Distillation Scale up:
In an experiment 100 lb-mol of 47 lb-mol % ethanol, 53 lb mol % water sol'n is fed into distillation column and separated into two streams:
100lb-mol
0.470 lb-mol ethanol
0.530 lb-mol water
goes to:
steam 1:
17 lb-mol
0.890 lb-mol Ethanol
0.110 lb-mol Water
Stream 2:
31.9 lb-mol ethanol
51.1 lb-mol water
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Scale-up: want to produce 733 lb-mol/hr of 0.890 lb-mol ethanol
How would I scale it up? Would I only need to multiply each value by 43.11 from the end? i.e. 17lb mol (of 0.890 ethanol) x 43.11 (from 733/17) to give me 732.xx mol of that ethanol?
To scale up the process, you need to maintain the same composition ratio for the ethanol and water streams. In this case, the composition ratio is 0.470 lb-mol ethanol to 0.530 lb-mol water.
To produce 733 lb-mol/hr of 0.890 lb-mol ethanol, you can follow the steps below:
1. Find the total number of lb-mol/hr of the ethanol stream:
Total lb-mol/hr of ethanol = 733 lb-mol/hr * 0.890 lb-mol ethanol/1 lb-mol ethanol = 652.87 lb-mol/hr
2. Determine the total lb-mol/hr of the water stream:
Total lb-mol/hr of water = Total lb-mol/hr of ethanol * (0.530 lb-mol water / 0.470 lb-mol ethanol)
Total lb-mol/hr of water = 652.87 lb-mol/hr * (0.530 lb-mol water / 0.470 lb-mol ethanol) = 734.75 lb-mol/hr
3. Calculate the lb-mol/hr of ethanol in Stream 1:
lb-mol/hr of ethanol in Stream 1 = Total lb-mol/hr of ethanol * (lb-mol ethanol in Stream 1 / Total lb-mol/hr)
lb-mol/hr of ethanol in Stream 1 = 652.87 lb-mol/hr * (17 lb-mol ethanol / 100 lb-mol) = 111.03 lb-mol/hr
4. Calculate the lb-mol/hr of water in Stream 1:
lb-mol/hr of water in Stream 1 = Total lb-mol/hr of water - lb-mol/hr of water in Stream 2
lb-mol/hr of water in Stream 1 = 734.75 lb-mol/hr - 51.1 lb-mol/hr = 683.65 lb-mol/hr
5. Calculate Stream 2 lb-mol/hr of ethanol:
lb-mol/hr of ethanol in Stream 2 = Total lb-mol/hr of ethanol - lb-mol/hr of ethanol in Stream 1
lb-mol/hr of ethanol in Stream 2 = 652.87 lb-mol/hr - 111.03 lb-mol/hr = 541.84 lb-mol/hr
6. Calculate Stream 2 lb-mol/hr of water:
lb-mol/hr of water in Stream 2 = Total lb-mol/hr of water - lb-mol/hr of water in Stream 1
lb-mol/hr of water in Stream 2 = 734.75 lb-mol/hr - 683.65 lb-mol/hr = 51.10 lb-mol/hr
So, the scaled-up values are as follows:
Stream 1:
- lb-mol/hr: Ethanol = 111.03 lb-mol/hr, Water = 683.65 lb-mol/hr
Stream 2:
- lb-mol/hr: Ethanol = 541.84 lb-mol/hr, Water = 51.10 lb-mol/hr
Please note that these calculations assume that the composition ratios remain constant during the scale-up process.
To scale up the process, you need to determine the new flow rates of the streams that will produce 733 lb-mol/hr of ethanol with the desired composition.
Let's start with Steam 1:
Currently, Steam 1 has a flow rate of 17 lb-mol with a composition of 0.890 lb-mol ethanol and 0.110 lb-mol water. You want to find the new flow rate of Steam 1 to produce 733 lb-mol/hr of 0.890 lb-mol ethanol.
To calculate the new flow rate of Steam 1, you can use the equation:
New Steam 1 Flow Rate = (Desired Ethanol Flow Rate / Ethanol Composition in Steam 1) x lb-mol Feed Ethanol Flow Rate
Plugging in the values:
New Steam 1 Flow Rate = (733 lb-mol/hr / 0.890 lb-mol ethanol) x 17 lb-mol
New Steam 1 Flow Rate = 18,940.45 lb-mol/hr
Therefore, the new flow rate of Steam 1 should be approximately 18,940.45 lb-mol/hr to produce 733 lb-mol/hr of 0.890 lb-mol ethanol.
Now let's move on to Stream 2:
Currently, Stream 2 has a flow rate of 31.9 lb-mol ethanol and 51.1 lb-mol water. You want to find the new flow rate of Stream 2 to maintain the same composition.
To calculate the new flow rate of Stream 2, you can use the equation:
New Stream 2 Flow Rate = (Desired Ethanol Flow Rate / Ethanol Composition in Stream 2) x lb-mol Ethanol Flow Rate in Stream 2
Plugging in the values:
New Stream 2 Flow Rate = (733 lb-mol/hr / 0.470 lb-mol ethanol) x 31.9 lb-mol ethanol
New Stream 2 Flow Rate = 50,309.36 lb-mol/hr
Therefore, the new flow rate of Stream 2 should be approximately 50,309.36 lb-mol/hr to maintain the same composition.
In summary, to scale up the distillation process and produce 733 lb-mol/hr of 0.890 lb-mol ethanol, you would need to have Steam 1 with a flow rate of approximately 18,940.45 lb-mol/hr and Stream 2 with a flow rate of approximately 50,309.36 lb-mol/hr.