Centrifugal Compressor Horsepower

GAS COMPRESSION INTRODUCTION In gas production operations, it is sometimes necessary for the pressure of the gas to be raised to a higher value. Some of these reasons are shown below: 1. To supplement the reservoir energy (as the gas reservoir depletes) so as to overcome all the pressure losses in the system and the pressure of the line into which the gas is being delivered. 2. To overcome the losses incurred in the long distance transportation of natural gas through transmission lines. 3. For re-injection of gas for pressure maintenance, gas cycling or gas lifting 4. For injection of gas into storage fields.

TYPES OF COMPRESSORS To achieve this step change in the pressure of the gas, a compressor is used. Compressors can be classified into two main types: 1. Positive-displacement, or intermittent flow units and 2. Continuous flow units.

Continuous flow units are those in which a rapidly rotating element accelerates the gas as it passes through the element, converting the velocity head into pressure. Centrifugal compressors are continuous flow units in which one or more rotating impellers, usually shrouded on the sides, accelerate the gas.

CENTRIFUGAL COMPRESSORS

Compression in a centrifugal compressor depends on the transfer of energy from a rotating set of blades to the gas. The rotor accomplishes this energy transfer by changing the momentum of gas. In the process, the momentum (related to kinetic energy) is converted into useful pressure energy by slowing the gas down in a stationary diffuser. The centrifugal designation is used because the gas flow is radial, and the energy transfer is predominantly due to a change in the centrifugal forces acting on the gas. The centrifugal compressor has an impeller with radial or backward slanted vanes. The gas is forced through the impeller by the mechanical action of the rapidly rotating impeller vanes. The velocity generated is then converted into pressure. The attached diagram below illustrates a single-stage centrifugal compressor with radial vanes. This utilizes a radial diffuser and a volute gas collector ending in a volute diffuser. Multistage centrifugal compressors utilize two or more impellers arranged for series flow, each with a radial diffuser and return channel separating impellers. A section of a typical uncooled multistage compressor is attached.

Single-Stage Centrifugal Compressor with Radial Vanes

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THE AIM OF THIS PROJECT IS TO CALCULATE THE HORSEPOWER REQUIRED BY A CENTRIFUGAL COMPRESSOR. The question was taken from, Gas Production Operations, Beggs 1984: Example5-5: Using the following data, estimate the horsepower required for a centrifugal compressor to compress 50MMscfd of a 0.6 gravity gas. p1 = 100psia p2 = 400psia Psc = 14.65psia Z1 = 0.988 T1 = 80oF k =1.28 Tsc =60oF Bg = 0.131 ft3/scf

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MEASUREMENT AND CALCULATIONS Step 1: Calculate the Actual Inlet Volume. Actual Inlet Volume, q = qwBg = 50 x 10

scf day

6

x 0.131

ft 3 scf

x

day 1440 min

3

= 4548.61

ft min

Step 2: Determine the Polytropic Efficiency of the Dynamic Compressor. Using Figure 1 in the Appendix: 3

ft With an inlet capacity of 4548.61 min

, the approximate polytropic efficiency is

72%

Step 3: Calculate (n-1)/n Adiabatic compression is obtained when there is no heat added to or removed from the gas during compression. The compression process is expressed by:

p1 V 1k =p 2 V 2k Dynamic units generally are designed based on the polytropic cycle where the pV relationship is: n

n

p1 V 1 =p 2 V 2

; Where n ≠ k

The quantity (n-1)/n is frequently needed as can be obtained from the equation below

n−1 k −1 = n k ηp Therefore:

1.28−1 1.28 (0.72)

= 0.304

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Step 4: Calculate Discharge Temperature of the gas. T 1 = 80oF = 460 +80 =540oR r=

p2 p1

=

400 100

=4

Discharge Temperature,

T 2 =T 1 r (n−1)/n =¿

0.304

540 (4 )

= 822.96 oR

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Step 5: Calculate Average Compressibility of the gas Calculate the discharge compressibility, Z 2 using the Figures 2 & 3 shown in Appendix. Determine the Pseudo Critical Pressure and Pseudo Critical Temperature from Figure 2 using the Specific Gravity, γg = 0.6: Pseudo Critical Pressure, Pc = 670 psia Pseudo Critical Temperature, Tc = 360 oR Pseudo Reduced Pressure, Ppr = 400/670 = 0.597 Pseudo Reduced Temperature, Tpr = 822.96/360 = 2.286 Determine the Discharge Compressibility from Figure 3 using the Pseudo Reduced Pressure and the Pseudo Reduced Temperature: Discharge Compressibility, Z2 =0.991 Average Compressibility,

Z´

=

0.988+ 0.991 2

= 0.99

Step 6: Calculate the Atomic Mass of the gas Atomic Mass, M= 28.96 γ g Atomic Mass, M = 28.96 (0.6) = 17.38 lbm/lb-mole

Step 7: Calculate Polytropic Head

Polytropic Head, Hp =

=

r (¿¿(n−1)/n)−1 ¿ R T 1 n ´z ¿ M (n−1)

; where R is the gas constant

540 (¿)(0.99) ¿ 4 (¿¿ 0.304)−1 ¿ 1545 ¿ ¿

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ft−lb lb m

= 81,911.26

Step 8: Calculate the Mass Flow Rate Mass Flow Rate, w = 50 x 106

scf 17.38 lb m 1 day day 379 scf 1440 min

= 1591.91

lbm min

Step 9: Calculate the Power Required Horsepower Horsepower, Hp =

w Hp 33,000 η p

=

1591.91( 81,911.26) (33,000)(0.72)

= 5490.02 Hp

APPENDIX

Figure 1: Approximate polytropic efficiency vs inlet volume

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Figure 2: Pseudo critical properties of natural gas

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Figure 3: Compressibility factors for natural gas

References: (Beggs, 1984) 8 | Page