Master En Ciencias De La Ingeniería

HANDLING UNCERTAINTIES IN PROCESS OPTIMIZATION
Daniel Navia, Gloria Gutiérrez, César de Prada
Systems Engineering and Automatic Control Department. University of Valladolid.
Paseo Prado de la Magdalena s/n, 47003 Valladolid, Spain.
Email: daniel.navia@autom.uva.es
Workpackage 3: System-wide coordination and control
1. INTRODUCTION
Process optimization is a key issue to increasecompetitiveness in the industry. Using
optimization it is possible to improve the use of raw materials and the energy to produce a
finished product, leading to a sustainable production as well as increasing the profit margin in
the operation of processes. The generality of the optimization methodologies, allows using it in
a great variety of production processes, which represents a huge advantage in thedesign of any
process.
Process optimization needs, in general, a model of the reality with the aim to forecast the
behavior of the process and calculate predictive actions that optimize the system. These models
can be derived from physical phenomena like:
-

Conservation of Mass and Energy
Thermodynamic considerations (1st and 2nd law)
Transfer phenomena: Mass, heat and momentum
Kineticexpressions, among others…

Even though models based in physical phenomena have a strong basis that allows to predict a
particular behavior, their predictions have an important degree of uncertainty fundamentally
because of a partial understanding of the physical phenomena along with the random behavior
that some process variables may have. Therefore, the management of these uncertainties inprocess optimization is very important to ensure feasibility as well as optimality in real
processes. In fact, neglecting these uncertainties can produce important economic losses and
even safety issues in real systems.
In this research, two methods of handling the uncertainty in process optimization are being
studied: Stochastic Optimization (SO) and (Dynamic) Real Time Optimization((D)RTO). Each
of them attempts to take into account the partial knowledge of a process for different points of
view.
2. STOCHASTIC OPTIMIZATION
Stochastic optimization tries to overcome the stochastic behavior of random variables that
affects the processes (Birge & Louveaux, 1997; Dantzig, 1955; Grossmann et al., 1983). To do
this, there are several alternatives in the literature to take intoaccount explicitly this behavior in
optimization (Ruszczynski & Shapiro, 2003). In particular, in his thesis two methods have been
studied:

Two-Stage Stochastic Optimization: this assumes that there are two stages of knowledge
of the random variable. In the first one an optimal decision must be obtained and
applied to the process knowing only the probability distribution of the random variables(obtained for example from an historic process data). As time passes, the real value of
the random variable can be revealed (measured from experimental analysis or estimated
indirectly), and corrective actions must be applied (Dantzig, 1955; Ruszczynski &
Shapiro, 2003).
Chance Constrained Optimization: unlike two-stage stochastic optimization, chance
constrained optimization tries tocalculate a decision variable that optimizes the system
ensuring a determined degree of feasibility of the entire process, knowing only the
probability distribution function of the random variables. The probability of feasibility
is obtained reformulating the constraints using their probability distribution function
(Charnes & Cooper, 1959; Li et al., 2008).
Both methods have been tested in amodel of a hydrodesulphuration unit from an oil refinery
(Figure 1), that presents three different sources of hydrogen to remove the sulphur content of a
hydrocarbon to produce a sulphur – free fuel.

Figure 1. Hydrodesulphuration system
Because every hydrogen source comes from different production units their qualities as well as
their production cost are not the same; therefore, the...