We can break the problem down into multiple parts:
1. First, we determine the amount of water that needs to be evaporated.
2. Then, we find the heat required to evaporate the water.
3. Finally, we calculate the cost of fuel to provide the required heat.
Let's do this step by step:
1. Amount of water to evaporate:
Mass of wet sugar = 100 kg
Mass fraction of water in wet sugar = 1/5
Mass of water in wet sugar = (1/5) * 100 kg = 20 kg
The evaporator removes 85% of the entering water:
Mass of water evaporated = 0.85 * 20 kg = 17 kg
2. Heat required to evaporate water:
1 kg of water = 2.205 lbm (pounds mass)
17 kg of water = 37.485 lbm
1 lbm of water requires 1000 Btu to evaporate:
Heat required to evaporate 17 kg (37.485 lbm) of water = 37,485 Btu
3. Calculate the cost of fuel
As of October 2021, the cost of a barrel of oil is around $80 USD (source: https://www.macrotrends.net/1369/crude-oil-price-history-chart). Therefore:
1 barrel of oil = 6,000,000 Btu
1 Btu of oil = $80 / 6,000,000 = $0.0000133
Cost of fuel to evaporate 37,485 Btu = 37,485 Btu * $0.0000133 = $0.498
Now, let's consider the change in cost based on efficiency:
First-stage drying efficiency = 80% (0.8)
Remaining drying efficiency = 50% (0.5)
The heat required in both stages will be the same due to needing to evaporate the same amount of water, but the energy input into the system will differ based on efficiency.
First stage required energy input:
37,485 Btu / 0.8 = 46,856.25 Btu
Remaining stage required energy input:
37,485 Btu / 0.5 = 74,970 Btu
Total energy input with efficiency included = 46,856.25 + 74,970 = 121,826.25 Btu
Cost of fuel with efficiency considered:
121,826.25 Btu * $0.0000133 = $1.62
So, the cost to dry the sugar increases to $1.62 with the efficiency changes considered.
Wet sugar, containing one-fifth water by mass is conveyed through an evaporator in which 85.0% of the entering water is vaporized. Taking a Basis of 100 kg of feed to the evaporator
A barrel of oil contains about 6 million Btu and about 1000 Btu is needed to evaporate one lbm of water. Find the current cost of a barrel of oil (document your source) and determine the cost of fuel per 1 lbm to dry the sugar. How does your cost change if the first stage drying (to 85% of the water is evaporated) is only 80% thermally efficient and the remaining drying is 50% efficient?
After calculation, I figure out that I need to find the cost to dry 200 tons of water to get sugar. However, when "the first stage drying (to 85% of the water is evaporated) is only 80% thermally efficient and the remaining drying is 50% efficient", I feel like it just costs the same amount of money because we still need to dry 200 tons of water. However, i am not sure if it is right?
Any help is greatly appreciated
1 answer
1 answer