:
Given:
Flow = 10 MMscfd at inlet conditions
Inlet P = 400 psia, T = 90°F
Discharge P = 1200 psia
k = 1.27, Z_avg = 0.90, η = 0.82
Step 1: Convert to ACFM
Q_std = 10,000,000 scfd / 1440 min/day = 6944 scfm
Q_actual = Q_std × (14.73/400) × (550/520) × (Z/1.0)
Q_actual = 6944 × 0.0368 × 1.058 × 0.90
Q_actual = 243 ACFM
Step 2: Compression ratio
r = 1200 / 400 = 3.0
Step 3: Calculate BHP
BHP = (243 × 400 × 1.27 / 0.27 × 229) × [(3.0^0.213 - 1)] / 0.82
BHP = (243 × 400 × 4.70 / 229) × [(1.251 - 1)] / 0.82
BHP = 1987 × 0.251 / 0.82
BHP = 608 HP
Round up: Select 650 HP driver
4. Fuel Consumption Rates
Fuel consumption calculations determine gas or liquid fuel requirements for engines, turbines, heaters, and other combustion equipment.
Gas Engine Fuel Consumption
Natural Gas Engine Fuel Rate:
Fuel = BHP × BSFC
Where:
Fuel = Fuel consumption (BTU/hr)
BHP = Brake horsepower output
BSFC = Brake specific fuel consumption (BTU/HP-hr)
Typical BSFC for natural gas engines:
Rich burn: 8500-9500 BTU/HP-hr
Lean burn: 7500-8500 BTU/HP-hr
High efficiency: 7000-7500 BTU/HP-hr
Convert to volumetric flow:
scf/hr = (BHP × BSFC) / HHV
Where HHV = Gas heating value (BTU/scf)
Efficiency calculation:
η = 2545 BTU/HP-hr / BSFC
For BSFC = 8000: η = 2545/8000 = 31.8%
Gas Turbine Fuel Consumption
Gas Turbine Fuel Rate:
Fuel = (kW × 3412.14) / (HHV × η)
Where:
Fuel = Fuel consumption (scf/hr)
kW = Power output (kilowatts)
3412.14 = Conversion BTU/hr per kW
HHV = Gas heating value (BTU/scf)
η = Thermal efficiency (0.25-0.40 typical)
Heat rate (HR):
HR = 3412.14 / η (BTU/kWh)
For η = 0.32:
HR = 3412.14 / 0.32 = 10,663 BTU/kWh
Fuel flow:
scf/hr = (kW × HR) / HHV
Fired Heater Fuel Consumption
Heater Fuel Requirements:
Fuel_input = Heat_duty / η
Where:
Fuel_input = Fuel consumption (MMBtu/hr)
Heat_duty = Process heat duty (MMBtu/hr)
η = Burner/heater efficiency (0.80-0.90)
Calculate from process requirements:
Heat_duty = ṁ × Cp × ΔT / 1,000,000
Where:
ṁ = Mass flow (lb/hr)
Cp = Specific heat (BTU/lb·°F)
ΔT = Temperature rise (°F)
Gas volume:
scf/hr = (Fuel_input × 1,000,000) / HHV
Diesel Engine Fuel Consumption
Diesel Fuel Rate:
Fuel = BHP × BSFC
Where:
BSFC = Brake specific fuel consumption (lb/HP-hr)
Typical diesel BSFC:
Naturally aspirated: 0.40-0.45 lb/HP-hr
Turbocharged: 0.36-0.42 lb/HP-hr
High efficiency: 0.32-0.36 lb/HP-hr
Convert to gallons:
gal/hr = (BHP × BSFC) / (ρ_diesel × 8.34)
Where:
ρ_diesel = Diesel specific gravity ≈ 0.85
8.34 = lb/gal for water
For BSFC = 0.38 lb/HP-hr, SG = 0.85:
gal/hr = BHP × 0.38 / (0.85 × 8.34)
gal/hr = BHP × 0.0536
Fuel Consumption Comparison
| Equipment | Fuel Type | Consumption Rate | Efficiency |
|---|---|---|---|
| Rich burn gas engine | Natural gas | 9000 BTU/HP-hr | 28% |
| Lean burn gas engine | Natural gas | 8000 BTU/HP-hr | 32% |
| Gas turbine (simple cycle) | Natural gas | 10,500 BTU/kWh | 32% |
