Process Integration and Optimization for Sustainability
https://doi.org/10.1007/s41660-019-00096-5
ORIGINAL RESEARCH PAPER
Synthesis of Heat-Integrated Water Allocation Networks
Through Pinch Analysis
Shweta Kamat 1 & Santanu Bandyopadhyay 1
Received: 14 February 2019 / Revised: 25 April 2019 / Accepted: 10 June 2019
# Springer Nature Singapore Pte Ltd. 2019
Abstract
Thermal energy (or utility consumption) and water can be optimized through the synthesis of heat-integrated water allocation
networks (HIWANs). Various numerical optimizations, pinch-based and hybrid tools, have been proposed for HIWAN synthesis.
Numerical optimization techniques make it difficult to visualize the problem due to complex formulations involving non-linear
equations and/or integer variables. Pinch-based methods provide physical insights but are restricted to graphical techniques. As a
result of this, HIWAN synthesis through pinch-based techniques gets tedious for medium-scale to large-scale data. HIWAN
synthesis can be solved using a hybrid technique that combines the physical understanding of pinch analysis with a series of
linear programming (LP) formulations. The proposed methodology converts the LP into an algebraic solution strategy and
thereby making the HIWAN synthesis procedure entirely based on pinch analysis. Unlike the other pinch-based methods that
rely on temperature-based heuristics to guide the water re-use streams, this method synthesizes HIWAN as an outcome of a utility
minimization algorithm. This algorithm is an extension of the compression work minimization algorithm in hydrogen networks.
The nature of these two problems differs due to the requirement of two entities (heating and cooling) in the former instead of one
entity (compression work) in the latter. Besides freshwater minimization, this methodology can be applied for the conservation of
other resources as well. Illustrative examples of three water allocation networks (one with regeneration) and an ammonia
allocation network demonstrate the proposed methodology.
Keywords Heat-integrated water allocation networks . Process integration . Pinch analysis . Isothermal mixing . Interplant flow
Introduction
Some industrial processes (e.g., pulping, smelting) extensively
use water at specified temperatures to ensure a desirable output.
Other than water, the processes may require fuels (e.g., coal,
natural gas) to generate utilities such as steam and/or cooling
water to achieve specified temperatures in supply waters. With
industrial growth and population rise, the annual rate of increase in water consumption is 1% (WWAP 2018), and that
of energy consumption is 1.2% (IEA 2014). It is estimated that
around 3.6 billion of the world population already lives in
water-scarce regions (WWAP 2018). On the other hand, despite
growth in renewable technologies, a major share of energy is
met by fossil fuels (U.S. EIA 2017). To achieve market
* Santanu Bandyopadhyay
santanub@iitb.ac.in
1
Department of Energy Science and Engineering, Indian Institute of
Technology Bombay, Powai, Mumbai 400076, India
competitiveness and to follow a greener as well as a sustainable
production process, it is important to seek measures to conserve
resources such as water and energy. In some process industries,
energy and water needs are intertwined, thereby requiring
methods for their conservation simultaneously. Such optimization can be achieved through process integration techniques for
water re-use through water allocation networks (WANs), heat
recovery through heat exchanger networks (HENs), and finally
through the heat-integrated water allocation network
(HIWAN). HIWANs can be synthesized using numerical optimization tools (Bagajewicz et al. 2002), insight-based techniques like pinch analysis (Savulescu et al. 2005a, 2005b)
and concentration potentials (Zhao et al. 2019), or hybrid approaches (Sahu and Bandyopadhyay 2012). HIWANs have
been synthesized for a single plant (Hong et al. 2018a) as well
as multiple plants (Ibrić et al. 2017b; Liu et al. 2018).
Furthermore, the HIWAN synthesis methods are extended towards heat integration of non-water using processes (Ibrić et al.
2017a). Literature reviews on HIWANs were presented by
Ahmetović et al. (2015) and Kermani et al. (2018).
Process Integr Optim Sustain
Bogataj and Bagajewicz (2008) minimized water
requirement and reduced energy use by incorporating slack
variables for utility consumption along with the water
minimization objective. Dong et al. (2008) introduced stochastic perturbation, through a modified state-space representation, for the optimization of energy and water resources prior
to HEN synthesis. Ahmetović et al. (2014) synthesized the
HIWAN through a non-convex mixed-integer non-linear programming (MINLP) with a convex hull formulation but
lacked the heat integration while optimizing the water system.
To overcome this drawback, Ibrić et al. (2014) optimized the
water and energy targets through total operating cost minimization in the initial step. Ibrić et al. (2016) proposed a compact
superstructure for HIWAN synthesis by simplifying the model
developed by Ibrić et al. (2014). On the other hand, Liao et al.
(2008) targeted the resources through an MINLP formulation
using the transshipment model. Liao et al. (2011) defined the
problem in a way that identified the hot or cold streams prior
to HIWAN synthesis and thereby requiring a mixed-integer
linear programming (MILP) formulation. However, in both
these cases, HEN synthesis involved MINLP formulations.
Hong et al. (2017) modified the transshipment model to eliminate the non-linearity associated with the minimization of
total annualized costs, thereby requiring an MILP formulation. While Ghazouani et al. (2017) developed a temperature
scale with many divisions, Kermani et al. (2017) considered
all possibilities of known temperatures in order to develop
MILP models. These MILP formulations would be transformed into MINLP formulations upon the addition of regeneration units with fixed removal ratios (Hong et al. 2018a).
MINLP formulations would lead to complexities due to the
presence of non-linearity as well as integer variables. Zhou
et al. (2015) eliminated the binary variables from the
MINLP formulations by adding several equations and variables, resulting in a non-linear programming (NLP) model
for HIWAN synthesis. Yan et al. (2016) reformulated the
non-convex MINLP with convex hull formation for stream
identification (Ahmetović and Kravanja 2013) into an NLP
through non-linear equations to identify the streams as well
as the number of heat exchangers (Yan et al. 2016). Cheng and
Adi (2018) proposed an NLP model for HIWAN synthesis
using a superstructure that separated the hot and cold streams
prior to synthesis.
These simultaneous optimization techniques always provide cost-optimal results. However, the single-step models
involve a large number of variables and are difficult to solve
due to the computational burden. As a result of this,
researchers have focused on simplifying MINLP
formulations into NLP or MILP while compromising either
on accuracy and/or convergence. Further simplification is possible through the use of sequential techniques involving utility
minimization for the least amount of water consumption. The
sequential techniques can be useful in regions facing water
scarcity. Bagajewicz et al. (2002) proposed two linear programming (LP) models to sequentially minimize water and
energy followed by an MILP formulation for HIWAN
synthesis. Du et al. (2003) minimized water through an NLP
model, while Du et al. (2004) included piping costs to the
model, leading to the development of an MINLP approach.
Both these methods involved the HEN synthesis through
MINLP formulations using the stage-wise superstructure approach (Yee and Grossmann 1990). Li et al. (2013) developed
a four-step method to minimize freshwater requirement, piping cost, utility requirement, and design a HEN through alternate LP and MILP formulations. Despite simplification, the
numerical optimization techniques do not provide physical
insights into the problem. The use of pinch-based techniques
makes it easy to visualize the synthesis process and thus is
preferred by industrial experts.
