DOI: 10.3303/CET2188161 
 

 
 

 
 
 

 
 
 

 

 
 
 

 
 
 

 
 
 

 
 

 

 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 
 

 
 

Paper Received: 5 June 2021; Revised: 17 August 2021; Accepted: 4 October 2021 
Please cite this article as: Varbanov P.S., Chin H.H., Jia X., Sher F., Klemeš J.J., 2021, Environmental Impacts of Plastic Materials Flow 
Minimisation Using Data-Driven Pinch Method, Chemical Engineering Transactions, 88, 967-972  DOI:10.3303/CET2188161 

CHEMICAL ENGINEERING TRANSACTIONS 

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 Servizi S.r.l. 

ISBN 978-88-95608-86-0; ISSN 2283-9216 

Environmental Impacts of Plastic Materials Flow Minimisation 
Using Data-Driven Pinch Method 

Petar Sabev Varbanova,*, Hon Huin China, Xuexiu Jiaa, Farooq Sherb, Jiří Jaromír 
Klemeša

a Sustainable Process Integration Laboratory – SPIL, NETME Centre, Faculty of Mechanical Engineering, Brno University of 
Technology - VUT BRNO, Technická 2896/2, 616 69 Brno, Czech Republic 

b Department of Engineering, School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, UK 
varbanov@fme.vutbr.cz 

Plastics recycling, as a subclass of material recovery and recycling, features extensive and intensive properties. 
The intensive properties can be used to define a recyclability criterion and to classify the plastic materials for a 
symbiotic system (industrial, municipal and commercial) into recyclability categories, where the materials with 
higher recyclability can be either recycled/reused within the same category or cascaded and made available to 
categories with lower recyclability. The potential surplus waste materials of lowest-grade recyclability would be 
destined for waste treatment and disposal, while the potential deficit of materials in the highest-grade 
recyclability category would have to be fulfilled by supplying fresh plastic material produced from primary raw 
materials. The current contribution takes this problem formulation as a basis to optimise the plastics recycling 
of industrial symbiotic systems. It defines a Plastic Material Cascade Diagram and an associated set of Supply-
Demand Composite Curves, identifying the recycling bottleneck – a Pinch Point limiting the rate of recycling and 
determining the most efficient material recycling network design. A case study is formulated to illustrate the 
usefulness of the new concept in reducing the consumption of raw materials and final waste. 

1. Introduction

There has been a surge in plastic packaging use as a result of the COVID-19 induced measures, adding to the 
already substantial volume of plastics produced annually (Klemeš et al., 2020). Ritchie and Roser (2018) 
reported that the annual production of plastic waste had reached 400 Mt in 2015. Jambeck et al. (2015) 
forecasted that the amount of ocean plastic waste would increase to 150 Mt by 2025. This results in a significant, 
simultaneous increase of the released plastic waste, the use of primary resources to produce the material, and 
the environmental footprints. The highest priority measure to minimise these impacts is the planning of plastics 
reuse and recycling in an optimal way. Chin et al. (2021) have proposed a data-driven framework for identifying 
the recyclability and compatibility between sets of plastic waste material sources and demand sinks. The plastic 
waste issues considerably increased when fighting COVID-19 and vaccinations (Klemeš et al., 2021). Recycling 
plastic waste requires a definition of the quality of the stream. Huysman et al. (2017) have analysed the 
compatibility between different polymers on the interfacial tension between them. They defined the substitution 
ratio of recycled plastic, correlated to the compatibility and derived a quality indicator. Eriksen et al. (2018) have 
explored various scenarios of plastic recycling and qualitatively defined the plastic waste categorisation based 
on EU standards. They assessed the polymeric composition and other general residues of the polymers. 
Brouwer et al. (2019) studied the post-consumer plastic packaging waste in a Dutch recycling plant between 
2014 and 2017. They reported that most of the recycled plastics are still suited only for open-loop applications 
due to impure plastic waste. Brouwer et al. (2020) proposed a categorisation of plastic package waste based 
on the degradation properties, chemical contamination and physical strength. The categorisation is qualitative , 
ambiguous and preventing proper threshold for plastic waste categorisation. 
Material Pinch Analysis has been proven to be an efficient tool in synthesising resources conservation networks. 
Water Pinch Analysis was initiated by Wang and Smith (1994) based on the Pinch Analysis concept for heat 
recovery systems (Linnhoff et al., 1994). El-Halwagi et al. (2003) introduced a graph-based method called 

