Page 60 - Sustainability in the Process Industry Integration and Optimization

Pro c ess O p timization 37

often viable, additional analyses are required to ensure that
the linearization does not result in an inadequate (inaccurate)
model. Similar problems also exist for Heat Exchanger
Networks, where nonisothermal mixing leads to equations
containing bilinear terms: products of mass flow rates and
enthalpies.

Process-specific constraints are also included in the optimization
problem. The mass balances are supplemented in the model by lower
and upper bounds on the stream flow rates and component
concentrations. Another source of constraints is the temperature
feasibility of interequipment connections. For example, water coming
from a blanching operation may be too hot to be used for washing
fresh fruits and so may require cooling (perhaps by mixing with a
colder stream) before this use; alternatively, this may be rejected as an
unacceptable connection, leading to a forbidden match. In MPR, such
constraints usually contain integer variables.
A frequent problem when synthesizing process networks is
obtaining extremely low flow rates for some interconnections. When
the model to optimize accounts for the complete capital costs, this
problem is less likely to appear. However, if capital costs are
underestimated (or disregarded) for some reason, then operating costs
may dominate, resulting in “degenerate” solutions with impractically
small flow rates. Practical solutions require reasonably accurate
estimates of the capital cost, especially if there are fixed costs. A more
straightforward option is to stipulate a lower bound on all network
flow rates.
Another important part of creating a process model is identifying
the energy needs of various operating units. It is crucial to account
for the heating and cooling needs of the process operations, and these
are established by formulating enthalpy balances (Linnhoff et al.,
1982). Most process streams need to be transported between the
operating units and also moved through them, and such transport
involves overcoming certain pressure drops (for fluids) and
performing mechanical work (for solids). These operations require
mechanical shaft power, which can be supplied by direct-drive
machines or electrical motors—elements that define the power
requirements of a process. In many cases, additional equations are
needed (e.g., constitutive relations as well as calculations of reaction
rates and equilibriums).

3.10.3 Choosing an Objective Function
The objective function to choose depends on the goal of the
optimization. It is possible to choose from a number of criteria,
including (1) maximizing profit; (2) minimizing operating cost;
(3) minimizing total annualized cost (TAC); (4) minimizing
consumption of certain resources or consumption per unit of product;