Question

In binary distillation, the number of bubble cap per tray primarily depends on:

• A. Allowable gas velocity
• B. Allowable liquid velocity
• C. Tray spacing
• D. Purge rate

Hint:

Key Design Rule for Trays: - Vapor handling capacity determines the active bubbling area and the number of caps/perforations (\( \text{Number of Caps} \propto \text{Vapor Flow Rate} / \text{Allowable Gas Velocity} \)). - Liquid handling capacity determines the downcomer area and weir length configurations.

Answer 1

The Correct Option is A

Concept: Bubble cap trays use individual risers and caps to distribute the rising vapor stream evenly into the liquid layer on each tray. The number of bubble caps required on a single tray is determined by balancing the total volumetric vapor flow rate against the allowable slot velocity of the vapor through each individual cap assembly. This balance ensures stable bubbling without causing excessive pressure drops or vapor entrainment.

Step 1: Examining the fluid mechanics of bubble caps.
The total volumetric flow rate of the vapor phase rising through the column is denoted as \( V_v \, (\text{m}^3/\text{s}) \). This flow rate is related to the linear vapor velocity (\( u_v \)) and the active bubbling area (\( A_a \)) by the expression: \[ V_v = A_a \cdot u_v \] The vapor must pass through the slot openings of the bubble caps. The total slot area required to handle this vapor flow depends directly on the

allowable gas velocity (\( u_{slot} \)) through the slots to maintain stable operation: \[ A_{slots, \text{total}} = \frac{V_v}{u_{slot}} \]

Step 2: Determining the total number of caps.
Let \( a_c \) represent the structural slot area provided by a single standard bubble cap assembly. The total number of bubble caps required on the tray (\( N_{caps} \)) is calculated by dividing the total required slot area by the area of a single cap: \[ N_{caps} = \frac{A_{slots, \text{total}}}{a_c} = \frac{V_v}{u_{slot} \cdot a_c} \] This relation shows that the total number of bubble caps per tray is determined primarily by the volumetric vapor flow rate and the allowable gas velocity limits. The design must maintain the gas velocity within an optimal range to prevent jet entrainment at high rates and bubbling instability or pulsations at low rates.

Step 3: Comparing with other parameters.
While the liquid flow velocity influences features like weir length and downcomer area, and tray spacing affects the total column height and entrainment limits, the total number of bubble caps on a tray is determined primarily by the allowable gas velocity.