Development of Methodology for Quantifying Collection Rate of Post ...

Materials Transactions, Vol. 48, No. 3 (2007) pp. 574 to 578 #2007 The Japan Institute of Metals

Development of Methodology for Quantifying Collection Rate of Post-Consumer Products Based on Material Flow of Steel* Ichiro Daigo1 , Yasunari Matsuno1 and Yoshihiro Adachi1 1

Department of Materials Engineering, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan

Currently, some post-consumer products are not collected appropriately and remain or are disposed of by unknown ways. In order to conserve resources, the collection rate of such products should be increased. To date, few definitive methods to quantify the collection rate have been developed due to the difficulties in monitoring the amounts of the uncollected products. We have no other choice but to estimate the collection rate. In this paper, a new statistical method was developed to quantify the collection rate of post-consumer products. This method is based on the identification of dynamic material flow of steel used in several kinds of products. The steel-contained products were categorized into six categories: buildings, civil engineering, machines, automobiles, containers, and ‘‘others.’’ The collection rates of buildings, civil engineering, and machines were estimated. As the denominator of the collection rate, the amount of discarded post-consumer products during a year was calculated dynamically from their lifetime distributions and production history in which steel was used prior to that year. As the numerator of the collection rate, the amount of collected steel scraps for recycling domestically and exports was obtained from statistics. Furthermore, uncertainty derived from the lifetime distributions was considered in the calculations. The estimated collection rates obtained with these methods were 1.00 for buildings, 0.00 to 0.22 for civil engineering, and 0.39 to 0.52 for machines. [doi:10.2320/matertrans.48.574] (Received October 12, 2006; Accepted December 20, 2006; Published February 25, 2007) Keywords: material flow analysis, population balance model, lifetime distribution, dissipative materials

1.

Introduction

When we consider the recycling of materials, it is crucial to learn how many post-consumer products are lost in the process of collection because of the huge volume involved.1) Although the recycling rate works as an index to evaluate the recycling process, there is almost no example of considering the quantity lost in the collection process, except for the recycling rate of beverage cans whose product life is short.2) Responding to this situation, for buildings,3) electric devices,4,5) and automobiles,6) research has been conducted to estimate the amount of post-consumer products discarded over the years, using dynamic analysis of the amount of product demand. MFA/SFA (Material flow analysis/Substance flow analysis) have also been used, but there are only a few studies that quantify overall material flows. In their previous paper,1,7) the authors showed that the loss in the collection process could be distinguished from the increase of the accumulation by considering the dynamic material flow, and we were able to quantify all the material flows. Other research efforts8–11) have studied the quantity lost in the invisible collection process. In spite of all these efforts, because the amount of the collected products is too large to quantify by an actual measurement, the collection rates in the previous studies had to depend on subjective values obtained from interviews with the industries involved. Therefore, in this study, the authors intended to establish a method of quantitatively estimating a collection rate by the mathematical processing of statistical data. 2.

(1)

(2)

Materials in postconsumer products

Materials in collected products

(3) Collected materials

(4) Recycled materials

Uncollected materials Materials in uncollected post-consumer products

Fig. 1 Schematic illustration of material flow from discarded materials as components of post-consumer products to recycled materials.

as the rate in which the numerator is the amount going into the material recycling process (3), and the denominator is the quantity of the material contained in the estimated amount of discarded post-consumer products (1). The term loss refers to the amount of the materials contained in the uncollected postconsumer products, as well as the amount of the material that fails to be collected in the dismantling, separating, and sorting process. Usually, the collection rate takes as its denominator the quantity of the material contained in the collected post-consumer products. In the conventional accounting system, the uncollected quantity referred in (1) and (2) of Fig. 1 is counted as a part of the stock due to its invisibility.

Definitions and Data

2.1 Definition of a collection rate As illustrated in Fig. 1, this study defines a collection rate *This

Paper was Originally Published in Japanese in J. Japan Inst. Metals 70 (2006) 114–117.

