1. Overview
Reciprocating compressors generate pulsating flow due to the intermittent nature of piston displacement. Without proper pulsation control, pressure pulsations cause piping vibration, valve failures, inaccurate metering, and potential fatigue failures in piping and vessels.
Suction Bottle
Upstream Dampener
Smooths flow to cylinder; prevents piping pulsation
Discharge Bottle
Downstream Dampener
Attenuates high-pressure pulsations
Choke Tube
Acoustic Resistance
Provides filtering between volumes
Internals
Baffles & Plates
Create acoustic chambers within bottle
Why Pulsation Control Matters
| Problem | Cause | Consequence | Industry Impact |
|---|---|---|---|
| Piping vibration | Pressure pulsation at pipe natural frequency | Fatigue failure, leaks | Safety hazard, downtime |
| Valve failure | Reflected pulsation waves at cylinder | Valve plate flutter, breakage | $50K-200K/event |
| Metering error | Pulsating flow through orifice meters | 5-30% measurement error | Revenue loss |
| Performance loss | Pulsation-induced pressure drop | 2-8% efficiency reduction | Higher fuel costs |
| Noise | Acoustic radiation from piping | Exceeding OSHA limits | Regulatory compliance |
Rule of thumb: Pulsation control costs typically represent 10-20% of the compressor package cost but prevent far greater expenses from piping failures, valve replacements, and unplanned shutdowns.
2. Pulsation Sources
The pulsation spectrum depends on compressor configuration, speed, number of cylinders, and whether single-acting or double-acting.
Flow Characteristics by Configuration
| Configuration | Dominant Harmonics | Flow Variation | Relative Pulsation |
|---|---|---|---|
| 1-cyl, single-acting | 1x, 2x, 3x | 100% | Very high |
| 1-cyl, double-acting | 1x, 2x | 30-40% | High |
| 2-cyl, 180 deg crank | 2x, 4x | 20-30% | Moderate |
| 3-cyl, 120 deg crank | 3x, 6x | 5-15% | Low |
| 4-cyl, 90 deg crank | 4x, 8x | 3-8% | Low |
| 6-cyl, 60 deg crank | 6x, 12x | 1-5% | Very low |
Pulsation Frequency Spectrum
Fundamental pulsation frequency:
f_1 = N * RPM / 60 (Hz)
Where N = number of compression events per revolution
For double-acting, single-cylinder: N = 2
For single-acting, single-cylinder: N = 1
For n cylinders on common header with equal crank spacing: N = n (or 2n if DA)
Harmonic frequencies:
f_n = n * f_1 (where n = 1, 2, 3, ...)
Example: 2-cyl DA compressor at 900 RPM
f_1 = 4 * 900 / 60 = 60 Hz (4x because 2 cyl x 2 events each)
f_2 = 120 Hz, f_3 = 180 Hz, ...
3. Sizing Methods
Three primary methods exist for sizing pulsation bottles, ranging from simple volume ratios to full acoustic simulation.
Method 1: Volume Ratio (Preliminary)
Simple volume bottle (no internals):
V_bottle >= F * V_swept
Where:
V_bottle = Internal volume of bottle (in^3 or ft^3)
V_swept = Cylinder swept volume (in^3 or ft^3)
F = Volume multiplier
Recommended multipliers (F):
Suction bottle: F = 10 to 15
Discharge bottle: F = 5 to 10
High ratio (> 3:1): Increase F by 50%
Swept volume:
V_swept = (pi / 4) * D_bore^2 * Stroke
For double-acting:
V_swept_HE = (pi/4) * D^2 * Stroke
V_swept_CE = (pi/4) * (D^2 - d_rod^2) * Stroke
V_swept_total = V_swept_HE + V_swept_CE
Method 2: Volume-Choke-Volume (Acoustic Filter)
Low-pass acoustic filter design:
The bottle is divided into two chambers connected by a choke tube.
This creates a Helmholtz resonator / low-pass filter.
