- Email: [email protected]
A model of plastics recycling: Does recycling reduce the amount of waste?
resources,
Resources, Conservation and Recycling 17 (1996) 141-151
ELSEVIER
conservation and recycling
A model of plastics recycling: does recycling reduce the amount of waste? Brenton L. Fletcher, Michael E. Mackay* Department of Chemical Engineering, The University of Queensland, Brisbane 4072, Queensland, Australia
Received 3 March 1995;revision received 19 July 1995;accepted 27 July 1995 Ab.ShCt
A model for recycling plastics is made to ‘phase in’ recycling over a given period. The recycled plastic can either replace virgin plastic or enter a new market where plastics are not normally used. The former is denoted as ‘true recycling’and the latter, ‘newmarket recycling’. It is shown that ‘true recycling’will eventually reduce the amount of waste by the same amount of plastic that is recycled. On the other hand, ‘new market recycling’will not reduce the amount of plastic waste and after a given period the overall result is that there is no effect on the amount of plastic waste generated. This is due to the fact that plastics in general have a finite lifetime. Keywords:Plastic; Plastic recycling; Municipal solid waste; Waste reduction
1. IntroduetIon
Australia produces approximately 1 million tonnes of plastic resins annually. Of this, 450 000 tonnes are discarded in landfill waste sites throughout the country and represents between 5 and 15% of the total weight of the landfill waste stream [l]. There are 50 million tonnes of plastic resin produced per annum in the world, however, the total amount recycled is difficult to quantify. The high volume to weight ratio of plastics means that on a volume basis, plastics represent between 10 and 30% of waste going to landfill. The volume of plastics in landfill is difficult to quantify since the amount of compaction has a definite impact on figures quoted in the literature. It is difficult to ascertain whether these volume Corresponding author.
??
0921-3449196/$15.000 1996 Elsevier Science B.V. All rights reserved PII 0921-3449(96)01068-3
142
B.L. Fletcher, ME.
Mackay/
Resources, Conservation and Recycling 17 (19%)
141-151
figures are based on uncompacted material, material that has been compacted once in the garbage truck, or material that has been further compacted by heavy machinery at the landfill site. In addition, the methods used for compaction of rubbish vary between landfill sites. Therefore, volume figures quoted tend to have a large uncertainty. Landfill sites tend to ‘fill up’ rather than become ‘overweight’ [2], so, the volume occupied by plastics in landfills should represent reasonable concern. Targets have been set by various organisations in an attempt to reduce waste problems. At the end of this decade, the Commonwealth Environmental Protection Agency (CEPA) wishes to reduce total municipal solid waste (MSW) by 50%, the Australian and New Zealand Environment and Conservation Council (ANZECC) aims to reduce packaging waste by 50% in a similar time, and KEMCOR, the supplier of 90% of the high density polyethylene (HDPE) used for milk packaging in Australia, has set a target of reducing the amount of HDPE sent to landfill by 50% 131.This follows the worldwide trend of various organisations that have sent similar goals. Approaches to address the problem of plastic waste have included recycling. In house recycling of industrial scrap waste has long been practiced at a high percentage by the plastics industry. However, recycling of household plastic waste has been virtually non-existent. Plastics recovered from household waste in 1989 represented only 0.4% of plastic consumed in households in Australia [l]. The recent introduction of curbside recycling bins concentrating mainly on the collection of polyethyleneterephthalate (PET) and HDPE beverage bottles and a small amount of polypropylene (PP), has definitely increased the level of plastics recycling. Currently, approximately 60 000 tonnes of plastic are recycled throughout Australia representing 6% of what is produced annually. @LB.: The percentage of plastic recycled could be much lower since many plastic articles are imported.) Victoria is the leading state regarding recycling and accounts for 60% of all recycling operations [3]. As more bins are distributed into the community and people become more educated in recycling, the amount of plastic recycled will inevitably increase in the following years. Ironically though, efforts to increase the amount of recycling are retarded by the lack of established markets for the reprocessed products [3]. Plastics recycling, as an industry, faces a number of hurdles before establishing itself as an effective means of reducing the amount of plastic waste contributing to landfill and litter problems. Currently, the level of recycling occurring in the household waste sector is not high enough to provide an appreciable effect on the problem of plastic waste. Solid markets for the recycled and reprocessed products are yet to be secured as a result of economic, technological and institutional barriers. How effective is recycling plastic waste, and how effective can it be? This paper attempts to address the feasibility of plastics recycling using a mass balance for the flow of plastics in our society. 2. Development of tbe model Three quarters of the plastic consumed in Australia are used in long life applications [3] while the remainder is used for packaging requirements. This is identical
B.L. Fletcher, M. E. Mackay/Resources,
Conservation and Recycling 17 (19%)
141-151
143
to the world average. The short one trip lifetime of plastic packaging leads it to be the major contributor to the problem of plastic waste and litter, and consequently plastic packaging is the focus of most household recycling efforts. However, when plastic packaging is recycled, it is reprocessed into items other than for direct food contact applications due to stringent regulations. In effect, this means that an entirely new market is created for this type of recycled and reprocessed plastic. Products currently processed from recycled plastics include garbage bins, crates, piping, pip ing joints and structural items for timber and concrete alternatives (these products are not necessarily made from recycled packaging). Recycled plastics are not regulated to be used for certain products, with the exception of direct food contact applications, so, the products made from recycled plastics can penetrate markets where virgin plastic is not used. This, in effect, increases the total market for plastics. Infinite recycling of plastic is technically impossible since the molecules degrade during repeated processing and places a finite lifetime on plastics. The model introduced below takes into account these two phenomena and is used to determine whether recycling plastics reduces the amount of plastic waste which eventually reaches landfill. A schematic for the general recycling scheme is shown in Fig. 1. Units for each symbol have either dimensions of mass (A4)or mass per unit time (MB). Plastic products leave the virgin market, M&W), at a rate of@/@ where without recycling become unaccounted waste at a rate, Uv (MO), or reach landfill at a rate, WV (MB). Unaccounted waste represents litter, exported products or products used in long term applications, such as electrical conduit in buildings, which will eventually reach landfill. The size of the virgin market is assumed constant here and the average
Fig. 1. Schematic of the genera&d recycling scheme.