2.2 Data used For this research, the authors tried to obtain collection rates of different kinds of products by focusing on the material flow of steel, i.e., the products covered here were exclusive to steel-containing products. Accordingly, our research was restricted to the statistical categorizations of steel. Products

Development of Methodology for Quantifying Collection Rate of Post-Consumer Products Based on Material Flow of Steel 1 0.8 Collection rate

under consideration were classified into six categories; namely buildings, civil engineering, machines, automobiles, containers, and ‘‘others.’’ Here, civil engineering includes tunnels, dams, etc., and machines include both machinery and transportation machines other than automobiles. As described above, for the discarded quantity contained in post-consumer products (1), which is the denominator of the collection rate, the quantity of the post-consumer products discarded after their product life needs to be identified. However, the actual quantity is hard to measure. Two reasons for the difficulty is that the number of consumers (the primary point of product disposal) and the number of collectors (the primary point of product collection) are immeasurable and their locations are very dispersed. There are, however, some exceptions products, such as automobiles. Because by law each automobile has to be registered, how many of them are actually discarded after use can be identified.12) We also assumed that the amount of post-consumer containers discarded each year was equivalent to that of the corresponding year’s demand for containers. As most containers are used for food or beverage, their product life is relatively short; their product life is considered to be less than a year, which is the same time period used in the statistics. For the products of the other four categories, we focused on each product’s lifetime distribution (distribution of years of use) and, based on the past demand for the product and the lifetime distribution of products under consideration, applied the population balance model (PBM).4,7,8,13) From this, the amount of discarded post-consumer products was derived. In this model, the discarded quantity of steel contained in postconsumer products (1) were able to be estimated by considering the statistical record of domestic demand for steel up to now,14,15) and the products’ lifetime distributions.7,8,13,16,17) The amount of steel indirectly imported and exported (i.e., the amount of steel contained in imported and exported products) were taken into account as well.18) For the four categories of products other than containers and automobiles, we defined the lifetime distributions of the products as follows. For the lifetime distribution of buildings and civil engineering, we followed the former research16) that identified the actual lifetime distribution of buildings, and used the Weibull distribution as the survival function, which set the shape parameter as 3.127, the scale parameter as 40.44, and the average lifetime as 28.4 years. To define the lifetime distribution of the machines and ‘‘others’’ categories, we employed the normal distribution of the common distribution function as our probability density function. The average lifetime was set at 12.1 years for both categories, with the assumption that 99% of the products would be discarded in a time period twice as long as the average. The numerator of our collection rate was the quantity of collected steel scrap that was consumed in steelmakers (3). To obtain the numerator, we followed statistics regarding the raw materials of steel.19) Note that the amount of collected steel scrap considered in our study was that of obsolete steel scrap obtained by deducting the amount of collected industrial scrap from the statistical value of the amount of domestic market scrap. Although the obsolete scrap usually

575

0.6 0.4

Containers Automobiles Others

0.2 0 1990

1992

1994

1996 Year

1998

2000

2002

Fig. 2 Collection rates of automobiles, containers, and ‘‘others’’ obtained during 1988–2000.

includes scrap from repairs, we assumed that all the scrap was from post-consumer products. The collection rates of automobiles, containers, and ‘‘others’’ were determined as follows. For automobiles, we assumed that the used cars exported from Japan could be regarded as uncollected post-consumer products. We therefore obtained the collection rate of automobiles from the recorded number of exported used cars.20) For containers, the recycle rate of major container products—steel cans—has been recorded each year, and we adopted these figures.21) Regarding ‘‘others’’, many of them are used as secondary products for bolts, nuts, screws, springs, etc., and they should be categorized into one of the four categories. For this reason, we assumed that the collection rate of ‘‘others’’ was the average of the collection rates of all the products. Similarly, the collection rate of ‘‘others’’ was obtained by dividing the amounts of total collected scrap by the estimated amounts of total discarded steel. Figure 2 shows the yearly change in the product collection rates we obtained. 2.3 Uncertainty As Nakajima et al. pointed out,22) while production statistics use categories defined by end-use category, scrap statistics are based on the classification defined at by shape and size. For this reason, there is currently no way to classify the collected scrap in terms of end-use category. That is to say, even if we try to figure out collected scrap according to its end-use category, it is not possible; only the sum of all the collected scrap is available. Also, in many of the existing studies predicting the amount of post-consumer products and discarded materials,1,3,8,13,17) the lifetime distribution is uniquely determined according to a parametric lifetime distribution function. The actual lifetime distribution exists just within 95% confidence interval of the parametric lifetime distribution function. It was substantiated by Komatsu in the case of the lifetime distributions of several kinds of buildings.16) That is to say, a parametric lifetime distribution has uncertainty. Our study employed the method described in Section 3.1 below to handle the different categorizations of statistical data between steel production and steel scrap, as well as the one described in Section 3.2, which considers the confidence interval of the lifetime distribution.

