Page 93 - Compression Machinery for Oil and Gas

82 SECTION II Types of Equipment

On straight thru compressors, a balance piston is placed adjacent to the last
stage impeller to partially balance the thrust from the impellers and seals within
the compressor. The force acting on the balance piston is opposite of the impel-
lers and is due to the differential pressure across the piston between the high-
pressure cavity at the last stage impeller and the lower-pressure cavity outboard
of the balance piston, which is connected to the compressor suction. The bal-
ance piston is sized to reduce the overall thrust load.
As compared to the impeller, the thrust at the balance piston and other seals
is a more straightforward calculation. The sum of the loads is the thrust. Due to
multiple conditions of operation, the total thrust will vary. On determining the
expected range of thrust loading, an appropriate thrust bearing can be selected.
Thrust loads of centrifugal impellers are a result of a pressure imbalance
between the front face and the rear face of the impeller. The sum of these forces
over all impellers and the forces created by the balance piston are the resulting
load on the compressor thrust bearing [19a].
From the axial momentum equation, which takes into account the change of
the axial momentum of the gas, and the forces due to the static gas pressure in
the axial direction:
ðð þ
! ! ! ! !
ρ C C dA ¼ p dA + F (3.3)
we get the resulting forces on the impeller as (Fig. 3.47)

! ! !
ð
F impeller ¼ F momentum c exit , c inlet Þ F pressure p cavity, front , p cavity,rear , p inlet , p exit
(3.4)
The front and rear cavities are formed between the impeller tip and the lab-
yrinth seals at the impeller inlet, and the impeller hub seals, respectively.
The force on the thrust bearing is thus (Fig. 3.48)
! ! !
(3.5)
F thrust bearing ¼ F impeller F balance piston p discharge , p suction
In the simplest approach to calculate the forces on the impeller, one would
assume the pressure in the front and rear cavities to be equal to the pressure at
the impeller tip. In a shrouded impeller, however, the gas in the cavity is subject
to swirl, and as a result, the static pressure at lower radii is lower than at the tip.
The amount of swirl is a function of the cavity geometry, and the leakage flows
through the labyrinths.
The cavity static pressure distribution can be calculated by
1 2 2 2
prðÞ ¼ p tip ρ qωð Þ r r (3.6)
tip
2
accounting for the cavity characteristics by introducing a cavity swirl coeffi-
cient q.