[Luyben] Process Mod.. - Student subdomain for University of Bath

84 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
level controllers. Reflux flows are fixed. Steam flows to the reboilers are set by
temperature controllers. Assume equimolal overflow, negligible vapor holdup, and
negligible condenser and reboiler dynamics. Use a linear liquid hydraulic relationship
where L and fi, are the initial steadystate liquid rate and holdup and fl is a constant
with units of seconds.
3.18. The rate of pulp lay-down F on a paper machine is controlled by controlling both
the pressure P and the height of slurry h in a feeder drum with cross-sectional area
A. F is proportional to the square root of the pressure at the exit slit. The air vent
rate G is proportional to the square root of the air pressure in the box P. Feedback
controllers set the inflow rates of air G, and slurry F, to hold P and h. The system is
isothermal.
Derive a dynamic mathematical model describing the system.
Restriction
FIGURE P3.18
3.19. A wax filtration plant has six filters that operate in parallel, feeding from one
common feed tank. Each filter can handle 1000 gpm when running, but the filters
must be taken off-line every six hours for a cleaning procedure that takes ten
minutes. The operating schedule calls for one filter to be cleaned every hour.
How many gallons a day can the plant handle? If the flow rate into the feed
tank is held constant at this average flow rate, sketch how the liquid level in the feed
tank varies over a typical three-hour period.
3.20. Alkylation is used in many petroleum refineries to react unsaturated butylenes with
isobutane to form high octane iso-octani: (alkylate). The reaction is carried out in a
two liquid-phase system: sulfuric acid/hydrocarbon.
The butylene feed stream is split and fed into each of a series of perfectly
mixed tanks (usually in one large vessel). This stepwise addition of butylene and the
large excess of isobutane that is used both help to prevent undesirable reaction of
butylene molecules with each other to form high-boiling, low octane polymers. Low
temperature (40°F) also favors the desired iC,/Ch reaction.
The reaction is exothermic. One method of heat removal that is often used is
autorefrigeration: the heat of vaporization of the boiling hydrocarbon liquid soaks
up the heat of reaction.