Content uploaded by Philippe Nimmegeers
Author content
All content in this area was uploaded by Philippe Nimmegeers on Mar 24, 2021
Content may be subject to copyright.
sustainability
Article
Extending Multilevel Statistical Entropy Analysis towards
Plastic Recyclability Prediction
Philippe Nimmegeers 1,2 , Alexej Parchomenko 3,4 , Paul De Meulenaere 5,6 , Dagmar R. D’hooge 7,8,
Paul H. M. Van Steenberge 7, Helmut Rechberger 3and Pieter Billen 1,*
Citation: Nimmegeers, P.;
Parchomenko, A.; De Meulenaere,
P.D.; D’hooge, D.R.; Van Steenberge,
P.H.M.; Rechberger, H.; Billen, P.
Extending multilevel statistical
entropy analysis towards plastic
recyclability prediction. Sustainability
2021,13, 3553. https://doi.org/
10.3390/su13063553
Academic Editor: Carlos Sanz-Lazaro
Received: 15 February 2021
Accepted: 17 March 2021
Published: 23 March 2021
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
1Intelligence in Processes, Advanced Catalysts and Solvents (iPRACS), Faculty of Applied Engineering,
University of Antwerp, Groenenborgerlaan 171, 2020 Antwerp, Belgium;
philippe.nimmegeers@uantwerpen.be
2Environmental Economics (EnvEcon), Department of Engineering Management, Faculty of Business and
Economics, University of Antwerp, Prinsstraat 13, 2000 Antwerp, Belgium
3Institute for Water Quality and Resource Management, TU Wien, Karlsplatz 13/226, 1040 Vienna, Austria;
alexej.parchomenko@vito.be (A.P.); helmut.rechberger@tuwien.ac.at (H.R.)
4VITO, 200 Boeretang, 2400 Mol, Belgium
5CoSys-Lab, Faculty of Applied Engineering, University of Antwerp, Groenenborgerlaan 171,
2020 Antwerp, Belgium; paul.demeulenaere@uantwerpen.be
6Flanders Make—Ansymo/Cosys Core Lab, 2020 Antwerp, Belgium
7Laboratory for Chemical Technology, Ghent University, Technologiepark 125, 9052 Ghent, Belgium;
dagmar.dhooge@ugent.be (D.R.D.); paul.vansteenberge@ugent.be (P.H.M.V.S.)
8Centre for Textiles Science and Engineering, Ghent University, Technologiepark 70a, 9052 Ghent, Belgium
*Correspondence: pieter.billen@uantwerpen.be
Abstract:
Multilevel statistical entropy analysis (SEA) is a method that has been recently proposed to
evaluate circular economy strategies on the material, component and product levels to identify critical
stages of resource and functionality losses. However, the comparison of technological alternatives
may be difficult, and equal entropies do not necessarily correspond with equal recyclability. A
coupling with energy consumption aspects is strongly recommended but largely lacking. The aim
of this paper is to improve the multilevel SEA method to reliably assess the recyclability of plastics.
Therefore, the multilevel SEA method is first applied to a conceptual case study of a fictitious bag
filled with plastics, and the possibilities and limitations of the method are highlighted. Subsequently,
it is proposed to extend the method with the computation of the relative decomposition energies of
components and products. Finally, two recyclability metrics are proposed. A plastic waste collection
bag filled with plastic bottles is used as a case study to illustrate the potential of the developed
extended multilevel SEA method. The proposed extension allows us to estimate the recyclability of
plastics. In future work, this method will be refined and other potential extensions will be studied
together with applications to real-life plastic products and plastic waste streams.
Keywords:
statistical entropy analysis; recycling; plastic waste; waste management; resource effi-
ciency; circular economy
1. Introduction
The same properties that make plastics into incredibly versatile materials—malleability
and tuneability—also challenge the transition toward a circular economy for plastics.
Indeed, polymers are often mixed at various scales, a wide diversity in compounds exists,
and polymers are subject to degradation. Large efforts are being undertaken in numerous
projects to increase the recycling rates for various post-industrial and post-consumer
end-of-life plastics, leading to new developments in sorting and refining technologies, as
well as mechanical and chemical recycling technologies (see for instance [
1
–
12
]). Even
on a societal level, changes are being made in how post-consumer plastics are collected,
either by curbside bags or container collection, deposit systems or centralized collection
Sustainability 2021,13, 3553. https://doi.org/10.3390/su13063553 https://www.mdpi.com/journal/sustainability
Sustainability 2021,13, 3553 2 of 21
facilities. Many of these efforts, however, interfere with the ever-increasing complexity
of plastic formulations and products. At the front end of their lifecycle, some initiatives
have been implemented with the aim of designing plastic products for circularity [
13
–
15
].
This can range from design-for-disassembly [
16
,
17
] and design-for-recycling [
18
–
20
]—
both on a molecular level as well as on a product/object level—to assisting in the rapid
detection/identification of material types by (chemical) labelling. Nevertheless, disruptive
new ideas often fail to be adopted, as they are faced with existing, rigid, large-scale material
flow infrastructures.
When assessing the sustainability of various new technological alternatives for plastics
circularity, the past decades have seen a shift from using traditional ex post methodologies
toward ex ante methodologies. The two major study areas are life cycle assessment (LCA)
and techno-economic assessment (TEA), as well as approaches integrating both. To effec-
tively serve as decision supports for research and development trajectories, applying these
assessment methods at low technology readiness levels (TRL) is imperative. Various strate-
gies exist, including the assumptions of ideal (thermodynamic) systems, the use of proxy
technology transfers, participatory methods and the application of learning
curves [21]
. Es-
sentially, the lower the technology readiness level, the more generic the study intrinsically
becomes, as detailed information about full-scale processes and commercialized products
in society is lacking.
Almost all sustainability assessments used for plastics cycles start by establishing
mass and energy balances, which can further be translated into a life cycle inventory or
into economic data. However, this approach requires quite advanced knowledge about the
potential unit processes involved. A key factor in both LCA and TEA, from which many
other indicators are derived, is the energy performance of systems. Indeed, if less energy is
required to recycle waste plastics into a product, this option may be chosen over its linear
economy alternative; e.g., producing virgin products that are incinerated at their end-of-life
or landfilling (not taking resource scarcity or other environmental indicators into account).
However, an energy balance and therefore quite detailed knowledge ofs unit processes
is needed to get to this point. Transformative materials innovations (based on disruptive
technologies) may in particular therefore fail to demonstrate their environmental and/or
economic potential, as the background technological system—a collection of the currently
employed methods—is usually considered in LCA or TEA.
Despite the large efforts dedicated to making the transition towards a more circu-
lar economy, an important challenge remains in assessing the recyclability of plastics
(
e.g., [22]
). A reduced level of recyclability of plastics can result (i) from the difficulty to
separate different plastic types [
23
], (ii) from the heterogeneity and mixing of collected
plastic fractions, (iii) from degradation processes during the recycling process that impact
crucial mechanical properties of recycled plastics [
24
,
25
], (iv) from the efforts related to
the recycling processes (e.g., [
26
])) and (v) from the presence of adverse effects; e.g., con-
taminations and the accumulation of substances in the recyclate that may pose a health
risk [27]
. This shows that assessing plastic recyclability is a complex task that requires
further research.
Often, users of the term recyclability fail to connect their design-for-recycling aspira-
tions with the current complex reality of post-consumer plastic waste handling, sorting
and recycling, or even worse, they are bound to a rigid background system. From an
engineering point of view, all materials are 100% recyclable, as long as enough energy
is available and the size of the cycle does not matter. This supports the aforementioned
focus on energy aspects to investigate the feasibility and sustainability of recycling. Again,
when making the claim that a material is “recyclable”, it can/should be supported by an
integrated sustainability assessment. However, given the strict requirement of mass and
energy balance estimations, as mentioned above, this analysis and therefore such claims
can only be made for existing platform materials and objects, for which at least proxy tech-
nologies and products exist. The outcome of these studies is subject to several constraints
corresponding to the scope of the study; the studied market, applied technologies, waste
Sustainability 2021,13, 3553 3 of 21
collection and sorting, access to manual labor or automation. These constraints regarding
the applicability of the outcomes relate the specific contributions of waste transportation,
sorting and refining to the overall impact/cost and are mostly case-specific. Again, judging
the potential merits of transformative materials or disruptive system innovations may be
inaccurate given the limited forecasting ability of traditional assessment methods.
