System Analysis and Optimization of Multi-Contaminant Water Reuse Network with and without Regeneration using a Hybrid Genetic Algorithm- Juniper Publishers
Juniper Publishers- Journal of Civil Engineering
Abstract
This paper proposed methodology to analyse the
possibility of combination of hybrid optimization function with
Single-Objective genetic algorithm (SOGA) for solving the
multi-contaminant water reuse network with and without regeneration
design problem. A non-linear model was considered due to non-linear
multicontaminant constraints system. The freshwater use and wastewater
production has been minimized, by applying the proposed method.
Moreover, the parameters related to the implementation of the genetic
algorithm that increase computer speed and satisfy optimum result were
tuned before the result is confirmed. The solutions and parametric
values so obtained have been further compared with the existing
literature values. The results obtained are in agreement and comparable
to those obtained from other methodologies and it even shows better
result in considering multi-contaminant water reuse with regeneration.
Keywords: Optimization; Genetic algorithm; UNESCO; Heat-integrated water; Computational strategies
Abbreviations:
SOGA: Single-Objective Genetic Algorithm; WNS: Water Network
Synthesis; WNA: Water Network Analysis; WAP: Water Allocation Planning;
WAN: Water Allocation Networks; OTWA: Optimal Total Water Network; GA:
Genetic Algorithm; IWN: Industrial Water Networks
Introduction
Water is a key element for the normal functioning of
many industries. It is intensively utilised in food, pulp or paper,
pharmaceutical, petrochemical and chemical industries, and so on. The
industrial revolution inspired many industrial processes that utilize
water and dispose of it with a certain concentration of pollutant. The
waste water generated from industrial processes is usually treated in a
central common facility in order to remove contaminants and to meet
regulatory specifications for wastewater disposal.
However, as opposed to this conventional approach,
reusing and re-routing the water streams in an integral water network
helps in reducing the consumption of freshwater in the system, and
minimizes the amount of wastewater to be treated and disposed of in to
the environment. Reusing and re-routing the water streams can account
for significant financial investment in a plant (industry), as the cost
of the treatment units is dependent on the volume of wastewater that
requires treatment. Furthermore, in certain instances the level of
treatment required is quite substantial. Hence, it would be favourable
if the volume of water that requires treatment were reduced.
This leads to research in water-reuse, recycling, and
regeneration-reuse/recycle as a means of minimising freshwater use and
wastewater production. Regeneration involves partial treatment by using
water treatment and purification technologies such as membrane and steam
stripping prior to reuse or recycle. These different options for
minimising the volume of water used by the industries combined together
are termed water network synthesis (WNS) or water network analysis (WNA)
or water allocation planning (WAP).
Some of the works done in the area of water
minimization in continuous and batch processes are described by the
detailed reviews of [1], Foo, Khor et al. and Gouws et al. The previous
works that involve wastewater recycle, treatment and reuse within
(industrial) consuming processes dates back to 1970's. The critical need
in reducing both contaminants and consumption of water and energy
necessitate most of them, due to the fact that twenty percent of the
world's total water consumption (this widely exceeds fifty percent in
many industrialised countries) has been recently attributed to
industries by UNESCO.
The scientific community has been largely involved in
the topic of the design of optimal water networks in the last three
decades, through minimizing both economic and environmental objectives.
The design of Water Allocation Networks (WAN) is a complex task,
especially when multiple contaminants are treated in the same plant with
particular emphasis on the decision about the use of many regeneration
units. This problem has been identified in previous works (e.g.
Gunaratnam et al., Feng et al., Boix et al.) and formulated as a generic
framework considering one or several objctive functions. The analysis
of the dedicated literature shows that a robust approach that can take
into account large problems is far from being straightforward. Also, the
definition of constraints or assumptions must be specified and adapted
to a case study, thus hindering the development of a standard approach.
Although, the model-based optimisation approach allows handling of water
network synthesis problems in their full complexity by considering
representative cost functions, multiple contaminants and various
topological constraints, it frequently presents major challenges of high
computational burden to achieve optimality, and it does not guarantee
global optimum which provides the lowest value (known as global
minimum).
Some of the significant achievements in water network
analysis that utilizes optimization-based modelling techniques and
computational strategies are the work of Takama et al. [2] which provide
seminal work on water network synthesis using optimization approach.
