PROCESSES: BASICS OF PROCESS DESIGN - Biomass as a Sustainable Energy Source for the Future - page 199

design objective function and perform optimization. Thus, in mathematical terms, one
obtains a mixed integer optimization problem Equation (7.1):

F ðÞ x ðÞ , c ðÞ , d ðÞ ; p Maximize ð design objective function Þ

:

d ðÞ , c ðÞ

= 0

g ðÞ x ðÞ , c ðÞ , d ðÞ ; t l −ð , p

ð process model equality equations Þ

Subject to

:

h ðÞ x ðÞ , c ðÞ , d ðÞ ; t l −ð , p

0 ð process model inequality equations Þ

≥

c ðÞ

continuous decision variables at level ðÞ l , to be optimized

:

d ðÞ :

discrete decision variables at level ðÞ l , to be optimized

p fixed parameters in themodel, prone to some uncertainty

:

t l −ðÞ :

targets already fixed at preceeding level ðÞ l − 1

x ðÞ

dependent process variables at level ðÞ ð Eq : 7 : 1 Þ

:

It is not that a design problem simply reduces to a mathematical optimization. Often,
the key conceptual design effort is the generation of a superstructure of alternative
building blocks that can be connected by streams in multiple ways. Another challenge
is the representation of this superstructure by means of discrete decision variables,
along with making choices among alternative design models. Last but not least,
the outcome of a design optimization must be assessed with respect to its practical
significance while accounting for the underlying parametric uncertainties.

7.5.6 Conceptual Design Matrix as a Summary of the Design Procedure

The two dimensions of the design procedure (levels and engineering design steps) can
be brought together in a matrix, as presented in Table 7.1. The purpose of this matrix is
to serve as a mental frame for structuring the design process. It is advised to work top-
down and level by level and at each level perform the activities per design step (see
Section 7.5.5). The few promising design alternatives selected in steps (e) and (f ) at a
level [ i ] must be transferred to step (a) of level [ i + 1] for further expansion and refine-
ment. If at a particular level none of the generated alternatives meet the performance
criteria, one may challenge the wisdom of the evaluation criteria or decide to return to
preceding design levels and look harder for better options there.
The application of the design steps are illustrated for the first three levels in the
following sections. The leading example to illustrate these steps is the conversion of
biomass into syngas, followed by FT reactions to produce liquid fuels. The use of this
example does not imply that other conversion routes for biomass are less relevant.
The passes through the can be visualized as a helix-like staircase

(see Figure 7.6). One full cycle involves passing through the seven engineering design
steps. Then one arrives at the next level of design at the initial step again.

“ design matrix ”