The pinch-based methods for HIWAN synthesis involve
three steps, namely freshwater (and regeneration) minimization, synthesis of WAN consuming minimum utility, and HEN
synthesis for the obtained WAN. After fresh resource minimization through re-use, the WAN was designed using a twodimensional grid representation to minimize the utility requirement (Savulescu et al. 2005b). A water-energy balance
diagram was introduced to improve the stream temperature
representation of the two-dimensional grid diagram
(Leewongtanawit and Kim 2009). Other techniques to minimize the energy while designing the WAN were heat surplus
diagram (Manan et al. 2009), super-imposed mass-energy
curves (Wan Alwi et al. 2011), and temperatureconcentration diagram (Martínez-Patiño et al. 2011). The
temperature-concentration diagram was extended to include
regeneration units (Shen et al. 2017). The HEN can be developed through separate systems (Savulescu et al. 2005a,
2005b), matching composite curves (Liao et al. 2016), or heat
transfer block diagrams (Hong et al. 2018b). This paper focuses on the second step in the synthesis of HIWAN through
pinch analysis. The existing methods are graphical and restricted to temperature-based heuristics that guide the synthesis of WANs. The use of graphical methods makes the solution
of medium- to large-scale problems tedious.
The complexity associated with numerical optimization
and the tedious nature of pinch-based techniques can be reduced by incorporating pinch analysis within the mathematical framework of the HIWAN. These approaches are known
as hybrid techniques. Most of these methods involve HEN
synthesis through pinch-based methods (Linnhoff and
Hindmarsh 1983). Ataei et al. (2009) developed an NLP,
while Tan et al. (2012, 2014) developed MINLP formulations
to minimize the total operating costs. George et al. (2011)
formulated LP models based on the transshipment model for
freshwater and utility minimization through isothermal
mixing. Kamat et al. (2019) extended this problem to include
regeneration units and eliminated the non-linearity associated
Process Integr Optim Sustain
with the model. Sahu and Bandyopadhyay (2012)
reformulated the LP model proposed by George et al. (2011)
to reduce the number of variables by using the concepts of the
modified problem table algorithm (Bandyopadhyay and Sahu
2010). Although the problem was simplified, it needed to be
solved as an LP within the pinch interval. This LP model
requires iterative algorithms like the simplex algorithm to converge to the solution. The need to use iterative algorithms can
be eliminated through algebraic or graphical techniques. In
order to save additional amount of freshwater, as compared
with the method proposed by Sahu and Bandyopadhyay
(2012), regeneration unit needs to be incorporated.
The proposed methodology is an algebraic as well as a
graphical technique for HIWAN synthesis. In contrast to the
existing pinch-based techniques, this method is applicable to
non-mass transfer processes. The existing pinch-based techniques comprised of rules to guide the WAN such that the
utility is minimized. However, the proposed method minimizes the utility, and the optimal HIWAN is an outcome of
this utility minimization algorithm. The principle behind the
proposed methodology is adapted from the compression work
minimization in hydrogen networks through interplant flow
minimization (Bandyopadhyay et al. 2014). The proposed
methodology differs from the above-mentioned technique
due to the requirement of heating and cooling in the former
rather than only compression work in the latter. The structure
of the paper is as follows. First, the problem is defined, and
models for freshwater and utility minimizations are formulated. An algebraic technique to minimize the utility requirement
is proposed next. The methods for water conservation can be
used for the conservation of other resources (e.g., ammonia,
hydrogen) as well. Subsequently, the methodology for
HIWAN synthesis has been demonstrated using the examples
of three water allocation networks, one of which consists of a
regeneration unit and an ammonia allocation network.
Fig. 1 Schematic representation
of HIWAN with isothermal
mixing
Fresh Resource
Problem Definition and Model Formulation
The general structure of a HIWAN is expressed in Fig. 1.
Internal water sources and demands in a process industry are
characterized by flow rate, contaminant concentration, and
temperature. Each internal source can provide water to the
internal demands to meet the flow and temperature requirements while ensuring that the upper limit on the contaminant
concentration is not exceeded. In case of unsatisfied flow and/
or concentration limits of internal demands, an external freshwater source is used. Any unallocated portion of the source is
disposed of as waste. Source streams to be allocated to demands need to be heated (cold streams) or cooled (hot
streams) to meet demand temperatures. Heat is transferred
from hot streams to cold streams in a heat exchanger. A minimum temperature difference needs to be maintained in the
heat exchanger to ensure a reasonable investment cost. To
satisfy the demand temperatures, hot and/or cold utility may
be required. A single hot and cold utility are assumed in this
paper. The specific heat capacity for water streams is assumed
to be constant, 4.2 kJ/kg °C, and its variations due to change in
temperature as well as concentration are ignored.
& A set of Ns internal sources is provided. Each internal
source provides a flow rate of Fsi, at a temperature of
Tsi, and contaminant concentration of Csi.
& There is a set of Nd internal demands. Each internal demand requires a flow of Fdj at a temperature Tdj. The
maximum contaminant concentration that can be allowed
to enter the jth demand is Cdj.
& Demand flow and quality requirements are matched by the
internal sources through isothermal mixing.
& It is possible that insufficient flow is available and/or demand quality restrictions are violated. In this case, freshwater, Fs0, which is available at a specified a temperature,
Ts0, and a contaminant concentration of Cs0, is required.
Qhu
Waste Resource
i=0 (Fs0, Cs0, Ts0)
j=0 (Fd0, Cd0, Td0)
i=1 (Fs1, Cs1, Ts1)
j=1 (Fd1, Cd1, Td1)
i=k (Fsk, Csk, Tsk)
j=k (Fdk, Cdk, Tdk)
i=Ns (FNs, CNs, TsNs)
j=Nd (FNd, CNd, TdNd)
Qcu
Process Integr Optim Sustain
&
&
&
&
Start
Any unallocated source flow will be disposed as waste.
Waste is represented as an external demand with no limit
on contaminant concentration. The waste flow rate is denoted by Fd0. The upper limit on the temperature of resource to be disposed of, Td0, is specified by the environmental norms.
A set of Ns internal sources along with freshwater source
(i = 0,1,.., Ns) and Nd internal demands along with wastewater (j = 0,1,.., Nd) are considered for heat integration.
Maximum heat is recovered from hot streams (T si > T dj )
Determine the minimum resource requirement
Complete the source and demand data
Identify the potential pinch intervals, P
p=P
Find hot utility above Thp,
Shift every source and demand above and below Thp and Tcp to Thp
and Tcp respectively
and transferred to cold streams (T si ≤ T dj ). The heat recovery potential is constrained by the minimum approach
temperature (ΔTmin) of the heat exchangers.
As a result of this, hot utility, Qhu, and/or cold utility, Qcu,
may be required to match the demand temperature
requirements.
The objective of this paper is to optimize freshwater
and utility requirements by synthesizing a HIWAN using
pinch analysis. In locations suffering from water scarcity,
freshwater is costly. Thus, the use of sequential strategy,
which minimizes utility for a minimum freshwater, provides cost-optimal results. Simultaneous optimization
technique provides cost-optimal results in other cases
but is not efficient computationally. To enhance the efficiency of the solution, sequential methods are developed.
The sequential strategy minimizes utility requirements in
a HIWAN for targeted freshwater. The mathematical
models for freshwater and utility minimization are provided. An algebraic methodology to obtain HIWAN
through utility minimization is proposed using the concept of interplant flow minimization.
