INTRODUCTION
Chemical industry plays an important role in the daily life of our society.
The purpose of a chemical process is to convert some (cheap) materials into
other desirable and valuable products. Innovation in chemical process design
is a key issue in today’s chemical industry. Process synthesis is an important
part of the overall chemical innovation process which starts with identification
of the process needs prior to construction and operation of the process plant.
Conceptual design is the initial stage of chemical process design where the
conceptual synthesis of a process flowsheet is developed. Chemical process synthesis
is an important activity to the industry and academia as it deals with the problem
of how to develop and integrate flowsheets to search for the best design alternative
for chemical product manufacturing processes (Alqahtani, 2008).
Optimization is the use of specific methods to determine the most costeffective
and efficient solution to a problem or design for a process. This technique
is a major quantitative tool in industrial decision making regarding problems
in the design, construction, process operation, plant, company level etc. (Edgar
et al., 2001). It deals with finding the optimum design parameters
for maximizing the profit or minimizing the total investment on a process plant
with tradeoffs between capital and operating costs (Alqahtani,
2008). As the power of computers has increased, optimization technique has
been expanded and applicable for more complex problems.
Operational optimization of either a section or the entire chemical plant starting
from the design stage has been a task of growing interest in the chemical industry.
Traditionally, it has been performed using the standard optimization tool of
commercial flowsheeting program or through an optimizersimulator program (Diaz
and Bandoni, 1996). The optimal design of chemical plant involves discrete
and continuous choices. The selection of the process unit among a number of
possible alternatives as optimization variables is a discrete choice. Continuous
choice refers to the selection of the optimal size and the operating conditions
(temperature, pressure, flowrates, compositions, conversions, etc.) of the selected
process unit as the optimization variables (Lee et al.,
2003). The applications of optimization have been mainly accomplished by
using continuous choice while the flowsheet topology (discrete choice) has been
kept fixed. The combination of discrete and continuous choices can be done but
the optimization problem will become more complex and difficult to solve. Therefore,
to apply optimization effectively in the chemical industries, both the theory
and practice of optimization must be understood.
THE NATURE OF OPTIMIZATION
Optimization concepts: Optimization has become a major enabling area
in Process System Engineering (PSE). It has evolved from methodology of academia
interest into a technology that has and continues to make significant impact
in industry (Biegler and Grossmann, 2004). PSE has been
evolving into a specialized field at the interface between chemical engineering,
applied mathematics and computer science with specific modelbased methods and
tools as its core competencies to deal with the inherent complexity of chemical
processes and the multiobjective nature of decisionmaking during the lifecycle
of the manufacturing process of chemical products (Klatt
and Marquardt, 2009). Typical problems in chemical process design or plant
operation have many possible solutions. Optimizations have been implemented
to find the values of variables in the process that yield the best value of
the performance criterion.
Every optimization problem contains three essential features which are (1)
at least one objective function to be optimized, also known as economic model,
(2) equality constraints and (3) inequality constraints. Features 2 and 3 constitute
the model of the process or equipment (Edgar et al.,
2001). Optimization solutions must not only satisfy all of the constraints,
but also must achieve the objective function. In mathematical term, optimization
problem can be represented by this notation:
where, x is a vector of n variables (x_{1}, x_{2}, …., x_{n}), h(x) is a vector of equations of dimension m_{1}, and g(x) is a vector of inequalities of dimension m_{2}. The total number of constraints is m = (m_{1} + m_{2}).
The formulation of the objective functions is one of the crucial steps in the
application of optimization. In the chemical industries, the objective function
often is expressed in units of currency (cost) because the goal of the enterprise
is to minimize costs or maximize profits subject to a variety of constraints.
The objective function can also be expressed in term to solve the problem in
maximization of the yield of component or minimization of the use of utilities
or minimizing difference between a model and some data and so on (Edgar
et al., 2001). Mass and energy balances are written as equality constraints
while inequalities constraints are represented by the design specifications
and logical constraints (Diaz and Bandoni, 1996).
