condition for obtaining a global minimum of the nonlinear problem is that both
the objective function and the constraint set must be convex. Otherwise, there is
no guarantee that the reached local optimum will be the global optimum.
As discussed in chapter ‘‘Modelling Superstructure for Conceptual Design of
Syngas Generation and Treatment’’, most commonly used optimization software,
such as GAMS or MatLab packages, includes several well-known optimization
algorithms as SQP. Other techniques include solvers such as NPSOL which is
especially effective for nonlinear problems whose functions and gradients are
expensive to evaluate.
Because of the complexity included in the set of constraints of Eq. 3, process
simulation environments are used to solve them with ease, as discussed in
chapters ‘‘Modelling Syngas Generation, Main Purification Operations and
Modelling Superstructure for Conceptual Design of Syngas Generation and
Treatment’’. Consequently, the application of DR techniques requires frame-
works that use the process simulation data together with other optimisation
algorithms. In such frameworks, the simulation environment usually acts as a
server of the optimisation algorithm by providing the value of Eq. 3 for the
different values of the variables being optimised. The following examples try to
clarify on this sense.
3.2 Examples of Data Reconciliation in obtaining Synthesis Gas
3.2.1 Case A: DR Applied to a Claus Desulphurisation Process
Recovery of sulphur from industrial waste gases is an important problem from the
environmental point of view, and as it was discussed in chapter ‘‘Main Purification
Operations’’, it is of paramount importance in the case of IGCC power plant
operation. The rise of sulphur volumes in waste gases together with tightening
emission regulations leads to the increase of sulphur-recovering needs [9].
In gasification plants, the main source of sulphur recovered is hydrogen sulphide
produced in the gasification step as a sub-product. The most widely used method to
treat H
2
S is based on oxidation of hydrogen sulphide into sulphur by adding oxy-
gen, further details are discussed in chapter ‘‘Main Purification Operations’’ .
The global sulphur recovering in Claus plants containing recirculation is around
99.8% of the sulphur content in the input gas. All the equipments and process units
involved in the model are put together as a whole operational unit. Six streams are
considered to link the Claus plant to the rest of the whole process equipments and
facilities, see Fig. 2.
The proposed strategy described in Eq. 2 has been applied to the above
described Claus plant to reduce the noise level in the inputs and output streams.
The set of constraints are modelled using the process simulator (in this case,
AspenHysys). These constraints include: mass and energy balances together with
the corresponding thermodynamic models for the calculation of phase distribution.
Clearly, the simulation environment eases the implementation of such framework
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