Page 169 - Sustainability in the Process Industry Integration and Optimization

146 Cha p te r S i x

Here A is the system availability in operation mode i for the jth
i
design, and x is the mode i’s ratio of actual to maximum capacity for
i
the jth design.
6.6.2 Optimization
Within the optimization framework for integrating RAM into process
synthesis, the mathematical model aims to minimize the life-cycle
cost. In its general form (Yin and Smith, 2008), the optimization
problem can be summarized as follows:

Minimize: the objective function (expected cost)
Subject to: process model constraints, preventive maintenance
constraints, process system availability constraints

The objective function is usually formulated as
Annual cost = Annualized capital cost + Annualized
operational cost + Annual lost production
penalty + Other costs (6.7)

6.7 Pressure Drop and Heat Transfer Enhancement in
Process Integration

Various factors—including flow rate, composition, temperature, and
phase—can affect heat capacity C . Another factor that should be
p
taken into account is pressure. Polley, Panjeh Shahi, and Jegede (1990)
extended the Heat Exchanger Network (HEN) targeting procedure
by considering pressure drop. They used the following relationship
between the pressure drop ΔP, the heat transfer coefficient h, and the
heat transfer area A:

P KAh m (6.8)
where K is a pressure-drop relationship constant and m reflects the
heat exchanger’s tube- and shell-side–specific coefficients. The
allowable pressure drop (rather than the heat transfer coefficient) is
specified for each stream. Then the heat transfer coefficients are
calculated iteratively to minimize the total area. Thus, when
approaching area targets the design is modified based on the fixed
pressure drops rather than fixed film coefficients.
Ciric and Floudas (1989) suggested a Mathematical Programming–
based, two-stage approach to HEN retrofits that includes a match
selection stage and an optimization stage. The match selection
stage uses an MILP transshipment model to select process stream
matches and match assignments. The optimization stage uses an NLP
formulation to optimize the match order and flow configuration of
matches.