144
B.L. Fletcher. ME.
Mackay/ Resources, Conservation and Recycling 17 (19%)
141-151
life time of the products is assumed to be equal to tav. We can write this mathematically as,
-Mv =
tRV
f
where in engineering terms tav is the mean residence time in the market (or really the mean time a consumer uses a product before discarding it). Because the virgin market is assumed constant in size and the products have a finite lifetime the rate plastics leave the market is always constant regardless of whether recycling occurs or not (Eq. 1). If recycling is introduced at a rate, R (M/O), then not all the waste is immediately discarded. The recycling rate is assumed to be a fraction of the rate plastic leaves the virgin market, xa. In addition, the rate of recycling is assumed to be ‘phased in’ with a time constant, tP, which is written as, R = x&l
-
e%]
However, the target recycling rate will be essentially reached after sufficient time. Other mathematical expressions could be used rather than the exponential, however, the type of expression does not affect any of our general conclusions. The recycled plastic can either be put back into the virgin market at a rate, RV(A4/O),or into a new market for recycled plastics, Ma(M), at a rate of RR(MM). If the recycled plastic is put back into the virgin market then it will be combined with the plastic fabricated at a rate, F(MA9).On the other hand, if the plastic enters the new recycled plastics market then it will eventually leave this market at a rate, r(M/8), when the product breaks or is no longer useful. We do not assume the recycled plastic in Ma can be recycled again after leaving this market since the products will be of such a type that inhibits repeated recycling. Examples of these products are mixed plastic waste used to make benches, posts and the like where the original raw material is replaced by the recycled plastic (the original raw material may be wood or metal, for example). The product becomes unaccounted waste generated at a rate, &@f/e), or directly reaches landfill at a rate, &(M/@. Our model could be relined to include the possibility of recycling the products leaving Ma. Yet, this would only serve to create a very complicated model with little benefit and will also not affect the general conclusions we draw below. The fraction of recycled plastic, ya, that reaches Ma is written as,
R R=YRR The lifetime of plastics in Ma is written similar to that for virgin plastics in Es. 1,
B.L. F’lercker. M.E. Mackay/
Resources, Conservation and Recycling 17 (1996) 141-151
145
where tan represents the mean lifetime of a recycled plastic product in this market. Referring to Fig. 1 the mass balances over the various subsystems as well as the entire system are, I:
dMv -=G-f
dt
II:
d&t -=RR-r dt
III:
d& -=Fdt
WV-
IV: f=R+
WV+ U,
V:
VI:
VII:
WR-
Uv .- VR=F-T
R = RR + Rv
t =
w, + u,
F + R, = G
where M&W) is the total plastic market (= Mv + MR) and Z&&f/O) is the total waste rate (= WV + Uv + WR + UR). Mass balances IV-VII do not have any accumulation and it is assumed at each of these points the mass is directed to each stream on a time scale much less than the mean lifetime of plastic products in the two markets. The first quantity we want to determine is the total waste rate, T. Using mass balances IV and VI as well as Eq. 2 one obtains, T = [l - %Rlf + X&6+
+ r
(9
The rate of plastic leaving the new recycled plastics market, r, is found from mass balance II and Fqs. 2-4,
(6) which is easily solved with the condition that r is initially zero, -&RR +
a
-emr/aR
l-a
1
146
B.L. Fletcher, M.E. Mackay/ Resources, Conservation and Recycling 17 (19%) 141-151
where a is equal to trot/t,,. 1’Hopitals rule may be easily applied for the case of a equal to 1 to eliminate the singularity in the denominator of the fractions. The quantity, f, represents the amount of plastic that will become waste when there is no recycling and T is normal&d with this to determine the dimensionless waste rate when the recycling scheme is in operation. This dimensionless waste rate is defined as P (= T/n and is given by Eqs. 5 and 6 as, P = 1 - xx[l - e-a’/tRR] + Xr&
1- -
1 1-U
a e -&RR + -e-‘/‘RR 1-U
1
(7)
If the amount of plastic waste is reduced with recycling, the waste rate, T*, will be less than one since the original dimensionless waste rate with no recycling is one (XR= 0). We again emphasise that the virgin market size, Mv, is assumed constant. The rate of plastic fabrication, F, is increasing at approximately 5% per annum indicating a possible increased virgin market size. Of course, an increase in the plastic fabrication rate could also be due to a decrease in the virgin market residence time, tav. We neglect these possibilities and any increases in plastic fabrication rate to obtain our general conclusions below. The rate of fabricated plastic, F, is determined next, subject to the above assumptions, to verify if recycling does help reduce the plastic made. The plastic fabrication rate without recycling is equal to fby application of mass balances I and VII. This is used to define the dimensionless fabrication rate, P (= F/j). From mass balance III, noting that Mv is constant and incorporating Eqs. 4, 6 and 7 the following results, F+ = 1 - xR[l
-
eeavtRR] + x~y~[l - e-at’tRR]
(8)
where if there is no recycling P will be equal to one. The total market available to virgin and recycled plastics, MT, is made dimensionless with the virgin market size, Mv, to yield iUr* (= &/A&). When the total market size is made dimensionless in this way it is equal to one when there is no recycling going to the new market for recycled plastics, MR. The equation for i&-* is determined by application of Eqs. 1, 4 and 6, M+ =
a --ot/tRR+ -e-t/‘ RR
1-U
1
(9)
Finally, we would like to determine an effectiveness for recycling, t. This quantity will be defined so it is zero for no recycling, is related to the number of times plastic is used and is defined by,
(10)
B.L. Fletcher, ME.
