Mechanistic Modelling of Chemical Processes
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Question 1
A well mixed tank is fed with a stream with total flowrate F
kmols/h containing x mol fraction of a solute.
The outflow is arranged so that the tank holdup will remain constant at
a value of M kmol. The mol fraction of solute in the
tank is equal to y - which is unknown.
- Set up the equations for the system.
- Determine the time constant and steady state gain associated with
y when the feed rate is 10 kmol/h and the
tank holds 20 kmols.
- Sketch the form of the response of y to a sudden
increase, or step change in x from an initial
steady state.
- If the solute reacts isothermally in a first order with rate
constant 0.5 /hr without change of volume in the tank,
what now will be the time constant for the system?
Question 2
A thermometer whose bulb has mass m, heat capacity
Cp and surface area A indicates a
temperature T. The temperature of its surroundings is
Te and heat is transferred convectively with overall heat
transfer coefficient U. Assume that the thermometer bulb
is at a uniform temperature. Choose realistic values for the parameters
and estimate how fast a typical thermometer indication might respond to
changes in the temperature being measured.
Question 3
A tank with input flowrate F kg/s has variable holdup
M(t) kg. The outlet flowrate L kg/s is a
function of holdup -
- Set up a model of the system.
- The tank is initially at steady state and contains 100
kg of liquid. Estimate the steady state gain for
changes in holdup w.r.t inlet flow and the time constant for the tank holdup.
- Suppose that the tank capacity is 500 kg and the
maximum feed flowrate is 2 kg/s. Given that there is 100
kg in the tank when there is a 50 % increase in feed
flowrate, evaluate the dimensionless gain.
- Sketch the response of the tank holdup to this sudden increase.
- Optional - perform a numerical simulation and compare the
results with the sketched response. Comment on how and why these differ.
Question 4
A well mixed vessel is fitted with a heating jacket whose
temperature is uniform and has value Tw. Fluid enters the
vessel at F kg/s and leaves at the same rate. The feed
temperature is Tf. The vessel holdup is M
kg and its temperature is T.
- Set up a model for the system.
- Derive expressions for the steady state gains for T w.r.t
A pressure vessel discharges to atmosphere through a relief valve
with square root characteristic.
- Set up a model for the system.
- Derive an approximate expression for its pressure time constant.
The vessel has a volume of 2 m3 and is initially at 10
bar. The relief valve has a diameter of 20 mm.
- Estimate how long it will take for the pressure to fall to 5
bar after the valve has opened.
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