| Gas turbine (combined cycle) | Natural gas | 6,800 BTU/kWh | 50% |
| Diesel engine | Diesel fuel | 0.38 lb/HP-hr | 38% |
| Electric motor | Electricity | 0.80 kWh/HP-hr | 93% |
| Line heater (gas fired) | Natural gas | N/A | 85% |
Example Calculation 4: Gas Engine Fuel Use
Calculate daily fuel consumption for a 1500 HP gas engine compressor:
Given:
Compressor BHP = 1500 HP
Engine BSFC = 8200 BTU/HP-hr
Gas HHV = 1020 BTU/scf
Operating hours = 24 hr/day
Step 1: Hourly fuel consumption
Fuel_hr = 1500 HP × 8200 BTU/HP-hr
Fuel_hr = 12,300,000 BTU/hr
Fuel_hr = 12.3 MMBtu/hr
Step 2: Gas volume
scf/hr = 12,300,000 / 1020
scf/hr = 12,059 scf/hr
Step 3: Daily consumption
scf/day = 12,059 × 24
scf/day = 289,412 scf/day
scf/day ≈ 0.29 MMscfd
Step 4: Annual consumption (365 days)
Annual = 0.29 MMscfd × 365 days
Annual = 105.7 MMscf/year
Engine efficiency:
η = 2545 / 8200 = 31.0%
5. Economic Energy Comparisons
Economic analysis compares operating costs for different fuel options, driver types, and energy sources to optimize facility design and operation.
Cost per Unit Energy
Normalized Energy Cost:
Cost_energy = Fuel_price / (Energy_content × Efficiency)
Where:
Cost_energy = Cost per useful energy ($/MMBtu delivered)
Fuel_price = Fuel cost in native units
Energy_content = HHV or energy value
Efficiency = Equipment efficiency
Examples:
Natural gas at $3.50/Mscf, 1020 BTU/scf, engine 32% efficiency:
Cost = $3.50 / (1.020 MMBtu/Mscf × 0.32)
Cost = $10.73 per MMBtu shaft work
Electricity at $0.10/kWh, motor 93% efficiency:
Cost = $0.10 / (0.003412 MMBtu/kWh × 0.93)
Cost = $31.52 per MMBtu shaft work
Diesel at $3.00/gal, 139,000 BTU/gal, engine 38% efficiency:
Cost = $3.00 / (0.139 MMBtu/gal × 0.38)
Cost = $56.80 per MMBtu shaft work
Annual Operating Cost
Annual Fuel Cost:
Cost_annual = Power × Hours × Fuel_rate × Fuel_price / (Energy_content × Efficiency)
Simplified:
Cost_annual = Load × Hours × Unit_cost
Where:
Load = Average power demand (HP, kW, MMBtu/hr)
Hours = Annual operating hours
Unit_cost = Fuel cost per unit energy delivered
For capacity factor:
Hours = 8760 hr/yr × CF
Where CF = capacity factor (0.0-1.0)
Breakeven Analysis
Electric vs. Gas Engine Breakeven:
Consider both capital and operating costs:
NPV = -Capital + Σ(Savings_annual / (1+r)^n)
Where:
NPV = Net present value
Capital = Additional capital cost
Savings_annual = Annual fuel cost difference
r = Discount rate
n = Year number
Simple payback (ignoring time value):
Payback = Capital_difference / Savings_annual
Example:
Electric motor: $200k capital, $150k/yr fuel
Gas engine: $150k capital, $80k/yr fuel
Capital difference: $200k - $150k = $50k higher for electric
Fuel savings: $150k - $80k = $70k/yr for electric
Payback = $50k / $70k = 0.7 years
In this case, gas engine has higher fuel cost,
so electric motor preferred if sufficient power available.
