Page 80 - Compression Machinery for Oil and Gas

70 SECTION II Types of Equipment

converging taper, a converging taper is recommended as the conservative
approach. While the direct damping increases as seal clearance divergence
increases (more diverging, more damping), a cliff is reached where the damping
suddenly becomes negative and the seal becomes destabilizing. In addition, the
seal clearance taper can be largely influenced by the seal carrier structure.
Deflection of the seal carrier or support structure can impact the taper, thus
influencing the available damping and resulting stability. Overall, seal taper
and carrier deflection should be considered in a rotordynamic analysis for all
honeycomb or hole-pattern seals.
Centrifugal impellers generate destabilizing aerodynamic forces. A widely
applied approach for predicting the bulk impeller aerodynamic cross-coupling
coefficients including eye and shaft seal effects is the Wachel method [11]. This
method was derived when the phenomenon of instability in high-pressure cen-
trifugal compressors first started to cause problems for oil and gas applications.
The original Wachel equation for cross-coupling is shown in Fig. 3.35. For com-
pressors with a single suction and no side streams, this formula may be
collapsed to a single stream.
API 617 provides a slightly different formulation of the Wachel number
known as a modified Wachel’s equation. It differs from the original Wachel for-
mulation in two ways. First, the mole weight variable is replaced with a constant
value of 30. Second, the density ratio is based on a particular impeller stage, not
the density ratio across a section. This density ratio difference can make a large
difference in beam-style compressors as opposed to an overhung design. In
addition, the CFD-based methods have been shown in literature for the calcu-
lation of impeller cross-coupling, including Moore et al. [12a]. While not as
widely used as the Wachel-based equations, CFD methods offer a more

FIG. 3.35 Wachel equation and input parameters [12].