Mackay/ Resources, Conservation and Recycling 17 (1996) 141-151
147
where tar is the mean residence time in the virgin market with the recycling rate Rv in place and will be discussed below. The first term on the right-hand side of Eq. 10 represents the fraction of material which is recycled back to the virgin market multiplied by a factor related to the new residence time in the virgin market due to ‘true recycling’, tar, divided by the residence time in the virgin market without recycling, tnv. The second term is the fraction of material that reaches the new recycled plastics market, &, and is multiplied by the total mean time this recycled plastic is used (tzr + txn) divided by the residence time in the virgin market without recycling. The residence time with ‘true recycling’, txr, is given by,
tRV =
MV
WV + Uv + RR
which represents the virgin market size divided by the amount of plastic which cannot re-enter the virgin plastic market. Application of mass balance IV and Eqs. l-3 yields,
tRT =
tRV
(11)
1 - _~a[1- ~a] 1 - e-ot/taa]
This result shows that with true recycling the actual time a plastic is used in the virgin market increases after recycling is in place. From mass balance V and Eqs. 2, 3, 10 and 11 the following results, xR[l
t=
-
emarhRR]
1 - ~n[l - yn][l - e-“‘Rx]
+
XuR[l
_
e-“‘/‘RR]
tRR t RV
(12)
The results for this section are summarised in Table 1 for sufficient time to achieve steady state (i.e. t - 00) and will be discussed in the next section. The various quantities are written as P(a), for example, to represent steady state values. 3. Discussion of the model If no plastic is truly recycled, YR equal to one, so that Rv is equal to zero then some interesting and, in hindsight, obvious conclusions can be drawn. We call this type of recycling ‘new market recycling,’ for obvious reasons, while the converse, ya equal to zero, is denoted as ‘true recycling.’ The first observation for new market recycling is that eventually the rate of waste generated, T*, is unchanged and is the same as if there was no recycling at all (Table 1). Also, eventually, regardless of the type of recycling scheme used, the rate of plastic fabricated, P, is equal to P. This is the result of the mass balance which at steady state can be written as ‘what goes in must go out.’ Yet, ‘new market recycling’ is not without advantage. The relative effectiveness, [, or relative time that plastic is used increases. The relative effectiveness is equal to
148
B.L. Fletcher, M.E. Mackay/
Resources, Conservation and Recycling 17 (19%)
141-151
Table 1 Summary of results for the model after sufficient time to achieve steady state Quantity
E4pRtiOIl
Result
Result (xR = 0.1,
YR= 0.5, tRR/tRV = 0.5) F(a)
I
I -XR+XR~R
0.95
mm)
8
l-XR+XRYR
‘+fT+tw)
9
1 + XtiRtRRitRV
0.95 1.025
xR
12
t(w)
1 -xR[l
tRR -YRl
+ xtiR-
0.130
tRV
zero without recycling and for a 10% recycling rate (xa = 0.1) with all the plastic going into the new market Cya = 1) [(a) is,
E(a) =
xR[l
+ fRRitRV1
Assuming that recycled plastics are less durable than virgin in the same application, due to degradation from processing, we would expect that tRR/tRv is 1eSSthan one. A value of 0.5 is used making I equal to 0.15. ‘True recycling’ will reduce the amount of waste generated and for a 10% true recycling rate (xa = 0.1, yR = 0) yields a reduction of waste by 10% (P(o0) = 0.9). The relative effectiveness is given by,
Ha) = ]
-xRx R
Interestingly, the effectiveness, as we have defined it, is less for this recycling scheme having a value of 0.111. This indicates that the relative usage time of the product is less than when a new market is created. This increase in the relative time is, however, at the sacrifice of the more important problem of not decreasing waste. One can also determine that the relative amount of plastic fabricated with ‘true recycling’ is directly reduced by the amount of plastic recycled which is not true for ‘new market recycling’ (no change in P(a) will occur). So, ‘true recycling’ reduces the impact on the environment by reducing the amount of oil that is processed to make plastics which ‘new market recycling’ will not do. Finally, the size of the market, &*(a), will directly increase by the amount recycled for the ‘new market recycling’ scheme (Table 1, ya > 0). There is no Change in the total market size for ‘true recycling’ @a = 0). An increased market size could have the deleterious effect that plastics gain hold in a new market albeit recycled plastics. In the future, virgin plastics could penetrate this market which would have the effect of increasing the virgin market size. More plastic would then have to be fabricated from oil and in turn more waste will be generated. This scenario is clearly undesirable.
B.L. Fletcher. ME. Mackay/ Resources, Conservation and Recycling 17 (19%) 141-151
149
An intermediate case to the above limiting cases for yR equal to 0.5 is given in Table 1. The values for the various quantities are the mean of the two limiting cases and may more accurately represent the true situation in plastics recycling. In other words, the amount of waste generated will not be equal to the amount of plastic recycled. The figure used of 50% going back to replace virgin plastics may be disputed. However, we are aware of several products being made from recycled plastics which are penetrating markets where plastics are not normally used. It may be that the original raw material is more harmful to the environment than recycled plastic which eventually reaches landfill. If this is true then ‘new market recycling’ is justified. Otherwise one can not truly warrant this type of recycling. Yet, there are economic [5,6], technological and societal reasons for not using recycled plastics in the virgin market, so, we can not condemn ‘new market recycling’. It may also come to fruition that ‘new market recycling’ is used to gain experience in plastics recycling and technological advances made during this occurrence could be used to facilitate ‘true recycling’. In order to obtain the mean residence time for our model, we define a distribution for the time it takes a plastic product to leave the market (i.e. presently this means disposal of a plastic product). A distribution function, F(t), which is fairly robust is, F(t) =
1 -
e-utR
(13)
where F(t) represents the fraction of products that would be disposed between zero time and the present time, c (this is referred to as a cumulative distribution function). The time constant, ta, is the mean residence time and is equivalent to tav, tan and tar. This form for the distribution function has applications in many flow processes, radioactive decay, etc. There are data for how much of a plastic type are disposed in a certain time and we have converted this to the mean residence time in Table 2. The mean residence time for applications A, B, and C were calculated by assuming the percentage of plastics were disposed in 1.5 years and application D in 10 years. Mean residence times were calculated by ignoring the high and low values due to probable inaccuracies in the distribution function as well as error in the data. However, the value of LDPE for use in packaging and single-use containers, application A, is probably of the correct order. We are interested in the global residence time here and believe that the mean times are adequate for our purpose. The mean residence time for application D is much too high. This is most likely due to a failure of the assumed distribution function which may, for this application, be inappropriate since the products will more than likely not begin to be disposed for a certain time and then show a form similar to Eq. 13 (this is mathematically equivalent to a phase lag time). Two parameters would be needed in this model, ta and the phase lag time, and since only one data point is available for each plastic (i.e. the amount of plastic disposed in lO+ years) it is impossible to determine them. The mean residence time can not be calculated for this application with the data available. A mean residence time of 7.1 i 4.1 years is the average of applications A-C which Will be uSed in the CdCUkiOnS belOW. This VdUC Will repreSCnt tRV. The
150
B.L. Fletcher. ME.
