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:
C = constant
k = ratio of specific heats
Had = adiabatic head, ft
x = a factor created for convenience
T2(theo) = adiabatic discharge temperature (theoretical absolute discharge
temperature assuming 100% adiabatic efficiency)
had = adiabatic efficiency
T2 = Actual discharge temperature, °R
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.
Since the change in entropy is not zero in an actual adiabatic compression process, an adiabatic efficiency (had) is used in Equation 100-23 and 100-24. In order to calculate MCp at average compression temperature, it is necessary to estimate the adiabatic efficiency to arrive at a discharge temperature per Equation 100-23. If the estimate is inaccurate, a second iteration may be required.