DOI: 10.3303/CET2188029 
 

 
 

 
 
 

 
 

 
 

 
 
 

 
 
 

 

 
 
 

 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

Paper Received: 22 April 2021; Revised: 20 August 2021; Accepted: 14 October 2021 
Please cite this article as: Haider M.A., Chaturvedi N.D., 2021, Segregated Targeting for Resource Conservation with Dedicated Sources for 
Batch Process, Chemical Engineering Transactions, 88, 175-180  DOI:10.3303/CET2188029 

CHEMICAL ENGINEERINGTRANSACTIONS 

VOL. 88, 2021 

A publication of 

The Italian Association 
of Chemical Engineering 
Online at www.cetjournal.it 

Guest Editors:Petar S. Varbanov, Yee Van Fan, Jiří J. Klemeš

Copyright © 2021, AIDIC ServiziS.r.l. 

ISBN978-88-95608-86-0;ISSN 2283-9216 

Segregated Targeting for Resource Conservation with 
Dedicated Sources for Batch Process 

Md Alquma Haider, Nitin Dutt Chaturvedi* 
Department of Chemical and Biochemical Engineering, Indian Institute of Technology Patna, Bihta, Patna, 801106, Bihar, 
India 
nitind@iitp.ac.in 

Conversation of natural resources is one of the most important steps towards sustainability and market 
competitiveness. Process Integration techniques have been successfully applied for conserving natural 
resources. High value-added products are the best suited in batch processes. The conservation of natural 
resources in batch processes is an important concern. A segregated targeting problem for the batch process is 
presented in this paper. This paper is focused on segregated targeting problems for optimal use of resources in 
the batch process through Pinch Analysis. The segregated targeting problem consists of internal sources, 
resources, dedicated sources and demands. Resource and dedicated sources of a given zone are used by 
demands of that zone only for a given period of time. Resources are time-independent and with no flow 
restrictions. Internal sources are also time-independent. Internal sources can be optimally used by any zones 
in a given time interval. An algorithm is developed so that internal sources can be used in such a way as to 
minimize resource requirements. This algorithm can be applicable for both semi-batch and batch processes. 
The applicability of the proposed algorithm is demonstrated through an illustrative example. 

1. Introduction

Chemical process industries utilize a very large amount of freshwater, cooling water, energy, hydrogen, raw 
materials and many other resources. These resources must be utilized in such a manner that they meet the 
needs of present without compromising with the needs of future i.e., resources must be utilized in sustainable 
manner. Efforts have been done by governments, industries and researchers to improve process efficiencies. 
These efforts have been done in different ways like to improve process methods, to improve energy efficiency, 
to utilize energy in optimal manners etc. The efficient uses of valuable resources like natural gas, coal, utility 
gas, steam, freshwater etc. have a good impact on environment. Conversation of natural resources is the most 
important step towards sustainability and market competitiveness. Process integration plays an important role 
in resources conservation. Many researchers proposed various methodologies to minimize resource 
requirements for continuous processes. These methodologies can’t be directly applied for batch processes. 
Batch processes are more complex due to presence of an additional time dimension.  
Bandyopadhyay et al. (2010) used concepts of Pinch Analysis to develop a decomposition algorithm. This 
algorithm is used to determine resource optimal solution for segregated targeting problems. Lee et al. (2009) 
worked on resource allocation network (RAN) in carbon –constrained energy sector planning for a special type 
of problem which consists of a set of sources and multiple sets of demands called zones. This type of problem 
is identified as a segregated targeting problem. Chaturvedi (2017) worked on minimizing energy requirements 
in batch water network using Pinch Analysis. Stampfli et al. (2019) worked on batch process integration and 
maximized the total heat recovery within the process. Chaturvedi (2020) used Pinch Analysis approach to 
calculate the power rating of resources required for minimizing the overall cost of electricity in hybrid power 
system. Foo et al. (2021) used P-graph methodology for watch batch process. Jain and Bandyopadhyay (2017) 
developed a rigorous methodology for segregated targeting problems with dedicated sources. These works on 
segregated targeting problems were focusing towards continuous processes. It can be noted that segregated 
targeting problems involving batch processes are not focused. The development of resource minimization 
techniques in segregated targeting problems for batch processes is not yet presented. It is so because 

