# Compressor Problem in thermodynamics

Hello, im working on the following problem:

## Homework Statement

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During the modifications in the process you are working on, your direct boss is interest in replacing a few equipment for new ones in order to improve the process and save some operational cost. One of the critical equipment is a compressor. The compressor needs to work using CO2 and due to the
process flow sheet, it will have a pressure of 100 kPa, a Temperature of 200 K and a velocity of 10 m/s when the flow goes into the compressor. The output is the inlet pressure increased by 1000 kPa, the temperature is 500 K and the speed is increased to 125 m/s. When talking to the different
suppliers you find out that there are three options to choose from, those are.

Supplier Maximum work [kJ/kg]
A 100
B 300
C 200
Values in the table are given in absolute numbers
From the supplier you will buy the equipment there are two options. Frontal and radial. Frontal equipment have a purchasing cost of 150000 NOK and an operational cost following the upcoming formula:
Operation cost: working hours (TOTAL) * work to be done [kJ/kg]* Converter factor.
For this case the converter factor is 0,07. The units of this factor are [NOK*kg/(kJ*years)]. This equipment must be replace every 10 years.
The radial equipment have a purchase of 110000 NOK and the operational cost is as the previous formula with a converter factor of 0,05 with the same units as before. This equipment must be changed every 5 years.
The process should run for 15 years. So, a) which supplier you will by it form? b) Which combination of equipment (frontal and/or radial) will you suggest to buy and why?

EXTRA INFO:
1 year = 8000 hours
Work in the operational cost is in absolute number.
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## The Attempt at a Solution

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I have found the solution in a) to be 274 kj/kg, so that supplier B would be preferred. What i dont get is task b). I assume that the task b is solved by finding the combination of Frontal or Radial equipment that gives the lowest total cost for a operation period of 15 years (either 1 frontal + 1 radial or 3 * radial), that includes the price cost + the operational cost. When i calculate f.ex. 10 years of operational time of the frontal equipment, by using the formula provided, i put in the total amount of hours (10 * 8000) multiplied with the work that i got out in task a) and the conversion factor. Since the units of the conversion factor is (NOK * kg)/(kj * years), i have to convert it so that i have in units of (NOK * kg)/(kj * hours).
The problem is when i do that, i get a very small number compared to the buying price of the equipment and unlikely to be the operational cost of 10 or 5 years for the frontal or radial equipment. Could the unit of the conversion factor be in (NOK * kg)/(kj * hours) or have i misunderstood the task? I get more reasonable answer if the unit was that.