Reciprocating Compressor Discharge Temperature Fundamentals

1. Overview

Discharge temperature is one of the most critical parameters in reciprocating compressor design. Excessive temperatures degrade lubricating oil, damage valve components, reduce packing life, and can cause safety hazards. Accurate prediction enables proper staging decisions, intercooler sizing, and material selection.

Valve Life

Temperature-Dependent

Every 20 F above 300 F halves valve plate life

Lube Oil

Flash Point Limit

Mineral oils degrade above 350 F

Packing

PTFE: 500 F Max

Bronze/carbon: higher limits

Cylinder

Thermal Stress

Temperature differentials cause distortion

Design rule: Keep discharge temperature below 300 F for standard services with mineral oil lubrication. For sour gas (H2S), keep below 275 F to prevent sulfide stress cracking and accelerated corrosion.

2. Adiabatic Compression Process

Reciprocating compressors approximate an adiabatic (isentropic) process because compression occurs rapidly with minimal time for heat transfer through cylinder walls. The theoretical discharge temperature depends on the compression ratio and the specific heat ratio of the gas.

Isentropic Discharge Temperature (GPSA Eq. 13-18): T2_isen = T1 x (P2/P1)^((k-1)/k) Where: T2_isen = Isentropic discharge temperature (deg R) T1 = Suction temperature (deg R = deg F + 459.67) P2 = Discharge pressure (psia) P1 = Suction pressure (psia) k = Specific heat ratio (Cp/Cv) (k-1)/k = Isentropic temperature exponent Actual Discharge Temperature: T2_actual = T1 + (T2_isen - T1) / eta_isen Where: eta_isen = Isentropic efficiency (0.80-0.92 typical) Note: T2_actual > T2_isen because inefficiencies add heat to the gas beyond the ideal process.

Why Adiabatic Applies to Recips

Unlike centrifugal compressors where gas flows continuously through stages, reciprocating compressors compress gas in discrete cycles lasting milliseconds. This rapid compression leaves insufficient time for significant heat transfer to the cylinder walls, making the adiabatic assumption reasonable.

Process	Exponent	T2 Relative	Application
Isothermal	n = 1	Lowest (= T1)	Theoretical ideal; infinite cooling
Polytropic	1 < n < k	Intermediate	Water-jacketed cylinders
Isentropic	n = k	Reference	Ideal recip; no heat transfer
Actual	n > k	Highest	Real machine with losses

Efficiency Impact on Temperature

Lower isentropic efficiency increases the actual discharge temperature. This is counterintuitive: a less efficient compressor produces hotter gas because more of the input energy converts to heat rather than useful compression work.

Temperature Rise vs. Efficiency: Delta_T_actual = (T2_isen - T1) / eta Example at r = 3.0, k = 1.27, T1 = 100 F (559.67 R): T2_isen = 559.67 x 3.0^(0.2126) = 699.6 R = 239.9 F Delta_T_isen = 139.9 F At eta = 0.90: Delta_T = 139.9 / 0.90 = 155.4 F --> T2 = 255 F At eta = 0.85: Delta_T = 139.9 / 0.85 = 164.6 F --> T2 = 265 F At eta = 0.80: Delta_T = 139.9 / 0.80 = 174.9 F --> T2 = 275 F At eta = 0.75: Delta_T = 139.9 / 0.75 = 186.5 F --> T2 = 287 F

Practical note: Water-jacketed cylinders remove 5-15% of the compression heat, reducing actual discharge temperature below the adiabatic prediction. Use a polytropic exponent n = 1.0 to 1.05 times k for jacketed cylinders.

3. K-Value Effects on Discharge Temperature

The specific heat ratio k is the single most influential gas property affecting discharge temperature. Gases with higher k values produce significantly hotter discharge temperatures at the same compression ratio.

Gas	k (60 F)	MW	T2 at r=3.0	T2 at r=4.0	Notes
Hydrogen (H2)	1.41	2.02	280 F	350 F	Highest T2; staging critical
Nitrogen (N2)	1.40	28.01	278 F	347 F	Behaves like air
Air	1.40	28.97	278 F	347 F	Standard reference
Carbon Dioxide	1.29	44.01	247 F	304 F	Z-factor correction needed
Natural Gas (0.65 SG)	1.27	18.85	240 F	294 F	Typical pipeline gas
Ethane (C2H6)	1.19	30.07	215 F	259 F	Lower k = cooler discharge
Propane (C3H8)	1.13	44.10	195 F	233 F	Watch for condensation

All values at T1 = 100 F, eta = 0.85. Actual temperatures vary with Z-factor and real-gas effects.

