Compressor Problem in thermodynamics

[reh]

Hello, I am 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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Homework Equations

The Attempt at a Solution

[/B]

I have found the solution in a) to be 274 kj/kg, so that supplier B would be preferred. What i don't 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.

 

[anathema]

Thank you for sharing your thoughts and calculations on this problem. It seems like you have a good understanding of the task at hand. Regarding your question about the units of the conversion factor, it is possible that there is a mistake in the given units. It would be best to clarify this with your boss or the suppliers to ensure that your calculations are accurate.

In terms of finding the best combination of equipment, your approach is correct. You need to compare the total cost (purchase cost + operational cost) for each combination and choose the one with the lowest cost. Keep in mind that you also need to consider the lifespan of the equipment (10 years for frontal and 5 years for radial) when calculating the total cost.

I hope this helps and good luck with your project!