In the search for more generic assessment methods, Rechberger and Brunner [
28
]
developed statistical entropy analysis (SEA), which was initially applied to waste-to-energy
(WtE) plants to investigate whether this technology is a concentrating or diluting waste
treatment operation. Later, this method was adopted for predominantly inorganic/metallic
materials streams, such as the European [
29
] and Chinese [
30
] copper cycle and the Austrian
phosphorus cycle [
31
]. Other recent developments of SEA include the construction of a
modified statistical entropy function to assess the recyclability of e-waste [
32
], linking SEA
to exergy analysis applied to a crushed lithium-ion battery lab scale sieving experiment [
33
]
and the introduction of mass joint entropy as an indicator together with a combination of
SEA with substance flow analysis to evaluate phosphorus management in a food-based
bioethanol system [
34
]. However, for a decade, the method was only applied to individual
substances, limiting its applicability. Recently, however, Parchomenko et al., (2020) [
35
]
extended the method by addressing statistical entropies at the component (consisting
of multiple substances) and product (consisting of multiple components) levels, leading
towards multilevel statistical entropy analysis. This extension [
35
] allows us to investigate
such circular economy strategies as reuse, repair, remanufacturing or combinations of these.
It is important to stress that SEA is not intended as a sustainability metric, but it has been
developed to assess resource effectiveness, meaning the ability of a system to preserve
functionality on the highest level possible, measured in terms of the statistical entropy
changes performed by a system. As SEA is independent of any background systems (such
as energy mixes) that play an important role and influence the results of, e.g., LCA, SEA
only assesses if a specific state is achieved (product entropy, or entropy level of components
or of pure substances) and not how it is achieved (e.g., by a robot or by manual work).
Nonetheless, in assessing recyclability, the latter is equally relevant.
The goal of this paper is to highlight how multilevel SEA can also be used in predicting
the recyclability of plastics in very generic background systems, although the method alone
has some limitations. To overcome these, we propose to extend the assessment method
by coupling it with energy balances from generic transportation, sorting and refining
technologies. In doing so, we demonstrate that not all statistical entropies (typically
expressed as relative statistical entropies) calculated by this method are equal in meaning,
as two different waste streams with a similar relative statistical entropy may still differ
significantly in the way these waste streams can be separated or further recycled (or
reduced in relative statistical entropy). This paper does not present clear-cut formulations
to address these issues, but rather explores options for quantifying aspects playing a role
in recyclability. In addition, the authors propose a metric based on relative statistical
entropy and relative decomposition energy as a potential avenue to define the recyclability
of plastics. This is motivated by the fact that the energy required to reduce the relative
statistical entropy of two different waste streams with a similar relative statistical entropy
may differ significantly. Quantifying this generically, although still in its infancy, may
resolve this and yield a powerful predictive and generic tool to predict plastics’ circularity.
In this respect, this work can be considered as an addition to the work of Roithner and
Rechberger (2020) [
36
] in which a recyclability effectiveness metric was defined based on
classic SEA to quantitatively and qualitatively assess how effectively a studied recycling
process can separate and concentrate an input waste stream.
This paper starts by recapping the multilevel SEA method by Parchomenko et al.
(2020) [
35
] and applies this to a fictitious example of a collection bag for post-consumer
recyclable plastics. Subsequently, an extension of the multilevel SEA method with energy
consumption aspects is proposed together with a possible recyclability metric. Further-
more, a more realistic example of a collection bag with multiple different bottles, as a
Sustainability 2021,13, 3553 4 of 21
proxy for source-separated curbside collection systems such as the P + MD system—i.e.,
the waste collection bag for plastic packaging, metal packaging and drinking cartons
in
Belgium [37,38]
—is elaborated, highlighting how objects with similar relative statis-
tical entropy values may clearly require a different energy input for relative statistical
entropy reduction.
2. Methods
In this section, the extended multilevel statistical entropy analysis (SEA) method is
described for the assessment of the recyclability of plastics. Firstly, the multilevel statis-
tical entropy analysis method of Parchomenko et al., (2020) [
35
] is introduced with its
mathematical description. Subsequently, this methodology is applied to the conceptual
example of a fictitious plastic bag. Limitations of the multilevel statistical entropy analysis
method for a direct application as a recyclability metric are illustrated by this conceptual
example. To conclude this section, an extension of the multilevel SEA method is presented
in which energy consumption aspects are taken into account. Note that the statistical
entropy considered in this contribution is not the same as thermodynamic entropy. To
stress the difference with thermodynamic entropy (typically denoted by
S
in scientific
literature), the statistical entropy is denoted by
H
in this contribution (as is typically done
in information theory).
2.1. Description of the Multilevel Statistical Entropy Analysis (SEA) Method
Statistical entropy analysis (SEA) is a method based on Shannon’s statistical entropy
function [
39
–
41
] to quantify changes in the substance distribution pattern throughout a
system in which materials undergo transitions in different steps [
28
,
29
,
42
]. Among different
process steps in a system, the substances can be diluted (increase in statistical entropy),
concentrated (decrease in statistical entropy) or remain unchanged (unchanged statistical
entropy). The focus of the initial SEA that was applied to the results of material flow
systems was on the analysis of individual substances and did not consider components
or products. Consequently, SEA cannot be directly applied to the evaluation of circular
economy strategies such as reuse, repair, remanufacturing or combinations of these. To
evaluate such circular economy strategies, the multilevel SEA method has been developed
by Parchomenko et al., (2020) [
35
] in which, next to substance level entropies, component
and product level statistical entropies are considered. The multilevel SEA method [
35
]
is described in this subsection by making a distinction between the three different levels:
substance level, component level and product level.
2.1.1. Substance Level Entropy
Consider a flow rate
Mf
of a material flow
f
(which can be a component or a good
flow, in mass per time) and the (dimensionless) mass fraction
ci,f
of a substance
i
in the
material flow f. Thus, the substance flow rate Xi,f(in mass per time) can be calculated as
Xi,f=Mfci,f(1)
In addition, standardized (dimensionless) mass fractions
mi,f
can be computed by
dividing the material flow rate
Mf
by the total flow of a substance
i
, over the
F
material
flows ∑F
f=1Xi,fas indicated in Equation (2) [33].
mi,f=Mf
∑F
f=1Xi,f
(2)
The statistical entropy
Hi(ci,f
,
mi,f)
of a substance
i
(which is dimensionless) can be
defined as follows [42]:
Sustainability 2021,13, 3553 5 of 21
Hi(ci,f,mi,f) = −
F
∑
f=1
mi,fci,flog2ci,f(3)
In the SEA method, a dimensionless relative statistical entropy
Hi
rel (ci,f
,
mi,f)
is used,
which is the ratio of the statistical entropy value
Hi(ci,f
,
mi,f)
and the maximum statistical
entropy value Hi
max The relative statistical entropy is as indicated in Equation (4).
Hi
rel (ci,f,mi,f) = Hi(ci,f,mi,f)
Hi
max
(4)
Hi
max =
log21
ci,geo,min , for open systems
log2∑F
f=1mi,f, for closed systems (5)
where
ci,geo,min
is the minimum natural or geogenic concentration of substance
i
in the at-
mosphere and the hydrosphere, which corresponds with the concentration of the substance
iin a compartment where it is maximally diluted [28,35].
Note that, in a closed system, the maximum statistical entropy of a substance
i
is
reached when the substance is equally distributed among the material flows and the
concentrations in all material flows are the same for substance
i
. The minimum statistical
entropy is reached if a material flow consists of a single pure substance
i
(as in that situation,
log2ci,f=log2(1)=0).
In SEA, only the relative substance level statistical entropy is considered. For a more
detailed description of the SEA method, the reader is referred to [
28
,
29
,
42
]. If the research
question concerns one single substance and its use in material flow analysis, the calculation
of substance-level entropy can help in addressing this research question. If, however,
the research question concerns higher levels (e.g., multiple substances, components or
products), then an extended SEA approach should be applied in which the component or
product level is addressed.
2.1.2. Component Level Entropy
In multilevel SEA, the second step is to calculate component-level entropy values.
These component-level entropy values can subsequently be used for the calculation of the
product-level entropies. A similar expression to Equation
(3)
can be used to describe the
statistical entropy of a component n,Hc
n(ci,n,mc
n):
Hc
n(ci,n,mc
n) = −
I
∑
i=1
mc
nci,nlog2(ci,n)(6)
where
mc
n
is the normalized component mass (i.e., the mass fraction of component
n
com-
pared with all components at a stage in the system),
ci,n
is the concentration of substance
i
in component nand Iis the number of substances.
The main differences between Equations
(3)
and
(6)
are the normalization at the
component level and the summation over the different substances.
The relative statistical entropy of a component
n
can be expressed as the ratio be-
tween the component-level statistical entropy
Hc
n(ci,n
,
mc
n)
and the maximum component-
level entropy
Hc
max
. Both the relative component-level statistical entropy and maximum
component-level entropy are described in Equations (7) and (8).