Fuel Cost Comparison Example
| Driver Type | Fuel Price | Efficiency | Cost per HP-hr | Cost for 1500 HP × 8760 hr |
|---|---|---|---|---|
| Gas engine (rich burn) | $3.50/Mscf | 28% | $0.0299 | $393,066 |
| Gas engine (lean burn) | $3.50/Mscf | 32% | $0.0262 | $344,058 |
| Gas turbine | $3.50/Mscf | 30% | $0.0279 | $366,660 |
| Diesel engine | $3.00/gal | 38% | $0.0408 | $536,112 |
| Electric motor | $0.08/kWh | 93% | $0.0643 | $844,596 |
| Electric motor | $0.05/kWh | 93% | $0.0402 | $527,873 |
Assumes: Gas HHV = 1020 BTU/scf, diesel = 139,000 BTU/gal, 1 HP-hr = 0.746 kWh, 1500 HP continuous load
Economic decision factors: Fuel cost comparison alone insufficient - must consider capital cost, maintenance, availability, emissions compliance, and reliability. Remote locations favor gas engines (no electrical infrastructure). Urban areas may require electric motors (emissions). Gas turbines preferred for >5000 HP due to lower capital cost per HP.
📊 Image: Fuel Cost per HP-hr Comparison
Bar chart showing operating cost comparison: Gas engine $0.026/HP-hr, Electric motor at $0.05/kWh $0.04/HP-hr, Diesel $0.041/HP-hr
Example Calculation 5: Gas vs. Electric Economics
Compare 20-year lifecycle costs for 2000 HP compressor station:
Option 1: Gas engine driven
Capital cost: $1,500,000 (installed)
Fuel: $3.50/Mscf, consumption 16.4 MMscfd @ 28% efficiency
Maintenance: $0.015/HP-hr = $262,800/yr
Capacity factor: 0.85 (7446 hr/yr)
Overhaul: $300,000 every 5 years
Option 2: Electric motor driven
Capital cost: $2,200,000 (with electrical substation)
Electricity: $0.07/kWh
Motor efficiency: 94%
Maintenance: $0.005/HP-hr = $74,460/yr
Capacity factor: 0.85 (7446 hr/yr)
Gas engine annual costs:
Fuel: 16.4 Mscf/day × 365 days × $3.50/Mscf × 0.85 CF = $18,250/yr
Maintenance: $262,800/yr
Overhaul (annualized): $300,000 / 5 = $60,000/yr
Annual O&M: $341,050/yr
Electric motor annual costs:
Power: 2000 HP × 0.746 kW/HP / 0.94 × 7446 hr × $0.07/kWh
Power: 1492 kW × 7446 hr × $0.07 = $776,460/yr
Maintenance: $74,460/yr
Annual O&M: $850,920/yr
20-year NPV at 8% discount rate:
Gas: -$1,500k - $341k × 9.818 = -$4,849k
Electric: -$2,200k - $851k × 9.818 = -$10,555k
Gas engine wins by $5,706k NPV over 20 years
Breakeven electricity price:
Gas annual cost = $341k
Required electric annual = $341k
$341k = kW × 7446 hr × $/kWh + $74.5k
$266.5k = 1492 kW × 7446 hr × $/kWh
$/kWh = $0.024
At electricity prices below $0.024/kWh, electric motor preferred
At current $0.07/kWh, gas engine strongly preferred
Sensitivity Factors
- Gas price volatility: Natural gas prices vary seasonally and regionally ($2-6/Mscf typical range)
- Electricity demand charges: Commercial rates include demand charges ($10-20/kW-month) that increase costs
- Capacity factor: Low-utilization equipment favors lower capital cost options (gas engines)
- Emissions costs: NOx emissions penalties can add $5-15k/year for gas engines in non-attainment areas
- Maintenance inflation: Labor costs typically increase 3-5%/year
- Technology improvements: Modern lean-burn engines achieve 35-38% efficiency
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