Temperature Sensitivity to k

Exponent Analysis: The temperature exponent (k-1)/k controls how much the gas heats during compression: k = 1.10: (k-1)/k = 0.0909 (low heating) k = 1.20: (k-1)/k = 0.1667 k = 1.30: (k-1)/k = 0.2308 k = 1.40: (k-1)/k = 0.2857 (high heating) Rule of thumb: For every 0.01 increase in k, discharge temperature rises approximately 3-5 F at typical compression ratios.

K-Value Variation with Conditions

The specific heat ratio is not constant. It decreases with increasing temperature and pressure, and varies with gas composition. Using a fixed k-value can introduce errors of 10-20 F in discharge temperature predictions.

Condition	Effect on k	Effect on T2	Guidance
Higher temperature	k decreases	T2 decreases	Use k at average of T1 and T2
Higher pressure	k decreases	T2 decreases	Use equation of state for accuracy
Heavier gas (higher MW)	k decreases	T2 decreases	Heavier = cooler discharge
More CO2/H2S	k decreases	T2 decreases	Acid gas lowers k but adds corrosion

Best practice: For accurate predictions, evaluate k at the average temperature (T1 + T2_estimated)/2. Iterate if the predicted T2 differs significantly from the initial estimate. Process simulation software handles this automatically.

4. Intercooling Requirements

When the compression ratio produces a discharge temperature exceeding material or lubricant limits, multi-stage compression with intercooling is required. Intercoolers reduce gas temperature between stages, lowering the final discharge temperature and improving overall efficiency.

When Is Intercooling Required?

Gas Type	k Value	Max Single-Stage Ratio	Limiting Factor
Hydrogen	1.41	2.5	T2 > 300 F at r = 2.8
Air / Nitrogen	1.40	2.5-3.0	T2 > 300 F at r = 3.0
Natural Gas	1.27	3.5-4.0	T2 > 300 F at r = 4.2
CO2	1.29	3.5	T2 > 300 F at r = 3.8
Propane	1.13	5.0-6.0	Low k permits higher ratio

Intercooler Design Basis

Intercooler Approach Temperature: T_intercooler_outlet = T_cooling_medium + Approach Typical approach temperatures: Air-cooled: 15-30 F above ambient Water-cooled: 10-15 F above water inlet Chilled water: 5-10 F above chilled water temp Two-Stage with Intercooling: Stage 1: P1 --> P_inter at r1 Intercooler: cool to T_ic (near T1) Stage 2: P_inter --> P2 at r2 Optimal split: r1 = r2 = sqrt(P2/P1) P_inter = sqrt(P1 x P2) Three-Stage with Intercooling: r_per_stage = (P2/P1)^(1/3) P_inter1 = P1 x r P_inter2 = P1 x r^2

Power Savings from Intercooling

Intercooling reduces the inlet temperature to each subsequent stage, reducing the work per stage. The power savings increase with the overall compression ratio and the effectiveness of intercooling.

Overall Ratio	Configuration	T2 Final (F)	Relative Power
r = 6.0	Single stage	430 F	100%
r = 6.0	2-stage, IC to 120 F	255 F	87%
r = 9.0	Single stage	520 F	100%
r = 9.0	2-stage, IC to 120 F	285 F	84%
r = 9.0	3-stage, IC to 120 F	230 F	80%

Natural gas, k = 1.27, T1 = 100 F, eta = 0.85 per stage.

Economic consideration: Adding an intercooler stage typically costs $50K-$200K but can save 10-15% in operating power. For compressors above 500 HP running continuously, the payback period is typically 1-3 years through fuel savings alone.

5. Temperature Limits and Material Considerations

Discharge temperature limits are set by the weakest component in the gas path: valve plates, packing, lubricant, or cylinder material. Different services impose different constraints.