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Material Recovery Pinch Diagram to obtain a minimum supply of external resources by investigating the single 
quality resource conservation problems. This approach provides more accurate targets that account for source 
mixing, and the network design can be determined directly. The water cascade analysis was then developed by 
Manan et al. (2004) and widely applied to minimise freshwater targets. The Pinch Analysis tool is insightful with 
the graphical approach represented by the Composite Curves that can help to clearly identify the source 
imbalances and the targets through visual inspection. The recent development of utilising Pinch-based tools is 
shown by Jia et al. (2020), who proposed a Water Scarcity Pinch Analysis (WSPA) to quantify water scarcity in 
terms of water quality and quantity. They represent the multiple properties of the water streams as a single 
quality indicator based on certain pre-set rules on the water categorisation. The indicator is then used to 
construct the Composite Curves to identify the maximum water flows that can potentially be recycled. Based on 
the above literature review, the following research gaps can be identified: 
(i) There is a need for more studies that combine quantitative and data-driven waste categorisation with 
Process Integration tools to facilitate more accurate recycling planning. Multiple properties of plastic waste, 
including chemicals, metals, additives and degradation properties, are not yet considered simultaneously. 
(ii) A concept and a procedure are still necessary for obtaining the most resource-efficient plastic material 
network designs resulting in minimum waste treatment and pollution. 
Inspired by the WSPA concept, this work addresses the mentioned gaps by proposing a Plastic Pinch 
framework, using quality categorisation based on the properties to evaluate the recyclability of the plastic waste. 
The well-known tree-based classification models are applied, i.e. Decision Tree analysis and Random Forest 
algorithm (VanderPlas, 2016), to derive a set of interpretable if-then rules for quality patterns determination of 
the various plastic waste streams. This paper focuses on formulating a criterion for materials recyclability for a 
given batch of plastic material based on its condition. The criterion formulation is based on the evaluation of the 
rate of polymer degradation and the rate of leakage of fragments to the environment. The Plastic Pinch 
procedure then identifies the bottleneck of the recycling rate and facilitates the recycling network design. 

2. Data-driven Plastic Pinch Analysis Method

Plastic Pinch Analysis (PPA) is designed to evaluate the reusability of plastic waste, given sets of plastic material 
sources and demands. The evaluation builds upon the recyclability definition (Chin et al., 2021) for plastic waste 
and obtains targets for the minimum demand of new plastic and to minimise plastic waste sent for final treatment 
(incineration, landfilling). The procedure of the PPA following the stages: 
Step 1: Plastic quality categorisation – identification of the categories using the collected plastic waste data; 
Step 2: Identification of the available plastic material sources (samples) and the sinks;  
Step 3: Classification of the sources and the sinks (mapping) by the recovery categories (classes) from Step 1, 
and identification of the plastic material sinks by the same categorisation procedure; 
Step 4: Construction of the Composite Curves and identification of the targets: Plastic Pinch Point, minimum 
fresh plastics, minimum final waste plastics. 
Several assumptions are made in this work to simplify the considerations and establish the method: 
(1) The demands and supplies for plastic materials are put forward by the symbiosis network actors. This can 

be implemented with contracts between the actors – suppliers, users, the exchange hub. The current work 
assumes that these transactions are agreed upon and evaluates the technical recyclability. 

(2) The fresh plastic material is assumed to be always available. The system is considered at a steady state. 
(3) A class with a smaller number contains higher-quality plastic (waste) material. 
(4) The materials in each class are forward-compatible. The content of each category/class (except the 

lowest-quality category) is acceptable for intake by all quality categories/classes of lower quality. 
(5) Different plastic polymers are incompatible when they are mixed. 

Table 1: Plastic quality categories and recommended uses 

Categories (Classes) Intended fate 

Class 1: Virgin Fresh plastic as manufactured from virgin resources – petroleum-based or 
renewables-based 

Class 2: Industrial The material can be used for the industrial demands in the SN 
Class 3: Household The material can be used for household items in the SN 
Class 4: Waste The material cannot be reused/recycled (too contaminated or the polymer is too 

degraded) and has to be sent for final treatment. 

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2.1.  Step 1: Plastic Quality Categorisation 

Similar to the WSPA (Jia et al., 2020), the PPA method adopts quality classes instead of specific detailed plastic 
chemical/physical parameters. The assessed plastic is divided into several classes based on the suitability for 
reuse between the sources and the sinks. The exact system of classes can be determined by the engineers and 
stakeholders in the given system – either an industrial site or a Symbiosis Network (SN). An example of a 
possible selection of classes is shown in Table 1, and it is assumed that the categories comply with the 
requirement for cascading formulated just before Step 1. The defined scheme allows the possibility of material 
cascading in an SN for regional plastics flows optimisation. 

2.2.  Step 2: Identification of sources and sinks 

The actors in the SN are surveyed for the plastic materials they would like to share with others, and for the 
plastic material demands, they have to be satisfied by the SN. The data should include: actor data, source 
identifier, polymer composition, amount – either finite (t) or flowrates (t/d), heterogeneity – mainly the 
composition of metals, inclusions and contaminants, degradation state of the polymers. In this case, the Melt 
Flow Index (MFI) is used as an indicator for the degradation state indicator, but other properties can also be 
used (Turku et al., 2018). For simplicity, in the current work, the identities of the SN actors are omitted, and 
heterogeneity is characterised by the concentration of metals. The data collection template is shown in Table 2. 