Classification of problem types, variable types and equations: Optimization can be classified in terms of continuous and of discrete variables regardless of the solution methods. The major problems for continuous optimization include Linear Programming (LP) and nonlinear programming (NLP), with important subclass of Linear Complementarity Problem (LCP) for LP, while for NLP includes Quadratic Programming (QP) and semidefinite programming (SP). As for discrete problem, they are first classified into MixedInteger Linear Programming (MILP) and MixedInteger Nonlinear Programming (MINLP). For the former an important particular case is when all variables are integer, which gives rise to an Integer Programming (IP) problem. Regarding to the formulation in (1), algebraic form correspond to mixedinteger optimization problems have the following general form with x are continuous variables which generally correspond to state variables, while y are the discrete variables which generally are restricted to take 01 values to define for instance the assignments of equipment and sequencing of tasks:
An MIP problem corresponds to a MINLP when any of the functions involved in
optimization problem are nonlinear. If all the functions are linear it corresponds
to a MILP. If there are no 01 variables, the MIP problem reduce to a NLP or
LP depending on whether or not the functions are linear (Alqahtani,
2008; Biegler and Grossmann, 2004).
Caballero et al. (2007) had classified the different
types of variables arise in an optimization problem and also differentiated
two classes of equations. Implicit equations are equations that are solved by
each modules in the process simulator, or any other third party module added
to the model, while External/explicit equations are the equations over which
user have complete control, include dependent and independent variables. Design
or independent variables in a chemical process simulator are the variables that
must be specified to converge the flowsheet. The number of such variables matches
the degrees of freedom in the flowsheet. Variables calculated by the simulator
(or in general by any implicit model) is the variable calculated by the simulator.
The user has no direct control over these variables but in some simulator it
is possible to force these variables to take specific value through auxiliary
calculation blocks that change some of the design variables until the specification
is met. In optimization the system, it is faster and usually numerically more
reliable to introduce these specifications as constraints to the model. Variables
that must be fixed in a given topology of the flowsheet is refer to a subset
of variables that must be fixed in a given iteration when solving a NLP problem
with a given topology and a given set of fixed binary (Boolean or integer) variables.
Lastly are the variables that do not appear at the flowsheet level (or in other
implicit block of equations) but appear in explicit external constraints. No
special treatment of these variables is required.
General step to solve optimization problems: Edgar
et al. (2001) lists six general steps for the analysis and solution
of optimization problems. It may not be necessary to follow the cited order
exactly, but should cover all steps eventually. Shortcuts in the procedure are
allowable and the easier steps can be performed first.
• 
Analyze the process so that the process variables and specific
characteristics of interest are define; that is make a list of all the variables 
• 
Determine the criteria for optimization and specify the objective
function in terms of the variables defined in step 1 together with coefficients 
• 
Using mathematical expressions develop a valid process/equipment
model that relates the inputoutput variables of the process and associated
coefficients include both equality and inequality constraints. Identify
the dependent and independent variables to get the number of degrees of
freedom 
• 
If the formulated problem is too large in its scope: 
• 
Break it up into manageable part or 
• 
Simplify the objective function and model 
• 
Apply a suitable optimization technique to the mathematical
statement of the problem 
• 
Check the answer and examine the sensitivity of the result
to changes in the coefficients in the problem and the assumptions 
Applications: In practice, optimization can be applied in numerous ways
to chemical processes and plants. Typical example in which optimization has
been include are (1) determining the best sites for plant location, (2) routing
tankers for the distribution of crude and refined products, (3) sizing and layout
of a pipeline, (4) designing equipment and an entire plant, (5) scheduling maintenance
and equipment replacement, (6) operating equipment such as tubular reactor,
columns and reactor, (7) evaluating plant data to construct a model of a process,
(8) minimizing inventory charges, (9) allocating resources or services among
several processes and (10) planning and scheduling construction (Edgar
et al., 2001).
Table 1: 
Applications of mathematical programming in process systems
engineering 

Optimization methods take advantage of the mathematical structure of the economic
and the process models to locate the optimum. The method chosen for any optimization
purposes depends primarily on the character of the objective function and whether
it is known explicitly, the nature constraints and the number of independent
and dependent variables (Alqahtani, 2008). Mathematical
programming and optimization in general have found extensive use in process
system engineering. Referring to Table 1, as for specific
areas, process design problems tend to give rise to NLP and MINLP problems,
while scheduling and planning problems tend to give rise to LP and MILP problems.