Galan and Grossmann formulate optimization of distributed wastewater
treatment network using mixed integer nonlinear programming. Zamora and
Grossmann presented method for obtaining global optimization solution of
water network synthesis. Doyle and Smith proposed sequential
optimization approach in finding the optimal solution. Huang et al;
adopt a representation of fixed flow rate in the water network
synthesis. Savelski M and Bagajewicz M [1,3] provide rigorous proofs for
the necessary conditions of an optimal direct reuse/ recycle and
formulation of mixed integer linear programming for single contaminant
water network synthesis [1,3]. Koppol and Bagajewicz addressed the issue
of uncertainty in the water network synthesis problems.
Moreover, Faria and Bagajewicz proposed a planning
model and way of obtaining global optimum result with piecewise- affine
relaxation enhanced with bound contraction and also consider
pre-treatment for water network synthesis in their later work. Sujak et
al. [4] creates a model for the design of optimal total water network
(OTWN) [4]. Sharma and Rangaiah [5], proposed designing, retrofitting,
and revamping water networks in petroleum refineries using
multiobjective optimization [5]. Tan and Cruz apply stochastic
optimization based technique in water network synthesis problems.
Karuppiah and Grossmann proposed a piecewise-affine relaxation of non
convex terms in the solution of water network analysis. Tan et al.
consider membrane separation based water regenerators for total water
network synthesis. Hong et al. [6] proposed simultaneous optimization of
heat-integrated water allocation networks.
However, despite all the above mentioned significant
achievements in water network analysis research that utilizes
optimization-based modelling techniques and computational strategies
there are some challenges in the issues of non convexity (which leads to
the presence of multiple local optimal solutions), nonlinearity (which
is due to considering regeneration technologies as nonlinear mixed with
linear objective function), simultaneous optimization of the
interactions of rigorous design models for wastewater treatment
technologies and multiple water-using units, enabling faster numerical
solutions, development of more meaningful optimization-based
formulations, uncertainty (posed by the data obtained from the industry,
the assumed parameters in analysis of the problems), alternative
methods for optimization under uncertainty and extension to resource
recovery systems. However, all the above challenges and uncertainties
can be handled by using stochastic programming which is robust
optimisation method. The use of stochastic programming like Genetic
Algorithm (GA) can improve the potential future directions in water
network analysis and assist in developing feasible, cleaner and more
economic industrial water networks (IWN) that drastically reduced
freshwater consumption as well as wastewater, and ensure reasonable
costs and efficient productivity (Ramos et al.).
Inconsideration of the above, this paper developed a
general framework for water (fresh and waste) allocation planning (WAP)
that can be applied to different water allocation contexts e.g. oil
refinery, food production, pharmaceutical etc, by considering multiple
contaminants with and without regeneration. The WAP problem was solved
using a combination of stochastic genetic algorithm (GA) optimization
and hybrid function optimization method. The non-convexity and
nonlinearity challenges are adjusted by using reproduction parameters of
GA which includes Elite Count and Crossover fraction to obtain possible
solutions by the use of Population creation function
that is constraint dependent. The optimization method handles
interactions of rigorous design models for wastewater treatment
technologies and multiple water using units simultaneously. The
solutions and parametric values so obtained from a case study of three
processes have been further compared with the existing literature
values.
Methodology
Superstructure for integrated water network (IWN) allocation problem
The superstructure model for IWN allocation problem
as proposed by Ramos et al. is shown in Figure 1. It is generalization
of the model given by karuppiah and Grossman and Ahmetovic and Grossmann
[7]. The first part consists of freshwater source, water from
regeneration units and from other process units all linked in to a
mixer. This is followed by connection to different processes for further
operation and addition of more contaminants strictly based on the
acceptance level of contaminant concentrations of each process. The
output water flow is linked to the splitter that separate flow in to
discharge as wastewater, flow to regeneration units and to other
processes. The second part starts with the mixer of water from process
units and from other regeneration units link to further regeneration and
passed to splitter which link the water flow to other process units and
further regeneration units (Figure 1).
Formulising the water minimisation problem with and without regeneration
Multi-contaminant-water reuse without regeneration model
Fitness function: The fitness function for
multi- contaminant-water reuse without regeneration model which is the
sum of fresh water flow rates at the entrance of all water using
processes is presented in equation1 (Figure 2).
Where, F is the flow rate of freshwater entering operation in tons/h.