Mackay/
Resources, Conservation and Recycling 17 (1996) 141-151
Table 2 Mean residence times in years for various plastics in four applications Resin
Type
A
B
C
D
LDPE HDPE PP PVC PS Phenol Urea
Thermoplastic Thermoplastic Thermoplastic Thermoplastic Thermoplastic Thermoset Thermoset
0.14 (87) 3.9 (32) 2.8 (41) 1.6 (18) 2.0 (52) 14 (IO)
29 (5) 2.9 (40) 8.1 (17) 14 (10) 14 (10) 9.2 (15) 6.0 (22)
74 (2) 5.2 (25) 3.9 (32) 11 (13) 3.5 (35) 2.4 (47) 2.4 (47)
160 (6) 330 (3) 95 (10) II (59) 330 (3) 30 (28) 33 (26)
Average residence times without highest and lowest values (f standard deviation)
74 (2) 6.1 zt 4.9
10 f 4
5.2 f 3.4
?
A, packaging, single-use containers; B, household sundries, toys; C, containers, automobiles, electric ap pliances; D, pipes, construction materials, electric wire, furniture. Numbers in parentheses represent the percentage scrapped in l-2 years for applications A-C and in lO+ years for application D [7]. LDPE represents low density polyethylene; PVC, polyvinylchloride and PS, polystyrene.
mean residence time in the new market, tRR, is assumed to be 50% of tRV for sake of calculation. The time constant to phase in recycling, t,,, is set so that 95% of the target recycling percentage, xa, is obtained in 5 years. This makes tp equal to 1.67 years according to Eq. 2. A 10% recycling rate, x a, and 50% of the recycled plastic going to the new market, YR, are also assumed. The results for these assumed values are shown in Fig. 2 using equations developed above.
0.00 y * 0
’
n
’
’ * * * - ’ * - ’ * ’ ’ a’ -
5
10 Time (years)
15
’ 20
Fig. 2. Waste generated (7”. Eq. 7), rate of plastics fabrication (P, Eq. 8), total market size (MT*, Eq. 9), and relative effectiveness (.$ Eq. 12) of the plastics recycling scheme shown in Fig. I for the conditions given in the figure.
B.L. Fletcker. M.E. Mackay/ Resources, Conservation and Recycling 17 (19%)
141-151
151
An interesting observation is that the total waste generated, P, shows a minimum at 4 years. This occurs because the recycling scheme is phased in faster than the mean residence time in the new recycled plastics market, Ma. In effect this means that the products in this market are not disposed in sufficient time for waste to be truly generated in this time frame. However, they are eventually disposed and after approximately 15 years steady state is achieved. If the recycled products in the new market last an even longer time, tRa is larger, this minimum becomes more accentuated and lasts for a longer time. One could be lead into the false assumption that ‘new market recycling’ reduces the amount of waste generated directly in proportion to the amount recycled if the period of observation is not long enough. This is the central conclusion to our work and we would like to emphasise that ‘new market recycling’ does not reduce the total amount of waste generated. Note that even if ‘true recycling’ is not introduced then a minimum in P will always be apparent. The other quantities in Fig. 2, MT*, P and l, all behave in similar fashion by gradually achieving their steady state values given in Table 2 in a similar time frame to 7”. As mentioned above, the steady state values are intermediate to the two limiting cases of either total ‘true recycling’ or ‘new market recycling’. 4. Conclusions We have developed a model of plastics recycling which accounts for the gradual phasing in of recycling and the limited lifetime of plastics for use by the consumer. The mean lifetime of plastics in most applications is found to be approximately 7.1 f 4.1 years and the characteristic time for phasing in the recycling scheme in 5 years is determined to be 1.67 years. It is shown that ‘new market recycling’ does not ultimately reduce the amount of waste generated while ‘true recycling’ does. An interesting observation is made that the amount of waste shows a minimum whose depth and longevity depends on the relative values of the plastics lifetime in the new market and the phase in time for recycling. If the period of observation is not long enough one could be lead into the false conclusion that ‘new market recycling’ actually reduces the waste generated. References [l] [2] [3] [4] [S] [6] [7]
Australia, Industry Commission Report on Recycling, Volume II: Recycling of Products, February 1991, p. 77. Brisson, I., 1993. Packaging Waste and the Environment: Economics and Policy. Resour., Conserv., Recycling, 8: 183-292. APRI Recycling Seminar, Melbourne, 21 July 1994. Koshir, F. and Koiser, E., 1994. An Overview of the Australian Plastic Industry. Conference Proceedings, ANTEC, San Francisco. Grignaschi, C., 1988. Plastics recycling in Italy: legislation, industrial experiences and future developments. Resour., Conserv. Recycling, 2: 17-25. Armsen, R., 1988. Economic situation of regranulation plants. Resour. Conserv. Recycling, 2: 13-16. Saeki, Y., 1993. The challenges of waste toward the 2lst century. Int. Polymer Processing, 8: 3-17.
