You are performing a preliminary design for an ethylene (C2=)/ethane (C2) fractionation tower. Assume that under the specified operating conditions, αC2=,C2 is 1.14 at the top of the column and 1.42 at the bottom. The feed rate is 750. gmol/s of a 75.0 mol% ethylene and 25.0 mol% ethane saturated vapor. The required ethylene purity in the distillate product must be at least 99.9 mol% to be acceptable for polymerization. The bottoms product must contain no more than 1.00 mol% ethylene. Assuming these limits are the actual product mole fractions

What are the minimum number of stages (Nmin) required to accomplish this separation?

What is the minimum reflux ratio required (Rmin)?

If the actual reflux ratio is 1.10Rmin, how many actual stages (N) are required for the separation?

To determine the minimum number of stages (Nmin) required to accomplish the separation in the ethylene/ethane fractionation tower, we need to use the Underwood method.

This method uses the concept of minimum reflux ratio (Rmin) to calculate the number of stages needed. First, we need to calculate the actual mole fractions of ethylene and ethane in the distillate and bottoms products, based on the given purity limits. The distillate product must have at least 99.9 mol% ethylene, so the mole fraction of ethylene (xC2=) in the distillate (xD) is 0.999. The bottoms product must have no more than 1.00 mol% ethylene, so the mole fraction of ethylene (xC2=) in the bottoms (xB) is 0.01.

Next, we can use the operating conditions and the given values of αC2=,C2 at the top and bottom of the column to calculate the minimum reflux ratio (Rmin) using the Underwood equation: Rmin = (αC2=,C2 - 1) / (αC2=,C2 - xC2=,D)
In this equation, αC2=,C2 is the relative volatility of ethylene to ethane. Plugging in the given values, we get:
Rmin = (1.42 - 1) / (1.42 - 0.999) = 0.42 / 0.421 = 0.997
Therefore, the minimum reflux ratio required is approximately 0.997.
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