Component	Material	Max Temp (F)	Failure Mode
Valve plates	Stainless steel	350	Fatigue, warping
Valve plates	PEEK polymer	300	Softening, deformation
Piston rings	PTFE-filled	500	Accelerated wear
Piston rings	Bronze	600	Galling
Packing	PTFE	500	Extrusion, leakage
Lubricant	Mineral oil	350	Carbonization, coking
Lubricant	Synthetic (PAO)	400	Breakdown, deposit formation
Cylinder liner	Cast iron	450	Thermal distortion

Service-Specific Temperature Limits

Service	Max T2 (F)	Reason	Reference
Standard natural gas	300	Valve and lube life	GPSA, manufacturer
Sour gas (H2S > 100 ppm)	275	SSC prevention, corrosion	NACE MR0175
Hydrogen service	275-300	Embrittlement, decarburization	API 618
CO2 service	300	Carbonic acid corrosion	Operating experience
Oxygen service	250	Autoignition risk	CGA G-4.4
Non-lubricated	350	Ring/packing wear	Manufacturer limits

Temperature monitoring: Install discharge temperature transmitters on each cylinder end with high-temperature alarms at 275 F and shutdown at 300 F (or per manufacturer). RTDs preferred over thermocouples for accuracy at these temperatures.

6. Worked Examples

Example 1: Single-Stage Natural Gas Compression

Given: Gas: Natural gas, SG = 0.65 P1 = 250 psia, P2 = 800 psia T1 = 90 F, k = 1.27, eta = 0.85 Step 1: Compression ratio r = P2/P1 = 800/250 = 3.20 Step 2: Temperature exponent (k-1)/k = (1.27-1)/1.27 = 0.2126 Step 3: Isentropic discharge temperature T1_abs = 90 + 459.67 = 549.67 R T2_isen = 549.67 x 3.20^0.2126 T2_isen = 549.67 x 1.270 = 698.1 R = 238.4 F Step 4: Actual discharge temperature T2_actual = 549.67 + (698.1 - 549.67)/0.85 T2_actual = 549.67 + 174.6 = 724.3 R = 264.6 F Result: T2 = 265 F (Below 300 F limit) Single-stage compression is acceptable.

Example 2: Two-Stage with Intercooling

Given: Gas: Natural gas, SG = 0.65 P1 = 100 psia, P2 = 1000 psia T1 = 100 F, k = 1.27, eta = 0.85 Step 1: Overall ratio r_overall = 1000/100 = 10.0 (Too high for single stage) Step 2: Optimal staging r_per_stage = 10.0^(1/2) = 3.162 P_inter = sqrt(100 x 1000) = 316.2 psia Step 3: Stage 1 discharge temperature T1_abs = 559.67 R T2_stage1 = 559.67 x 3.162^0.2126 = 559.67 x 1.274 T2_stage1 = 713.0 R = 253.3 F (isentropic) T2_actual_s1 = 559.67 + (713.0 - 559.67)/0.85 T2_actual_s1 = 740.1 R = 280.4 F Step 4: After intercooler (approach = 15 F) T_ic_out = 100 + 15 = 115 F = 574.67 R Step 5: Stage 2 discharge temperature T2_stage2 = 574.67 x 3.162^0.2126 = 574.67 x 1.274 T2_stage2 = 732.1 R = 272.4 F (isentropic) T2_actual_s2 = 574.67 + (732.1 - 574.67)/0.85 T2_actual_s2 = 759.9 R = 300.2 F Result: T2_final = 300 F (At limit - acceptable) Intercooling reduced T2 from a projected 500+ F (single stage) to 300 F while saving approximately 15% power.

Quick Estimation Table

Compression Ratio	k = 1.15	k = 1.27	k = 1.40
r = 2.0	149 F	174 F	199 F
r = 2.5	173 F	207 F	241 F
r = 3.0	193 F	236 F	278 F
r = 3.5	210 F	261 F	311 F
r = 4.0	226 F	284 F	341 F
r = 5.0	254 F	324 F	396 F

Actual discharge temperatures at T1 = 100 F, eta = 0.85. Values in bold exceed 300 F limit.

Discharge Temperature Calculations

300-350 F

k = Cp/Cv

r > 3.5-4.0

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