Sustainability 2021,13, 3553 6 of 21
Hc
n,rel (ci,n,mc
n) = Hc
n(ci,n,mc
n)
Hc
max
(7)
Hc
max =−
I
∑
i=1
ci,tot log2(ci,tot)(8)
where ci,tot is the concentration of substance iin the total mixture/product/system stage.
The maximum component-level entropy corresponds with either the case in which all
substances are present in one material flow or equally distributed. Note that when dilution
takes place in compartments outside the system boundary, the maximum statistical entropy
is calculated as in Equation (5) for open systems.
2.1.3. Product Level Entropy
The final level that is considered in this paper is the product level. The product-level
statistical entropy is defined in Equation (9).
Hp(cn,p,Hc
n,rel (ci,n,mc
n)) = −
N
∑
n=1
log2cn,pHc
n,rel (ci,n,mc
n)(9)
cn,p=qn
Ntot (10)
where
cn,p
is the component concentration of component
n
in the product
p
,
qn
is the
number of entities of component nand Ntot is the total number of components.
From Equation
(9)
, it can be seen that the product-level entropy depends on the dis-
tribution of components (via the component concentration
cn,p
) and the distribution of
substances over the components (i.e., the relative statistical entropy values of the compo-
nents
Hc
n,rel (ci,n
,
mc
n)
). Consequently, an increase in product-level entropy can be caused by
either an increase in the number of distinct components in a product or through a higher
dilution or a more equal distribution of the substances over the product’s components.
In multilevel SEA, relative statistical entropies are considered. Therefore, the product-
level statistical entropy needs to be divided by the maximum product-level statistical en-
tropy to calculate the relative product-level statistical entropy. The maximum product-level
entropy corresponds with the situation in which every substance is uniformly distributed
over the product’s components. The maximum degree of substance dilution is in that case
determined by the total number of components
N
. Thus, the relative product level statistical
entropy and maximum product-level entropy can be expressed as in Equations
(11)
and
(12)
.
Hp
rel (cn,p,Hc
n,rel (ci,n,mc
n)) = Hp(cn,p,Hc
n,rel (ci,n,mc
n))
Hp
max
(11)
Hp
max =log2(Ntot)(12)
Note that the minimum
Hp
rel (cn,p
,
Hc
n,rel (ci,n
,
mc
n))
of 0 is reached in the situation where
the product consists of only one component or one type of component (i.e.,
cn,p=
1, thus
log2cn,p=
0) and the situation in which all components consist of a single substance (i.e.,
the component entropies equal zero).
2.2. Conceptual Example of Multilevel SEA: A Fictitious Plastic Bag
The multilevel SEA method is illustrated based on the conceptual example of a
fictitious plastic bag (product) which is filled with 10 components (four units of component
1 and six units of component 2). A unit of component 1 consists of one entity of red material
(2 g) and one entity of blue material (3 g). A unit of component 2 consists of one entity of
orange material (3 g) and one entity of blue material (3 g). In terms of mass fraction, the blue
material consists of 20% substance A and 80% substance B. The orange material consists of
40% substance A and 60% substance C. The red material consists of 50% substance B, 20%
substance C and 30% substance D. An illustration of this conceptual example is presented
Sustainability 2021,13, 3553 7 of 21
in Figure 1. In the next paragraphs, the substance-level, component-level and product-level
entropies are calculated for this example.
Figure 1. Illustration of the conceptual fictitious plastic bag example.
2.2.1. Substance Level Entropy Analysis
To study the transformation or distribution of substance
A
over the components by
any given operation, the substance-level entropy should be calculated. The substance-
level entropy could be of particular interest when studying sorting or refining processes,
targeted at a certain substance purity and yield. The statistical entropy for substance
A
can be computed by filling in the entries for substance
A
in Equation
(3)
. This results in
the following:
HA(cA,f,mA,f) = −mA,c1cA,c1log2(cA,c1)−mA,c2cA,c2log2(cA,c2)=1.977 (13)
The maximum substance-level statistical entropy can be calculated via Equation
(5)
for closed systems. This results in the following:
HA
max =log2 2
∑
f=1
mA,c f !=2.085 (14)
The relative substance-level statistical entropy can subsequently be calculated via
Equation (4):
HA
rel (cA,f,mA,f) = HA(cA,f,mA,f)
HA
max
=0.948 (15)
The exercise above could also be done for the other substances. Therefore, the entries
and results for the (relative) substance-level statistical entropies for the different substances
are summarized in Table 1. Substance D has the lowest substance-level relative statistical
entropy as it is only present in the first component. Substance B has the highest substance-
level relative statistical entropy as it is the most diluted substance. Substance A is more
diluted than substance C, reflecting the higher substance-level relative statistical entropy
of A compared to substance C.
Table 1.
Substance-level statistical entropy entries for the fictitious plastic bag example, with
Πc1=−mi,c1ci,c1log2ci,c1
and Πc2=−mi,c2ci,c2log2ci,c2. In bold are the resulting substance level relative statistical entropies.
mi,c1ci,c1log2(ci,c1)Πc1mi,c2ci,c2log2(ci,c2)Πc2HiHi
max Hi
rel
A 1.515 0.12 −3.059 0.556 2.727 0.3 −1.737 1.421 1.977 2.085 0.948
B 0.714 0.68 −0.556 0.270 1.286 0.4 −1.322 0.680 0.950 1 0.950
C 1.61 0.08 −3.644 0.470 2.903 0.3 −1.737 1.513 1.983 2.175 0.912
D 8.33 0.12 −3.059 3.059 15 0 0 0 3.059 4.544 0.673
Sustainability 2021,13, 3553 8 of 21
2.2.2. Component-Level Entropy Analysis for the Fictitious Bag Example
If the use and the fate of several related substances in the different components of
the system are considered, component-level entropies can be calculated. This could be
applicable in research questions regarding the distinct characteristics and composition of
various components in a product or system. The component-level entropies are calculated
for the two components in this example, component 1 and component 2, using Equation
(6)
.
To illustrate the use of the equations, this is elaborated for the first component. In order to
complete Equation
(6)
, the component mass fraction
mc
1
and and the substance concentra-
tions in component 1 are needed. These can be computed as indicated in Equations
(16)
and (17).
mc
1=Mc
1
Mc
1+Mc
2
=4×5
(4×5)+(6×6)=0.357 (16)
ci,1 =ci,blu e Mc
1cblue,1 +ci,oran ge Mc
1corange,1 +ci,re d Mc
1cred,1
Mc
1
(17)
Inputting the values for the different substances in Equation
(17)
results in following
substance concentrations in component 1:
cA,1 =
0.12,
cB,1 =
0.68,
cC,1 =
0.08 and
cD,1 =0.12. Thus, the statistical entropy of component 1 can be formulated as
Hc
1(ci,1,mc
1) = −(mc
1cA,1 log2(cA,1)+mc
1cB,1 log2(cB,1)+mc
1cC,1 log2(cC,1)+mc
1cD,1 log2(cD,1)) =0.501 (18)
The maximum component-level entropy can be calculated with Equation (8):
Hc
max =−
4
∑
i=1
ci,tot log2(ci,tot)=1.668 (19)
with ci,tot =ci,bl ue Mblue +ci,oran ge Morange +ci,re d Mred
Mtot (20)
where
Mtot
is the total mass (equal to 56 g for this case study). Consequently, the relative
statistical entropy for component 1 can be calculated via Equation (7):
Hc
1,rel (ci,1,mc
1) = Hc
1(ci,1,mc
1)
Hc
max
=0.301 (21)
The entries and results for the (relative) component-level statistical entropies for the
different components are summarized in Table 2. The last column of Table 2indicates
that the first component has a lower component-level relative statistical entropy than the
second component. This can be explained by the higher degree of dilution (40% B, and 30%
A and 30% C) of component 2 in its substances compared to component 1 (68% B, 12% A,
12% D and 8% C), as depicted in the second column of Table 2.
Sustainability 2021,13, 3553 9 of 21
Table 2.
Component-level statistical entropy entries and value for the fictitious plastic bag example.
ci,nmc
nlog2(ci,n)−mc
nci,nlog2(ci,n)Hc
n,rel
cA,1 0.12 0.357 −3.059 0.131
cB,1 0.68 0.357 −0.556 0.135
cC,1 0.08 0.357 −3.644 0.104
cD,1 0.12 0.357 −3.059 0.131
Hc
10.501 0.301
cA,2 0.3 0.643 −1.737 0.335
cB,2 0.4 0.643 −1.322 0.340
cC,2 0.3 0.643 −1.737 0.335
cD,2 0 0.643 0 0
Hc
21.010 0.606
2.2.3. Product-Level Entropy Analysis for the Fictitious Bag Example
For this example, the final hierarchical level in the multilevel SEA method is the
product level, in which the use of components and several related substances in the
product are studied. The product-level entropy can be calculated with Equation
(9)
. For
the fictitious bag example, this results in the following expression:
Hp(cn,p,Hc
n,rel (ci,n,mc
n)) = −
2
∑
n=1
log2cn,pHc
n,rel (ci,n,mc
n) = 0.843 (22)
The maximum statistical entropy can be calculated via Equation and
Hp
max =log2(Ntot)
=log2(10)=
3.322. Consequently, the relative statistical entropy of the fictitious bag can
be written as (Equation (11)).