Arrange all sources and demands in increasing order of temperatures
(T1< T2<...<TN)
k=N
Consider all sources and demands at temperature Tk as plant A at Tk and all
other sources and demands as plant B at Tk-1
Find the minimum hot utility (Qhu)k by minimizing the interplant flow
between Tk and Tk-1
Consider flows from plant A to plant B as source at Tk-1 and flows from plant
B to plant A as demand at Tk-1
Yes
=
Minimum hot utility,
p=p-1
Is p=1?
+∑ (
)
No
Yes
Find pinch interval such that
= max
Obtain the WAN from the interplant flows for the pinch interval and
synthesize a HIWAN through pinch analysis
Fresh Resource Minimization
Let fij denote the water flow rate allocated from ith
source to jth demand. Let f0j denote the freshwater flow
rate accepted by the jth demand and f i0 denote the
waste generated by ith source. It is assumed that there
is no leakage or loss of water. Hence, the flow is conserved. The flow balance for every internal source and
demand is given by Eqs. 1 and 2. Equation 3 indicates
that a particular demand may accept flow at the desirable or superior quality. Freshwater to be minimized is
Fig. 2 Number of ways to
minimize utility in pinch interval
with four temperature levels
No
k=k-1
Is k=1?
S
T4
T3
T2
T1
Plant A
Plant B
End
Fig. 3 Flowchart for HIWAN synthesis
denoted by Fs0 and the objective function is provided
by Eq. 4.
Nd
∑ f i j ¼ F si
∀i∈f0; 1; …N s g
D
S
j¼0
T4
T3
Plant A
T2
T1
Plant B
ð1Þ
S
D
T4
T3
T2
T1
D
Plant A
Plant B
Process Integr Optim Sustain
Ns
∑ f i j ¼ F dj
i¼0
∀ j∈f0; 1; …N d g
Ns
∑ f i j C si þ f 0 j C s0 ≤ F dj C dj
ð2Þ
∀ j∈f0; 1; …N d g
i¼1
ð3Þ
d
f 0j
Minimize F s0 ¼ ∑Nj¼1
ð4Þ
The freshwater (Eq. 4) needs to be minimized subject to
source and demand flow constraints (Eqs. 1 and 2) and demand contaminant load constraints (Eq. 3). The freshwater
minimization problem is an LP. This problem can also be
solved algebraically or graphically applying techniques of
pinch analysis. Some of the techniques are water surplus diagram (Hallale 2002), material recovery pinch diagram (ElHalwagi et al. 2003; Prakash and Shenoy 2005), water cascade analysis (Manan et al. 2004), source composite curve
(Bandyopadhyay 2006), limiting composite curve (LCC)
(Agrawal and Shenoy 2006), improved problem table (Deng
and Feng, 2011, Deng et al., 2016), automated composite table
algorithm (Parand et al. 2016), etc. The amount of wastewater
or freshwater can be obtained from the overall flow balances
(Pillai and Bandyopadhyay 2007).
Minimization of Utility and HIWAN Synthesis
Once the freshwater consumption is minimized, the next step
is to minimize the utility requirement. The essential parameters (flow rate, contaminant concentration, and temperature)
for all the sources and demands are entirely known. For
known flow rate and temperature of sources and demands,
the hot and cold utilities are related by a constant, Δ, which
is expressed by Eq. 5 (Sahu and Bandyopadhyay 2012).
Therefore, minimization of either hot or cold utility leads to
the minimization of the other utility. A pinch-based model,
proposed in this paper, minimizes the hot utility.
"
#
Nd
Ns
j¼0
i¼0
Qhu −Qcu ¼ cp ∑ F dj T dj − ∑ F si T si ¼ Δ
Table 1
ð5Þ
Process data for Example 1
Flow rate (kg/s)
Demand
D0
–
D1
100
D2
40
D3
166.67
Source
S0
–
S1
100
S2
40
S3
166.67
Concentration (ppm)
Temperature (°C)
Prior to the model description, it is essential to explore the
pinch terminology and principles. As discussed in the
“Problem Definition and Model Formulation” section, a minimum approach temperature of ΔTmin needs to be maintained
in the heat exchanger. Thus, temperature difference between
any hot and cold stream cannot be less than ΔTmin. The temperatures of hot and cold streams at which this minimum
temperature difference is maintained are termed as hot and
cold pinch temperatures. The portion between the hot and cold
pinch temperatures is known as the pinch interval. The modified problem table algorithm was used to target the utility
requirement and identify the pinch interval for a WAN
(Bandyopadhyay and Sahu 2010). Unlike utility targeting
for an existing WAN, the synthesis of HIWAN to satisfy the
minimum utility criteria introduces variable heat capacity
rates. Sahu and Bandyopadhyay (2012) extended the modified
problem table algorithm for HIWAN synthesis. This model
identified the pinch interval based on the calculation of hot
utility requirement for potential pinch intervals, which were
obtained from source temperatures. Let p (p = 1,2,.., PI) be a
set of potential pinch intervals. As every source temperature is
a potential pinch interval, PI can range from 1 to 2 (Ns + 1).
The potential hot and cold pinch temperatures denoted by Thp
and Tcp and the potential pinch interval is expressed as Thp/Tcp.
External heating is done above Tcp and external cooling is
carried out below Thp. External heating would be required in
the region above Thp. Similarly, external cooling is required in
the region below Tcp. Thus, hot utility above Thp and cold
utility below Tcp can be obtained algebraically as the minimum temperature difference will always be maintained
(Sahu and Bandyopadhyay 2012).
Consider the minimization of hot utility (Eq. 6) for a potential pinch interval, Qhup, which is the sum of hot utility
required above Thp (denoted by μp) and in the pinch interval
(denoted by (Qhup)PI). The algebraic expression for μp is given
in Eq. 7:
PI
hu
∀ p∈f1; 2; ::; PI g
ð6Þ
Qhu
p ¼ μp þ Qp
μp ¼ ∑ F dj cp T dj −T hp − ∑ F si cp T si −T hp ∀T si ; T dj
j
> T hp ; p∈f1; 2; ::; PI g
–
50
50
800
30
100
75
100
0
100
800
1100
20
100
75
100
i
ð7Þ
Within the pinch interval, the streams could require external heating as well as cooling. Thus, (Qhup)PI cannot be algebraically determined. As μp is a constant, the objective reduces to the minimization of (Qhup)PI (Eq. 8):
PI
d
s
i f T dj
Minimize Qhu
¼
∑
f
c
T
−T
p
i
j
p
j
i
i; j
h
i
> T si ∀T dj ; T si ∈ T hp ; T cp ; p∈1; 2::; PI
ð8Þ
Process Integr Optim Sustain
Table 2 Hot utility for potential
pinch interval 100/70 °C for
Example 1
Flow transferred across (°C)
Contaminant concentration (ppm)
Flow rate (kg/s)
Qhu/Qcu (MW)
Interplant flow between plants at 100 °C and 75 °C
75 to 100
100 to 75
0
100
50
11.69
5.25
− 1.23
75 to 100
800
38.96
4.09
77.27
1.62
10.96
Interplant flow between plants at 75 °C and 70 °C
70 to 75
Total hot utility requirement
0
Hot utility required in the potential pinch interval (Eq. 8)
needs to be minimized subject to the flow balances (Eqs. 2 and
3), demand contaminant load constraint (Eq. 4), and freshwater and waste targets from the results of the freshwater minimization problem. From the modified problem table algorithm, the interval having the least amount (largest negative
magnitude before cascading) of cascaded heat is the pinch
interval. This is shown in Eq. 9. In the modified problem table
algorithm, a positive sign is associated with the flows arising
from sources and negative sign with the flows entering a demand. Note that the signs are reversed in this paper according
to the definition of hot utility shown in Eq. 8:
Qhu ¼ max Qhu
ð9Þ
for p ¼ 1 to 2 ðN s þ 1Þ
p
The modified problem table algorithm (Bandyopadhyay
and Sahu 2010) was algebraic, but this model was a LP. As
compared with other techniques (e.g., George et al. 2011), the
domain for using LP was reduced. This problem was LP only
when a source and/or demand lied within the pinch interval.