Constraints
Linear Constraints functions: The linear
constraint function of the water mass balance of all processes involved
in Multi contaminant water reuse is presented in equation 2.
Where, Xi ? is the flow rate of water reuse form to in tons/h, and
W is the wastewater flow rate out of the process in tons/h.
Nonlinear constraints functions
i. The nonlinear constraint function of the
contaminant mass balance of all processes involved in multi-contaminant-
water reuse is presented in equation 3:
Where, c,,k is the average inlet concentration of contaminant to process in ppm.
ΔMjk is the average mass load of each contaminant for each operation in g/h.
i. The nonlinear constraint function of maximum contaminant inlet concentration involved in
multi-contaminant-water reuse is presented in equation 4:
Where, Cj,k,in is the average inlet concentration of contaminant k to process in ppm.
Cj,k,out , is the average outlet concentration of contaminant k to process in ppm.
Multi-contaminant water reuse with regeneration model
Fitness function: The fitness function for
multi-contaminant water reuse with regeneration model which is the sum
of fresh water flow rates at the entrance of all water using processes
is as presented in equation 1: (Figure 3).
Constraints
Linear Constraint functions: The linear
constraint function of the water mass balance of all process involved in
multi-contaminant- water reuse with regeneration is presented in
equation 5.
i. The nonlinear constraint function of the
contaminant mass balance of all processes involved in
multi-contaminant-water reuse with regeneration is presented in equation
6.
Where, Cok , is the average regeneration outlet concentration of contaminant in ppm.
ii. The nonlinear constraint function of the Maximum Contaminant inlet concentration involved in
multi-contaminant-water reuse with regeneration is presented in equation 7:
Where, all the symbols are as described in the first model description.
The main difference between multi-contaminant-water
reuse with and without regeneration model is that the later has
reconnection of water reuse after regeneration which includes the
processes and streams connected to the regeneration unit, and the former
has no regeneration that links to the processes and streams after use.
Solving the water minimisation problem using a GA Algorithm
For solving the equations above (1-7) the SOGA was
used and in order to further improve the diversity and convergence of
the solutions obtained by SOGA, a hybrid function was incorporated. The
hybrid function "fmincon" is adopted to prevent the GA from getting
stuck in the local minimum solution of the WAP. "Fmincon" uses a Hessian
as an optional input.
Initial generation of chromosomes: The initial chromosomes were randomly generated by the Matlab software using boundary limits of all positive real values i.e Xu} >
0 . The binary values (1 and 0) of all the variables in each equation
were identified. A value of 1 is assigned to the position of the
variable if it exists in the equation and 0 otherwise. The values of
contaminants were directly used in the equations as either the
coefficient of the variable or as a constant.
Genetic algorithm in matlab:The SOGA is the basis used for solving the proposed optimization
model in Matlab, and in order to further improve the
diversity and convergence of Pareto optimal solutions obtained by SOGA, a
hybrid function is incorporated. The hybrid function works after the
exhaustion of the combined crossover and mutation operator that improved
the search ability of the algorithm.
Method for the hybrid approach: Incorporating a
search method within a genetic algorithm can improve the search
performance on the condition that their roles cooperate to achieve the
optimization goal [8] (Tarek et al). The hybrid function "fmincon" is
adopted to prevent the GA from getting stuck in the local minimum
solution of the WAP. "Fmincon" uses a Hessian as an optional input. This
Hessian is the matrix of second derivatives of the Lagrangian equation.
The Hessian is the matrix of second derivatives of the objective
function.
In single objective GA the hybrid function starts at
the best point returned by the GA. The method involves combining
principles of Genetic Algorithms (GA) and SQP algorithm that performs
the computation of the Hessian of the objective function and its
non-linear constraints. The hybrid function prevents the GA from being
stuck in the local minimum solution of the WAP problem.
The Hessian for a constrained problem is the Hessian
of the Lagrangian of an objective function f, nonlinear inequality
constraint vector c, and nonlinear equality constraint vector ceq, the
Lagrangian is given by equation 8.
The are Lagrange multipliers.
The Hessian of the Lagrangian is shown in equation 9.
Matlab software provide SQP as "fmincon" which
minimise constraint function based on a powerful concept in optimization
known as trust regions. "Fmincon" uses a Hessian as an input function.
Key steps in waste water minimization for multiple contaminant problems
A number of key steps are to be followed for implementing a Wastewater minimization project [9].
