Calculation of distillation column bottom discharge
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The feed to the butadiene column is 3.5 t/h, with a butadiene content of 98.4%. It is required that the purity of butadiene in the top product be greater than 99.2%, while the butadiene content in the bottom of the column should be less than 30%. What is the minimum amount of material that must be taken out from the bottom of the column to meet these requirements? Solution: Using the mass balance formula: W = F × (XD – XF) / (XD – XW). Substituting the values: W = 3500 × (99.2 – 98.4) ÷ (99.2 – 30) = 40.5 kg/h. Answer: The amount of material taken out from the bottom of the column should not be less than 40.5 kg/h. Could that expert please give an explanation? Thank you
We define the following variables: F: feed flow rate (kg/h), which is given as 3500 kg/h in the problem (note that 3.5 t/h needs to be converted to kg/h, i.e., 3.5 × 1000 = 3500 kg/h). XF: The mass fraction (or molar fraction) of butadiene in the feed, given as 98.4% in the problem. XD: The target purity of butadiene in the overhead product is given as 99.2% in the question. XW: The maximum allowable content of butadiene in the tower bottom, given in the question as 30%. W: Bottom draw rate (kg/h), which is what we need to determine. The material balance equation is used to calculate the flow relationships of various components in a distillation column. In this problem, what concerns us is the flow rate of butadiene. The material balance equation can be expressed as: W = F × (XD - XF) / (XD - XW). The meaning of this equation is that, in order to maintain material balance of butadiene inside the tower, the amount of butadiene taken out at the bottom of the tower, W, must equal the excess amount of butadiene in the feed (i.e., F × (XD - XF)) divided by the difference in purity of butadiene between the top and bottom of the tower (i.e., XD - XW). Now we will substitute the values given in the question into the formula for calculation: W = 3500 × (99.2% - 98.4%) / (99.2% - 30%) = 3500 × 0.008 / 0.692 ≈ 40.5 kg/h. Therefore, in order to meet the requirements that the purity of butadiene in the product at the top of the tower be >99.2% and the butadiene content at the bottom of the tower be <30%, the output rate from the bottom of the tower should not be less than 40.5 kg/h.