A distillation column has a federate of 100 kmol/h consisting of 10 mol% light nonkey (LNK), 60 mol% light key (LK) and the rest is heavy key (HK) components. The feed is saturated liquid. The actual L/D value is 1.2 times the minimum L/D value. As an engineer, you are instructed to design the column so that it can recover 99.5% of the LK in the distillate. The mole fraction of the LK in the distillate is 0.75. (OLNK= 4.0; a[k= 1.0; ahk= 4.0) Use the Fenske-Underwood-Gilland approach to find: a. Number of stages at total reflux. b. Minimum reflux ratio. c. Actual number of stages and the feed stage location.

Part (a) Number of Stages at Total Reflux (NTR)

To determine the number of stages at total reflux (NTR), we can use the Fenske-Schmidt equation:

ln(x_D/x_F) = NTR * ln(α)

where:

• x_D is the mole fraction of LK in the distillate (0.75) • x_F is the mole fraction of LK in the feed (0.6) • α is the relative volatility of LK to HK (α_LK/α_HK = 4/1 = 4)

Plugging in the values, we get:

ln(0.75/0.6) = NTR * ln(4)

Solving for NTR, we get:

NTR = 1.08

This means that at total reflux, we need 1.08 stages to achieve the desired separation.

Part (b) Minimum Reflux Ratio (R_min)

To determine the minimum reflux ratio (R_min), we can use the Underwood equation:

R_min = (q - qD)/(xD - xB)

where:

• q is the molar flow rate of the feed (100 kmol/h) • qD is the molar flow rate of the distillate (qD = L * xD, where L is the molar flow rate of the reflux) • xB is the mole fraction of LK in the bottoms (xB = 0)

Since we want to recover 99.5% of the LK in the distillate, we can calculate qD as follows:

qD = (0.995)(0.6)(100 kmol/h) = 59.7 kmol/h

Plugging in the values, we get:

R_min = (100 kmol/h - 59.7 kmol/h)/(0.75 - 0)

Solving for R_min, we get:

R_min = 1.19

This means that the minimum reflux ratio required to achieve the desired separation is 1.19.

Part (c) Actual Number of Stages and Feed Stage Location

To determine the actual number of stages (N) and the feed stage location (N_F), we can use the Gilliland correlation:

N = NTR + (NTR - 1) / (R_actual - R_min)

where:

• R_actual is the actual reflux ratio (R_actual = 1.2 * R_min = 1.43)

Plugging in the values, we get:

N = 1.08 + (1.08 - 1) / (1.43 - 1.19)

Solving for N, we get:

N = 1.78

Since we cannot have a fraction of a stage, we round up to 2 stages. Therefore, the actual number of stages required is 2.

The feed stage location can be determined using the following equation:

N_F = N + (x_F - x_D)/(xD - xB)

Plugging in the values, we get:

N_F = 2 + (0.6 - 0.75)/(0.75 - 0)

Solving for N_F, we get:

N_F = 1.25

Since we cannot have a fraction of a stage, we round up to 2 stages. Therefore, the feed stage location is at stage number 2.

Conclusion

To design the distillation column so that it can recover 99.5% of the LK in the distillate with a mole fraction of 0.75 in the distillate, we need 2 actual stages with a feed stage location at stage number 2. The minimum reflux ratio required is 1.19, and the actual reflux ratio is 1.43.

Leave a Comment