Table 2. Data collection template 

Streams Polymer Flow (t) Properties 
Sources e.g. 
SR1 
… 
SR(n) 

Polymer type, e.g. 
PE 

Flow rate values, e.g. 
150 
… 
50 

Properties, e.g. 
(i) Polymer compositions,  
(ii) Contaminant compositions,  
(iii) Degradation/mechanical properties  

Sinks 
SK1 
… 
SK(m) 

Polymer type, e.g. 
PE 

Flow rate values, e.g. 
150 
… 
50 

Properties, e.g. 
(iv) Polymer compositions,  
(v) Contaminant compositions,  
(vi) Degradation/mechanical properties 

2.3.  Step 3: Classification of the Sources and Sinks 

The classification of the sources or sinks is based on the collected plastic waste properties data in any recycling 
system. A logical data analysis with a Machine Learning approach helps in deriving a more informative quality 
definition of the plastic streams. This study applies the well-known tree-based classification models, i.e. Decision 
Tree algorithm and Random Forest algorithm, to derive a set of if-then rules for quality patterns determination 
of the various plastic waste streams, where the qualities can be pre-defined by the stakeholders in the system. 
By using these if-then rules allow the classification of the sources or sinks into the proper categories. 
A traditional decision tree algorithm can be solved by the well-known algorithm, known as the ID3 algorithm, 
and the improved version called the C4.5 algorithm. These algorithms mainly use the indicators called the 
Shannon entropy - Eq(1) and information gain- Eq(2) to identify the split points (or thresholds) of the dataset. 
Another well-known index is the Gini index- Eq(3), which is the basis of the CART algorithm. The Gini index is 
mainly used for binary classification problems with categorical variables but is also applicable to a continuous 
dataset with binary splits. Random Forest algorithm is built upon the concept of bagging method, where multiple 
decision trees are ensemble and return the average results from different runs. The open-source Python 
package; scikit-learn (VanderPlas, 2016) is used to perform the data-driven classification of the plastic waste 

𝐸𝑛𝑡𝑟𝑜𝑝𝑦(𝐶) = ∑ −𝑝𝑖 log2 𝑝𝑖  

𝑖

(1) 

𝐺𝑎𝑖𝑛(𝐶, 𝑋) = 𝐸𝑛𝑡𝑟𝑜𝑝𝑦(𝐶) − 𝐸𝑛𝑡𝑟𝑜𝑝𝑦(𝐶, 𝑋) 
(2) 

𝐺𝑖𝑛𝑖 = 1 − ∑(𝑝𝑖 )
2

𝑖

(3) 

where 'C' represents a class, 'pi' represents the probability of attribute/variable 'i' in class 'C', 'X' is the split point. 
Gain (C, X) represents the entropy difference after a split on the data using attribute/variable 'X'. 

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2.4.  Step 4: Targeting with Plastic Pinch Analysis 

Based on the quantity and quality of the plastic sources and sinks, the Composite Curves for supply and demand 
can be constructed (Figure 1) – the Plastic Source Composite Curve and the Plastic Sink Composite Curve. In 
Figure 1, the Y-axis denotes the plastic waste quality classes from 1 to 4 (from the highest to lowest quality). 
The classes are assigned to each source or sink in the previous step. The X-axis denotes the plastic amount. 
The supplies or the sinks are plotted in stacked curves representing the amount of plastic waste/demands in 
each quality class quality category. The Source Composite Curve is then shifted horizontally to the right until it 
is at the right of the Sink Composite Curve. The segment where they touch represents the ‘Pinch’ quality of the 
plastic wastes recycling system. The minimum required input raw plastic is represented by the non-overlapping 
sink segment in the bottom-left of the diagram, and the minimum plastic waste for disposal is represented by 
the non-overlapping source segment. 

Figure 1: An example of The Source and Sink Composite Curves 

Figure 2: Plastic Material Cascade Diagram – (a) Infeasible and (b) Feasible 

This kind of recycling planning enables a cascading use of the plastic waste sources - high-quality sources can 
be used by the demands requiring higher quality first, and then by any lower quality demands - Figure 2. If the 
Composite Curves are overlapped with a crossover in the case of Figure 1 or a negative flow balance as in 
Figure 2a, there is insufficient higher quality plastics to meet the demands of the network. In the cascade 
diagram (Figure 2b), the Pinch Point is identified by the zero flow. This also indicates additional input of plastic 
materials in class ‘1’ can be added to the system to meet the demands. 

