chemical engineering homework project

1 Process Description The process used throughout this assignment is an isothermal distillation column with eight trays:

Figure 1: A two cut splitter.

The column splits a feed in the two components A and B, where A is the lighter component. According to customer specifications, the mole fraction of A in the distillate xD should be at least 0.98. It is assumed that for economic reasons (avoid too much loss of A) the mole fraction of A in the bottom xB should be no more than 0.05. The feed F is determined by the upstream chemical reactor. The feed flow rate and the mole fraction of A in the feed (i.e., zF) vary according to the profiles shown in Figure 2. The control valves VL and VS are designed to manipulate the reflux L and the boil-up V, respectively.

Figure 2: The feed (left) and the mole fraction of A in the feed (right) over time.

2 Modeling You are provided with the nonlinear, dynamic model of the process at hand. The process model is implemented in Simulink (DC.mdl). The file PDC.m contains the parameter values. Run this file before running the Simulink model.

3 Questions 1. Based on the process description, accurately formulate the control objectives. Discuss the order of

importance of the control objectives.

2. Using mass balance equations, derive an expression relating the various input and output streams for each stage of the distillation column. State all your assumptions. Hint: you can replace vapor mole fractions with liquid mole fractions using Dalton's Law, Raoult's Law, and the equation for relative volatility: αAB= ____

3. Relate your mass balance equations to the equations in the Fcn blocks of the Simulink process model. Then, perform a degrees-of-freedom analysis on the distillation column. Hint: observe that Simulink integrates the result of each Fcn block, so each Fcn block's equation should be in the form of an ODE.

4. Quantify the effect that changing the disturbance variables F and zf has on the steady-state values of V, B, L, and D that are required to maintain the output mole fractions at xD = 0.98 and xB = 0.05. Based on these results, which disturbance variable do you consider to be the most demanding disturbance?

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