175



continuous processes produce much larger volume of wastewater and also minimize much more resource as 
compared to batch processes. This is the reason industrial practitioners and researchers are more focused in 
continuous processes. High value-added products are the best suited in batch processes. This paper is focused 
on developing an algorithm for segregated targeting problems with dedicated sources in the batch process. The 
segregated targeting problem consists of internal sources, resources, dedicated sources and demands. There 
are different zones. Each zone consists of dedicated sources, demands and resources. Resources and 
dedicated sources of a given zone are used by demands of that zone only for a given period of time. Resources 
are time-independent and with no flow restrictions. Internal sources are also time- independent. Internal sources 
can be used by any zones in a given time interval.  

2. Problem Statement and Mathematical Formulation

The general problem for segregated targeting for resource conservation with dedicated sources in the batch 
process may be mathematically stated as follow: 
A set of NS internal sources (I.S) is given. Each source (i=1, 2,….,NS) produces a flow of Fsi with quality of qsi at 
a definite time interval. A set of multiple zones (k=1,2,….Nk) is also present. Each zone consists of dedicated 
sources (D.S), demands and one resource at a definite time interval. Each dedicated source (l=1, 2,…NDSlk) of 
kth zone produces flow FDSlk with quality qDSlk at a given time interval. Resources are time-independent and have 
no flow restrictions. Each resource of a given zone (say kth) has a quality qrk. Each demand (j=1,2,…NDk) of kth 
zone accepts a flow FDk with a maximum allowable quality of qDjk from dedicated sources ,and resource of its 
own zone. It can also be accepted from internal sources at a given time interval. 

Figure 1: Superstructure of segregated targeting problem for a definite time interval 

Flows and quantities are balanced based on superstructure as follow: 

∑ . ∑ . 𝑓𝑖𝑗𝑘
𝑁𝑑𝑘
𝑗=1

𝑁𝑘
𝑘=1 (𝑡) +  𝑓𝑖𝑤 (𝑡) =  𝐹𝑠𝑖 (𝑡)                            ∀ i

(1) 

∑ . 𝑋𝑙𝑗𝑘
𝑁𝑑𝑘
𝑗=1 (𝑡) + 𝑋𝑙𝑤𝑘 (𝑡) = 𝐹𝐷𝑠𝑙𝑘  (𝑡)    ∀ l 

(2) 

     Internal source 

   Dedicated source 

         Demands 

 Resource 

    Waste 

Flow coming from outside of the zone and entering to the demand 

176



∑ .𝑁𝑠𝑖=1 𝑓𝑖𝑗𝑘 (𝑡) +  ∑ . 𝑋𝑙𝑗𝑘
𝑁𝐷𝑆𝑘
𝑙=1 (𝑡) +  𝑓𝑟𝑗𝑘 (𝑡) = 𝐹𝑑𝑗𝑘 (𝑡)       ∀ j 

(3) 

𝐹𝑟𝑗𝑘 𝑞𝑟𝑘 (𝑡) + ∑ .
𝑁𝑠
𝑖=1 𝑓𝑖𝑗𝑘 𝑞𝑠𝑖 (𝑡) + ∑ .

