PROCESSES: BASICS OF PROCESS DESIGN - Biomass as a Sustainable Energy Source for the Future - page 196

type A or B or C; connectivity, should there be a solvent recycle between unit U1 and
U2: Y/N? The other decision variables are continuous within a constrained interval:
e.g., 298 < temperature (K) < 348.
This brief sketch shows that there are many design decision variables of a discrete
and continuous nature, which turns design into a huge combinatorial problem.

7.5.2 What Is the Problem in Generating Designs?

Structuring of process design by means of a certain procedure is necessary, because
one wants to avoid a situation in which an astronomical number of alternative
designs are created, which are all logically possible and must be evaluated with
respect to performance. A simple example indicates the enormity of this problem.
Let there be N units in a process, and each unit has, on average, M design decision
variables, where each decision variable can attain, on average, K discrete values. Let
us assume that the design decision variables are fully independent; i.e., picking a
value for one variable does not impair the freedom of decision for any of other deci-
sion variables. The number of logically possible designs becomes D = K M . N .Ifthere
is one choice per variable, K = 1, only one design is possible: D = 1. Things start to
get out of hand when the choices ( K ) increase. Even for a very simple process ( K =2;
M =4; N = 5), a million

can be logically generated, D =2 20 =~10 6 ,while
for a more complicated process ( K =4; M =8; N = 20), the outcome is D =4 160 =
~10 96 . The problem with this combinatorial approach is that almost all of the result-
ing alternative designs that are logically possible do not make sense from physical
and economic points of view. Generating all alternatives and filtering out the very
few feasible ones is a prohibitive effort. The practical failure of this brute force com-
binatorial approach is caused by assuming that the decision variables are independ-
ent while they are not. For instance, it does not make sense to place a product
purification unit before the reactor making the product. There are many physical
constraints connecting the decision variables and constraining the choices. The core
challenge is how to cope with very many design decision variables with almost as
many constraints between them and arrive at a small number of the better design
alternatives.

“ designs ”

7.5.3 Hierarchical Decomposition Approaches for Process Design

The time-honored practical approach is to apply a hierarchical decomposition
approach to process design. Here, the design decision variables are partitioned in a
hierarchy of many smaller clusters, as explained by Douglas (1988). The aim is to
structure the design procedure in such a way that the decision variables with a poten-
tially high impact on the economic performance are covered first and the ones with a
lesser impact later. This approach implies a more sequential way of decision making,
one cluster after the other. The clusters are organized according to design levels . The
economic impact is highest at the top level, where decisions are made on the nature of
products, feeds, capacity, type of processing agents (e.g., catalysts, solvents), mode