Hp
rel (cn,p,Hc
n,rel (ci,n,mc
n)) = Hp(cn,p,Hc
n,rel (ci,n,mc
n))
Hp
max
=0.254 (23)
2.3. Limitation of Multilevel SEA if Separation Energy Matters: A Counter Example
Consider a variation on the fictitious bag example, illustrated in Figure 2. In this
example, two components (which could be any plastic packaging objects, ranging from
packaging trays to bottles with caps) are present in the product mixture. Both components
have the same substance concentrations (with three substances, A, B and C, and two
materials, blue and orange). However, both components have a different structure and are
linked differently to one another. One component could, for instance, be glued, whereas
the other could be screwed. A comparable situation would be a bag filled with multilayer
plastics and monolayer plastics, both with the same substance composition.
Figure 2. Illustration of the counter example, also a conceptual fictitious plastic bag.
Sustainability 2021,13, 3553 10 of 21
In this counter example, it is clear that the relative component statistical entropies will
be the same; i.e., 0.500 (see Table 3for details on the calculation of the component level
entropies). However, both components are not necessarily as easily separated. Multilevel
statistical entropy analysis does not account for the energy that is needed to separate these
components in its constituent building blocks. Therefore, the efforts to reduce the relative
statistical entropy could strongly differ for the various components, although they have
the same relative component statistical entropy. In order to use the concept of multilevel
SEA for the evaluation of recyclability, an extension is required which addresses the effort
needed to separate the components into their building blocks. Therefore, the authors
present such an extension using energy consumption aspects in the next subsection.
Table 3. Component-level statistical entropy entries and value for the counter example.
ci,nmc
nlog2(ci,n)−mc
nci,nlog2(ci,n)Hc
n,rel
cA,1 0.300 0.500 −1.737 0.261
cB,1 0.400 0.500 −1.322 0.264
cC,1 0.300 0.500 −1.737 0.261
Hc
10.785 0.500
cA,2 0.300 0.500 −1.737 0.261
cB,2 0.400 0.500 −1.322 0.264
cC,2 0.300 0.500 −1.737 0.261
Hc
20.785 0.500
2.4. Extension of the Multilevel SEA Method with Energy Consumption Aspects to
Assess Recyclability
As indicated in the counter example of the previous subsection, an extension of the
multilevel SEA method is needed. The authors propose to extend the multilevel SEA
method by including energy consumption aspects to assess the recyclability of a product
or its components. Firstly, the extension with energy consumption aspects is illustrated for
the component level. Subsequently, it is extended to the product level.
Consider a component
n
that consists of
M
different materials that are linked together
to form the component
n
. Such a material
m
consists of
I
different substances that are
mixed or blended in a certain way (note that a substance is indicated by
i
). As indicated
in the counter example, the relative statistical entropy concept does not account for the
often distinct way in which materials and/or substances are linked. Depending on the
linking of the materials and/or the substances, different processes exist to decompose
the component
n
in its constituting materials
m
and/or its constituting substances
i
. The
energies required to decompose a component into its materials
Ec
n(π
,
ηc
m)
or decompose
a component into its substances
Ec
n(π
,
ηc
i)
can be defined per unit mass of component
(
units: J/kg
). A conceptual representation of how these decomposition energies are linked
to the recycling of the components is indicated by the full blue arrows in Figure 3. Note
that these energies depend on the process
π
that is used, which in turn depends on the
required decomposition efficiency to either the materials
ηc
m
or the substances
ηc
i
. All
decomposition efficiencies defined in this contribution have a value between 0 and 1,
corresponding with no decomposition and full decomposition into materials or substances,
respectively. In addition, it should be stated that, in practice, processes can exist that do
both; i.e., decomposing the components partially into their materials and partially into their
substances. Therefore, a generic decomposition energy of a component
n
can be defined as
Ec
n(π,ηc
m,ηc
i)(in J/kg).
Next, a product
p
can be considered which consists of
N
different components
n
.
The energy required to decompose the product into its components can be defined as
Ep(π
,
ηp
n)
, where
ηp
n
is the decomposition efficiency of the product to its components, per
unit mass of product (units: J/kg). A product
p
could also be decomposed directly by a
process in its constituent materials using a decomposition energy from a product to its
Sustainability 2021,13, 3553 11 of 21
materials described by
Ep(π
,
ηp
m)
, where
ηp
n
is the decomposition efficiency of the product
to its components. Similarly, a product could be decomposed in its constituent substances
with decomposition energy from a product to its substances
Ep(π
,
ηp
i)
, where
ηp
i
is the
decomposition efficiency of the product to its components. These decomposition energies
are presented conceptually by the red dotted arrows in Figure 3. The generic energy
of decomposition of a product
p
, decomposing the product partially in its components,
materials and substances, can denoted by Ep(π,ηp
n,ηp
m,ηp
i)(in J/kg).
Figure 3.
Conceptual representation of the decomposition energies for the counter example. For the
sake of completeness, the decomposition energy from a material
k
to its substances
i
, denoted by
Em
k(π,ηm
i), has also been depicted.
In order to use these concepts of decomposition energy to evaluate the recyclability
of different components or products, a relative metric is needed. Therefore, a maximum
decomposition
Emax
(in J/kg) is defined. This maximum decomposition energy corresponds
with the energy that is needed to produce the amount of virgin substances that are present
at the highest hierarchical level of the system that is studied, per kg (units: J/kg). In our
contribution, this is the product level. This allows us to compare the relative decomposition
energies of components with one another, as the same maximum decomposition energy
value is used. In the case that the energy required to produce all virgin substances that
are present at a lower hierarchical level is used (such as for a component), the relative
decomposition energies of different components could not be compared to one another.
Therefore, the energy required to produce all virgin substances that are present at the
highest hierarchical level—in this contribution, the product level—has been chosen to
define the maximum decomposition energy. A mathematical formulation for the maximum
decomposition energy is presented in Equation (24).
Emax =1
Mtot
N
∑
n=1
I
∑
i=1
qnci,nMneproduction
i, (24)
where
Mtot
is the total mass of the studied system (i.e., the mass of the highest hierarchical
level that is considered),
qn
is the number of components
n
in the product (dimensionless),
ci,n
is the mass fraction of substance
i
in component
n
(dimensionless),
Mn
is the mass of
component
n
(in kg) and
eproduction
i
is the energy that is needed to produce 1 kg of virgin
substance i(expressed in J/kg).
The maximum decomposition energy defined in Equation
(24)
can be used to de-
fine the relative decomposition energy of a component
Ec
rel (π
,
ηc
m
,
ηc
i)
and of a product
Ep
rel (π
,
ηp
n
,
ηp
m
,
ηp
i)
in Equations
(25)
and
(26)
, respectively. In practice decomposition to
Sustainability 2021,13, 3553 12 of 21
the materials is often the goal as these materials (e.g., blends) have been designed with a
specific purpose in mind.
Ec
n,rel (π,ηc
m,ηc
i) = Ec
m,i(π,ηc
m,ηc
i)
Emax (25)
Ep
rel (π,ηp
nηp
m,ηp
i) = Ep
n,m,i(π,ηp
n,ηp
m,ηp
i)
Emax (26)
Note that the relative decomposition energy (either at component or product level)
typically has a value between 0 and 1. However, situations exist in which the relative
decomposition energy is greater than 1. In such a situation, the considered decomposition
requires more energy per kg than producing the virgin substances that are present per kg.
From an energetic point of view, such a recycling route is undesirable. However, such a
situation could on the other hand be justifiable in the case of the absence (or an extreme
scarcity) of sources to produce the virgin substances.
A first possible recyclability metric for a component based on relative statistical
entropy and relative decomposition energies for a component
R(1)
n
or product
R(1)
p
can be
formulated in Equations (27) and (28), respectively.
R(1)
n=1−Hc
n,rel (ci,n,mc
n)1−Ec
n,rel (π,ηc
m,ηc
i)(27)
R(1)
p=1−Hp
rel (cn,p,Hc
n,rel (ci,n,mc
n))1−Ep
rel (π,ηp
n,ηp
m,ηp
i)(28)
Note that the recyclability metrics
R(1)
n
and
R(1)
p
typically have a value between 0
and 1 (assuming that the relative decomposition energies have a value between 0 and 1).