The proposed methodology makes the problem completely
algebraic, thereby eliminating the need to use a LP software.
Methodology for HIWAN Synthesis
At first, the freshwater is minimized by using the LCC
(Agrawal and Shenoy 2006; Bandyopadhyay 2006). Once
Contaminant concentration (ppm)
1200
1000
800
all the source and demand flows, and contaminant concentrations are known, this method targets the minimum utility
through pinch analysis. In order to identify the temperature
pinch interval, all the potential pinch intervals are considered
one by one. The hot utility above Thp is found from Eq. 7. All
the source and demand temperatures above Thp and below Tcp
are equated to Thp and Tcp. The hot utility minimization within
the pinch interval is analogous to the compression work minimization in hydrogen networks (Bandyopadhyay et al. 2014).
The concept of interplant water flow minimization is used to
minimize hot utility in the pinch interval. Two plants are considered at different temperatures, which are consecutive when
the temperatures are arranged in increasing order. If the same
methodology, which minimizes the interplant flow, is adopted
without dividing the problem into above/below pinch and
pinch interval, then the condition which ensures minimum
driving force in the heat exchangers cannot be imposed algebraically through known techniques.
The methodology follows a stepwise minimization, where
utility is minimized for temperature levels from the highest to
the lowest set of temperatures. Considering each potential
pinch interval one by one, the following methodology is
adopted. The sources and demands at the highest temperature
(TN) are considered to be as plant A, while the sources and
demands at all other temperatures are considered as plant B at
the second highest temperature (TN-1). This interval is denoted
as [TN°C, TN-1°C]. Any flow from plant B to plant A will
require heating, while any flow from plant A to plant B will
require cooling. Hence, the objective boils down to the minimization of the interplant flow. The hot utility at this stage
(Qhup)(N/N-1) can be calculated as follows:
Qhu
¼ F BA cp ðT N −T N −1 Þ ∀p∈f1; 2; ::; PI g ð10Þ
p
ðN =N−1Þ
Interplant flow
600
400
Table 3
200
Thp/Tcp°C
100/70
105/75
75/45
50/20
20/− 10
μp
(Qhup)PI
Qhup
0
10.96
10.96
0
9.34
9.34
0
9.74
9.74
0
9.74
9.74
3.25
0
3.25
0
0
10
20
30
Quality load (g/s)
40
50
60
Fig. 4 Minimum interplant flow between plants at 100 °C (A) and 75 °C
(B) for Example 1
Hot utility (MW) for all potential pinch intervals for Example 1
Process Integr Optim Sustain
Fig. 5 a A HIWAN for Example
1. b Alternate HIWAN for
Example 1
11.69 kg/s
50 kg/s
6300 kW
S1 (100, 100, 100)
H
D1 (100, 50, 100)
38.31 kg/s
89.4 kg/s
D3 (166.7, 800, 100)
77.27 kg/s
50 kg/s
S3 (166.7, 1100, 100)
4090.91 kW
38.96 kg/s
H
C
D2 (40, 50, 75)
S2 (40, 800, 75)
1227.16 kW
572.75 kW
27.27 kg/s
H
1.04 kg/s
o
o
70 C
70 C
D0 (77.3, 1100, 30)
S0 (77.3, 0, 20)
10500 kW
5726.7 kW
C
o
50 C
6490.68 kW
(a) A HIWAN for Example 1
11.69 kg/s
50 kg/s
6300 kW
45.5 kg/s
H
38.31 kg/s
S1 (100, 100, 100)
D1 (100, 50, 100)
4.5 kg/s
4.5 kg/s
84.9 kg/s
77.3 kg/s
50 kg/s
S3 (166.7, 1100, 100)
D3 (166.7, 800, 100)
H
4090.91 kW
38.96 kg/s
C
D2 (40, 50, 75)
S2 (40, 800, 75)
H
27.27 kg/s
1227.16 kW
572.75 kW
1.04 kg/s
o
o
70 C
70 C
S0 (77.3, 0, 20)
5726.7 kW
10500 kW
o
50 C
D0 (77.3, 1100, 30)
C
6490.68 kW
(b) Alternate HIWAN for Example 1
where FBA is the minimum flow transferred from plant B to
plant A.
Similarly, the hot utilities are calculated for other temperature intervals. The total hot utility is obtained as follows:
PI Qhu
¼ Qhu
p
p
þ ⋯ þ Qhu
p
þ Qhu
p
∀p∈f1; 2; ::; PI g
ðN =N −1Þ
ð2=1Þ
ð3=2Þ
ð11Þ
The possibility of achieving different results by changing
the search direction is investigated. Suppose there are N temperature levels in the selected pinch interval including Thp and
Tcp, the problem can be solved in N-1 ways. For example, the
different ways for solving the problem for four temperature
levels are shown in Fig. 2.
There are sources (open dots) and demands (closed dots) at
the temperature levels within the pinch interval. Here, T4 = Thp
and T1 = Tcp. In the first case, the first step involves the interplant minimization of plants A (at T2) and plant B (at T1). Note
Process Integr Optim Sustain
Contaminant Concentration (ppm)
1200
Table 5
1000
780 ppm
800
600
400
Hot utility (MW) for all potential pinch intervals for Example 2
Thp/Tcp°C
100/90
85/75
75/65
40/30
30/20
μp
(Qhup)PI
Qhup
0
3.44
3.44
0
3.44
3.44
0
4.82
4.82
0
4.82
4.82
0
0
0
200
39 ppm
0
0
20
40
60
80
100
Quality load (g/s)
Fig. 6 Graphical targeting of freshwater and regeneration flow rates
that all the sources and demands above T2 will be considered
to be at T2 in the first step. The second way considers plant A
to be at T4 and plant B at T3, while the third way considers
plant A to be at T3 and plant B to be at T2. Irrespective of the
way adopted to find the solution, the same results are
obtained. Bandyopadhyay et al. (2014) proposed that the total
compression work within a pressure interval is the sum of
compression work for each consecutive pair of pressure levels
in that interval. Owing to the analogy between the compression work and heat minimization, this theorem could be extended to the utility minimization problem. However, the stated theorem may be incorrect. Thus, the proposed methodology results in an approximate solution for the hot utility requirement in the potential pinch interval. Once the minimum
hot utility requirements in the potential pinch intervals are
found out using the proposed methodology, the total hot utility
can be obtained from Eq. 6. The interval for which the hot
utility is at maximum is the pinch interval (Eq. 9). The cold
utility (Qcu) is evaluated from the enthalpy balance given in
Eq. 5. The interplant flows for the pinch interval result into the
required HIWAN. A flowchart depicting the methodology for
the synthesis of the HIWAN is given in Fig. 3.