Cutoff frequency of filter:
f_c = (c / 2*pi) * sqrt(A_c / (L_c * V_1 * V_2 / (V_1 + V_2)))
Where:
c = Speed of sound in gas (ft/s)
A_c = Cross-sectional area of choke tube (in^2)
L_c = Length of choke tube (in)
V_1 = Volume of first chamber (in^3)
V_2 = Volume of second chamber (in^3)
Design criterion:
f_c < 0.5 * f_1 (cutoff below half the fundamental pulsation freq)
Attenuation above f_c:
Attenuation = 20 * log10(f/f_c)^2 dB per octave above cutoff
Typical: 12-18 dB/octave for well-designed V-C-V filter
Method 3: Digital Acoustic Simulation
| Analysis Type | Tool | Output | When Required |
|---|---|---|---|
| 1-D acoustic | Specialized software | Pressure pulsation spectrum | API 618 Approach 2 |
| Forced mechanical response | FEA + acoustic | Piping vibration, stress | API 618 Approach 3 |
| Transient analysis | Time-domain simulation | Startup/shutdown pulsation | Variable-speed units |
| 3-D acoustic (CFD) | CFD software | Internal flow patterns | Complex geometries |
Choke Tube Sizing
Choke tube diameter:
D_choke = (0.35 to 0.50) * D_nozzle
Where D_nozzle = cylinder nozzle diameter
Choke tube length:
L_choke = (3 to 8) * D_choke
Pressure drop through choke:
delta_P = f * (L/D) * (rho * v^2 / 2)
Keep steady-state pressure drop < 0.25% of line pressure
to avoid excessive performance loss.
Acoustic resistance (impedance):
Z_choke = rho * c * (A_pipe / A_choke)
Higher Z_choke = better filtering but more pressure drop.
4. API 618 Requirements
API 618 (Reciprocating Compressors for Petroleum, Chemical, and Gas Industry Services) defines three approach levels for pulsation and vibration control, each with increasing rigor and cost.
API 618 Approach Levels
| Level | Scope | Analysis Method | Cost Impact |
|---|---|---|---|
| Approach 1 | Pulsation suppression devices (analog study or guidelines) | Volume-ratio rules, simple acoustic filters | Baseline |
| Approach 2 | Approach 1 + digital acoustic simulation | 1-D acoustic model of piping system | +5-10% |
| Approach 3 | Approach 2 + mechanical response analysis | Acoustic + piping FEA for vibration/stress | +10-20% |
API 618 Pulsation Limits
Allowable peak-to-peak pressure pulsation at line connection:
P_pulsation (%) = R_L / (P_line * sqrt(D_pipe / ID_ref))
API 618 5th Ed. guideline values:
At cylinder flange: 7% peak-to-peak of line pressure
At line connection: 2% peak-to-peak of line pressure
Simplified API 618 line-side criterion:
P_pulsation_allow = P_line * (R_L / ID_factor)
Where:
R_L = Line pulsation factor (typically 0.02 = 2%)
P_line = Average line pressure (psia)
Pulsation-induced pressure drop (API 618):
delta_P_pulsation < 1% of average line pressure for suction
delta_P_pulsation < 2% of average line pressure for discharge
When to Use Each Approach
| Application | Recommended Approach | Rationale |
|---|---|---|
| Small field gas compressor (< 500 HP) | Approach 1 | Standard bottles adequate |
| Medium process compressor (500-3,000 HP) | Approach 2 | Acoustic verification needed |
| Large pipeline compressor (> 3,000 HP) | Approach 3 | Full mechanical response required |
| High-speed units (> 1,200 RPM) | Approach 2 or 3 | Higher harmonic content |
| Variable-speed operation | Approach 3 | Multiple resonance crossings |
| Critical/unspared service | Approach 3 | Reliability justifies cost |
5. Acoustic Design Considerations
Proper acoustic design requires understanding the speed of sound, acoustic resonance, and the interaction between bottle geometry and piping system.
Speed of Sound in Gas
Speed of sound:
c = sqrt(k * Z * R * T / MW) (ft/s)
Where:
k = Specific heat ratio (Cp/Cv)
Z = Compressibility factor
R = 1545.35 ft-lbf/(lbmol-R)
T = Temperature (R = F + 459.67)
MW = Molecular weight (lb/lbmol)
Typical values:
Natural gas (SG=0.65), 100F, 500 psia: c ~ 1,300 ft/s
Natural gas (SG=0.65), 100F, 100 psia: c ~ 1,400 ft/s
Air, atmospheric: c ~ 1,130 ft/s
Hydrogen, atmospheric: c ~ 4,300 ft/s
Acoustic Resonance in Piping
Open-open pipe (both ends open to volumes):
f_n = n * c / (2 * L) (n = 1, 2, 3, ...)
Open-closed pipe (one end open, one closed):
f_n = (2n - 1) * c / (4 * L) (n = 1, 2, 3, ...)