576

Calculation Method

(a) 1991 0.03

0.01

0 −1000

i

0 Difference from average, W 1991 −W1991 /1000t

1000

(b) 1997 0.03

Frequency

0.02

0.01

0 −1000

0 Difference from average, W1997 −W 1997 /1000t

1000

Buildings

Civil engineering

Machines

Frequency

Fig. 3 Distribution of the amount of discarded steel expressed as a difference from the average in (a) 1991 and (b) 1997.

Frequency

Here, Sy refers to the amount of scrap collected in the year y. Wi;y is the estimated amount of discarded steel contained in post-consumer products i in the year y. The term ri denotes the collection rate of products i, which can vary from 0 to 1. The years y covered by the study were 1991 through 1997. The end-use category i indicates any and all of the six categories. Also, we assumed that the collection rates of buildings, civil engineering and machines remained at constant across the years. It would be ideal if the average of the collection rates of all the products remained at constant during the years covered here. Looking at the yearby-year change in the collection rate of ‘‘others’’ shown in Fig. 2 as the average of the collection rates of all the products, the average of the collected rates remained almost the same from 1991 through 1997. For this reason, we evaluate the collection rate by using the data of this time period. A nonlinear optimization problem was then derived from one of the mathematical optimization solutions, the descent method. It should be noted that the minimum sum of residual errors obtained here would be a local minimum within the restraint conditions. This was confirmed by defining an initial value at 3,125 points. The collection rates obtained this way were 1.000 for buildings, 0.041 for civil engineering, and 0.509 for machines. The coefficient of determination R2 was 0.57, revealing that our analysis was of low precision due to the limited number of observation points.

0.02

Frequency

3.1 How to obtain the collection rate The estimated amounts of scrap generation were categorized by end-use of products from which the scraps come. Scrap statistics do not have the categorization. Only the total amounts of scraps in the statistics can be compared with the estimated amounts. In order to estimate the collection rates of the three categories, namely buildings, civil engineering, and machines, the least-square approach was applied in eq. (1). X Sy ¼ ri
Wi;y ð1Þ

Frequency

3.

I. Daigo, Y. Matsuno and Y. Adachi

1

1.00 93.5%

0.38−0.46 6.1%

0.5 0

0.2

0.00−0.22 93.5%

0.1 0 0.4

1.00 6.1%

0.39−0.53 100%

0.2 0 0

3.2 Confidence interval of the lifetime distribution This study took into consideration the uncertainty of the lifetime distribution function, as pointed out by Komatsu.16) We examined the uncertainty by the following method. Whether an individual product is discarded within a year (the year t) is supposed to be an independent event. Accordingly, the number of discarded products within this single year can be obtained by the Bernoulli trials. This then suggests that the number of discarded products can be regarded as a random variable which has the binomial distribution. On this assumption, we estimated the confidence interval of the lifetime distribution by the following method. Let us suppose that the number of products initially introduced in the market is N0 , the number of survival products at the beginning of the year t is Nt , the survival distribution of the product is FðxÞ, and the probability density function of disposal is f ðxÞ. Then, the disposal probability whose denominator is N0 in the year t can be expressed by f ðtÞ in eq. (2). Here, 1, the exponent of the function F, is F’s inverse function.

0.1

0.2

0.3

0.4 0.5 0.6 Collection rate

0.7

0.8

0.9

1

Fig. 4 Estimated collection rates of buildings, civil engineering, and machines.

f ðtÞ ¼ Fðxt Þ  Fðxt þ 1Þ

  Nt Nt  F F 1 þ1 ¼ N0 N0

ð2Þ

We use uniform random numbers which are generated by the rand function of MS Excel 2002. The uniform random numbers are converted into wt , random number with the binomial distribution that follows B (Nt , f ðtÞ). Since Ntþ1 is obtained by deducting wt from Nt , the same calculations for the year t þ 1 are also calculated. This calculation was conducted 1,000 times to find that the amount of discarded material contained in the post-consumer products differed by 0.5 million tons, as shown in Fig. 3. Then, the method described in the previous section derived the collection rates