The minimum recyclability should correspond with the situation in which the relative
statistical entropy is either maximal and/or the relative decomposition energy is maximal.
The maximum recyclability corresponds with the situation in which the relative statistical
entropy equals zero and the relative decomposition energy equals zero. However, negative
values of the recyclability metric are possible in which the relative decomposition energy is
greater than 1. As mentioned earlier, in such a situation, more energy is required to achieve
the preset decomposition than the energy that is needed to produce the virgin substances
that are present in the product. In the case of a negative recyclability metric value (
R(1)
n<
0
or
R(1)
p<
0), recycling can only be justifiable if sources to produce the virgin substances
are not available or extremely scarce.
The potential negative value of
R(1)
n
or
R(1)
p
could be considered to be less elegant.
Therefore, the following alternative recyclability metrics
R(2)
n
and
R(2)
p
are proposed at the
component and product level:
R(2)
n=1−Hc
n,rel (ci,n,mc
n)
Ec
n,rel (π,ηc
m,ηc
i)(29)
R(2)
p=1−Hp
rel (cn,p,Hc
n,rel (ci,n,mc
n))
Ep
rel (π,ηp
n,ηp
m,ηp
i)(30)
The minimum value of the alternative recyclability metrics R(2)
nand R(2)
pequals zero
and corresponds with the maximum component and product-level relative statistical
entropy, respectively. The maximum value of the alternative recyclability metric equals
infinity and corresponds with the situation in which the relative decomposition energy
equals zero (i.e., no energy is needed to decompose the component or product). Note that
negative values of the recyclability metrics
R(2)
n
and
R(2)
p
are impossible as the relative
statistical entropy values cannot exceed 1 and the relative decomposition energy values
Sustainability 2021,13, 3553 13 of 21
cannot be smaller than 0. In addition, a situation in which the recyclability metrics
R(2)
n
and
R(2)
p
are smaller than the contributions coming from the relative statistical entropies
at the component
1−Hc
n,rel (ci,n,mc
n)
and product level
1−Hp
rel (cn,p,Hc
n,rel (ci,n,mc
n))
,
respectively, correspond with the situation of a negative recyclability metric value of
R(1)
n
and R(1)
p.
In the case studies presented in this contribution, we focus on the recyclability of the
components. The two recyclability metrics that have been presented at the component level,
R(1)
n
and
R(2)
n
, are evaluated in the next section. The maximum recyclability corresponds
with the situation in which a relative statistical entropy value of zero is exhibited for a
component (i.e., the component consists of one single substance or one material) and the
situation in which no energy is required for further refinement.
3. Results and Discussion
In this section, the results obtained with the proposed extension of multilevel SEA
with energy consumption aspects are presented and discussed. Firstly, the assumptions
that have been made to calculate the decomposition energies in this paper are introduced.
Subsequently, the two proposed recyclability metrics are evaluated for the counter example
presented in Section 2.3. Next, the case study of a plastic waste collection bag filled with
plastic bottles is introduced, and multilevel SEA and the proposed extension of multilevel
SEA are applied to this case study. To conclude this section, the potential of the proposed
extension of multilevel SEA for plastic waste recycling is discussed.
3.1. Assumptions for the Calculation of Decomposition Energies
Although the relative statistical entropy difference between a waste collection bag
with different monolayer labels versus a bag with multilayer label bottles can be quite small
(even zero in the counter example introduced in Section 2.3), we know intuitively that
multilayer plastic composites are much harder to recycle. Indeed, the various layer materi-
als are often chemically incompatible, limiting the potential for mechanical recycling [
43
].
Disentangling the layers in order to lower the relative statistical entropy of a component or
product would require custom technologies such as selective dissolution–precipitation [
43
],
delamination [44] or selective hydrolysis of one of the constituting substances [45].
Sorting and pretreating polymers, employing techniques such as washing, shredding,
grinding, sink–float and near-infrared separations, reduces the statistical entropy of a collec-
tion of plastic waste objects, such as the components and subcomponents (bottles, labels and
caps) of the exemplary collection bags. Altogether, with a uniform allocation, such sorting
is responsible for about 0.36 MJ energy consumption per kg of plastic [
22
]. In order to get to
recycled pellets via mechanical recycling, an additional 0.32 MJ/kg energy is required [
46
],
leading to a total energy requirement of 0.68 MJ/kg. When multilayer labels are present, to
achieve approximately the same relative statistical entropy level, the polylactic acid (PLA)
of the labels should be selectively dissolved, corresponding to an energy consumption of
1.23 MJ/kg (0.36 MJ/kg (Faraca et al., 2019) [
22
] + 0.87 MJ/kg (Maga et al., 2019) [
46
])).
Note that these numbers are an estimate based on the literature and are only for illustration
purposes. In addition, the case studies in this contribution are rather simple and do not
account for the complexity of the constituents of the components and their mixtures. In
practice, this can have implications for the effective decomposition energies.
The maximum decomposition energy has been defined as the energy that is needed
to produce all virgin substances present per kg of the product (in this case, the plastic
bag). Three substances (PET, PE and PLA) are considered in this contribution, and the
energies needed to produce the virgin materials have been assumed based on the literature:
83 MJ/kg for PET [47], 76 MJ/kg for PE [48] and 58.9 MJ/kg for PLA [49].
Sustainability 2021,13, 3553 14 of 21
3.2. Recyclability Metrics for the Counter Example
Consider the counter example from Section 2.3 in which we have two types of compo-
nents which are equal in substance composition (both having a relative statistical entropy
of 0.500), but where one component consists of 100% monolayers and the other of 100%
multilayers. Assuming that the substance A is PE, B is PET and C is PLA and that the mul-
tilayer components are selectively dissolved, the following decomposition energies can be
calculated:
Emax
= 73.7 MJ/kg,
Emono
= 0.68 MJ/kg,
Emono
rel =
0.00923,
Emulti = 1.23 MJ/kg
and
Emulti
rel
= 0.0167. The values of the recyclability metrics for the monolayer and multilayer
components are depicted in Table 4.
Table 4.
Values of the recyclability metrics and difference between the recyclability metrics for the
monolayer and multilayer components in the counter example.
R(1)
nR(2)
n
Monolayer 0.495 54.2
Multilayer 0.492 29.9
Monolayer–Multilayer 0.003 24.3
From Table 4it can be seen that both recyclability metrics are higher for the monolayer
component than for the multilayer component, reflecting that the monolayer components
are easier to recycle than the multilayer components (as expected). However, the difference
between the recyclability metrics of the monolayer and multilayer components is more
pronounced in
R(2)
n
than in
R(1)
n
. Therefore, we consider the second recyclability metric
R(2)
n
as being more attractive than the first one
R(1)
n
in terms of quantifying the effect of
decomposition energy on recyclability.
In the next section, a plastic waste collection bag filled with plastic bottles is studied
as a more complex system. This waste stream differs from the counter example, in the
sense that the plastic bottles are very similar and only differ in the composition of the
labels and the way these labels are constructed (i.e., monolayers versus multilayers). Both
recyclability metrics are compared to see whether these are capable of capturing the slight
difference in recyclability.
3.3. Case Study: Plastic Waste Collection Bag Filled with Plastic Bottles
As a case study, a simplified plastic waste collection bag filled with plastic bottles (the
product for this case study) has been studied, as illustrated in Figure 4. Three types of
components are considered: a plastic bottle with a monolayer PLA label (referred to as
monolayer PLA bottle), a plastic bottle with a monolayer PE label (referred to as monolayer
PE bottle) and a plastic bottle with a multilayer PLA and PE label (referred to as multilayer
PLA bottle). Five materials are present in the studied system: a bottle cap, bottle material,
monolayer PLA label, monolayer PLA label, multilayer PLA and PE label. Four substances
are considered: PET, PLA, PE and X (an adhesive component that can be present on the
label). It should be noted that this example is hypothetical and does not represent common
bottle labels.
The concentrations of the substances in the components and products are summarized
in Table 5. The concentrations of the materials in the components and the concentrations of
the components in the product are summarized in Table 6.
Sustainability 2021,13, 3553 15 of 21
Figure 4. Illustration of the plastic waste collection bag filled with plastic bottles.
Table 5.
Concentrations of substances in the components and product for plastic waste collection bag
filled with plastic bottles.
PET PE PLA X
Components
Monolayer bottle (PLA) 0.8 0.05 0.145 0.005
Monolayer bottle (PE) 0.8 0.145 0.05 0.005
Multilayer bottle (PLA and PE) 0.8 0.0975 0.0975 0.005
Product Blue bag 0.8 0.0975 0.0975 0.005
Table 6.