𝑁𝐷𝑆𝑘
𝑙=1 𝑋𝑙𝑗𝑘 𝑞𝐷𝑆𝑙𝑘 (𝑡)  ≤ 𝐹𝑑𝑗𝑘 𝑞𝑑𝑗𝑘 (𝑡)

(4) 

𝑊(𝑡) = ∑ .𝑁𝑠𝑖=1 𝑓𝑖𝑤 (𝑡) =  𝑅(𝑡) + ∆(𝑡)
(5) 

∆(𝑡) = ∑ .𝑁𝑠𝑖=1 𝐹𝑆𝑖 (𝑡) − ∑ .
𝑁𝑑
𝑗=1 𝐹𝑑𝑗 (𝑡)

(6) 

∑ .𝑁𝑠𝑖=1 𝑓𝑖𝑤 (𝑡) = W(t) =  𝑅(𝑡) + ∑ .
𝑁𝑠
𝑖=1 𝐹𝑆𝑖 (𝑡) − ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 (𝑡) (7) 

𝑅(𝑡) + ∑ .𝑁𝑠𝑖=1 𝐹𝑆𝑖 (𝑡) = 𝑊𝑝𝑖𝑛𝑐ℎ (𝑡) + ∑ .
𝑁𝑑
𝑗=1 𝐹𝑑𝑗 (𝑡) (8) 

𝑅𝑞𝑟𝑠(𝑡) + ∑ .
𝑁𝑠
𝑖=1 𝐹𝑆𝑖 𝑞𝑠𝑖 (𝑡) ≤ 𝑊𝑝𝑖𝑛𝑐ℎ 𝑞𝑝(𝑡) + ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 𝑞𝑑𝑗 (𝑡) (9) 

𝑅𝑞𝑟𝑠(𝑡) + ∑ .
𝑁𝑠
𝑖=1 𝐹𝑆𝑖 𝑞𝑠𝑖 (𝑡) ≤ 𝑅𝑞𝑝(𝑡) + ∑ .

𝑁𝑠
𝑖=1 𝐹𝑆𝑖 𝑞𝑝(𝑡) − ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 (𝑡)𝑞𝑝(𝑡) + ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 𝑞𝑑𝑗 (𝑡) (10) 

𝑅𝑞𝑟𝑠(𝑡) − 𝑅𝑞𝑝(𝑡) ≤ ∑ .
𝑁𝑠
𝑖=1 𝐹𝑆𝑖 𝑞𝑝(𝑡) − ∑ .

𝑁𝑠
𝑖=1 𝐹𝑆𝑖 𝑞𝑠𝑖 (𝑡) − ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 (𝑡)𝑞𝑝(𝑡) + ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 𝑞𝑑𝑗 (𝑡) (11) 

𝑅(𝑞𝑟𝑠 − 𝑞𝑝)(𝑡) ≤ ∑ .
𝑁𝑠
𝑖=1 𝐹𝑆𝑖 (𝑞𝑝 − 𝑞𝑠𝑖 )(𝑡) − ∑ .

𝑁𝑑
𝑗=1 𝐹𝑑𝑗 (𝑞𝑝 − 𝑞𝑑𝑗 )(𝑡) (12) 

𝑅(𝑡) ≥ ∑ .𝑁𝑑𝑗=1 𝐹𝑑𝑗
(𝑞𝑑𝑗−𝑞𝑝)

(𝑞𝑟𝑠−𝑞𝑝 )
(𝑡) +∑ .𝑁𝑠𝑖=1 𝐹𝑆𝑖

(𝑞𝑝 −𝑞𝑠𝑖 )

(𝑞𝑟𝑠−𝑞𝑝)
(𝑡) (13) 

The objective is to minimize resource requirements 

Minimize 𝑅 = ∑ .𝑁𝑑𝑗=1 𝐹𝑑𝑗
(𝑞𝑑𝑗−𝑞𝑝)

(𝑞𝑟𝑠−𝑞𝑝 )
(𝑡) +∑ .𝑁𝑠𝑖=1 𝐹𝑆𝑖

(𝑞𝑝−𝑞𝑠𝑖 )

(𝑞𝑟𝑠 −𝑞𝑝)
(𝑡) (14) 

For minimizing R, the quantity 
(𝑞𝑝−𝑞𝑠𝑖 )

(𝑞𝑟𝑠 −𝑞𝑝)
(𝑡) must be maximized. This quantity is known as Time Benefit Number 

(TBN). 

