| name | reciprocating-compressor |
| description | Reciprocating compressor design — thermodynamic cycle (isentropic, polytropic), volumetric efficiency, valve dynamics (spring-mass, flow coefficient), rod load calculation (tension/compression), piston rod packing, API 618 design criteria, pulsation analysis (acoustic analog), cylinder sizing and staging, intercooler design, gas force diagram, and ASME/API standards for industrial reciprocating compressors. |
| metadata | {"priority":7,"promptSignals":{"phrases":["reciprocating compressor","piston compressor","API 618","compressor valve","pulsation analysis","cylinder rod load"],"minScore":3}} |
Reciprocating Compressor — Complete Skill
Thermodynamic Cycle
Indicator Diagram
Ideal indicator diagram:
Suction → compression (isentropic) → discharge → re-expansion of clearance gas
Four processes on PV diagram:
- 1→2: Isentropic compression from suction (p₁) to discharge (p₂)
- 2→3: Discharge at constant p₂ (discharge valve open)
- 3→4: Isentropic re-expansion of clearance volume gas
- 4→1: Suction at constant p₁ (suction valve open)
Volumetric efficiency:
η_v = 1 − c × (r_p^(1/n) − 1) [c = clearance ratio = V_clearance/V_displacement; r_p = p₂/p₁ pressure ratio; n = polytropic exponent]
For isentropic: n = γ = c_p/c_v; practical n = 1.3–1.4 (heat transfer effects)
Example:
r_p = 4.0; c = 0.05; n = 1.35 (methane, γ ≈ 1.31)
η_v = 1 − 0.05 × (4.0^(1/1.35) − 1) = 1 − 0.05 × (4.0^(0.741) − 1) = 1 − 0.05 × (2.68 − 1) = 1 − 0.084 = 0.916 = 91.6%
Actual volumetric efficiency: corrected for valve pressure drop, gas heating, leakage
η_v_actual ≈ η_v_ideal × 0.85–0.97 (depending on design quality)
Compression Power
Theoretical and Actual Power
Isentropic power:
W_is = (n/(n−1)) × p₁ × V₁ × (r_p^((n−1)/n) − 1) [per stage; V₁ = actual suction flow in m³/s]
Or: W_is = ṁ × (H₂ − H₁) [ṁ = mass flow; H = enthalpy from gas properties/equation of state]
Shaft power:
W_shaft = W_is / (η_compression × η_mechanical)
η_compression: accounts for heat transfer during compression; typically 0.80–0.95
η_mechanical: accounts for bearing friction, drive losses; 0.95–0.98
Staging for high pressure ratio:
For overall r_p large → divide into N stages with intercooling between
Optimal r_p per stage: r_stage = r_p_total^(1/N) (equal ratios minimize total work with perfect intercooling to T₁)
Total work with N stages < single stage (intercooling restores T to T₁ between stages → lower compression work)
Example (methane, p₁ = 1 MPa, p₂ = 10 MPa, 2 stages):
r_stage = √10 = 3.162 per stage (with intercooling)
T₂_stage1 = T₁ × r_stage^((n-1)/n) = 293 × 3.162^(0.248) = 293 × 1.345 = 394 K = 121°C
Intercooler cools back to 40°C; stage 2 starts at 313 K
W_total = 2 × W_stage ≈ 2 × (1.35/0.35) × 1×10⁶ × V₁ × (3.162^0.259 − 1)
Valve Dynamics
Automatic Compressor Valves
Valve type: flat disk, ring plate, poppet, channel/plastic flexing plate
Self-actuating: valve opens when differential pressure across valve exceeds spring force
Spring-mass model:
m_valve × ẍ + c × ẋ + k × x = F_pressure(t) − F_spring
F_pressure = ΔP(t) × A_valve_seat
Natural frequency of valve: f_n = 1/(2π) × √(k/m_valve) [must be >> operating frequency to avoid resonance]
Valve flow coefficient (Cv):
Flow through open valve: Q = Cv × √(ΔP / ρ_gas) [standard form]
Or: ΔP_valve = ṁ² / (2 × ρ × A_eff²) [A_eff = effective flow area = lift × port perimeter × Cd]
Target: ΔP_valve < 3% of stage pressure ratio × p₁ (API 618 guidance)
Impact velocity:
Valve closes at end of stroke; valve plate impacts seat at v_impact
API 618: v_impact ≤ 0.5 m/s for standard materials; poppet: ≤ 1.5 m/s
High impact velocity → shortened valve life (fatigue); measure with dynamic pressure transducers
Rod Load Calculation
Gas Force Analysis
Combined rod load (CRANKSHAFT end analysis):
F_rod = F_gas − F_inertia [net rod load seen by crosshead pin, crankshaft; alternates sign]
Gas force:
F_gas = (p_DE × A_piston) − (p_CE × A_rod_end) [for double-acting; DE = drive end; CE = crank end; A_rod_end = A_piston − A_rod²]
Inertia force:
F_inertia = m_reciprocating × a_max [a_max = r × ω² at TDC/BDC; r = crank throw; ω = angular velocity]
m_reciprocating = m_piston + m_piston_rod + m_crosshead × fraction
Maximum tension/compression rod load:
Tension: F_tension = F_gas_max_suction_stroke − F_inertia (at BDC)
