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CHEMICAL ENGINEERING DEPARTMENT UNIVERSITI TEKNOLOGI PETRONAS

JAN 2015 SEMESTER CCB 3013 – Chemical Process Dynamics, Instrumentation and Control

Assignment 2 Submission due date: 05 Mar 2015

Q#1

A perfectly stirred, constant-volume tank has two input streams, both consisting of the same liquid. The temperature and flow rate of each of the streams can vary with time.

(a) Derive a dynamic model that will describe transient operation. Make a degree of freedom analysis assuming that both Streams 1 and 2 come from upstream unit (i.e., their flow rates and temperatures are known functions of time). (b) Simplify your model, if possible, to one or more differential equations by eliminating any algebraic equations. Also simplify any derivatives of products of variables. Notes: wi denotes mass flow rate for stream i. Liquid properties are constant (not functions of temperature).

Q#2

A completely enclosed stirred-tank heating process is used to heat an incoming stream whose flow rate varies. The heating rate from this coil and the volume are both constant.

(a) Develop a mathematical model (differential and algebraic equations) that describes the exit temperature if heat losses to the ambient occur and if the ambient temperature (Ta) and the incoming stream’s temperature (Ti) both can vary. (b) Discuss qualitatively what you expect to happen as Ti and w increase (or decrease). Justify by reference to your model. Notes: ρ and Cp are constant. U, the overall heat transfer coefficient, is constant. As is the surface area for heat losses to ambient. Ti >Ta (inlet temperature is higher than ambient temperature).

Q#3

Two tanks are connected together in the following unusual way as shown in Fig.

(a)

Develop a model for this system that can be used to find h1, h2, w2 and w3 as functions of time for any given variation in inputs.

(b)

Perform a degree of freedom analysis. Identify all input and output variables.

Notes: The density of the incoming liquid, ρ, is constant. The cross sectional areas of the two tanks are A1 and A2. w2 is positive for flow from Tank 1 to Tank 2. The two valves are linear with resistances R2 and R3.

Q#4

Consider a liquid flow system consisting of a sealed tank with non-condensable gas above the liquid as shown in Fig. Q#4. Derive an unsteady state model relating the liquid level h to the input flow rate qi. Is operation of this system independent of the ambient pressure Pa? What about for a system open to the atmosphere? You may make the following assumptions: (i)

The gas obeys the ideal gas law. A constant amount of mg/M moles of gas are present in the tank.

(ii) The operation is isothermal. (iii) A square root relation holds for flow through the valve. (iv)

Fig. Q#4

Q#5

Using the blending process described in Q#1, calculate the response of x to a change in x1 (the disturbance from 0.4 to 0.5 and a change in w2 from 200 to 100 kg/min. Plot the response using appropriate software for 0 ≤ 𝑡 ≤ 25 min. Explain physically why the composition increases or decreases.