Concentrations of materials in the components and the concentrations of the components in the product for the
plastic waste collection bag filled with plastic bottles.
Bottle
Cap
Monolayer Label
(PLA)
Bottle
Material
Multilayer
Label
Monolayer Label
(PE)
Mass Fraction in
Product
Monolayer bottle (PLA) 0.1 0.1 0.8 0 0 0.25
Monolayer bottle (PE) 0.1 0 0.8 0 0.1 0.25
Multilayer bottle (PLA and PE) 0.1 0 0.8 0.1 0 0.5
3.3.1. Multilevel SEA Results
Based on the data in Tables 5and 6, the component-level and product-level relative
statistical entropies can be calculated. The results are depicted in Table 7. The component-
level relative statistical entropy value of the multilayer bottle is higher (0.5) compared to
the monolayer bottles (0.241). This is due to two factors: (i) the number and total mass of
multilayer bottles is higher than the number of monolayer bottles (PLA) and monolayer
bottles (PE) individually, and (ii) the multilayer bottle has a label that consists of PE, PLA
and X, while the monolayer bottles only have a label that consists of PE and X or PLA and X.
Note that, although the sum of the masses of the two monolayer bottle components equals
the mass of the multilayer bottle components, the sum of the component-level relative
statistical entropies of the monolayer bottles is still lower than the relative statistical entropy
of the multilayer bottle due to the difference in the composition of the label.
As a first variation on this case study, the relative statistical entropies are calculated in
the case that no PE monolayer bottles were present in the bag and four PLA monolayer
bottles and four multilayer bottles were present in the bag. The relative statistical entropy
of the multilayer bottle remains unchanged. However, the relative statistical entropy of
the monolayer bottle (PLA) changes to 0.486, which is close to the value of 0.504 for the
multilayer bottle. The slight difference in component-level relative statistical entropy is
Sustainability 2021,13, 3553 16 of 21
caused by the label composition. However, the product-level relative statistical entropy
decreases from 0.488 to 0.33 as the number of distinct components has reduced.
Table 7.
Component-level and product-level relative statistical entropies for the plastic waste collec-
tion bag filled with plastic bottles.
Relative Statistical Entropy
Monolayer bottle (PLA) 0.241
Monolayer bottle (PE) 0.241
Multilayer bottle (PLA and PE) 0.5
Plastic bag (product) 0.488
A second variation is the situation in which the bag is only filled with eight multilayer
bottles. In this situation, the product consists of only one type of component, rendering the
concept of product-level relative statistical entropy much less useful. The component-level
relative statistical entropy is at its maximum value of 1, as all substances are concentrated
in the same manner in the different components.
A third variation is the situation in which the bag is only filled with four monolayer
bottles (PLA) and four monolayer bottles (PE). In this case, the component level entropies
equal 0.482. The product-level relative statistical entropy changes to 0.32, which is close to
the product-level relative statistical entropy of the first variation.
In essence, the multilayer presence does not dramatically increase the relative statis-
tical entropy, whereas the recyclability of multilayers is clearly dramatic. This appears
especially from the comparison of variation 1 and variation 3.
3.3.2. Extending the SEA Results with Energy Considerations
The assumptions from Section 3.1 are followed when calculating the relative decom-
position energies. Since the labels account for 10% of the total mass in the collection bags
in our example, the additional energy requirement to achieve a similar statistical entropy
is thus 4% higher for the first variation (half of the bottles having multilayer labels) and
8% higher for the second variation (all bottles having multilayer labels). If hydrolysis
(Maga et al., 2019) [
46
] is used instead of dissolution–precipitation, these numbers would
change to 7% and 14%, respectively. Note that these numbers are an authors’ estimate and
are only for illustration purposes.
Consider the plastic waste collection bag filled with four monolayer PLA bottles and
four multilayer bottles (i.e., the first variation with component-level relative statistical
entropies of 0.488 and 0.500, respectively). If we consider recyclability at the component
level, we study the relative statistical entropy at the component level and the relative
decomposition energy at the component level. This means that, for the relative decompo-
sition energies, the relative decomposition energy of a monolayer bottle and the relative
decomposition energy of a multilayer bottle are calculated for the recyclability metrics. If
we consider the selective dissolution of the multilayer labels, we can conclude from the pre-
vious paragraph that 8% more energy is needed to recycle a multilayer bottle compared to
a monolayer bottle. This would lead to the expressions of the proposed recyclability metric
at the component level being
Rmono
and
Rmulti
, where
Emono
rel
is the relative decomposition
energy of a monolayer PLA bottle:
Rmono =(1−0.486)(1−Emono
rel )(31)
Rmulti =(1−0.504)(1−1.08Emono
rel )(32)
For the monolayer PLA bottle, we assume that it is decomposed by a sorting and
pretreatment step, followed by a mechanical recycling step. For this situation, we calculated
a total energy requirement of 0.68 MJ kg
−1
[
22
,
46
]. For substance X, we assume no energy
requirement, as it is not considered to be a valuable raw substance in this case study. In the
first variation, four monolayer PLA bottles and four multilayer bottles are present in the
Sustainability 2021,13, 3553 17 of 21
product. The substance concentrations and the substance masses in the bag filled with four
monolayer PLA bottles and four multilayer bottles (first variation of the case study) are
summarized in Table 8. Note that the total mass of the product equals 0.2 kg.
Table 8.
Concentrations and masses of substances in the product for the first variation of the plastic
waste collection bag (filled with four monolayer PLA bottles and four multilayer bottles.
PET PE PLA X
Concentration (-)
0.8 0.074 0.121 0.005
Mass (kg) 0.16 0.015 0.024 0.001
The maximum decomposition energy for the first variation can be calculated by
combining Equation
(24)
with the substance masses depicted in Table 8and the ener-
gies needed to produce the virgin materials. This results in
Emax
= 79.1 MJ/kg and
Emono
rel =0.00860 and Emulti
rel =0.00928 and in the values presented in Table 9.
Table 9.
Values of the recyclability metrics and difference between the recyclability metrics for the
first variation of the plastic waste collection bag (filled with four monolayer PLA bottles and four
multilayer bottles.
R(1)
nR(2)
n
Monolayer PLA bottle 0.510 59.8
Multilayer bottle 0.491 53.4
Monolayer PLA bottle—Multilayer bottle 0.019 6.4
Both recyclability indicators in Table 9indicate a slightly easier recyclability of the
monolayer PLA bottles compared to the multilayer bottles. However, the first recyclability
metric shows a substantial difference of 0.019. This is counterintuitive when comparing
this with the difference in the counter example of 0.003 for the first recyclability metric.
This would imply that the difference in recyclability between the two types of bottles is
higher than the difference in recyclability between the monolayers and the multilayers in
the counter example. The decomposition energy contribution seems undervalued when
using the first recyclability metric
R(1)
n
. Comparing the difference in recyclability between
the monolayers and the multilayers in this case study and the counter example gives more
expected results. The monolayers are substantially easier to recycle than the multilayers
in the counter example (a difference of 24.3 in
R(2)
n
), while the monolayer PLA bottles
and multilayer bottles differ less in recyclability (difference of 6.4 in
R(2)
n
) for the second
recyclability metric. The results for
R(2)
n
correspond more with what is expected intuitively,
as the monolayer bottle and the multilayer bottle only differ in terms of the labels (which is
only 10% of the bottle mass), which explains the small difference in recyclability. Based on
this reasoning, we consider the second recyclability metric
R(2)
n
as being most suited to the
proposed recyclability metrics in this contribution.
It should be stressed that different options exist to define recyclability metrics based
on relative statistical entropy and relative decomposition energies. One option would be to
use a recyclability metric in which the relative statistical entropy is put in the denominator
(for instance,
(1−Ec
n,rel (π,ηc
m,ηc
i))
Hc
n,rel (ci,n,mc
n)
for the component level) or both relative decomposition
energy and relative statistical entropy are put in the denominator (
1
Hc
n,rel (ci,n,mc
nEc
n,rel (π,ηc
m,ηc
i)
).
Another option could be to define the maximum decomposition energy in another way; an
option could be to define the maximum decomposition energy as the maximum energy
from a group of currently existing/considered recycling processes that is needed to achieve
the required decomposition efficiencies. For the examples elaborated in this paper, this
would correspond with the energy needed for a hydrolysis process. However, this would
Sustainability 2021,13, 3553 18 of 21
be a definition that is less generic. In future work, different definitions of recyclability
metrics using the concepts of relative statistical entropy and relative decomposition energy
will be studied with real life case studies, and it will be assessed whether these can be
computed in a generic and practical way (i.e., whether the information needed to compute
these can be made available in a relatively easy manner).
