Compressor Station Spacing Fundamentals

1. The Pressure Budget

A compressor station raises gas to its discharge pressure. From there the gas loses pressure to friction and to any rise in ground elevation until it arrives at the next station. The difference between the pressure a station can put into the line and the lowest pressure the next station will accept is the pressure budget for that section. Station spacing is simply the distance over which the budget is spent.

• Upper limit: discharge pressure cannot exceed the MAOP of the pipe, which ASME B31.8 sets from the pipe wall, grade and location class.
• Lower limit: the minimum suction pressure the next station is designed to take. Letting pressure fall further raises the compression ratio, the horsepower and the discharge temperature at that station.
• End condition: the gas must still arrive at the delivery point at the pressure the customer or downstream system requires.

Plotted against milepost, the result is the familiar sawtooth: pressure jumps at each station and decays toward the next. For gas, each tooth is curved rather than straight, for reasons covered in section 3.

2. MAOP per ASME B31.8

ASME B31.8 para. 841.1.1 gives the design pressure of steel gas pipe:

• S = specified minimum yield strength, psi
• t = nominal wall thickness, in
• D = nominal outside diameter, in
• F = design factor from Table 841.1.6-1
• E = longitudinal joint factor from Table 841.1.7-1 (1.00 for seamless, ERW and DSAW pipe)
• T = temperature derating factor from Table 841.1.8-1 (1.000 at 250 °F or lower)

Worked example. 24 in OD, 0.375 in wall, X52 (S = 52,000 psi), Class 1 Division 2, ERW:

Stations on this line can discharge at up to 1,170 psig. The example that follows uses 1,100 psig, leaving margin below MAOP.

3. Gas Flow Between Stations

GPSA Engineering Data Book Section 17 gives the transmission flow equations used for pipeline design. All share one structure: flow is proportional to the square root (or a similar power) of the difference of the squared pressures.

For example, the Panhandle B equation (Eq 17-27), with Q in scfd, L in miles, d in inches, T in °R and P in psia:

Why the pressure curve bends

For a fixed flow, these equations say that P² falls roughly linearly with distance. Pressure itself therefore falls along a curve that steepens as pressure drops: the gas expands, speeds up and loses more pressure per mile. A section that starts at 1,100 psig loses its first 100 psi over a much longer distance than its last 100 psi. A straight line drawn between the station pressures overstates the pressure at mid section.

Average pressure

Compressibility Z is evaluated at the average line pressure, GPSA Eq 17-16:

This is the exact average of pressure along a section in which P² falls linearly, and it sits slightly above the arithmetic mean.

4. Elevation in Gas Lines

Gas is light, but not weightless. At transmission pressure a column of gas has real density, and lifting it costs pressure. GPSA Eq 17-15 is printed for a horizontal line; GPSA notes that in the term giving the effect of elevation change the pressure is taken as constant at the average value. The corrected pressure squared term is:

ΔH is the downstream elevation minus the upstream elevation in feet, positive uphill. The constant is not empirical. A gas column has dP/dh = P M / (Z R T × 144) psi per foot with M = 28.9625 G and R = 10.7316; doubling for pressure squared gives 2 × 28.9625 / (10.7316 × 144) = 0.03748.

Values are for G = 0.6 at 60 °F. The static head scales with pressure, so a fixed allowance per foot of rise is wrong at one end of the pressure range or the other. On a long line with rolling terrain the effect largely cancels, but a net rise to the delivery point, or a single large climb, shifts station locations and adds horsepower.

5. Placing the Stations

The calculator places stations by walking the line in short steps, solving the flow equation with the elevation term over each step.

1. March backward from delivery. Starting at the delivery point with the required delivery pressure, step upstream and compute, at every milepost, the pressure needed there to reach delivery with no further compression.
2. Walk forward from receipt. Starting at the receipt pressure, step downstream. While the local pressure is still below the pressure needed to coast to delivery, a station will be required somewhere ahead.
3. Place a station at the suction limit. The station goes at the last point before line pressure would fall below the minimum suction pressure. This spreads the stations as far apart as the suction limit allows.
4. Size the last station to delivery. Once full discharge pressure would carry the gas to delivery, that station is the last one, and it only needs the pressure the backward march calls for at its location.

