Page 58 - Sustainability in the process industry

Pro c ess O p timization 35

Network and Topology Data Identification
Obtaining network-related information is needed to account for
constraints that are related to the system topology and to the limits
imposed by operating units on the suitability of various process
streams to serve as inputs or outputs. In water networks, such
considerations include the acceptability (or unacceptability) of using
the water output from some operations as inputs for other operations.
For instance, the final washing of sugar crystals in sugar production
would require pure water, and for this the outputs from other water-
using operations would be unacceptable. On the otherhand, used
water from blanching might be perfectly acceptable for the initial
washing or rinsing of fruits. This type of information is used to
formulate additional constraints on the compatibility of different
process streams. When supplied to automated process optimization
algorithms, these constraints serve to eliminate a number of infeasible
combinations of process units. When building pure MPR models
(Williams, 1999), network-related information is transformed into
explicit mathematical constraints involving expressions with binary
selection variables. When using the graph-theoretic approach and/or
the P-graph framework (Friedler et al., 1993) to construct a process
model, such information is explicitly encoded in the P-graph building
blocks (materials and operations) and is then used by algorithms that
generate only those topologies that are combinatorially feasible.

3.10.2 Mathematical Modeling of Processes:
Constructing the Equations
After the conceptual basis has been established, it is time to begin
constructing the explicit mathematical formulations of the problem.
The standard procedure in this regard is first to build a super-
structure—one that incorporates all possible options and combin-
ations of operating units—and then to reduce the superstructure via
optimization techniques. In this context, a superstructure is the union
of several feasible flowsheets (see Figure 6.2 for an example of a water
reuse network superstructure). When this union includes all possible
flowsheets, the superstructure is called the maximal structure
(Friedler et al., 1993) or the hyperstructure (Papalexandri and
Pistikopoulos, 1996).
There are two basic approaches to formulating the superstructure
and subjecting it to reduction optimization.
1. Explicit formulation of a superstructure by the design engineer,
followed by translation of that structure into an integer programming
model: The generated problem is then solved by the
corresponding MPR algorithm. Popular codes for solving
MILP problems are OSL (GAMS, 2009) and CPLEX (ILOG,
2009); both are included in such commercial optimization
software packages as GAMS (2009). If the model does not