3.4. Potential for Plastic Waste Recycling
Different pathways exist to recycle plastic waste, which are typically subdivided into
mechanical and chemical recycling processes. A recent review on the current state of the art
processes for solid plastic waste recycling has been presented by Ragaert et al., (2017) [
50
].
The different mechanical recycling steps that are typically needed to separate plastic waste
collection bags into their different plastic components can be summarized as follows [
50
]:
(s) bag opening/cutting, (ii) separation by size (progressive rotating sieve), (iii) blowing
out of loose contents (labels or bags) with wind sifters, (iv) removal of ferrous materials by
an overhead magnet, (v) removal of cartons by optical sorting, (vi) removal of non-ferrous
metals (e.g., aluminum) with eddy currents and (vii) removal of soft plastics (e.g., foils)
using a ballistic separator. The authors stress that, in this contribution, a simplified situation
has been studied in which the plastic waste collection bag only contains bottles, while in
practice other plastic packaging objects, such as trays, foils and bags, are present [
37
]. In
addition, it is clear that a substantial number of process steps (and an associated substantial
energy consumption) are needed.
Multilayer plastics are widely used (e.g., in food packaging applications) as the
properties of different raw materials can be combined to optimize performance with
respect to the packaging requirements (e.g., preventing contaminations, serving as an
oxygen barrier and extending shelf life). The review of Kaiser et al., (2018) [51] addressed
the recycling of multilayer plastic packaging by making a distinction between (i) methods
that separate multilayer plastic packaging into its constituting components (delamination
and selective dissolution precipitation) and (ii) compatibilization, wihch processes the
mixture in one step. The delamination of multilayer plastics is challenging and complex,
making the separation costly and time-consuming, and the recycled material is often of
low quality. Therefore, another option is to avoid separating the multilayer plastic waste
into its separate components but instead blend the polymer. Typically, compatibilization
is applied, in which a compatibilizer (e.g., a graft or block copolymer) is used to improve
the miscibility of the overall blend, reducing the energy requirements. Compatibilization,
typically achieved in a rather well-defined extrusion process, results in a system with a
high entropy state. However, the energy needed to reduce the entropy in a delamination
process might be too high.
Reactive extrusion and multiphase blending with extrusion technology is currently
being developed to combine the recycling of polymers or plastic waste and synthesize
new polymers or plastic products [
52
–
54
]. Similarly, reactive extrusion typically keeps the
system at a high relative statistical entropy state but offers benefits from an energetic point
of view compared with other technologies (that aim at reducing the entropy) for the same
waste stream. This feature makes reactive extrusion an interesting application that can be
analyzed with the proposed extension in this contribution. Therefore, in future work, the
extended multilevel statistical entropy methodology will be further developed and applied
to support the development of reactive extrusion technology.
The proposed methodology in this paper, in which multilevel statistical entropy
analysis has been extended with energy consumption aspects, can be used to evaluate
these different recycling options from a recyclability point of view. However, in terms of
sustainable plastic waste treatment, additional aspects need to be addressed. Therefore, the
authors see opportunities to integrate the proposed extended multilevel statistical entropy
analysis methodology with energy consumption aspects in a multi-objective environmental
techno-economic assessment framework [55].
Sustainability 2021,13, 3553 19 of 21
Other perspectives for future work are the refinement of the proposed recyclability
metric and the inclusion of energy consumption aspects, the application of the proposed
methodology to real-life plastic products and plastic waste streams and integration of
different levels of entropy (e.g., at the molecular and geographical level).
4. Conclusions
In this paper, the multilevel statistical entropy analysis (SEA) method has been re-
viewed and discussed in the context of evaluating the recyclability of plastics. We have
illustrated how the concept of multilevel SEA can be extended to allow the assessment
of the recyclability of plastics based on a conceptual example of a fictitious plastic bag.
As a potential avenue to assess the recyclability of plastics, we proposed an extension
of multilevel SEA with energy consumption aspects (relative decomposition energy) to
formulate recyclability metrics for components and products. In other words, we took into
account the energy required to reduce the relative statistical entropy of components or
products. This methodology has been applied to the case study of a plastic waste collection
bag. This paper explored which aspects play a role in recyclability and which options exist
to quantify this. Future work will involve further refinement using realistic case studies as
well as complex processes such as reactive extrusion.
Author Contributions:
Conceptualization, P.N., A.P., P.D.M. and P.B.; methodology, P.N. and A.P.;
software, P.N., A.P., P.B.; validation, P.N., A.P. and P.B.; formal analysis, P.N., A.P. and P.B.; investiga-
tion, P.N. and P.B.; writing—original draft preparation, P.N. and P.B.; writing—review and editing,
P.N., A.P., P.D.M., D.R.D., P.H.M.V.S., H.R. and P.B.; visualization, P.N.; supervision, H.R. and P.B. All
authors have read and agreed to the published version of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Data is contained within the article.
Conflicts of Interest: The authors declare no conflict of interest.
References
1. MMAtwo Project. Available online: https://www.mmatwo.eu/ (accessed on 11 February 2021).
2. CIRC-PACK Project. Available online: https://www.circpack.eu/ (accessed on 11 February 2021).
3. iCAREPLAST Project. Available online: https://www.icareplast.eu/ (accessed on 11 February 2021).
4. MultiCycle Project. Available online: http://multicycle-project.eu/ (accessed on 11 February 2021).
5. PlastiCircle Project. Available online: https://www.plasticircle.eu/ (accessed on 11 February 2021).
6. PolyCE Project. Available online: https://www.polyce-project.eu/ (accessed on 11 February 2021).
7. PolynSPIRE Project. Available online: https://www.polynspire.eu/ (accessed on 11 February 2021).
8. ResolVe Project. Available online: https://depolymerisation.com/ (accessed on 11 February 2021).
9. PLASTECO Project. Available online: https://www.interregeurope.eu/plasteco/ (accessed on 11 February 2021).
10.
BIOCOMPACK-CE Project. Available online: https://www.interreg-central.eu/Content.Node/BIOCOMPACK-CE.html (ac-
cessed on 11 February 2021).
11.
MATTER Project. Available online: https://catalisti.be/project/sidestream-valorization/matter/ (accessed on 11 February 2021).
12. P2PC Project. Available online: https://catalisti.be/project/sidestream-valorization/p2pc/ (accessed on 11 February 2021).
13.
European Commission. Communication from the Commission to the European Parliament, the Council, the European Economic and Social
Committee and the Committee of the Regions A European Strategy for Plastics in a Circular Economy; COM/2018/028 final; European
Commission: Brussels, Belgium, 2018.
14.
European Commission. Directive (EU) 2019/904 of the European Parliament and of the Council. On the Reduction of the Impact of Certain
Plastic Products on the Environment; European Commission: Brussels, Belgium, 2019.
15.
Gall, M.; Schweighuber, A.; Buchberger, W.; W. Lang, R. Plastic Bottle Cap Recycling—Characterization of Recyclate Composition
and Opportunities for Design for Circularity. Sustainability 2020,12, 378. [CrossRef]
16.
Peeters, J.R.; Vanegas, P.; Dewulf, W.; Duflou, J.R. Economic and environmental evaluation of design for active disassembly.
J. Clean. Prod. 2017,140, 1182–1193. [CrossRef]
17.
Vanegas, P.; Peeters, J.R.; Cattrysse, D.; Tecchio, P.; Ardente, F.; Mathieux, F.; Dewulf, W.; Duflou, J.R. Ease of disassembly of
products to support circular economy strategies. Resour. Conserv. Recycl. 2018,135, 323–334. [CrossRef] [PubMed]
18.
Radusin, T.; Nilsen, J.; Larsen, S.; Annfinsen, S.; Waag, C.; Eikeland, M.S.; Pettersen, M.K.; Fredriksen, S.B. Use of recycled
materials as mid layer in three layered structures-new possibility in design for recycling. J. Clean. Prod.
2020
,259, 120876.
[CrossRef]
Sustainability 2021,13, 3553 20 of 21
19.
Ragaert, K.; Hubo, S.; Delva, L.; Veelaert, L.; Du Bois, E. Upcycling of contaminated post-industrial polypropylene waste: A
design from recycling case study. Polym. Eng. Sci. 2018,58, 528–534. [CrossRef]
20.
Gradus, R. Postcollection Separation of Plastic Recycling and Design-For-Recycling as Solutions to Low Cost-Effectiveness and
Plastic Debris. Sustainability 2020,12, 8415. [CrossRef]
21.
Buyle, M.; Audenaert, A.; Billen, P.; Boonen, K.; Van Passel, S. The Future of Ex-Ante LCA? Lessons Learned and Practical
Recommendations. Sustainability 2019,11, 5456. [CrossRef]
22.