𝑇𝐵𝑁 = {

(𝑞𝑝−𝑞𝑠𝑖)

(𝑞𝑟𝑠−𝑞𝑝)
(𝑡), 𝑞𝑟𝑠 ≥ 𝑞𝑝

(𝑞𝑝−𝑞𝑠𝑖 )

(𝑞𝑝 −𝑞𝑟𝑠)
(𝑡), 𝑞𝑟𝑠 ≤ 𝑞𝑝

(15) 

3. Proposed Algorithm

The following algorithm is proposed for solving segregated targeting problems with dedicated sources to 
minimize resource utilization in the batch process:  
Step 1: Streams present in each zone are divided into definite time intervals. This step provides the availability 
of dedicated sources, demands, resources, and internal sources in a particular time interval 
Step 2: Each zone is solved to determine resource requirements without use of internal sources in a particular 
time interval. This can be done by Pinch Analysis technique like Source Composite Curve, Limiting Composite 
Curve etc. This step provides resource requirements, pinch points etc. in a particular time interval. 
Step 3: Calculate TBN Eq(15) in each zone for a particular time interval. The highest TBN is taken. The higher 
the value of TBN, the lower will be the resource requirement. 
Step 4: Transfer a definite amount of flow from I.S to that zone which corresponds to the highest TBN. This step 
reduces resource requirements 
Step 5: Transfer a definite amount of flow from I.S to that zone which corresponds to the next highest TBN. 
Continue this step until all TBNs of a particular time interval used or pinch point jumped. If this occurs then go 
to step 3 
Step 6: Stop the algorithm if all internal sources are exhausted or all-time benefit numbers (TBNs) of all time 
intervals are used. 

177



Figure 2: Flowchart for the methodology of segregated targeting problem in batch process 

4. Illustrative example

The applicability of the proposed algorithm is demonstrated through an illustrative example. Consider a 
segregated targeting problem in which there are two zones and three internal sources. Each zone consists of 
three dedicated sources, three demands, and one resource. Dedicated sources and demands are time 
dependent while resources and internal sources are time –independent. 
According to step 1, streams present in each zone are divided into equal time interval i.e., 0-1, 1-2, and 2-3 (h). 
This can be done by Gantt chart. Because of briefly, Gantt charts for both zones are not shown. 
For zone 1, streams present in time interval 0-1,1-2, and 2-3(h) are R1, L2, D3; R1, L1, L2, L3, D1, D2, D3; and 
R1, L1, D1, D2, D3 respectively. For zone 2, the streams present in time interval 0-1, 1-2, and 2-3(h) are R2, 
L5, D4, D6; R2, L4, L5, L6, D5, D6; and R2, L4, D5, D6 respectively. After applying pinch analysis technique, 
freshwater requirements in zone 1 for time interval 0-1, 1-2 and 2-3(h) are 12.4667, 26.8 and 26.8t/h 
respectively. Pinch points in zone 1 for time interval 0-1, 1-2 and 2-3(h) are 20, 15 and 15 ppm respectively. 
Similarly freshwater requirements in zone 2 for time interval 0-1, 1-2 and 2-3(h) are 44.875, 39.22 and 39.22t/h 
respectively. Pinch points in zone 2 for time interval 0-1, 1-2 and 2-3(h) are 23, 17, and 17 ppm respectively. 
TBN for each zone at different time interval along with internal sources are calculated. For time interval 0- 1(h), 
TBNs for S1, S2 and S3 in zone 1 are 0, 0.33 and 0.467 respectively. Similarly, for time interval 0-1 (h), TBNs 
for S1, S2 and S3 in zone 2 are 0.231, 0.6154 and 0.769 respectively. 

Start 

Divide streams of each zone in time intervals 

Calculate resource requirement of each zone at different time intervals without using I.S 

Calculate T.B.N of each zone at a particular time and select highest TBN 
intervals

Is any next TBN available 
for a particular time 

interval?

 Is pinch point jumped 
or TBN of a particular 
time interval used? 