Helmholtz resonator (volume + neck):
f_H = (c / 2*pi) * sqrt(A / (L_eff * V))
Where:
L = Pipe length (ft)
c = Speed of sound (ft/s)
A = Neck cross-sectional area (ft^2)
L_eff = Effective neck length (physical + end corrections)
V = Cavity volume (ft^3)
Critical rule: No acoustic natural frequency should coincide
with any compressor excitation harmonic (1x through 10x RPM).
Bottle Geometry Guidelines
| Parameter | Guideline | Rationale |
|---|---|---|
| Bottle diameter | 2-3x pipe diameter | Area ratio for acoustic impedance change |
| Bottle length | 3-5x bottle diameter | Avoid internal acoustic resonance |
| Nozzle location | Offset from centerline | Avoid exciting longitudinal modes |
| Baffle spacing | Avoid L = c/(2f) | Prevent standing waves between baffles |
| Choke location | Between 1/3 and 2/3 point | Optimal volume split for filtering |
| Bottle orientation | Horizontal preferred | Liquid drainage, support simplicity |
Design verification: After preliminary sizing, always verify that no acoustic natural frequency of any pipe segment between the bottle and the nearest branch or volume coincides with any compressor harmonic from 1x to 10x RPM. A 20% separation margin is the minimum acceptable.
6. Worked Examples
Example 1: Simple Volume Bottle Sizing
Given:
Single-cylinder, double-acting compressor
Bore = 12 in, Stroke = 8 in, Rod = 3.5 in
Speed = 900 RPM, P_suction = 200 psia, P_discharge = 600 psia
Step 1: Swept volume
V_HE = (pi/4) * 12^2 * 8 = 904.8 in^3
V_CE = (pi/4) * (12^2 - 3.5^2) * 8 = 827.9 in^3
V_swept = 904.8 + 827.9 = 1,732.7 in^3
Step 2: Suction bottle volume (F = 12)
V_suction = 12 * 1,732.7 = 20,792 in^3 = 12.03 ft^3
Step 3: Discharge bottle volume (F = 8)
V_discharge = 8 * 1,732.7 = 13,862 in^3 = 8.02 ft^3
Step 4: Bottle dimensions (suction)
Pipe OD = 8 in, so bottle ID = 2.5 * 8 = 20 in
V = (pi/4) * 20^2 * L = 20,792
L = 20,792 / 314.16 = 66.2 in (5.5 ft)
L/D = 66.2/20 = 3.3 (within 3-5 guideline -- OK)
Example 2: Acoustic Filter Cutoff Frequency
Given:
Same compressor, V-C-V suction bottle
Two chambers: V_1 = V_2 = 10,396 in^3 (equal split)
Choke tube: D = 4 in, L = 24 in
Gas: Natural gas, c = 1,350 ft/s at suction conditions
Step 1: Choke tube area
A_c = (pi/4) * 4^2 = 12.57 in^2
Step 2: Effective volume term
V_eff = V_1 * V_2 / (V_1 + V_2) = 10,396^2 / 20,792
V_eff = 5,198 in^3
Step 3: Cutoff frequency
(Convert to consistent units: c = 1,350 * 12 = 16,200 in/s)
f_c = (16,200 / (2*pi)) * sqrt(12.57 / (24 * 5,198))
f_c = 2,578.3 * sqrt(12.57 / 124,752)
f_c = 2,578.3 * sqrt(0.0001008)
f_c = 2,578.3 * 0.01004 = 25.9 Hz
Step 4: Check against pulsation frequency
f_1 = 2 * 900 / 60 = 30 Hz (double-acting, 1 cylinder)
f_c / f_1 = 25.9 / 30 = 0.86
Problem: f_c should be < 0.5 * f_1 = 15 Hz
Need larger volumes or smaller choke tube.
Solution: Increase total volume to 30,000 in^3
V_eff = 7,500 in^3
f_c = 2,578.3 * sqrt(12.57 / (24 * 7,500))
f_c = 2,578.3 * sqrt(0.0000698) = 2,578.3 * 0.00835
f_c = 21.5 Hz ... still marginal.
Reduce choke diameter to 3 in: A_c = 7.07 in^2
f_c = 2,578.3 * sqrt(7.07 / (24 * 7,500))
f_c = 2,578.3 * sqrt(0.0000393) = 2,578.3 * 0.00627
f_c = 16.2 Hz -- approaching target.
Increase L_c to 30 in:
f_c = 2,578.3 * sqrt(7.07 / (30 * 7,500))
f_c = 2,578.3 * sqrt(0.0000314) = 2,578.3 * 0.00561
f_c = 14.5 Hz < 15 Hz -- ACCEPTABLE
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