Faraca, G.; Martinez-Sanchez, V.; Astrup, T.F. Environmental life cycle cost assessment: Recycling of hard plastic waste collected
at Danish recycling centres. Resour. Conserv. Recycl. 2019,143, 299–309. [CrossRef]
23.
Foschi, E.; Zanni, S.; Bonoli, A. Combining Eco-Design and LCA as Decision-Making Process to Prevent Plastics in Packaging
Application. Sustainability 2020,12, 9738. [CrossRef]
24.
Eriksen, M.; Christiansen, J.; Daugaard, A.; Astrup, T. Closing the loop for PET, PE and PP waste from households: Influence of
material properties and product design for plastic recycling. Waste Manag. 2019,96, 75–85. [CrossRef]
25.
Fiorio, R.; D’hooge, D.R.; Ragaert, K.; Cardon, L. A Statistical Analysis on the Effect of Antioxidants on the Thermal-Oxidative
Stability of Commercial Mass- and Emulsion-Polymerized ABS. Polymers 2019,11, 25. [CrossRef] [PubMed]
26.
Paletta, A.; Leal Filho, W.; Balogun, A.L.; Foschi, E.; Bonoli, A. Barriers and challenges to plastics valorisation in the context of a
circular economy: Case studies from Italy. J. Clean. Prod. 2019,241, 118149. [CrossRef]
27.
Alassali, A.; Barouta, D.; Tirion, H.; Moldt, Y.; Kuchta, K. Towards a high quality recycling of plastics from waste electrical and
electronic equipment through separation of contaminated fractions. J. Hazard. Mater. 2020,387, 121741. [CrossRef] [PubMed]
28.
Rechberger, H.; Brunner, P.H. A New, Entropy Based Method To Support Waste and Resource Management Decisions. Environ. Sci.
Technol. 2002,36, 809–816. [CrossRef] [PubMed]
29.
Rechberger, H.; Graedel, T. The contemporary European copper cycle: Statistical entropy analysis. Ecol. Econ.
2002
,42, 59–72.
[CrossRef]
30. Yue, Q.; Lu, Z.; Zhi, S. Copper cycle in China and its entropy analysis. Resour. Conserv. Recycl. 2009,53, 680–687. [CrossRef]
31.
Laner, D.; Zoboli, O.; Rechberger, H. Statistical entropy analysis to evaluate resource efficiency: Phosphorus use in Austria.
Ecol. Indic. 2017,83, 232–242. [CrossRef]
32.
Zeng, X.; Li, J. Measuring the recyclability of e-waste: an innovative method and its implications. J. Clean. Prod.
2016
,131, 156–162.
[CrossRef]
33.
Velázquez Martínez, O.; Van Den Boogaart, K.; Lundström, M.; Santasalo-Aarnio, A.; Reuter, M.; Serna-Guerrero, R. Statistical
entropy analysis as tool for circular economy: Proof of concept by optimizing a lithium-ion battery waste sieving system. J. Clean.
Prod. 2019,212, 1568–1579. [CrossRef]
34.
Wang, X.; Miao, J.; You, S.; Ren, N. Statistical entropy analysis as a proxy method for quantitative evaluation of phosphorus of a
food-based bioethanol system. Resour. Conserv. Recycl. 2021,164, 105125. [CrossRef]
35.
Parchomenko, A.; Nelen, D.; Gillabel, J.; Vrancken, K.C.; Rechberger, H. Evaluation of the resource effectiveness of circular
economy strategies through multilevel Statistical Entropy Analysis. Resour. Conserv. Recycl. 2020,161, 104925. [CrossRef]
36.
Roithner, C.; Rechberger, H. Implementing the dimension of quality into the conventional quantitative definition of recycling
rates. Waste Manag. 2020,105, 586–593. [CrossRef] [PubMed]
37.
Roosen, M.; Mys, N.; Kusenberg, M.; Billen, P.; Dumoulin, A.; Dewulf, J.; Van Geem, K.M.; Ragaert, K.; De Meester, S.
Detailed Analysis of the Composition of Selected Plastic Packaging Waste Products and Its Implications for Mechanical and
Thermochemical Recycling. Environ. Sci. Technol. 2020,54, 13282–13293. [CrossRef] [PubMed]
38.
Kleinhans, K.; Hallemans, M.; Huysveld, S.; Thomassen, G.; Ragaert, K.; Van Geem, K.M.; Roosen, M.; Mys, N.; Dewulf, J.;
De Meester, S. Development and application of a predictive modelling approach for household packaging waste flows in sorting
facilities. Waste Manag. 2021,120, 290–302. [CrossRef] [PubMed]
39. Shannon, C. A mathematical theory of communication, I and II. Bell Syst. Tech. J. 1948,27, 379–423. [CrossRef]
40. Shannon, C. A mathematical theory of communication, III–V. Bell Syst. Tech. J. 1948,27, 623–656. [CrossRef]
41. Shannon, C.; Weaver, W. The Mathematical Theory of Communication, 7th ed.; University of Illinois Press: Urbana, IL, USA, 1949.
42.
Rechberger, H. Entwicklung einer Methode zur Bewertung von Stoffbilanzen in der Abfallwirtschaft. Ph.D. Thesis, TU Wien,
Vienna, Austria, 1999.
43.
Walker, T.W.; Frelka, N.; Shen, Z.; Chew, A.K.; Banick, J.; Grey, S.; Kim, M.S.; Dumesic, J.A.; Van Lehn, R.C.; Huber, G.W. Recycling
of multilayer plastic packaging materials by solvent-targeted recovery and precipitation. Sci. Adv. 2020,6. [CrossRef]
44.
Ügdüler, S.; De Somer, T.; Van Geem, K.M.; Roosen, M.; Kulawig, A.; Leineweber, R.; De Meester, S. Towards a better
understanding of delamination of multilayer flexible packaging films by carboxylic acids. ChemSusChem 2021. [CrossRef]
45.
Ügdüler, S.; Van Geem, K.M.; Denolf, R.; Roosen, M.; Mys, N.; Ragaert, K.; De Meester, S. Towards closed-loop recycling of
multilayer and coloured PET plastic waste by alkaline hydrolysis. Green Chem. 2020,22, 5376–5394. [CrossRef]
46.
Maga, D.; Hiebel, M.; Thonemann, N. Life cycle assessment of recycling options for polylactic acid. Resour. Conserv. Recycl.
2019
,
149, 86–96. [CrossRef]
47. Gleick, P.; Cooley, H.S. Energy implications of bottled water. Environ. Res. Lett. 2009,4, 014009. [CrossRef]
48. Boustead, I. Eco-profiles of the European Plastics Industry: High density polyethylene (HDPE). PlasticsEurope 2005.
Sustainability 2021,13, 3553 21 of 21
49.
Guo, Q.; Crittenden, J. An energy analysis of polylactic acid (PLA) produced from corn grain and corn stover integrated system.
In Proceedings of the 2011 IEEE International Symposium on Sustainable Systems and Technology, Chicago, IL, USA, 16–18 May
2011; pp. 1–5. [CrossRef]
50.
Ragaert, K.; Delva, L.; Van Geem, K. Mechanical and chemical recycling of solid plastic waste. Waste Manag.
2017
,69, 24–58.
[CrossRef]
51.
Kaiser, K.; Schmid, M.; Schlummer, M. Recycling of Polymer-Based Multilayer Packaging: A Review. Recycling
2018
,3, 1.
[CrossRef]
52. Moad, G. The synthesis of polyolefin graft copolymers by reactive extrusion. Prog. Polym. Sci. 1999,24, 81–142. [CrossRef]
53.
Hernández-Ortiz, J.C.; Van Steenberge, P.H.M.; Duchateau, J.N.E.; Toloza, C.; Schreurs, F.; Reyniers, M.F.; Marin, G.B.; D’hooge,
D.R. The Relevance of Multi-Injection and Temperature Profiles to Design Multi-Phase Reactive Processing of Polyolefins.
Macromol. Theory Simul. 2019,28, 1900035. [CrossRef]
54.
Wang, S.; Daelemans, L.; Fiorio, R.; Gou, M.; D’hooge, D.R.; De Clerck, K.; Cardon, L. Improving Mechanical Properties
for Extrusion-Based Additive Manufacturing of Poly(Lactic Acid) by Annealing and Blending with Poly(3-Hydroxybutyrate).
Polymers 2019,11, 1529. [CrossRef]
55.
Thomassen, G.; Van Dael, M.; You, F.; Van Passel, S. A multi-objective optimization-extended techno-economic assessment:
Exploring the optimal microalgal-based value chain. Green Chem. 2019,21, 5945–5959. [CrossRef]