Worked example

180 miles of 24 in × 0.375 in X52 (MAOP 1,170 psig), 500 MMSCFD of 0.6 gravity gas at 60 °F, Panhandle B with E = 0.95, receipt 700 psig, discharge 1,100 psig, minimum suction 700 psig, delivery 600 psig, over rolling terrain from 780 to 1,380 ft:

Gas arrives at 600.8 psig. Had CS-3 discharged at the full 1,100 psig, delivery would have been 826 psig and the station would have needed about 11,500 hp. Sizing it to delivery saves roughly 4,000 hp, 11% of the line total. On the same line with flat terrain, CS-2 and CS-3 move downstream by about 0.7 mile and the total falls by about 270 hp, the cost of the 430 ft net rise to delivery.

6. Station Horsepower

GPSA Section 13 (centrifugal compressor calculations, page 13-28) gives the polytropic method used here. Suction is taken at the flowing gas temperature, assuming the gas is cooled after each station.

Mass flow is w = Q / (379.5 × 1440) × MW in lb/min, with MW = 28.9625 G.

Worked example: CS-1

• Suction 714.7 psia, discharge 1,114.7 psia, ratio r = 1.560
• k = 1.28 and η_p = 0.82 give (n−1)/n = 0.28 / (1.28 × 0.82) = 0.2668
• Discharge temperature T₂ = 519.67 × 1.560^0.2668 = 585 °R, or 125 °F
• Average compressibility Z_avg = 0.897 (suction and discharge averaged)
• Polytropic head H_p = 19,566 ft·lbf/lbm
• Mass flow w = 500,000,000 / (379.5 × 1440) × 17.378 = 15,899 lb/min
• Gas horsepower = 15,899 × 19,566 / (0.82 × 33,000) = 11,496 hp
• Brake horsepower = 11,496 + 11,496^0.4 = 11,538 hp

As a cross check, GPSA Eq 13-4, the quick estimate of 16 to 18 hp per MMcfd per unit of ratio for ratios of 1.5 to 2.0, gives 12,500 to 14,000 hp. GPSA notes that the quick estimate tends to read high, which is consistent with the rigorous figure above.

7. Assumptions and Limits

• Steady, isothermal flow at the stated flowing temperature. Real lines warm near each station discharge and cool toward ground temperature downstream.
• One pipe size and one location class for the whole line. Class changes along a route change MAOP section by section.
• Z from Beggs-Brill, a fit of the Standing-Katz chart with Sutton pseudocritical properties, typically within 2 to 3% at transmission conditions. Custody and permit work uses AGA-8 or GERG-2008.
• Downhill pressure recovery can push pressure above MAOP between stations on steep terrain. The calculator checks for this and reports where it happens.
• Screening guard: designs that need stations closer than 10 miles apart are refused, because they indicate an undersized pipe rather than a workable layout.
• No transients. Line pack swings, station trips and demand changes need transient simulation before final design.

Standards & References

• ASME B31.8: Gas Transmission and Distribution Piping Systems. Para. 841.1.1 design formula; Tables 841.1.6-1, 841.1.7-1 and 841.1.8-1; para. 840.2.1 location classes.
• GPSA Engineering Data Book, Section 17: Eqs 17-15, 17-16, 17-18, 17-22, 17-25 and 17-27 for transmission line gas flow.
• GPSA Engineering Data Book, Section 13: Eqs 13-33 to 13-39 for polytropic head, gas horsepower, discharge temperature and brake horsepower; Fig. 13-8 for heat capacity ratio.
• Beggs and Brill (1973) compressibility correlation; Sutton (1985) pseudocritical properties.