Resources, Conservation and Recycling 17 (1996) 141-151
ELSEVIER
conservation and recycling
A model of plastics recycling: does recycling reduce the amount of waste? Brenton L. Fletcher, Michael E. Mackay* Department of Chemical Engineering, The University of Queensland, Brisbane 4072, Queensland, Australia
Received 3 March 1995;revision received 19 July 1995;accepted 27 July 1995 Ab.ShCt
A model for recycling plastics is made to ‘phase in’ recycling over a given period. The recycled plastic can either replace virgin plastic or enter a new market where plastics are not normally used. The former is denoted as ‘true recycling’and the latter, ‘newmarket recycling’. It is shown that ‘true recycling’will eventually reduce the amount of waste by the same amount of plastic that is recycled. On the other hand, ‘new market recycling’will not reduce the amount of plastic waste and after a given period the overall result is that there is no effect on the amount of plastic waste generated. This is due to the fact that plastics in general have a finite lifetime. Keywords:Plastic; Plastic recycling; Municipal solid waste; Waste reduction
1. IntroduetIon
Australia produces approximately 1 million tonnes of plastic resins annually. Of this, 450 000 tonnes are discarded in landfill waste sites throughout the country and represents between 5 and 15% of the total weight of the landfill waste stream [l]. There are 50 million tonnes of plastic resin produced per annum in the world, however, the total amount recycled is difficult to quantify. The high volume to weight ratio of plastics means that on a volume basis, plastics represent between 10 and 30% of waste going to landfill. The volume of plastics in landfill is difficult to quantify since the amount of compaction has a definite impact on figures quoted in the literature. It is difficult to ascertain whether these volume Corresponding author.
??
0921-3449196/$15.000 1996 Elsevier Science B.V. All rights reserved PII 0921-3449(96)01068-3
142
B.L. Fletcher, ME.
Mackay/
Resources, Conservation and Recycling 17 (19%)
141-151
figures are based on uncompacted material, material that has been compacted once in the garbage truck, or material that has been further compacted by heavy machinery at the landfill site. In addition, the methods used for compaction of rubbish vary between landfill sites. Therefore, volume figures quoted tend to have a large uncertainty. Landfill sites tend to ‘fill up’ rather than become ‘overweight’ [2], so, the volume occupied by plastics in landfills should represent reasonable concern. Targets have been set by various organisations in an attempt to reduce waste problems. At the end of this decade, the Commonwealth Environmental Protection Agency (CEPA) wishes to reduce total municipal solid waste (MSW) by 50%, the Australian and New Zealand Environment and Conservation Council (ANZECC) aims to reduce packaging waste by 50% in a similar time, and KEMCOR, the supplier of 90% of the high density polyethylene (HDPE) used for milk packaging in Australia, has set a target of reducing the amount of HDPE sent to landfill by 50% 131.This follows the worldwide trend of various organisations that have sent similar goals. Approaches to address the problem of plastic waste have included recycling. In house recycling of industrial scrap waste has long been practiced at a high percentage by the plastics industry. However, recycling of household plastic waste has been virtually non-existent. Plastics recovered from household waste in 1989 represented only 0.4% of plastic consumed in households in Australia [l]. The recent introduction of curbside recycling bins concentrating mainly on the collection of polyethyleneterephthalate (PET) and HDPE beverage bottles and a small amount of polypropylene (PP), has definitely increased the level of plastics recycling. Currently, approximately 60 000 tonnes of plastic are recycled throughout Australia representing 6% of what is produced annually. @LB.: The percentage of plastic recycled could be much lower since many plastic articles are imported.) Victoria is the leading state regarding recycling and accounts for 60% of all recycling operations [3]. As more bins are distributed into the community and people become more educated in recycling, the amount of plastic recycled will inevitably increase in the following years. Ironically though, efforts to increase the amount of recycling are retarded by the lack of established markets for the reprocessed products [3]. Plastics recycling, as an industry, faces a number of hurdles before establishing itself as an effective means of reducing the amount of plastic waste contributing to landfill and litter problems. Currently, the level of recycling occurring in the household waste sector is not high enough to provide an appreciable effect on the problem of plastic waste. Solid markets for the recycled and reprocessed products are yet to be secured as a result of economic, technological and institutional barriers. How effective is recycling plastic waste, and how effective can it be? This paper attempts to address the feasibility of plastics recycling using a mass balance for the flow of plastics in our society. 2. Development of tbe model Three quarters of the plastic consumed in Australia are used in long life applications [3] while the remainder is used for packaging requirements. This is identical
B.L. Fletcher, M. E. Mackay/Resources,
Conservation and Recycling 17 (19%)
141-151
143
to the world average. The short one trip lifetime of plastic packaging leads it to be the major contributor to the problem of plastic waste and litter, and consequently plastic packaging is the focus of most household recycling efforts. However, when plastic packaging is recycled, it is reprocessed into items other than for direct food contact applications due to stringent regulations. In effect, this means that an entirely new market is created for this type of recycled and reprocessed plastic. Products currently processed from recycled plastics include garbage bins, crates, piping, pip ing joints and structural items for timber and concrete alternatives (these products are not necessarily made from recycled packaging). Recycled plastics are not regulated to be used for certain products, with the exception of direct food contact applications, so, the products made from recycled plastics can penetrate markets where virgin plastic is not used. This, in effect, increases the total market for plastics. Infinite recycling of plastic is technically impossible since the molecules degrade during repeated processing and places a finite lifetime on plastics. The model introduced below takes into account these two phenomena and is used to determine whether recycling plastics reduces the amount of plastic waste which eventually reaches landfill. A schematic for the general recycling scheme is shown in Fig. 1. Units for each symbol have either dimensions of mass (A4)or mass per unit time (MB). Plastic products leave the virgin market, M&W), at a rate of@/@ where without recycling become unaccounted waste at a rate, Uv (MO), or reach landfill at a rate, WV (MB). Unaccounted waste represents litter, exported products or products used in long term applications, such as electrical conduit in buildings, which will eventually reach landfill. The size of the virgin market is assumed constant here and the average
Fig. 1. Schematic of the genera&d recycling scheme.