Illustrative Examples
Example 1: WAN with three temperature levels
Table 1 provides the limiting process data for a WAN
(Bagajewicz et al. 2002). A minimum approach temperature
of 30 °C is considered. The specific heat capacity is considered to be 4.2 kJ/kg °C. The minimum freshwater required and
Table 4 Hot utility for potential
pinch interval 75/65 °C for
Example 2
Flow transferred across (°C)
wastewater discharged are found to be 77.273 kg/s using
pinch analysis, which is comparable with literature
(Bagajewicz et al. 2002). Freshwater is available at 20 °C
and wastewater is to be discharged at 30 °C. The other source
and demand temperatures are 75 °C and 100 °C (see Table 1).
As any source can control the pinch temperature
(Bandyopadhyay and Sahu 2010), the potential pinch points
(Thp/Tcp) are identified to be 130/100 °C, 100/70 °C, 105/
75 °C, 75/45 °C, 50/20 °C, and 20/− 10 °C. As there is no
source or demand above 130 °C, and between 130 and
100 °C, no hot utility would be required for the potential pinch
interval of 130/100 °C. Thus, it can be eliminated from the
analysis. The proposed methodology is used to find the minimum hot utility for each potential pinch interval. The procedure is discussed for one of the potential pinch intervals (100/
70 °C). The hot utility above the hot pinch temperature is
found to be 0 kW from Eq. 7. All the sources and demands
above Thp (i.e., 100 °C for this case) and below Tcp (i.e., 70 °C
for this case) are shifted to Thp and Tcp respectively. Source S2
and demand D2 have temperature of 75 °C which is within the
potential pinch temperatures. Now, all the sources and demands are arranged in an increasing order of temperature. In
this case, there are three temperature levels (70 °C, 75 °C, and
100 °C). All the sources (S1 and S3) and demands (D1 and
D3) at 100 °C are considered as plant A while the rest are
considered as plant B (i.e., S0, S2, D0, and D2). The minimum
interplant flow is found out across plants A and B and shown
in Table 2 (this is visually represented in Fig. 4). It can be
observed that there is flow from plant A to plant B, and vice
versa at different contaminant concentrations. In the next step,
all flows at 75 °C are considered as plant A, while flows at
70 °C are considered as plant B. The sources provided to plant
A are S2 and flow from 100 to 75 °C (11.69 kg/s at 100 ppm).
The demands included in plant A are D2 and flows from 75 to
100 °C (50 kg/s at 0 ppm, and 38.96 kg/s at 800 ppm). Plant B
comprises all flows at and below 70 °C (S0, D0), as it is the
lowest temperature of the considered potential pinch interval.
Contaminant concentration (ppm)
Interplant flow between plants at 75 °C and 65 °C
65 to 75
39
75 to 65
100
Total hot utility requirement
Flow rate (kg/s)
Qhu/Qcu (MW)
114.74
114.74
4.82
− 4.82
4.82
Process Integr Optim Sustain
Fig. 7 HIWAN with regeneration
for Example 2
7.2 kg/s
o
40 C
24.7 kg/s
50 kg/s
116.7 kg/s
o
D1 (100, 50, 100)
H 65 C
3442.1 kW
o
65 C
D3 (166.7, 800, 100)
18833.7 kW
758 kW
S3 (166.7, 1100, 100)
50 kg/s
18.1 kg/s
S1 (100, 100, 100)
81.9
kg/s
SR (114.7, 39, 30)
o
75 C
32.8 kg/s
o
S2 (40, 800, 75)
40 C
40 kg/s
H 1376.8 kW
1364 kW
4818.9 kW
C 4818.9 kW
DR (114.7, 790, 30)
D2 (40, 50, 75)
The minimum interplant flow between plants A and B can be
found in a way similar to that shown in Fig. 4, and the results
are shown in Table 2.
As there are three temperature levels, the problem can
be solved in two ways. The second way of solving the
problem is by minimizing the utility in the interval
[75 °C, 70 °C] followed by the minimization of hot utility
in the interval [100 °C, 75 °C]. The amount of flow transferred is the same irrespective of the direction of solving.
The hot utility, indicated by a positive sign, is shown in
Table 2 for each interplant flow. All the hot utilities are
added in order to obtain the minimum hot utility in the
Table 6 Limiting process data for
Example 3
Flow rate (kg/s)
pinch interval (Eq. 11). The total hot utility is found to be
10,963.64 kW from Eq. 6.
The same method is used to obtain the hot utility for all the
potential pinch intervals, which are listed in Table 3. As described in the proposed methodology, the pinch interval is
100/70 °C where the hot utility requirement is the maximum
(Eq. 9). Upon using the hot utility result (10,963.64 kW) in the
heat balance equation (Eq. 5), the cold utility is found to be
7718.15 kW. A large number of WANs can be synthesized by
fixing the minimum interplant flow and varying the remainder
such that the constraints are satisfied. The pinch design method (PDM) is used to synthesize the HEN (Linnhoff and
Concentration
(ppm)
Temperature
(°C)
Temperature (with a drop of 5 °C) (°C)
–
20
40
20
40
40
20
–
0
0
50
75
150
100
30
60
75
71
73
90
80
30
60
75
71
73
90
80
–
20
40
20
40
40
20
0
100
50
100
150
200
200
20
60
75
71
73
90
80
20
55
70
66
68
85
75
Demand
D0
D1
D2
D3
D4
D5
D6
Source
S0
S1
S2
S3
S4
S5
S6
Process Integr Optim Sustain
Contaminant concentration (ppm)
250
LCC of Plant A
200
150
Interplant Flow
100
Reflected LCC
of Plant B
50
0
0
1
2
3
4
5
Quality load (g/s)
Fig. 8 Minimum interplant flow between plants at 80 °C (A) and 75 °C
(B) for Example 3
Hindmarsh 1983). The HEN for all the possible WANs would
be the same as the flow transferred at different temperature
levels is fixed through this method. Two HIWANs are shown
in Fig. 5a, b. There are two hot streams, three cold streams,
and four bypass (neither hot nor cold) streams in Fig. 5a.
Figure 5b consists of two hot streams, four cold streams, and
five bypass streams. The interconnections which are different
are represented by dashed lines. Both the HIWANs require
two process–to–process heat exchangers, three heaters, and
two coolers with the same duties. The results are comparable
with the results reported by George et al. (2011) by solving 2
LPs.
This example was solved by other authors using sequential
(Bagajewicz et al. 2002) and simultaneous (Tan et al. 2014)
techniques by considering the minimum approach temperature to be 10 °C. The proposed methodology is applied for
this ΔTmin value, and freshwater consumption of 77.273 kg/s,
hot utility of 3736 kW, and cold utility of 490 kW are found.
Table 7 Hot utility for potential
pinch interval 80/70 °C for
Example 3
Flow transferred across (°C)
These values are comparable with those of literature results
(Bagajewicz et al. 2002; Tan et al. 2014).
Typically, the utility requirement and the number of exchangers, to exchange heat in a HIWAN, are lower for nonisothermal mixing problems. The methodology proposed in
this paper targets utility by allowing only isothermal mixing.
