A mixed metal material that is recovered from MSW is further processed by using a magnetic binary separator that separates ferrous metals from non-ferrous metals. The mixed metal material enters the separator at a rate of 2.5 tons per day. Ferrous metal makes up 65% of this material. The product recovery stream leaves the separator at a rate of 1.75 tons per day with 88% of that being ferrous metals. The remainder of the material leaves the separator in the material reject stream.
a) Calculate the percent of ferrous metal recovery
b) Calculate the purity of the ferrous metal in the product recovery stream
c) Calculate the overall efficiency of the separator
a) To calculate the percent of ferrous metal recovery, we need to determine the total amount of ferrous metal in the input material and compare it to the amount of ferrous metal in the product recovery stream.
The total amount of ferrous metal in the input material can be calculated by multiplying the rate at which the mixed metal material enters the separator (2.5 tons per day) by the percentage of ferrous metal in the input material (65%):
Total amount of ferrous metal in input material = 2.5 tons/day * 0.65 = 1.625 tons/day
The amount of ferrous metal in the product recovery stream can be calculated by multiplying the rate at which the product recovery stream leaves the separator (1.75 tons per day) by the percentage of ferrous metal in the product recovery stream (88%):
Amount of ferrous metal in product recovery stream = 1.75 tons/day * 0.88 = 1.54 tons/day
So, the percent of ferrous metal recovery can be calculated by dividing the amount of ferrous metal in the product recovery stream by the total amount of ferrous metal in the input material and multiplying by 100:
Percent ferrous metal recovery = (Amount of ferrous metal in product recovery stream / Total amount of ferrous metal in input material) * 100
Percent ferrous metal recovery = (1.54 tons/day / 1.625 tons/day) * 100
Percent ferrous metal recovery = 94.77%
b) To calculate the purity of the ferrous metal in the product recovery stream, we divide the amount of ferrous metal in the product recovery stream by the total material in the product recovery stream and multiply by 100.
The total material in the product recovery stream is the rate at which the product recovery stream leaves the separator (1.75 tons per day). Therefore, the purity of the ferrous metal in the product recovery stream can be calculated as follows:
Purity of ferrous metal in product recovery stream = (Amount of ferrous metal in product recovery stream / Total material in product recovery stream) * 100
Purity of ferrous metal in product recovery stream = (1.54 tons/day / 1.75 tons/day) * 100
Purity of ferrous metal in product recovery stream = 88%
c) To calculate the overall efficiency of the separator, we need to compare the amount of material in the reject stream to the total amount of material in the input material.
The amount of material in the reject stream can be calculated by subtracting the rate at which the product recovery stream leaves the separator (1.75 tons per day) from the rate at which the mixed metal material enters the separator (2.5 tons per day):
Amount of material in reject stream = 2.5 tons/day - 1.75 tons/day = 0.75 tons/day
The overall efficiency of the separator can be calculated by dividing the total material recovered (the sum of the product recovery stream and the reject stream) by the total material entering the separator and multiplying by 100:
Overall efficiency of separator = ((Product recovery stream + Reject stream) / Total material entering the separator) * 100
Overall efficiency of separator = ((1.75 tons/day + 0.75 tons/day) / 2.5 tons/day) * 100
Overall efficiency of separator = 100%
So, the overall efficiency of the separator is 100%.