91Ó°ÊÓ

A distillation column having eight theoretical stages (seven in the column + partial reboiler + total condenser) is being used to separate 100 krnollh of a saturated-liquid feed containing 50 mol% A into a product stream containing 90 mol% A. The liquid-to-vapor molar ratio at the top plate is 0.75. The saturated-liquid feed is introduced on plate 5 from the top. Determine: (a) The composition of the bottoms, (b) The L/V ratio in the stripping section, and (c) The moles of bottoms per hour. Unbeknown to the operators, the bolts holding plates 5, 6, and 7 rust through, and the plates fall into the still pot. If no adjustments are made, what is the new bottoms composition? It is suggested that, instead of returning reflux to the top plate, an equivalent amount of liquid product from another column be used as reflux. If this product contains 80 mol% A, what now is the composition of: (a) The distillate, and (b) The bottoms. EQUILIBRIUM DATA, MOLE FRACTION OF A y 0.19 0.37 0.5 0.62 0.71 0.78 0.84 0.9 0.96 x 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Step by step solution

01

Understanding the Problem

The problem involves a distillation column with eight theoretical stages and asks for (a) the composition of the bottoms, (b) the L/V ratio in the stripping section, and (c) the moles of bottoms per hour. We also need to find new compositions after plates 5, 6, and 7 fall, and when an 80 mol% A liquid is used as reflux.

02

McCabe-Thiele Method for Distillation Columns

Use the McCabe-Thiele method to understand the column performance. The given equilibrium data helps in constructing the equilibrium curve for separation. The number of stages, feed condition, reflux condition, and product compositions guide the operating lines.

03

Construct Equilibrium Curve

Plot the equilibrium curve using the provided data: y = [0.19, 0.37, 0.5, 0.62, 0.71, 0.78, 0.84, 0.9, 0.96] versus x = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]. This graph visually represents the separation potential for this distillation setup.

04

Calculate Operating Lines

To find the operating lines, use the reflux ratio ( R = 0.75 ) and top product purity (90 mol% A). The rectifying line connects this point with the top corner (0,0) of the diagram. Calculate the bottom line using the material balance and the new position of the bottom stage after the plates fall.

05

Material and Energy Balances

Perform a mass balance over the column: Feed is 50 mol% A, Distillate is 90 mol% A. Overall: F = D + B and the component balance: Fz_F = Dx_D + Bx_B . Pre-failure, the reboiler and condenser assist define x_B.

06

Solve for Bottoms Composition (x_B) and L/V Ratio

Use the McCabe-Thiele graph or iterative balances through the stripping section to find x_B. Similarly, determine the L/V ratio in the stripping section (via a line from x_B matching the end equilibrium state).

07

Calculate Moles of Bottoms per Hour

Using F = 100 kmol/h and D = D_x = 90 kmol/h, solve for B in B = F - D . Factor in flows changed by plate failure.

08

Adjustments After Plates Fail

Without plates 5, 6, 7, recalculate x_B considering fewer theoretical stages. The product composition still leads rectifying calculations but the new stripping section is much less efficient.

09

Using 80 mol% A as Reflux

The new reflux (80 mol% A) shifts operating lines. Recalculate using 80% in reflux: expect composition shifts in distillate and bottoms, requiring transfer to McCabe-Thiele method again.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

McCabe-Thiele method

The McCabe-Thiele method is a graphical design technique widely used in chemical engineering to estimate how effectively a distillation column can separate components. It's especially effective for binary mixtures. This method involves plotting the equilibrium curve of the mixture and the respective operating lines to visualize the number of required stages for the desired separation.

• Start by plotting an equilibrium curve that represents the vapor-liquid equilibrium data.
• Add operating lines for the rectifying and stripping sections using the reflux ratio, which defines the slope of these lines.
• The intersection of the operating line with the equilibrium curve represents a theoretical stage needed for separation.

Whether you're dealing with this method for a stable column or recalculating after changes, such as the failure of plates, this graphical tool gives a clear insight into how many theoretical stages are required under given conditions. It's a robust method because it visualizes changes like altered feed quality or modified reflux ratios.

Equilibrium curve plot

The equilibrium curve plot is a crucial part of the McCabe-Thiele method. This plot visually represents how the compositions of vapor and liquid are related as they come into equilibrium at different stages in the distillation process.

• Using the given equilibrium data, plot the mole fractions of component A in the vapor phase (y-axis) versus the liquid phase (x-axis).
• The equilibrium line typically bows downwards, reflecting how vapor composition changes at near-optimal separation.
• This curve acts as a basis to optimize the operating lines which affect the efficiency and the number of stages in the distillation column.

It facilitates understanding how changes in feed or reflux conditions will push the system towards or away from efficient separation. The plot is essential for visualizing the impact of disturbances, like falling plates, on the separation process.

Mass and energy balances

Mass and energy balances are fundamental concepts used to ensure conservation principles are followed in the distillation process. In the context of this exercise, mass balances focus on how the feed, distillate, and bottoms relate.

• The overall mass balance is defined by the equation: \ F = D + B \ where \( F \) is the feed, \( D \) is the distillate, and \( B \) is the bottoms.
• You also have to perform a component balance to maintain the mole balance of the component within the product streams: \ Fz_F = Dx_D + Bx_B. \
• Knowing how energy moves within the column complements these mass balances by ensuring efficient heat supply to separate components properly.

Mass balance calculations help determine how disturbances like lost stages or alternative reflux sources affect the column's efficiency by shifting the balance calculations.

Material balance calculations

Material balance calculations in distillation are crucial to determine how changing the input or operational conditions impacts the product compositions. These balances are the practical tools used alongside the McCabe-Thiele method to quantify distillate and bottoms flow rates and compositions.

• Apply the overall and component balances to find unknown stream flows or compositions.
• In scenarios like lost plates, material balances show how the reduced number of theoretical stages impacts the concentration of components in the bottom product (\( x_B \)).
• Incorporating alternative reflux compositions, such as with an 80 mol% A product, involves recalculating the operational efficiencies and expected output compositions.

These material balances allow engineers to project and adjust to physical changes in the equipment or feed conditions, ensuring the operation remains efficient and the desired product purity is achieved.