144
B.L. Fletcher. ME.
Mackay/ Resources, Conservation and Recycling 17 (19%)
141-151
life time of the products is assumed to be equal to tav. We can write this mathematically as,
-Mv =
tRV
f
where in engineering terms tav is the mean residence time in the market (or really the mean time a consumer uses a product before discarding it). Because the virgin market is assumed constant in size and the products have a finite lifetime the rate plastics leave the market is always constant regardless of whether recycling occurs or not (Eq. 1). If recycling is introduced at a rate, R (M/O), then not all the waste is immediately discarded. The recycling rate is assumed to be a fraction of the rate plastic leaves the virgin market, xa. In addition, the rate of recycling is assumed to be ‘phased in’ with a time constant, tP, which is written as, R = x&l
-
e%]
However, the target recycling rate will be essentially reached after sufficient time. Other mathematical expressions could be used rather than the exponential, however, the type of expression does not affect any of our general conclusions. The recycled plastic can either be put back into the virgin market at a rate, RV(A4/O),or into a new market for recycled plastics, Ma(M), at a rate of RR(MM). If the recycled plastic is put back into the virgin market then it will be combined with the plastic fabricated at a rate, F(MA9).On the other hand, if the plastic enters the new recycled plastics market then it will eventually leave this market at a rate, r(M/8), when the product breaks or is no longer useful. We do not assume the recycled plastic in Ma can be recycled again after leaving this market since the products will be of such a type that inhibits repeated recycling. Examples of these products are mixed plastic waste used to make benches, posts and the like where the original raw material is replaced by the recycled plastic (the original raw material may be wood or metal, for example). The product becomes unaccounted waste generated at a rate, &@f/e), or directly reaches landfill at a rate, &(M/@. Our model could be relined to include the possibility of recycling the products leaving Ma. Yet, this would only serve to create a very complicated model with little benefit and will also not affect the general conclusions we draw below. The fraction of recycled plastic, ya, that reaches Ma is written as,
R R=YRR The lifetime of plastics in Ma is written similar to that for virgin plastics in Es. 1,
B.L. F’lercker. M.E. Mackay/
Resources, Conservation and Recycling 17 (1996) 141-151
145
where tan represents the mean lifetime of a recycled plastic product in this market. Referring to Fig. 1 the mass balances over the various subsystems as well as the entire system are, I:
dMv -=G-f
dt
II:
d&t -=RR-r dt
III:
d& -=Fdt
WV-
IV: f=R+
WV+ U,
V:
VI:
VII:
WR-
Uv .- VR=F-T
R = RR + Rv
t =
w, + u,
F + R, = G
where M&W) is the total plastic market (= Mv + MR) and Z&&f/O) is the total waste rate (= WV + Uv + WR + UR). Mass balances IV-VII do not have any accumulation and it is assumed at each of these points the mass is directed to each stream on a time scale much less than the mean lifetime of plastic products in the two markets. The first quantity we want to determine is the total waste rate, T. Using mass balances IV and VI as well as Eq. 2 one obtains, T = [l - %Rlf + X&6+
+ r
(9
The rate of plastic leaving the new recycled plastics market, r, is found from mass balance II and Fqs. 2-4,
(6) which is easily solved with the condition that r is initially zero, -&RR +
a
-emr/aR
l-a
1
146
B.L. Fletcher, M.E. Mackay/ Resources, Conservation and Recycling 17 (19%) 141-151
where a is equal to trot/t,,. 1’Hopitals rule may be easily applied for the case of a equal to 1 to eliminate the singularity in the denominator of the fractions. The quantity, f, represents the amount of plastic that will become waste when there is no recycling and T is normal&d with this to determine the dimensionless waste rate when the recycling scheme is in operation. This dimensionless waste rate is defined as P (= T/n and is given by Eqs. 5 and 6 as, P = 1 - xx[l - e-a’/tRR] + Xr&
1- -
1 1-U
a e -&RR + -e-‘/‘RR 1-U
1
(7)
If the amount of plastic waste is reduced with recycling, the waste rate, T*, will be less than one since the original dimensionless waste rate with no recycling is one (XR= 0). We again emphasise that the virgin market size, Mv, is assumed constant. The rate of plastic fabrication, F, is increasing at approximately 5% per annum indicating a possible increased virgin market size. Of course, an increase in the plastic fabrication rate could also be due to a decrease in the virgin market residence time, tav. We neglect these possibilities and any increases in plastic fabrication rate to obtain our general conclusions below. The rate of fabricated plastic, F, is determined next, subject to the above assumptions, to verify if recycling does help reduce the plastic made. The plastic fabrication rate without recycling is equal to fby application of mass balances I and VII. This is used to define the dimensionless fabrication rate, P (= F/j). From mass balance III, noting that Mv is constant and incorporating Eqs. 4, 6 and 7 the following results, F+ = 1 - xR[l
-
eeavtRR] + x~y~[l - e-at’tRR]
(8)
where if there is no recycling P will be equal to one. The total market available to virgin and recycled plastics, MT, is made dimensionless with the virgin market size, Mv, to yield iUr* (= &/A&). When the total market size is made dimensionless in this way it is equal to one when there is no recycling going to the new market for recycled plastics, MR. The equation for i&-* is determined by application of Eqs. 1, 4 and 6, M+ =
a --ot/tRR+ -e-t/‘ RR
1-U
1
(9)
Finally, we would like to determine an effectiveness for recycling, t. This quantity will be defined so it is zero for no recycling, is related to the number of times plastic is used and is defined by,
(10)
B.L. Fletcher, ME.
