﻿ Adiabatic Relationships | Process Engineering

Isentropic means constant entropy (a definition of entropy is beyond the scope of this manual). Adiabatic describes a process wherein no heat is added or subtracted.

For the sake of this discussion, it can be assumed that isentropic and adiabatic are the same (although different thermodynamically). Adiabatic compression is commonly assumed for reciprocating, but not centrifugal compressors.

In isentropic processes, the following relationships apply: where:
C = constant
k = ratio of specific heats where: where:
x = a factor created for convenience where:
T2(theo) = adiabatic discharge temperature (theoretical absolute discharge where:
T2 = Actual discharge temperature, °R where:
Ghp = gas horsepower

Notice that Equation 100-20 has been corrected by an average compressibility, (Z1 + Z2) / 2. Averaging is a fairly accurate approximation of the correction required.

Because of the non-ideal (non-perfect) behavior of many gases, the k exponent does not remain constant during compression. For air, diatomic gases, and inert gases, the change in k is small when the pressures are moderate. However, for most hydrocarbon gases, the variance of k during compression is substantial. The usual correction is to calculate k using MCp (see Equation 100-7) at the average of the compressor (or stage) suction and discharge temperature. MCp values at 14.7 psia are given in the Appendix of this manual.

Using the MCp at atmospheric pressure and average compression temperature for compressor head and power calculations is sufficiently accurate for most applications. However, for very high pressures or other unusual conditions, further corrections are necessary.