Simultaneous mixed-integer disjunctive optimization for synthesis of petroleum refinery topology Processing Alternatives for Naphtha Produced from Atmospheric Distillation Unit

In this work, we propose a logic-based modeling technique within a mixed-integer
disjunctive superstructure optimization framework on the topological optimization
problem for determining the optimal petroleum refinery configuration. We are interested
to investigate the use of logic cuts that are linear inequality/equality constraints to the
conceptual process synthesis problem of the design of a refinery configuration.
The logic cuts are employed in two ways using 0-l variables: ( l) to enforce certain
design specifications based on past design experience, engineering knowledge, and
heuristics; and (2) to enforce certain structural specifications on the interconnections of
the process units. The overall modeling framework conventionally gives rise to a mixedinteger
optimization framework, in this case, a mixed-integer linear programming model
(because of the linearity of the constraints). But in this work, we elect to adopt a
disjunctive programming framework, specifically generalized disjunctive programming
(GDP) proposed by Grossmann and co-workers (Grossmann, l. E. (2002). Review of
Nonlinear Mixed-Integer and Disjunctive Programming Techniques. Optimization &
Engineering, 3, 227.) The proposed GOP-based modeling technique is illustrated on a
case study to determine the optimal processing route of naphtha in a refinery using the
GAMS/LogMIP platform, which yields practically-acceptable solution. The use of
LogMIP obviates the need to reformulate the logic propositions and the overall
disjunctive problem into algebraic representations, hence reducing the time involved in
the typically time-consuming problem formulation. LogMIP typically leads to less
computational time and number of iterations in its computational effort because the
associated GDP formulation involves less equations and variables compared to MILP.
From the computational experiments, it is found that logical constraints of design
specifications and structural specifications potentially play an important role to
determine the optimal selection of process units and streams. Hence, in general, the GDP
formulation can be improved by adding or eliminating constraits that can accelerate or
slow-down the problem solution respectively.