Mackay/ Resources, Conservation and Recycling 17 (1996) 141-151
147
where tar is the mean residence time in the virgin market with the recycling rate Rv in place and will be discussed below. The first term on the right-hand side of Eq. 10 represents the fraction of material which is recycled back to the virgin market multiplied by a factor related to the new residence time in the virgin market due to ‘true recycling’, tar, divided by the residence time in the virgin market without recycling, tnv. The second term is the fraction of material that reaches the new recycled plastics market, &, and is multiplied by the total mean time this recycled plastic is used (tzr + txn) divided by the residence time in the virgin market without recycling. The residence time with ‘true recycling’, txr, is given by,
tRV =
MV
WV + Uv + RR
which represents the virgin market size divided by the amount of plastic which cannot re-enter the virgin plastic market. Application of mass balance IV and Eqs. l-3 yields,
tRT =
tRV
(11)
1 - _~a[1- ~a] 1 - e-ot/taa]
This result shows that with true recycling the actual time a plastic is used in the virgin market increases after recycling is in place. From mass balance V and Eqs. 2, 3, 10 and 11 the following results, xR[l
t=
-
emarhRR]
1 - ~n[l - yn][l - e-“‘Rx]
+
XuR[l
_
e-“‘/‘RR]
tRR t RV
(12)
The results for this section are summarised in Table 1 for sufficient time to achieve steady state (i.e. t - 00) and will be discussed in the next section. The various quantities are written as P(a), for example, to represent steady state values. 3. Discussion of the model If no plastic is truly recycled, YR equal to one, so that Rv is equal to zero then some interesting and, in hindsight, obvious conclusions can be drawn. We call this type of recycling ‘new market recycling,’ for obvious reasons, while the converse, ya equal to zero, is denoted as ‘true recycling.’ The first observation for new market recycling is that eventually the rate of waste generated, T*, is unchanged and is the same as if there was no recycling at all (Table 1). Also, eventually, regardless of the type of recycling scheme used, the rate of plastic fabricated, P, is equal to P. This is the result of the mass balance which at steady state can be written as ‘what goes in must go out.’ Yet, ‘new market recycling’ is not without advantage. The relative effectiveness, [, or relative time that plastic is used increases. The relative effectiveness is equal to
148
B.L. Fletcher, M.E. Mackay/
Resources, Conservation and Recycling 17 (19%)
141-151
Table 1 Summary of results for the model after sufficient time to achieve steady state Quantity
E4pRtiOIl
Result
Result (xR = 0.1,
YR= 0.5, tRR/tRV = 0.5) F(a)
I
I -XR+XR~R
0.95
mm)
8
l-XR+XRYR
‘+fT+tw)
9
1 + XtiRtRRitRV
0.95 1.025
xR
12
t(w)
1 -xR[l
tRR -YRl
+ xtiR-
0.130
tRV
zero without recycling and for a 10% recycling rate (xa = 0.1) with all the plastic going into the new market Cya = 1) [(a) is,
E(a) =
xR[l
+ fRRitRV1
Assuming that recycled plastics are less durable than virgin in the same application, due to degradation from processing, we would expect that tRR/tRv is 1eSSthan one. A value of 0.5 is used making I equal to 0.15. ‘True recycling’ will reduce the amount of waste generated and for a 10% true recycling rate (xa = 0.1, yR = 0) yields a reduction of waste by 10% (P(o0) = 0.9). The relative effectiveness is given by,
Ha) = ]
-xRx R
Interestingly, the effectiveness, as we have defined it, is less for this recycling scheme having a value of 0.111. This indicates that the relative usage time of the product is less than when a new market is created. This increase in the relative time is, however, at the sacrifice of the more important problem of not decreasing waste. One can also determine that the relative amount of plastic fabricated with ‘true recycling’ is directly reduced by the amount of plastic recycled which is not true for ‘new market recycling’ (no change in P(a) will occur). So, ‘true recycling’ reduces the impact on the environment by reducing the amount of oil that is processed to make plastics which ‘new market recycling’ will not do. Finally, the size of the market, &*(a), will directly increase by the amount recycled for the ‘new market recycling’ scheme (Table 1, ya > 0). There is no Change in the total market size for ‘true recycling’ @a = 0). An increased market size could have the deleterious effect that plastics gain hold in a new market albeit recycled plastics. In the future, virgin plastics could penetrate this market which would have the effect of increasing the virgin market size. More plastic would then have to be fabricated from oil and in turn more waste will be generated. This scenario is clearly undesirable.
B.L. Fletcher. ME. Mackay/ Resources, Conservation and Recycling 17 (19%) 141-151
149
An intermediate case to the above limiting cases for yR equal to 0.5 is given in Table 1. The values for the various quantities are the mean of the two limiting cases and may more accurately represent the true situation in plastics recycling. In other words, the amount of waste generated will not be equal to the amount of plastic recycled. The figure used of 50% going back to replace virgin plastics may be disputed. However, we are aware of several products being made from recycled plastics which are penetrating markets where plastics are not normally used. It may be that the original raw material is more harmful to the environment than recycled plastic which eventually reaches landfill. If this is true then ‘new market recycling’ is justified. Otherwise one can not truly warrant this type of recycling. Yet, there are economic [5,6], technological and societal reasons for not using recycled plastics in the virgin market, so, we can not condemn ‘new market recycling’. It may also come to fruition that ‘new market recycling’ is used to gain experience in plastics recycling and technological advances made during this occurrence could be used to facilitate ‘true recycling’. In order to obtain the mean residence time for our model, we define a distribution for the time it takes a plastic product to leave the market (i.e. presently this means disposal of a plastic product). A distribution function, F(t), which is fairly robust is, F(t) =
1 -
e-utR
(13)
where F(t) represents the fraction of products that would be disposed between zero time and the present time, c (this is referred to as a cumulative distribution function). The time constant, ta, is the mean residence time and is equivalent to tav, tan and tar. This form for the distribution function has applications in many flow processes, radioactive decay, etc. There are data for how much of a plastic type are disposed in a certain time and we have converted this to the mean residence time in Table 2. The mean residence time for applications A, B, and C were calculated by assuming the percentage of plastics were disposed in 1.5 years and application D in 10 years. Mean residence times were calculated by ignoring the high and low values due to probable inaccuracies in the distribution function as well as error in the data. However, the value of LDPE for use in packaging and single-use containers, application A, is probably of the correct order. We are interested in the global residence time here and believe that the mean times are adequate for our purpose. The mean residence time for application D is much too high. This is most likely due to a failure of the assumed distribution function which may, for this application, be inappropriate since the products will more than likely not begin to be disposed for a certain time and then show a form similar to Eq. 13 (this is mathematically equivalent to a phase lag time). Two parameters would be needed in this model, ta and the phase lag time, and since only one data point is available for each plastic (i.e. the amount of plastic disposed in lO+ years) it is impossible to determine them. The mean residence time can not be calculated for this application with the data available. A mean residence time of 7.1 i 4.1 years is the average of applications A-C which Will be uSed in the CdCUkiOnS belOW. This VdUC Will repreSCnt tRV. The
150
B.L. Fletcher. ME.