End 

Transfer definite amount of corresponding I.S for the highest TBN 

All I.S exhausted or all TBNs used 

Yes 
No 

Yes 

No 

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Table 1: Internal Source Data 

Internal Source Quality(ppm) Flow(t/h) Duration(h) 
S1 20 22.45 0-3 
S2 15 30.02 0-3 
S3 13 58.96 0-3 

Table 2: Zone 1 Data 

Dedicated Source Quality(ppm) Flow(t/h) Duration(h) 
L1 15 40 1-3 
L2 20 15 0-2 
L3 22 7 1-2 
Demands Quality(ppm) Flow(t/h) Duration(h) 
D1 10 15 1-3 
D2 8 13 1-3 
D3 9 17 0-3 
Resource Quality(ppm) Flow(t/h) Duration(h) 
R1 5 0-3 

Table 3: Zone 2 Data 

Dedicated Source Quality(ppm) Flow(t/h) Duration(h) 
L4 17 50 1-3 
L5 23 41 0-2 
L6 25 50 1-2 
Demands Quality(ppm) Flow(t/h) Duration(h) 
D4 7 23 0-1 
D5 8 17 1-3 
D6 9 25 0-3 
Resource Quality(ppm) Flow(t/h) Duration(h) 
R2 10 0-3 

For time interval 0-1 (h), the highest TBN is 0.769 which corresponds to zone 2 of S3; 8.33t/h is added from S3 
to zone 2 which reduces freshwater requirement to 39.66t/h. The next highest TBN is 0.6154 which corresponds 
to zone 2 of S2, 0.0001t/h is added from S2 to zone 2, freshwater requirement does not change, it is still 39.66t/h 
(any amount of S2 does not change freshwater requirement). Again, the next highest TBN is 0.467 which 
corresponds to zone 1 of S3, 8.5t/h is added from S3 to zone 1, and freshwater requirement changes from 
12.4667t/h to 8.5t/h. Further the subsequent highest TBN is 0.33 which corresponds to zone 1 of S2, 0.001 t/h 
is added from S2 to zone 1, freshwater requirement does not change, it is still 8.499= (8.5) t/h (any amount of 
S2 does not change freshwater requirement). The next highest TBN is 0.231 which corresponds to zone 2 of 
S1, 0.001 t/h is added from S1to zone 1, freshwater requirement does not change, it is still 39.66t/h (any amount 
of S1 does not change freshwater requirement). 
For time interval 1-2 (h), TBN for S1, S2 and S3 in zone 1 are -0.5, 0 and 0.2 respectively. Similarly for time 
interval 1-2 (h), TBN for S1, S2 and S3 in zone 2 are -0.428, 0.2857 and 0.5714 respectively. The highest TBN 
is 0.5714 which corresponds to zone 2 of S3, 5t/h is added from S3 to zone 2 which changes freshwater 
requirement from 39.22t/h to37 t/h. The next highest TBN is 0.2857 which corresponds to zone 2 of S2, 0.0001 
t/h is added from S2 to zone 2 which does not change freshwater requirement, it is still 37 t/h (any amount of 
S2 does not change freshwater requirement). The next highest TBN is 0.2 which corresponds to zone 1 of S3, 
22.7498t/h is added from S3 to zone 1 which changes freshwater requirement from 26.8t/h to 22.25004t/h. 
For time interval 2-3 (h), TBN for S1, S2 and S3 in zone 1 are -0.5, 0 and 0.2 respectively. Similarly for time 
interval 2-3 (h), TBN for S1, S2 and S3 in zone 2 are -0.428, 0.2857 and 0.5714 respectively. The highest TBN 
is 0.5714 which corresponds to zone 2 of S3, 5t/h is added from S3 to zone 2 which changes freshwater 
requirement from 39.22t/h to 37t/h. The next highest TBN is 0.2857 which corresponds to zone 2 of S2, 0.0001 
t/h is added from S2 to zone 2 which does not change freshwater requirement, it is still 37t/h (any amount of S2 

179



does not change freshwater requirement). Further the next highest TBN is 0.2 which corresponds to zone 1 of 
S3, 9.39t/h is added from S3 to zone 1 which changes freshwater requirement from 26.8 to 24.922t/h. 