The reason for this is that design problems tend to rely more heavily on predictions
of process models, which are nonlinear, while in scheduling and planning the
physical predictions tend to be less important, since most operations are described
through time requirements and activities. In the case of process control the
split is about even (Biegler and Grossmann, 2004).
RECENT WORK: OPTIMIZATION INTEGRATED WITH PROCESS SIMULATOR
The goal of process engineers it to find among the large number of alternative
flowsheets, the least expensive one and to evaluate whether or not this alternative
is profitable. A synthesis approach can utilise the availability of effective
design methods aided by powerful simulation tools and other third party software
for flowsheet optimization, sizing and cost estimation.
Costa et al. (2005) present the utilization
of a process simulator in the operation and capacity expansion of Prosint Quimica
plant, the largest Brazilian methanol producer. The process constitutes process
line, fuel system and steam system which consist substantial models. Process
data necessary for the process simulation from plant was accessed using Exaquantum
software (Plant Information Management SystemPIMS tool) which can act as Excel
plug in when it is activated in a spreadsheet. Then the data collected will
be transport from Excel file to Aspen file (simulator) where simulation can
be executed through OLE links (object linking and embedding) previously establish
between the files. The results obtained are then transferred to an output Excel
file also using the OLE capabilities for several data presentation.
Subawalla et al. (2004) presented a multivariable
optimization (MVO) as a powerfull nonlinear steadystate flowsheet simulation
technique in the methylamines facilities to optimize plant performance by increasing
plant capacity and/reducing energy consumption. The MVO process flowsheet involves
three steps before it can be implemented in plant. First, develop models for
individual unit operations and build process flowsheet. Then, validate the process
flowsheet and the individual models with plant and laboratory data to minimize
the error between model predictions and plant data. The last step is to create
MVO flowsheet which involves defining the variables and their upper and lower
limits, the constraints (include equipment operating limits) and the objective
function. Common optimization variables include feed and recycle flow rates,
distillation mass and energy flows and flow rates of other energy stream. They
used AspenPlus® Simulator for the simulation.
Mahmood and Chng (2009) discussed the used of integrated
HYSYS model with Excelbased spreadsheet in debottlenecking and optimization
of oil and gas facilities. The debottlenecking study was split into three distinct
phase: (1) develop a HYSYS fully integrated facilities model and calibrate against
actual operating conditions, (2) collate design data for input into Meascap
Capacity models, (3) checking Meascap results and input data particularly for
items with Utilisation Factor > 100%. Meascap is a simple Excelbased
spreadsheet tools which extracts the process data generated by a HYSYS simulation
and uses it to calculate the actual design capacity (Capacity) and required
capacity (Demand) of the equipment items using Capacity Models. Utilisation
Factor for each piece of equipment is to indicate, in percentage, how close
the equipment is required to operate compared to its design capacity.
Caballero et al. (2007) addressed the design
and optimization of chemical processes using Chemical Modular Process Simulator
that include state of the art models, including discontinuous cost and sizing
equations. Using this modular framework, the problem is formulated as a generalized
disjunctive programming problem and reformulated and solved as a mixedinteger
nonlinear programming problem. Different algorithms (branch and bound, outer
approximation, and LP/NLP based branch and bound) have been adapted to deal
with implicit equations and their capabilities have been studied. These studies
relies on three steps which are (1) set up the process flowsheet (Aspen HYSYS®
simulator), determine the degrees of freedom and decide which of the independent
variables in the flowsheet are among the available options, (2) write the mathematical
programming model that includes explicit constraints ( sizing and cost models),
third party implicit models (other inputoutput models not included in the process
simulator). These new constraints can be only in term of the independent and/or
dependent variables that previously appear in the flowsheet and also in terms
of new external variables and (3) connecting the process simulator with the
rest of the model using a clientserver application through the windows component
object model (COM) interface. All the steps are controlled from MATLAB®,
where the different algorithms were implemented. NLP subproblems and Master
problems are solved using TOMLABMATLABan interface for accessing state of
the art NLP or MILP solvers.