Mackay/
Resources, Conservation and Recycling 17 (1996) 141-151
Table 2 Mean residence times in years for various plastics in four applications Resin
Type
A
B
C
D
LDPE HDPE PP PVC PS Phenol Urea
Thermoplastic Thermoplastic Thermoplastic Thermoplastic Thermoplastic Thermoset Thermoset
0.14 (87) 3.9 (32) 2.8 (41) 1.6 (18) 2.0 (52) 14 (IO)
29 (5) 2.9 (40) 8.1 (17) 14 (10) 14 (10) 9.2 (15) 6.0 (22)
74 (2) 5.2 (25) 3.9 (32) 11 (13) 3.5 (35) 2.4 (47) 2.4 (47)
160 (6) 330 (3) 95 (10) II (59) 330 (3) 30 (28) 33 (26)
Average residence times without highest and lowest values (f standard deviation)
74 (2) 6.1 zt 4.9
10 f 4
5.2 f 3.4
?
A, packaging, single-use containers; B, household sundries, toys; C, containers, automobiles, electric ap pliances; D, pipes, construction materials, electric wire, furniture. Numbers in parentheses represent the percentage scrapped in l-2 years for applications A-C and in lO+ years for application D [7]. LDPE represents low density polyethylene; PVC, polyvinylchloride and PS, polystyrene.
mean residence time in the new market, tRR, is assumed to be 50% of tRV for sake of calculation. The time constant to phase in recycling, t,,, is set so that 95% of the target recycling percentage, xa, is obtained in 5 years. This makes tp equal to 1.67 years according to Eq. 2. A 10% recycling rate, x a, and 50% of the recycled plastic going to the new market, YR, are also assumed. The results for these assumed values are shown in Fig. 2 using equations developed above.
0.00 y * 0
’
n
’
’ * * * - ’ * - ’ * ’ ’ a’ -
5
10 Time (years)
15
’ 20
Fig. 2. Waste generated (7”. Eq. 7), rate of plastics fabrication (P, Eq. 8), total market size (MT*, Eq. 9), and relative effectiveness (.$ Eq. 12) of the plastics recycling scheme shown in Fig. I for the conditions given in the figure.
B.L. Fletcker. M.E. Mackay/ Resources, Conservation and Recycling 17 (19%)
141-151
151
An interesting observation is that the total waste generated, P, shows a minimum at 4 years. This occurs because the recycling scheme is phased in faster than the mean residence time in the new recycled plastics market, Ma. In effect this means that the products in this market are not disposed in sufficient time for waste to be truly generated in this time frame. However, they are eventually disposed and after approximately 15 years steady state is achieved. If the recycled products in the new market last an even longer time, tRa is larger, this minimum becomes more accentuated and lasts for a longer time. One could be lead into the false assumption that ‘new market recycling’ reduces the amount of waste generated directly in proportion to the amount recycled if the period of observation is not long enough. This is the central conclusion to our work and we would like to emphasise that ‘new market recycling’ does not reduce the total amount of waste generated. Note that even if ‘true recycling’ is not introduced then a minimum in P will always be apparent. The other quantities in Fig. 2, MT*, P and l, all behave in similar fashion by gradually achieving their steady state values given in Table 2 in a similar time frame to 7”. As mentioned above, the steady state values are intermediate to the two limiting cases of either total ‘true recycling’ or ‘new market recycling’. 4. Conclusions We have developed a model of plastics recycling which accounts for the gradual phasing in of recycling and the limited lifetime of plastics for use by the consumer. The mean lifetime of plastics in most applications is found to be approximately 7.1 f 4.1 years and the characteristic time for phasing in the recycling scheme in 5 years is determined to be 1.67 years. It is shown that ‘new market recycling’ does not ultimately reduce the amount of waste generated while ‘true recycling’ does. An interesting observation is made that the amount of waste shows a minimum whose depth and longevity depends on the relative values of the plastics lifetime in the new market and the phase in time for recycling. If the period of observation is not long enough one could be lead into the false conclusion that ‘new market recycling’ actually reduces the waste generated. References [l] [2] [3] [4] [S] [6] [7]
Australia, Industry Commission Report on Recycling, Volume II: Recycling of Products, February 1991, p. 77. Brisson, I., 1993. Packaging Waste and the Environment: Economics and Policy. Resour., Conserv., Recycling, 8: 183-292. APRI Recycling Seminar, Melbourne, 21 July 1994. Koshir, F. and Koiser, E., 1994. An Overview of the Australian Plastic Industry. Conference Proceedings, ANTEC, San Francisco. Grignaschi, C., 1988. Plastics recycling in Italy: legislation, industrial experiences and future developments. Resour., Conserv. Recycling, 2: 17-25. Armsen, R., 1988. Economic situation of regranulation plants. Resour. Conserv. Recycling, 2: 13-16. Saeki, Y., 1993. The challenges of waste toward the 2lst century. Int. Polymer Processing, 8: 3-17.