Page 152 - Process Modelling and Simulation With Finite Element Methods

Extended Multiphysics 139

pressure at which separation of reacted propylene and unreacted cyclopropane
will occur. The compressed gas is then condensed to bubble-point liquid and
feed to a distillation column. The column has 31 ideal stages with the feed onto
the stage 16. It operates with a total condenser and a molar reflux ratio of 8.4
producing a distillate flow rate of 0.292 kg-molh.”
Sound familiar? Such scenarios populate modules on “Process Engineering
Fundamentals.” Why is it extended multiphysics? Each unit operation
constitutes its own logical domain, connected to the others by entry and exit
points. In the conceptual design stage of such a plant, the unit operations are
treated by simplified models to permit facile exploration of the configuration
space. Process integration by means of recycle and heat exchanger networks
adds greater complexity to the flowsheet, and greater scope for economies in
operating and capital costs. Eventually, however, the process engineer has to
give detailed designs for such plant. These days that includes process
simulation, typically including optimisation, parametric sensitivity studies and
transient analysis. And even if the plant were designed a generation ago, process
studies of this nature are common for retrofit and optimisation. In many cases,
plant were over designed by 30-50% (since such flexibility is a common
safeguard in design), so now that the plant is operational, efficiency savings of
30-50% should be achievable. Thus has grown the burgeoning field of process
systems optimisation. And this is a regime for extended multiphysics. If any of
the unit operations in Figure 4.1 are to be modelled in detail, that usually
involves a spatial-temporal PDE where the simplified model used in design
might have been a lumped parameter model. For instance, suppose the reactor in
Figure 4.1 is CSTR reactor which is jacketed by a bath of its product liquid (at
500°C) before entering the heat exchanger proper. Temporal fluctuations in the
reactor temperature propagate through the bath to the heat exchanger, requiring
control action, which in turn leads to transients in the compressor operation.
These feed into the distillation column. Presuming the separated unreacted
cyclopropane is recycled back to the feed to the reactor, the temperature
fluctuations into the distillation column will have translated into composition
fluctuations in the recycle stream, which will then effect the reactor conversion,
starting the whole cycle again. The plant should be designed to dampen
fluctuations back to the set point, rather than reinforce them. Extended
multiphysics is in play at every level of process coupling. In the linear flowsheet
of Figure 4.1, it is possible to isolate the modelling of each unit operation, since
the entry and exit points are the only overlaps. It is still extended multiphysics if
you want to link them up in FEMLAB, but the linkages are simple. But if
process integration enters in, then the linkages may be more thorough. For
instance, in distillation columns, differential heating and cooling of stages can be
done to influence separation efficiency (with multiple entry and exit points for
various “fractions”). These streams can be crossed for heat integration and