Medeiros et al. (2004) analyzes HDTLUB, aiming
to optimize the process and operational aspects under the constraints of product
specifications. The HDTLUB was approached on three levels: (1) development
of a steady state simulator to predict the final state of the product and hydrogen
and utilities consumption from process variables, (2) definition of the economic
objective, taking into account realistic aspects of process costs and the need
to achieve product specification. The installed costs (ISBL, US$) were determined
by the Guthrie models for year 1988 using the corresponding MarshallSwift (M
and S) index. Annual operational costs (UTIL, US$/year) were defined based on
respective consumption of utilities and (3) optimization of design and operation.
The HDTLUB process was optimized using the SIMPLEX NelderMead method in MATLAB
R12 environment.
Goel et al. (2002) presents an optimization
framework to identify an optimal process flowsheet structure and optimal equipment
availability requirements at the conceptual design stage. It is possible to
decompose the big synthesis, reliability and maintenance optimization problem
into manageable subproblems: reliability optimization and process synthesis,
and maintenance and design optimization problems. In the first subproblem,
efforts are focused on optimizing the inherent availability and obtaining the
optimal structure and optimal level of inherent availability required for equipment
in the final optimal structure. Once the optimal structure and optimal availability
of components have been obtained, detailed process models together with detailed
maintenance models using time dependent reliability functions, can be used to
obtain the optimal design parameters and a detailed maintenance schedule. The
effectiveness and usefulness of the proposed optimization framework is demonstrated
for the synthesis example of a HDA process.
Lee et al. (2001) illustrates a study project
that initiated to develop a realistic simulation of an FCC and its upstream
gas oil hydrotreater (HTR). The overall objective was to create a tool from
which multiple case studies could be easily developed to study the effects of
varying hydrotreater severity and FCC conversion on the product yields, properties
and economics of the hydrotreater/FCC complex. The final objective was the optimization
of the entire operation. For the purpose of the study, the individual HTRSIM
and FCCSIM reactor models were first separately tuned and calibrated to match
typical commercial unit operations. Calibration was required to allow a first
principles reactor model to match an observed unit’s performance. The matching
was accomplished by adjusting model parameters tied to the installed catalyst’s
activity, selectivity and stability. Also captured during the calibration are
nonidealities in the reactor system, such as divergence from plugflow (e.g.,
hydrotreater bed channeling). Then the entire gas plant is simulated using the
unit operations of HYSYS. Refinery including detailed traytotray fractionators,
heat exchangers, absorbers and the like. In situations in which the separation
section was at or near constraints, this detail may very well be necessary,
as these considerations may limit the reactor’s window of operations. In
order to demonstrate the full capabilities of HYSYS. Refinery, an optimization
case was created to maximize the HTR/FCC complex as an integrated economic unit.
CONCLUSION
The reviewed highlighted the basic concepts that must be understood before applying the optimization. The used of readily available process simulation software as an interface to structural and continuous optimization is possible and promising strategy. The used of Excel unit operation in iCON® simulation process that allows the user to embed Microsoft Excel spreadsheets directly into the flowsheet and allows easy twoway data transfers between the softwares helps to simplify the development of optimization tools. In the future work, this research aim to generate and simulate different process flowsheets at several levels of complexity. The proposed flowsheets are then be evaluated to determine the optimal design condition and perform economic evaluation via Excel spreadsheet using VBA. The results will be validated with existing optimizer software.
FUTURE WORK
The used of cheap and readily available process software as an interface to optimization is much desired. iCON® is a locally developed process simulator by PETRONAS with Graphical User Interface (GUI) that includes all the facilities one expects from a chemical process simulator such as unit operation forms, graphs, unit conversion and process flow diagrams. In addition, iCON® provides a powerful Excel unit operation that allows the user to embed Microsoft Excel spreadsheets directly into the flowsheet and allows easy twoway data transfers between the softwares. This new approach allowed the process information from process design simulator to be extracted and used in optimization problems. The data such as pressure, temperature, flow rate and composition are extracted from iCON process simulator using the Microsoft Excel spreadsheets which is already builtin in this simulator software to optimize chemical process plant based on continuous parameters. In addition, ICON®Excel® allows twoway data transfers that enable a cyclic optimization assessment procedure. Research is currently ongoing to develop the entire framework in Fig. 1.

Fig. 1: 
Optimization framework 
ACKNOWLEDGMENT
The authors wish to thank Universiti Kebangsaan Malaysia for funding this project under grant number UKMGUPNBT0826093.