5. Conclusions

In this paper, a Pinch Analysis-based methodology is developed for segregated targeting for resource 
conservation with dedicated sources for batch Process. Previous methodologies for resource optimization of 
segregated targeting problems with dedicated sources cannot directly be applied for the batch process. The 
applicability of the proposed algorithm is shown with help of an example. This algorithm gives an idea for those 
types of problems also in which sources are available for many parts or many zones of batch process plants. 
With help of this algorithm, these sources can be optimally utilized. The TBN used in this algorithm indicates 
that which zone and which internal source are first applied simultaneously for resource minimization because 
higher the value of the TBN, lower will be resource requirement. This algorithm minimizes resource requirement 
approximately 4.55t/h in the given example. This algorithm can be applied for cooling water network, carbon 
constrained energy sector planning, water allocation network, etc. Internal sources are available for all time. 
This makes the problem semi-batch process also. If internal sources are also present in different time intervals, 
then the problem becomes more complex and rigorous. A graphical method can be developed for this problem 
in future. 

Nomenclature

𝐹𝑠𝑖 (𝑡) Flow rate of 𝑖𝑡ℎ internal source at a particular time interval (t/h)  
𝐹𝑑𝑗𝑘 (𝑡) Flow rate of 𝑗𝑡ℎ  demand present in 𝑘𝑡ℎ zone at a particular time interval (t/h) 

𝐹𝐷𝑠𝑙𝑘  (𝑡) Flow rate of 𝑙𝑡ℎ dedicated source present in 𝑘𝑡ℎzone at a particular time interval (t/h) 
𝑓𝑖𝑗𝑘 (𝑡) Flow rate transferred from 𝑖𝑡ℎ internal source to 𝑗𝑡ℎ  demand present in 𝑘𝑡ℎzone at a particular 

time interval (t/h) 
𝑓𝑟𝑗𝑘 (𝑡) Flow rate transferred from 𝑟 𝑡ℎ resource to 𝑗𝑡ℎ  demand both present in 𝑘𝑡ℎ zone at a particular 

time interval (t/h) 
𝑓𝑖𝑤 (𝑡) Flow rate transferred from 𝑖𝑡ℎ internal source to waste at a particular time interval (t/h) 
𝑋𝑙𝑗𝑘 (𝑡) Flow rate transferred from 𝑙𝑡ℎdedicated source to 𝑗𝑡ℎ  demand both present in 𝑘𝑡ℎ zone at a 

particular time interval (t/h) 
𝑋𝑙𝑤𝑘 (𝑡) Flow rate transferred from 𝑙𝑡ℎdedicated source present in 𝑘𝑡ℎ zone to waste at a particular time 

interval (t/h) 
𝑞𝑠𝑖 (𝑡) Quality of 𝑖𝑡ℎ internal source at a particular time interval (ppm) 

𝑞𝑑𝑗𝑘 (𝑡) Quality of 𝑗𝑡ℎ  demand present in 𝑘𝑡ℎ zone at a particular time interval (ppm) 
𝑞𝐷𝑆𝑙𝑘 (𝑡) Quality of 𝑙𝑡ℎ dedicated source present in 𝑘𝑡ℎ zone at a particular time interval (ppm) 
𝑞𝑟𝑘 (𝑡) Quality of 𝑟 𝑡ℎ  resource  present in 𝑘𝑡ℎ zone at a particular time interval (ppm) 
𝑞𝑝𝑘 (𝑡) Quality of pinch point of 𝑘𝑡ℎ zone at a particular time interval (ppm) 
𝑅(𝑡) Resource at a particular time interval (t/h) 
𝑊(𝑡) Waste at a particular time interval (t/h) 

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