However, as proved by Sahu and Bandyopadhyay (2012), the
utility targets achieved in cases of isothermal as well as nonisothermal mixing are identical whenever there is no demand
within the pinch interval. Thus, the proposed technique is
applicable to non-isothermal mixing problems as and when
the previous condition is applicable. In order to understand
the applicability of the proposed methodology, the problem
is analyzed by varying ΔTmin. For a ΔTmin up to 10 °C, there
cannot be any demand within any of the potential pinch intervals. Therefore, the targets for isothermal and non-isothermal
mixing cases are identical. For a ΔTmin between 11 and 25 °C,
waste (i.e., demand D0) lies between one of the potential
pinch intervals (i.e., 20/31 °C to 20/45 °C). To achive nonisothermal mixing for this demand, freshwater (i.e., source S0)
has to be used. However, this is not possible from the optimality condition of the water network. Thus, non-isothermal
mixing within this interval is not possible and the target for the
non-isothermal mixing case is identical to that for the isothermal mixing case. Only for ΔTmin higher than 25 °C, nonisothermal mixing can reduce the total utility requirement.
Example 2: Water Regeneration Network
Example 1 is revisited to depict the proposed methodology for
the synthesis of HIWAN with a regeneration unit. A regeneration unit, at 30 °C with the removal ratio of 0.95, is
Contaminant concentration (ppm)
Interplant flow between plants at 80 °C and 75 °C
75 to 80
100
75 to 80
150
Interplant flow between plants at 75 °C and 73 °C
73 to 75
0
75 to 73
50
73 to 75
100
73 to 75
150
Interplant flow between plants at 73 °C and 71 °C
71 to 73
0
73 to 71
50
71 to 73
100
Interplant flow between plants at 71 °C and 70 °C
70 to 71
0
70 to 71
100
Total hot utility requirement
Flow rate (kg/s)
Qhu/Qcu (kW)
20
40
420
840
40
40
20
40
336
− 336
168
336
40
20
40
336
− 168
336
40
20
168
84
3024
Process Integr Optim Sustain
Table 8 Hot utility (MW) for all
potential pinch intervals for
Example 3
Thp/Tcp°C
μp
(Qhup)PI
Qhup
90/
80
85/
75
80/
70
83/
73
81/
71
75/
65
73/
63
71/
61
70/
60
60/
50
30/
20
20/
10
0
1.68
1.68
0
2.1
2.1
0
3.02
3.02
0
2.60
2.60
0
2.94
2.94
0
3.02
3.02
0
2.69
2.69
0
2.52
2.52
0
2.52
2.52
0
2.52
2.52
0
2.52
2.52
2.52
0
2.52
considered (Ibrić et al. 2014). Using the graphical insights (see
Fig. 6) from the automated composite table algorithm proposed by Parand et al. (2016 a, b), a case of zero freshwater
and wastewater is obtained. The amount of regeneration is
found to be 114.737 kg/s. These results are comparable with
those of the literature (Ibrić et al. 2014).
The regeneration unit acts as a source (SR) as well as demand (DR) as it provides purified water through the consumption of water of inferior quality from different sources. From
Fig. 6, the regeneration inlet contaminant concentration, Cdr,
is 780 ppm and the regeneration outlet contaminant concentration, Csr, is 39 ppm. Now, there are four sources (S1, S2,
S3, and SR) and four demands (D1, D2, D3, and DR) with
known temperatures, flow rate, and contaminant concentrations (upper limit in case of internal demands). From Table 1
and given regeneration temperature, the source temperatures
are identified to be 100 °C, 75 °C, and 30 °C. As the pinch is
controlled by the sources, the potential pinch intervals (Thp/
Tcp) to be considered for the analysis are as follows: 100/
90 °C, 85/75 °C, 75/65 °C, 40/30 °C, 30/20 °C. Using the
proposed methodology, the minimum hot utility is targeted
for all these potential pinch intervals. The procedure is shown
for one of the potential pinch intervals (75/65 °C). The hot
utility consumption above the temperature of 75 °C (Thp) is
obtained to be 0 kW from Eq. 7. In the next step, the sources
Fig. 9 HIWAN for Example 3
and demands at higher temperatures (S1, S3, D1, and D3) are
shifted to 75 °C. As S2 and D2 are at 75 °C, all the sources and
demands except the regeneration source and demand are considered to be a part of plant A, while the latter is considered to
be a part of plant B. The temperature of the regeneration
source and demand, being lower than 65 °C (Tcp) is shifted
to 65 °C. It can be noted that the LCC of plant A, which does
not include the regeneration sources and demands, is the same
as the LCC (without regeneration) in Fig. 6. Similarly, the
LCC of plant B, which only includes regeneration sources
and demands, is the same as the water supply line. As the
interplant flow line is the shortest possible distance between
the LCCs of plant A and plant B, it is along the LCC of plant B
or the water supply line. The interplant flow can be found out
from the water supply line, and the corresponding hot utility
requirement is given in Table 4.
Similarly, the hot utility is evaluated from the minimum
interplant flow for all the potential pinch intervals (Table 5).
As discussed earlier, the intervals 75/65 °C and 40/30 °C,
consuming the maximum hot utility of 4818.9 kW, are the
pinch intervals (Eq. 9). Using the heat balance equation (Eq.
5) and the hot utility result, the cold utility is obtained as
4818.9 kW. The utility requirements correspond to the literature results, where a NLP was used to optimize the energy and
water requirements (Ibrić et al. 2014). Using the PDM,
2856 kW
40 kg/s
H
S5 (40, 200, 90)
S6 (20, 200, 80)
S2 (40, 50, 75)
D5 (40, 150, 90)
9240 kW
o
20 kg/s
85 C
20 kg/s
D6 (20, 100, 80)
168 kW
C
20 kg/s
S4 (40, 150, 73)
H
20 kg/s
C
336 kW
S1 (20, 100, 60)
D3 (20, 50, 71)
D1 (20, 0, 60)
40 kg/s
40 kg/s
D4 (40, 75, 73)
168 kW
S3 (20, 100, 71)
S0 (60, 0, 20)
D2 (40, 0, 75)
20 kg/s
3360 kW
20 kg/s
840 kW
o
70 C
840 kW
D0 (60, 200, 30)
Process Integr Optim Sustain
Thp/Tcp°C
μp
(Qhup)PI
Qhu
95/
85
85/
75
80/
70
78/
68
76/
66
75/
65
70/
60
68/
58
66/
56
65/
55
55/
45
30/
20
20/
10
0
0.84
0.84
0.84
2.1
2.94
0.84
3.95
4.79
1.01
4.45
5.46
1.18
4.62
5.80
1.26
4.62
5.88
2.69
3.19
5.88
3.19
2.86
6.05
3.36
2.86
6.22
3.36
2.94
6.3
3.78
2.52
6.3
3.78
2.52
6.3
6.3
0
6.3
HIWAN with regeneration is synthesized for this example
(Fig. 7).
Example 3: Water Allocation Network with Five
Temperature Levels
The limiting process data for a WAN are shown in Table 6 (Li
et al. 2013). A minimum approach temperature of 10 °C is
considered. The specific heat capacity is considered to be
4.2 kJ/kg °C. The minimum freshwater requirement and waste
discharged are found to be 60 kg/s through pinch analysis,
which is comparable with those in literature (Li et al. 2013).
Freshwater is available at 20 °C and wastewater is discharged
at 30 °C. The source temperatures are 20 °C, 60 °C, 71 °C,
73 °C, 75 °C, 80 °C, and 90 °C. As the pinch temperature is
controlled by the source temperature, the potential pinch intervals (Thp/Tcp) are 20/10 °C, 30/20 °C, 60/50 °C, 70/60 °C,
71/61 °C, 81/71 °C, 73/63 °C, 83/73 °C, 85/75 °C, 75/65 °C,
80/70 °C, and 90/80 °C. The minimum utility requirement is
found out for each potential pinch interval by using the
Fig. 10 HIWAN for Example 3
(with temperature drop)
proposed methodology. The procedure is discussed for one
of the potential pinch intervals (80/70 °C). The hot utility
required above the hot pinch temperature is found to be
0 kW from Eq. 7.