Compression: F_compression = F_gas_max_discharge_stroke + F_inertia (at TDC)
API 618 rod load limit:
Maximum allowable rod load: depends on frame rating; per API 618 Table; typically 15–200 kN for small-medium frames
Compressive rod load limited by Euler column buckling of rod: F_Euler = π² × E × I / L_eff²
Rod cross-section: d_rod = √(4 × F_max / (π × σ_allow)) [σ_allow typically 120–150 MPa for forged alloy steel rod]
Piston Rod Packing
Pressure Packing Design
Rod packing: series of rings that seal against piston rod; prevent gas leakage
Ring types: full-face radial rings, partial pressure-balanced rings (tangential spring-loaded)
Material: PTFE (soft; low friction; moderate temperature); filled PTFE; carbon (higher T and pressure)
Leakage rate (per API 618):
Acceptable leakage: typically < 0.1% of throughput for non-lube packing
Vent connection between packing sets (for toxic/flammable gas); vent to flare/recovery
Packing cooling:
Water cooling of packing case if rod temperature > 130°C (from friction or hot gas)
Rod cooling: oil-flooded packing (lube systems); or dry-running PTFE (oil-free compressors)
Pulsation Analysis (API 618, Appendix M)
Acoustic Analog Method
Pulsation: pressure fluctuations caused by intermittent flow from cylinders → acoustic resonance in piping → vibration → fatigue failure
Acoustic length: L_acoustic = c_sound / (2 × f_excitation) [quarter-wave resonance; full-wave; modes]
c_sound in gas: c = √(γ × R × T / M_mol) [c [m/s]; R = 8.314 J/mol·K; M_mol = molar mass]
API 618 Approach 1: pulsation control without acoustic analysis (use pulsation bottles/dampeners per formula)
Pulsation bottle volume: V_bottle ≥ K × V_stroke [K = 5–10; V_stroke = cylinder displacement per stroke]
Bottle volume attenuates pressure pulsations by acting as capacitance in acoustic circuit
API 618 Approach 2/3: full acoustic simulation (PULS software, Expander, or similar)
Digital model of piping + compressor + vessels → solve acoustic pressure distribution → compare to API 618 limits
API limit: peak-to-peak pressure pulsation < 2% of mean line pressure (in pulsation-sensitive service)
Staging and Intercooling
Multi-Stage Design
Intercooler heat duty:
Q_intercooler = ṁ × c_p × (T_out_stage1 − T_cooler_outlet) [remove heat; T_cooler_outlet = 40–50°C typically]
Material: carbon steel tubes (for clean hydrocarbon gas); SS 316 for corrosive; fins if air-cooled
Stage pressure limits:
API 618: inter-stage temperature ≤ 160°C for hydrocarbon gas (auto-ignition risk)
Maximum discharge temperature per stage: T_max = T_suction × r_stage^((n-1)/n) ≤ 135°C (API) for lubricated
Discharge temp too high → oil breakdown → valve deposits → valve failure
Staging design table:
| Stage | p_in [MPa] | p_out [MPa] | T_in [°C] | T_out [°C] | Power [kW] |
|---|
| 1 | 0.1 | 0.35 | 40 | 97 | 150 |
| 2 | 0.35 | 1.05 | 40 | 97 | 140 |
| 3 | 1.05 | 3.5 | 40 | 97 | 135 |
Standards and References
| Standard | Scope |
|---|
| API 618 | Reciprocating compressors for petroleum industry |
| API 11P | Specification for packaged reciprocating gas compressor units |
| ASME PTC 9 | Performance test code for reciprocating compressors |
| ISO 13707 | Reciprocating compressors (general industry) |
| ASME B31.3 | Process piping (compressor inlet/outlet piping) |
| API 670 | Machinery protection systems (vibration monitoring) |
Output
Provide: service (gas: composition; MW [g/mol]; γ = c_p/c_v; Z compressibility; p₁ [MPa]; p₂ [MPa]; flow ṁ [kg/s] or Q₁ [m³/min]), staging (N_stages; r_stage = r_p_total^(1/N); intercooler T_out [°C]; max discharge T_check per stage), volumetric efficiency (c [%]; n; η_v = 1−c×(r_stage^(1/n)−1) [%]; actual flow = η_v×displacement [m³/min]), cylinder sizing (displacement V_d = Q₁/(η_v×n_rpm) [m³/rev]; bore D [mm]; stroke L [mm]; N cylinders; single/double acting), power (W_is per stage [kW]; η_comp; η_mech; shaft power [kW]; motor sizing [kW]), rod load (F_gas_max [kN]; F_inertia [kN]; F_tension [kN]; F_compression [kN]; API 618 frame limit [kN]; rod diameter [mm]; Euler check), valves (type: plate/ring/poppet; ΔP_valve [kPa] ≤ 3% × p₁×r; impact velocity [m/s] ≤ 0.5; material for discharge T), pulsation (approach: API 618 Approach 1/2/3; bottle volume [L]; pulsation level [%] ≤ 2%; piping resonance check), and applicable standard (API 618 for design; ASME PTC 9 for acceptance testing; API 670 for condition monitoring).