1: Virgin

Balance: -100

2: Industrial

Balance: 150

3: Household

Balance: -50

4: Waste

Balance: 350

500

450

0

400

600

200

200

Final 

treatment

Fresh supply

-100

0

150

-50

350

(a)

1: Virgin

Balance: 0

2: Industrial

Balance: 250

3: Household

Balance: 50

4: Waste

Balance: 450

500

450

0

400

600

200

200

Final 

treatment

Fresh supply

100

0

250

50

450

(b)

Pinch

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3. Case Study

An illustrative case study is used to demonstrate the Data-Driven Plastic Pinch framework. The first step 
identified plastic quality categories. Virgin plastic belongs to Class ‘1’, industrial plastic belongs to Class ‘2’, 
household plastic belongs to Class ‘3’, and waste belongs to Class ‘4’. It is to be noted that the plastic waste 
data sample can be collected from any system in a symbiosis network and form a database of plastic waste 
properties. The data of the plastic waste properties are not shown in this work and can be referred to Chin et al. 
(2021). The classification of the plastic wastes can then be performed based on the database and applied to 
any plastic wastes recycling network. The second step involves the identification of the sources and sinks of the 
system. Table 3 shows the sources and sinks data for the case study, PE denoting polyethylene. The last column 
of the data represents the quality class of the plastic sources or sinks that are identified with Step 3. 

Table 3. Case study of the sources and sinks 

Sources Polymer Flow (t) Al Metal 
Concentration (ppm) 

Degradation properties Quality (Class) 
Melt flow index 
(g/10 min) 

SR1 PE 150 100 0.5 Industrial (2) 
SR2 PE 300 50 1.5 Industrial (2) 
SR3 PE 400 500 0.1 Waste (4) 
SR4 PE 500 32 9.5 Virgin (1) 

Sinks Polymer 
Al Metal 
Concentration (ppm) 

Melt flow index 
(g/10 min) 

SK1 PE 300 100 7.7 Virgin (1) 
SK2 PE 200 37 5.6 Industrial (2) 
SK3 PE 200 200 7.1 Waste (4) 
SK4 PE 300 20 8.5 Virgin (1) 

The third step involves the identification of the classification rules based on the database. The Decision Tree 
algorithm and Random Forest algorithm are applied to the database, and the results show that the Random 
Forest algorithm yields better prediction accuracy. The confusion matrix and the classification rules can be found 
in (Chin et al., 2021). The identified if-then rules can then be applied to the sources and sinks to classify them 
into the proper classes (see the last column in Table 3). 

Figure 3: Composite Curves representation for the case study – (a) Infeasible cascade and (b) Feasible cascade 

After identifying the quality classes of the sources and sinks, the Composite Curves can then be plotted for the 
system. Figure 3(a) shows the Source and Sink Composite Curves for the case study. It can be seen that there 
are insufficient sources for the highest quality sink (Class ‘1’). The Source Composite Curve is then shifted to 
the right until it overlaps with the Sink Composite Curve- see Figure 3(b). Note that a total minimum of 100 t of 
virgin plastic is required for the system with the Pinch quality class between Class ‘1’ and ‘2’. The minimum 
plastic waste that is generated is 200 t that is to be sent to incineration or landfilled. 

4. Conclusions

This work has proposed a Plastic Pinch framework combining the Machine Learning approach to facilitate a 
more accurate recycling planning of the plastic wastes in any system. The first step includes defining the quality 
classes of the plastic wastes depending on the demands, and the second step is to identify the sources and 
sinks streams. In the third step, the Machine Learning-based classification approaches can be used to 

(a) (b) 

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distinguish the plastic sources and sinks into the pre-defined quality classes that segregate multiple properties 
of the plastic waste streams. The classification model can be trained with the sampled plastic waste data from 
different origins. Once the quality classes are defined, the Pinch Analysis framework can then be applied to 
determine the minimum raw plastic target or the plastic wastes to be disposed of. The Pinch framework is based 
on the quality class that has been defined by the previous classification approach. An illustrative case study is 
used to demonstrate the framework, and it shows that 85 % of plastic sources can be recycled. Future work 
could include more issues such as heterogeneity of plastic wastes, data variations on supplies or demands and 
unknown quality classes. Future work should also consider the economic and contractual implications of plastic 
material recycling – including direct exchanges and institutionalising the exchange hubs. Relaxing the steady-
state assumption to account for material supplies uncertainty is also important for obtaining practical 
implementations of the method. 

Acknowledgement 

The funding from the project 'Sustainable Process Integration Laboratory – SPIL funded by EU' CZ Operational 
Programme Research and Development, Education, Priority1: Strengthening capacity for quality research 
(Grant No. CZ.02.1.01/0.0/0.0/15_003/0000456) is gratefully acknowledged. 

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