All the sources and demands above Thp and below Tcp are
shifted to Thp and Tcp. There are five temperature levels: 70 °C,
71 °C, 73 °C, 75 °C, and 80 °C. Thus, four sub-problems with
the intervals [80 °C, 75 °C], [75 °C, 73 °C], [73 °C, 71 °C],
and [71 °C, 70 °C] need to be solved to obtain the minimum
interplant flow. The minimum interplant flow in the interval
[80 °C, 75 °C] is shown in Fig. 8. Similarly, the minimum
interplant flow can be obtained for the other temperature intervals as well, and then added to find out the hot utility requirement in this potential pinch interval (Eq. 11). Hot utility
resulting from this minimum interplant flow is presented in
Table 7. Using the same methodology, hot utility is found out
for all the potential pinch intervals which are summarized in
Table 8. As the total hot utility (Eq. 6) is maximum (3024 kW)
for the intervals 80/70 °C and 75/65 °C, these intervals are
found to be the pinch intervals (Eq. 9). The cold utility is
3696 kW
H
40 kg/s
S5 (40, 200, 85)
D5 (40, 150, 90)
1260 kW
9240 kW
40 kg/s
D6 (20, 100, 80)
S6 (20, 200, 75)
20 kg/s
H
D2 (40, 0, 75)
o
65 C
H
20 kg/s
D4 (40, 75, 73)
252 kW
D3 (20, 50, 71)
S2 (40, 50, 70)
H
84 kW
S4 (40, 150, 68)
S1 (20, 100, 55)
20 kg/s 588 kW
20 kg/s
S3 (20, 100, 66)
2940 kW
20 kg/s
Table 9 Hot utility (MW) for all
potential pinch intervals for
Example 3 (temperature drop)
o
55 C
H
420 kW
D1 (20, 0, 60)
D0 (60, 200, 30)
S0 (60, 0, 20)
40 kg/s
o
65 C
20 kg/s
840 kW
H
Process Integr Optim Sustain
Table 10
Limiting process data for Example 4
Flow rate (kg/s)
Concentration (ppm)
Temperature (°C)
D0
–
–
40
D1
D2
350
677
0
40
30
187
D3
D4
126
202
75
100
55
98
S0
S1
–
530
0
30
30
21
S2
S3
68
1130
150
300
43
130
S4
36
500
35
Demand
Source
obtained as 504 kW from the energy balance in Eq. 5. The
HIWAN satisfying the minimum interplant flow is shown in
Fig. 9.
The results obtained through the proposed methodology
match with the results from literature (Li et al. 2013). Li
et al. (2013) solved an LP to minimize freshwater, an MILP
to obtain a set of WANs while minimizing the number of
interconnections, an LP to target the utility, and a MILP to
minimize the heat transfer units. Four process–to–process heat
exchangers, two heaters, and two coolers were obtained. The
HIWAN shown in Fig. 9 has a similar HEN as Li et al. (2013).
Seven heat exchangers are obtained through PDM (Linnhoff
and Hindmarsh 1983). Three heat exchangers between
streams S5-D0, and S0-D2, resulting from the enthalpy balance above, below, and between the two pinch intervals, are
combined into a single heat exchanger. Similarly, two heat
exchangers between streams S6-D0 and S1-D6 have been
combined.
The limiting process data from Table 6 are modified by
incorporating a temperature drop of 5 °C. Thus, the
Contaminant Concentration (ppm)
600
500
400
300
Interplant flow
200
100
0
0
50
100
150
200
Quality load (g/s)
Fig. 11 Minimum interplant flow between plants at 130 °C (A) and 98 °C
(B) for Example 4
temperature of every internal source drops by 5 °C and the
resulting source temperatures are 20 °C, 55 °C, 70 °C, 66 °C,
68 °C, 85 °C, and 75 °C. The potential pinch intervals are
found to be 20/10 °C, 30/20 °C, 95/85 °C, 75/65 °C, 80/
70 °C, 70/60 °C, 78/68 °C, 68/58 °C, 76/66 °C, 66/56 °C,
65/55 °C, and 55/45 °C. The methodology of interplant flow
minimization is used to find out the minimum hot utility requirement for all potential pinch intervals. The results are
summarized in Table 9. The pinch intervals are found to be
20/10 °C, 30/20 °C, 65/55 °C, and 55/45 °C. Between these
temperature intervals, the heat provided by hot streams is exactly that amount of heat required by the cold streams. For the
pinch intervals 20/10 °C and 30/20 °C, there is no restriction
on the minimization of hot utility because no stream exists in
these intervals. The WAN must be obtained in such a way that
it satisfies the minimum interplant flow obtained in case the
pinch intervals are 65/55 °C and 55/45 °C. The HIWAN is
shown in Fig. 10. Three heat exchangers, obtained by PDM,
between streams S5-D0 and S0-D2 are combined into a single
heat exchanger. Similarly, two heat exchangers between
streams S6-D0 and S0-D1 are combined into a single heat
exchanger. Three heat exchangers and six heaters are used.
The proposed algorithm results in a minimum hot utility of
6300 kW, while the cold utility is found to be 0 kW from Eq.
5. The results are verified by solving the LP on GAMS 24.2.2
using the solver CPLEX (12.6.0.0).
Example 4: Ammonia Allocation Network
A process plant utilizes ammonia as a dust-cleaning agent and
as a mass-separating agent in a sour gas absorption column.
Ammonia with an unacceptable contaminant concentration is
produced in the CaCl2 production section. This ammonia is
regenerated. The limiting process data for an ammonia plant
are given in Table 8 (Wan Alwi et al. 2011). It is assumed that
there is no temperature change due to a chemical reaction
when ammonia streams are mixed. The minimum approach
temperature is given to be 35 °C. Specific heat capacity for
ammonia is 2.19 kJ/kg °C. Using pinch analysis, the minimum ammonia consumption is obtained as 654.9 kg/s and
the waste to be disposed is 1063.9 kg/s, the same as reported
by Wan Alwi et al. (2011).