Step 1: The need of waste water minimization identified based on limited availability of freshwater,
economic and environmental regulation consideration.
Step 2: Data related to plant/industry is collected
which include fresh water use by a particular unit, process quality
requirement, cost and capability of treating water for initial input to
the process and the wastewater generated in the end by the process.
Step 3: Drawing a flow sheet of the processes, which shows water balance diagram of the processes.
Step 4: Identification of the key contaminants for
the processes; these are the contaminants that are to be reduced so that
the discharged waste water can be reused or disposed under the
specified control standards for an industry.
Step 5: The approach applied for solving the
wastewater minimization problems. Mathematical programming approach: It
involves definition of superstructure by considering each process within
an industry to have a certain freshwater flow rate, output water from
other process and or regenerated water, the output from the process will
have effluent with certain level of pollutants concentration which can
be discharged, recycled or regenerated for reuse, mathematical
optimization and analysis of solution.
Step 6: After carrying out various analysis and calculations a Wastewater minimization project can be
implemented.
Algorithm implementation
The basic flow chart for the implementation of
Genetic Algorithm (GA) is shown in Figure 1. However, depending on the
optimization software used in finding the solution, the steps may
require a little adjustment in execution.
This paper uses Matlab software for implementing the
steps; as such the following adjustments were adopted in obtaining the
best result.
Steps in genetic algorithm implementation in Matlab:
a. Combining all variables in one vector.
b. Writing vector for lower and upper bounds ( lb and ub ).
c. Writing matrix and vector of inequalities ( A and b)
d. Writing matrix and vector of equalities ( Aeq and beq ).
e. Writing nonlinear constraint function.
f. Calling the solver: [x fval] = ga(fitnessfcn, nvars, A,b, Aeq, beq, lb, ub)
Algorithm testing
As the parameter setting that is good for one problem
may not be suitable for another one sensitivity analysis of the
parameters of the GA approach was done to identify the parameters that
produce quality solutions [10,11]. In this research all parameters
related to the implementation of the genetic algorithm were tuned before
the algorithm is confirmed. These parameters are Population, Fitness
Scaling, Selection, Reproduction, Mutation, Crossover, Migration,
Constraint Parameters, Hybrid Function and Function Evaluation (Table
1). These parameters were chosen so that the optimal, or at least a good
one, solution is found. Obviously, by the stochastic nature of Genetic
Algorithm (GA), multiple runs on the same problem are necessary to get a
good estimate of performance.
Furthermore, in order to verify the adopted methodology the solutions obtained have been further
compared with the existing literature obtained values.
Case Studies
The genetic algorithm program was used in two
important examples in chemical engineering industries. The examined
industrial cases have significant usage and discharge of fresh water and
wastewater. The first case has three industrial processes and three
contaminants but without regeneration. The second case is as the first
case but with addition of regeneration.
Multi-contaminant water reuse without regeneration for 3 (Three) industrial processes
Considering an integrated optimization approach in
multiple contaminant system that contains n operations, m contaminants,
the numbers of variables involved are and there are equality constraints
[12].
The Linear Constraint is derived from the water mass
balance and the nonlinear constraint is derived from the contaminant
mass balance and the maximum contaminant inlet concentration. The lower
bound was set to zero to control all variable as positive numbers,
while, the upper bounds was set to infinity.
Case Study: Input limiting process data The example
data used have three process units and three contaminants, is fMann and
Liu [13], with the limiting water data for the industrial process units
shown in Table 2
Final points: Optimization terminated because
the average change in the fitness value is less than function tolerance
and constraint violation is less than constraint tolerance. The solution
process further proceeds by switching to the hybrid optimization
algorithm (FMINCON) and satisfy the constraints. "Fmincon" stopped
because the size of the step is less than the default value of the step
size tolerance and constraints are satisfied to within the default value
of the constraint tolerance. FMINCON come to termination because the
objective function is non-decreasing in feasible directions, to within
the default value of the function tolerance, and constraints are
satisfied to within the default value of the constraint tolerance. The
final result is shown in Table 3.
The Superstructure representation of results for
three (3) processes is shown in Figure 4. This shows the optimum water-
using network for an example problem of multi-contaminant without
regeneration-water reuse.
Solution of the problem corresponding to the
diagrammatical Superstructure representation of the solution is shown in
Table 4. It described the obtained result, indicating that the minimum
total freshwater required by the industry is 70.0m3/h, 30m3/h for process 1 and 33.0m3/h for process 2 and 7.0m3/h for process 3. While, process 2 and 3 reuse 2.0m3/h and 21.0m3/h of wastewater respectively, from process 1.
