# 04.10 Pumps and Compressors

### Compressor Efficiency: Ideal gas

Compressor efficiency using an ideal gas assumption (uakron.edu, 13min) Propane is compressed from -100F and 1 bar to 180F and 10 bar. This is enough information to compute the efficiency of the compressor. In this video, we use the ideal gas assumption. We solve the same problem later using more accurate property estimates. Re-watching this video after you have solved the problem using the chart will help you to understand a lot about the influences of molecular interactions and their significance in accounting for the work that goes into designing a chemical engineering process.

Comprehension Questions:
1. An ordinary vapor compression cycle (OVC) is to be considered for cryogenic cooling. The process fluid is to be propane with a compression/expansion ratio (ie. PHi/PLo) of 5.2. The evaporator coils operate at 0.148MPa. The adiabatic compressor's actual exit temperature is 120°F. You may assume the ideal gas law. Hint: what temperature is implied by the pressure of 0.148MPa for the "evaporator." (cf. Eqn. 2.47).
(a) Write the energy balance for the compressor.
(b) Estimate the actual work required for this compressor.
(c) Write the entropy balance required to estimate the efficiency of the compressor.
(d) Estimate the reversible work required for this compressor.
(e) Estimate the compressor's efficiency.
2. HFC134a is to be considered as the working fluid in a prospective refrigeration system. HFC134a (MW=102) is compressed in an adiabatic compressor from 244K and saturated vapor to 316K and 0.9856MPa. Assume the ideal gas law.
(a)
Write the energy balance for the compressor.
(b) Estimate the actual work required for this compressor.
(c) Write the entropy balance required to estimate the efficiency of the compressor.
(d) Estimate the reversible work required for this compressor.
(e) Estimate the compressor's efficiency
.

1.     An ordinary vapor compression cycle (OVC) is to be considered for cryogenic cooling. The process fluid is to be propane with a compression/expansion ratio (ie. PHi/PLo) of 5.2. The evaporator coils operate at 0.148MPa. The adiabatic compressor's actual exit temperature is 120°F. Whenever using the chart, show your work on the attached chart.27%

a.      Write the energy balance for the compressor. (3)

b.     Estimate the required properties at the compressor inlet to estimate the work.(3)

c.      Estimate the required properties at the compressor outlet to estimate the work.(3)

d.     Estimate the actual work required for this compressor. (3)

e.      Estimate the coefficient of performance of a Carnot cycle operating between equivalent inlet and outlet conditions.(5)

f.      Write the entropy balance required to estimate the efficiency of the compressor.(3)

g.     Estimate the required properties to estimate the efficiency of the compressor.(4)

h.     Estimate the compressor's efficiency.(6)

How to read a pressure-enthalpy chart (uakron.edu, 9min) In principle, reading properties from a chart is no different from looking them up in a table (like the steam tables). In some ways, you could argue that it is easier because interpolation is unnecessary. On the other hand, there are so many lines of the propane chart, all going in different directions, it can be a little confusing at first. In general, the best approach is to use the saturation table when you can, and read the chart when necessary. This video walks you through the process.

Comprehension Questions:
1. HFC134a is to be considered as the working fluid in a prospective refrigeration system. HFC134a (MW=102) is compressed in an adiabatic compressor from 244K and saturated vapor to 316K and 0.9856MPa. (a) Estimate the pressure(MPa), enthalpy (J/g) and entropy(J/g-K) for the compressor inlet. (b) Estimate the enthalpy (J/g) and entropy(J/g-K) for the compressor outlet.

### Compressor Efficiency: Using the chart

Compressor efficiency using real propane (uakron.edu, 11min) Propane is compressed from -100F and 1 bar to 180F and 10 bar. This time we solve for the compressor efficiency using the chart to estimate the thermodynamic properties.

Comprehension Questions:
1. Re-watch the video showing the solution of this problem based on the ideal gas law. What is the temperature exiting an adiabatic, reversible compressor assuming the propane inlet above? How does that compare to the temperature for an adiabatic, reversible ideal gas? Explain why one is higher than the other.
2. HFC134a is to be considered as the working fluid in a prospective refrigeration system. HFC134a (MW=102) is compressed in an adiabatic compressor from 244K and saturated vapor to 316K and 0.9856MPa. (a) Write the relevant energy balance. (b) Write the relevant energy balance. (c) Solve for the actual work (J/g) (d) Estimate the efficiency of the compressor.

### Isothermal, Reversible Compression

Isothermal compression of steam (uakron, 11min) Compute the work of isothermally and reversibly compressing steam from 5 bars and 224°C to 25 bars. Pay close attention to the problem statement!

Comprehension Questions:
1. Two moles of methane at 3bar and 200K are isothermally and reversibly compressed to 30 bar in a piston/cylinder.
Assume the ideal gas law.
(a) Write the energy and entropy balances.
(b) Estimate the change in entropy (J/K) and enthalpy (J).
(c) Solve for the work(J/g).
2. Two moles of methane at 3bar and 200K are isothermally and reversibly compressed to 30 bar in a piston/cylinder.  Use the chart and table for methane.
(a) Write the energy and entropy balances.
(b) Estimate the change in entropy (J/K) and enthalpy (J).
(c) Solve for the work(J/g).
(d) Compare the changes in entropy and enthalpy for real methane to those for ideal gas methane.