Fresh ammonia is available at 30 °C and the temperature
limit on waste disposal is 40 °C. The other temperatures are
given in Table 10. As temperature pinch is controlled by the
source temperatures, the potential pinch intervals are 165/
130 °C, 130/95 °C, 78/43 °C, 70/35 °C, 65/30 °C, 56/21 °C,
43/8 °C, 35/0 °C, 30/− 5 °C, and 21/− 14 °C. The minimum
hot utility for each potential pinch interval is found out using
the proposed methodology. The solution strategy for one of
the potential pinch intervals (130/95 °C) is discussed. The hot
utility above Thp is found to be 84,509.9 kW from Eq. 7. All
the sources and demands above Thp (i.e., 130 °C in this case)
Process Integr Optim Sustain
Table 11 Hot utility for potential
pinch interval 130/95 °C for
Example 4
Flow transferred across (°C)
Contaminant concentration (ppm)
Flow rate (kg/s)
Qhu/Qcu (MW)
Interplant flow between plants at 130 °C and 98 °C
98 to 130
98 to 130
0
30
304.90
313.15
21.37
21.94
130 to 98
300
1071.05
− 75.06
Interplant flow between plants at 98 °C and 95 °C
95 to 98
95 to 98
0
30
304.90
451.25
2.00
2.96
95 to 98
150
20.75
0.14
300
1027.90
− 6.75
48.41
98 to 95
Total hot utility requirement
and below Tcp (i.e., 95 °C in this case) are shifted to Thp and
Tcp. The temperature of demand D4 is within the pinch interval, thereby requiring three temperature levels (95 °C, 98 °C,
130 °C). After the temperature shift, all sources (S3) and demands (D4) at 130 °C are considered as plant A, and the rest as
plant B (D0, D1, D2, D3, S0, S1, S2, S4). The interplant flow
between plants A and B is minimized, and the graphical representation is shown in Fig. 11. Now, sources and demands at
98 °C and 95 °C are considered as a part of plant A and plant
B. The flows from the plant at 130 °C to 98 °C are considered
as a source at 98 °C. Whereas, the flows from 98 to 130 °C are
demands at 98 °C. This sub-problem is solved in a similar
manner as that of plants at 130 °C and 98 °C. The interplant
flows and corresponding hot utility requirements for plants at
[130 °C, 98 °C] and [98 °C, 95 °C] are shown in Table 11.
Hot utility requirement at each of the flow transfer point
from Table 11 is added in order to obtain the total hot utility in
the potential pinch interval (Eq. 11). The overall hot utility
(Eq. 6) for this case is found out by adding the hot utility
required above pinch (Eq. 7) and the hot utility requirement
in the pinch interval (Eq. 11). A similar procedure is adopted
for all the potential pinch points. The resulting hot utility
(132.93 MW) obtained is given in Table 12. The pair with
the highest hot utility consumption is the pinch (Eq. 9), which
is 130/95 °C. Thus, the hot utility is 132.93 MW. The cold
utility is found out to be 79.23 kW from the Eq. 5. The
resulting heat-integrated ammonia allocation network is
depicted in Fig. 12.
The results from the proposed methodology match with the
results from the literature by using LPs to minimize freshwater
and energy requirement (Sahu and Bandyopadhyay 2012) or
total cost minimization using a MINLP complemented with
Table 12 Hot utility (MW) for all
potential pinch intervals for
Example 4
the floating pinch method (Tan et al. 2014) or a MILP
(Ghazouani et al. 2015). Ammonia is extremely costly as
compared with the utility (Tan et al. 2014). Thus, the minimization of fresh ammonia leads to the minimum operating
costs.
Conclusions
A novel methodology is proposed to algebraically target
energy and freshwater through pinch analysis. The method
used by Bandyopadhyay et al. (2014) to target minimum compression work in a hydrogen network is extended to minimize
hot utility requirement within the temperature pinch interval.
Once freshwater is minimized, sources and demands within
the pinch interval are divided into levels based on their temperatures. Two plants operating at different temperatures are
considered, and the energy requirement is found by minimizing the interplant flows. The flow transferred from sources of a
plant to the demands of the other plant provides the optimal
WAN. Pinch interval is located based on the ideology proposed by Sahu and Bandyopadhyay (2012).
One of the advantages of using a graphical tool (LCC) for
interplant minimization is that it provides better visualization.
The ability to solve an LP problem (Sahu and Bandyopadhyay
2012) algebraically has eliminated the need to use any programming software. As the solution does not get influenced
by the number of variables, the HIWAN can be synthesized
quickly for a large-scale industry. A water allocation network
problem with three (with and without regeneration) and five
temperature levels in the pinch interval, a water allocation
network with temperature drop, and an ammonia allocation
Thp/Tcp°C
165/130
130/95
78/43
70/35
65/30
56/21
43/8
35/0
30/− 5
21/− 14
μp
(Qhup)PI
(Qhu)p
32.6
51.9
84.5
84.5
48.4
132.9
41.7
62.9
104.6
37.3
64.3
101.6
34.6
59.6
94.2
29.7
60.0
89.7
25.8
34.6
60.4
34.1
19.6
53.7
43.2
10.5
53.7
53.7
0.0
53.7
Process Integr Optim Sustain
Fig. 12 Heat-integrated ammonia
allocation network
43402.5 kW
304.9 kg/s
o
95 C
61431.25 kW
H
63093.6kW
58.95 kg/s
D2 (677, 40, 187)
o
80.6 C
H
o
75.8 C
1027.9 kg/s
7358.98 kW
S3 (1130, 300, 130)
o
76.43 C
136.33 kW
20.75 kg/s
D4 (202, 100, 98)
H
o
105 C
C
2363.01 kW
S2 (68, 150, 43)
660.80 kW
47.25 kg/s
43.15 kg/s
D3 (126, 75, 55)
1241.7 kW
78567.35 kW
o
74.9 C
C
S4 (36, 500, 35)
350 kg/s
S0 (654.9, 0, 30)
D0 (1063.9, 306.7,
36 kg/s
394.2 kW
D1 (350, 0, 30)
313.15 kg/s
S1 (530, 30, 21)
50749 kW
o
95 C
78.75 kg/s
5863.73 kW
138.1 kg/s
network problem are used to demonstrate the proposed
algorithm.
Like any technique based on PA, this method cannot be
applied to process industries with multiple contaminants.
Future work is directed towards extending the proposed methodology to include multiple contaminants. The methodology
needs to be extended for problems in which utility requirements and heat exchanger duties can be reduced further
through non-isothermal mixing.
Compliance with Ethical Standards
H
22380.8 kW
o
95 C
907.33 kW
H
potential pinch interval, p (kW); (Qhup)PI, Hot utility in potential pinch
interval, p (kW); (Qhup)(N/N-1), Heat required for flow from N-1 to Nth
level in potential pinch interval (kW); Tcp, Potential cold pinch temperature (°C); Tdj, Temperature required by jth demand (°C); Thp, Potential hot
pinch temperature (°C); TN, Temperature of Nth level (°C); TN-1,
Temperature of N-1th level (°C); Tsi, Temperature of ith source (°C)
Abbreviations HEN, Heat exchanger network; HIWAN, Heat-integrated water allocation networks; LCC, Limiting composite curve; LP, Linear
programming; MILP, Mixed-integer linear programming; MINLP,
Mixed-integer non-linear programming; NLP, Non-linear programming;
PDM, Pinch design method; WAN, Water allocation network
Conflict of Interest The authors declare that they have no conflict of
interest.
References
Nomenclature Δ, Difference between hot and cold utility (kW); μp, Hot
utility above hot pinch temperature for potential pinch interval, p (kW);
ΔTmin, Minimum approach temperature of a heat exchanger; Cdj,
Maximum contaminant concentration acceptable by jth demand (ppm);
C dr, Regeneration inlet contaminant concentration (ppm); C sr,
Regeneration outlet contaminant concentration (ppm); Cs0, Contaminant
concentration in freshwater (ppm); Csi, Contaminant concentration of ith
source (ppm); cp, Specific heat capacity (kJ/kg °C); FBA, Flow transferred
from plant B to plant A; Fd0, Wastewater flow rate (kg/s); Fdj, Flow
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temperature levels in pinch region; Nd, Number of internal demands;
Ns, Number of internal sources; PI, Number of potential pinch intervals;
Qcu, Cold utility (kW); Qhu, Hot utility (kW); Qhup, Total hot utility for
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