Solution of the problem corresponding to the
diagrammatical Superstructure representation of the solution is shown in
Table 4. It described the obtained result, indicating that the minimum
total freshwater required by the industry is 70.0m3/h, 30m3/h for process 1 and 33.0m3/h for process 2 and 7.0m3/h for process 3. While, process 2 and 3 reuse 2.0m3/h and 21.0m3/h of wastewater respectively, from process 1.
Multi-contaminant water reuse with regeneration recycle for 3(Three) industrial processes
Considering an integrated optimization approach in
multiple contaminant system that contains n operations, m contaminants
and regeneration units, there are 2n variables more than water reuse
without regeneration. The numbers of variables involved are + 3n + nm and there are n + nm equality constraints [12].
The fitness function which is the sum of fresh water
flow rates at the entrance of each water using process is as presented
in equation 1.
Test problem: Input limiting process data: The
example data used have three process units and three contaminants, and
is taken from Mann and Liu (1999) and [13], with the limiting water data
for the process units shown in Table 2 is used with the limiting water
data for the process units shown in Table 2 is used with an assumed
regeneration contaminant concentration of 25ppm:
Final points: Optimization terminated because
the average change in the fitness value is less than function tolerance
and constraint violation is less than constraint tolerance. The solution
process further proceeds by switching to the hybrid optimization
algorithm (FMINCON) and satisfy the constraints. "Fmincon" stopped
because the size of the step is less than the default value of the step
size tolerance and constraints are satisfied to within the default value
of the constraint tolerance. FMINCON terminated. because the objective
function is nondecreasing in feasible directions, to within the default
value of the function tolerance, and constraints are satisfied to within
the default value of the constraint tolerance and the final result is
shown in Table 5.
The Superstructure representation of result for three
(3) the optimum water-using network for an example problem of processes
with regeneration is shown in Figure 5. This shows multi-contaminant
with regeneration-water reuse (Figure 6).
Solution of the problem corresponding to the
diagrammatical Superstructure representation of the solution is shown in
Table 6. It described the obtained result, indicating that the minimum
total freshwater required by the industry with regeneration of 25ppm is
51.0m3/h, 45m3/h for process 1 and 6.0m3/h for process 2. Process 2 use additional 19.0m3/h of wastewater. While, process 3 reuse 20.0m3/h of wastewater only, from process 1 after regeneration.
Comparison of the obtained result with the existing literature value
Table 7 shows that the result obtained from the
solution of multi-contaminant water reuse without regeneration for
minimum freshwater consumption or wastewater generated is equal to that
obtained from the literature. Moreover this study consider regeneration
in the second case i.e multi-contaminant water reuse with regeneration
with an assumption of 25ppm contaminant regeneration quality, while the
literatures mentioned [13] (i.e Mann and Liu) did not find solution to
that case.
Conclusion
The genetic algorithm has major advantages of
flexibility and robustness as a global optimum result search method.
Although, it uses stochastic optimization it can deal with highly
nonlinear problems and on differentiable functions as well as functions
with multiple local optima and is readily amenable to implementation,
which renders them usable in real-time problems of WAP. The nonlinear
programming solutions for multi-contaminant water network with and
without regeneration are presented. The approach was based primarily on
using MATLAB in implementing the genetic operators. A standard
formulation was proposed that can be modified to suite a wide variety of
WAP problems. The only data required are the number of processes, their
associated maximum inlet and outlet concentrations, the mass load
generated for each contaminant and the number of regeneration units with
the corresponding efficiency related to each contaminant [14-23].
The best genetic algorithm parameters for obtaining a
good result were presented, followed by the implementation. Finally the
obtained results were compared with the literature values.
The model shows better result in considering multi-contaminant water reuse with regeneration.
Moreover, the future study will consider
multi-objective optimization of water reuse network using multiobjective
genetic algorithm capabilities of Matlab.
Acknowledgment
I would like to knowledge Petroleum Technology Development Fund (PTDF) Nigeria for funding this research.
For More Open Access Journals Please Click on: Juniper Publishers
Fore More Articles Please Visit: Civil Engineering Research Journal
Fore More Articles Please Visit: Civil Engineering Research Journal
Comments
Post a Comment