Development of Methodology for Quantifying Collection Rate of Post-Consumer Products Based on Material Flow of Steel

577

Table 1 Comparison between collection rates estimated in this study and those in a previous study. Estimated collection rate With given lifetime distribution

With uncertainty of lifetime distribution Range of collection rates

Buildings

1.00

1.00

0.96

1.00

0.04

0.00–0.22

0.15

0.10

Machines

0.51

0.39–0.53

0.48

0.49

Results and Discussions

Table 1 summarizes the results obtained with the method we created in this study. We obtained weighted averages of the collection rates for buildings and civil engineering obtained with this study, and found that the collection rate was in the range of 0.55 to 0.70. The average and the median were both 0.60, which was slightly larger compared to the questionnaire survey value. Also, since the collection rate is expected to be larger for buildings than for civil engineering, the results we obtained are appropriate. Though the collection rate for buildings in this study was 1.00, it is possible that some of the steel scrap from the buildings was buried without being separated from other materials. However, the buried quantity is small, and therefore we can safely presume that almost all the steel was collected. For civil engineering, the obtained collection rate was 0.00 to 0.22. As stated above, civil engineering includes tunnels, dams, etc. A survey conducted in the past23) says 39.8% of civil engineering cannot possibly be collected. Accordingly, in terms of civil engineering that has the possibility of being collected, we estimate the collection rate would be between 0.00 to 0.37. In the future, further studies need to be conducted on classifying civil engineering into more detailed sub-categories, as well as on field surveys of the collection rate. The collection rate obtained in this study was estimated to be smaller than the one obtained from the questionnaire survey. One reason for this may be that machines include ships, almost all of which are dismantled outside Japan. Thus, the method we proposed in this study has presented the possibility of identifying product collection rates that are difficult to measure. While, in this study, we created an analytical method with the focus on steel, for which relatively well-structured statistical data is available, we believe that this method could also be applied to other materials. However, it should be noted that steel is easy to separate from other materials due to its magnetism, with the exception of austenitic stainless steel; consequently, for other materials one has to consider the yield from the process of disassembly and separation. 5.

Mean value

Civil engineering

of buildings, civil engineering, and machines from the results of these calculations, as shown in Fig. 4. In each collection rate, the existing range was identified with a probability of about 94%. 4.

Average

Questionn aire survey

Conclusion

In this study, based on material flow, we created a method to identify the collection rate of a product whose collection

0.50 0.80

rate is difficult to measure empirically. Considering the uncertainty of lifetime distribution functions, we created a method that derives collection rates for products with the confidence interval. In addition, by calculating the collection rate of steel used for three end-use categories, we verified the appropriateness of the collection rates obtained. In the future, more studies will be required to improve the analysis accuracy by establishing more detailed categories, and to identify product collection rates based on different kinds of data obtained by applying this method to other materials. Acknowledgment The authors hereby express our sincere gratitude to Mr. Seiichi Hayashi, a consultant at Japan Technical Information Service, who gave us very helpful and valuable advice for this study. This work was supported by K1810 of science foundation of Ministry of the Environment.

REFERENCES 1) I. Daigo, Y. Matsuno, K. N. Ishihara and Y. Adachi: Tetsu-to-Hagane´ 91 (2005) 159–166. 2) EcoMaterial Forum, Recycling criteria working group: Recycling indicator guideline, 2004.9, pp. 5–11. 3) S. Hashimoto and Y. Terashima: Waste Management Research 11 (2000) 271–279. 4) K. Yokota, Y. Matsuno, M. Yamashita and Y. Adachi: Int. J. LCA 8 (2003) 129–136. 5) T. Tasaki, M. Koguchi, T. Kameya and K. Urano: Waste management research 12 (2001) 29–58. 6) Y. Adachi, I. Daigo, H. Yamada and Y. Matsuno: Development Engineering 11 (2005) 19–29. 7) I. Daigo, Y. Igarashi, Y. Matsuno and Y. Adachi: Tetsu-to-Hagane´ 93 (2007) 66–70. 8) I. Daigo, D. Fujimaki, Y. Matsuno and Y. Adachi: Tetsu-to-Hagane´ 91 (2005) 171–178. 9) I. Daigo, D. Fujimaki, Y. Matsuno and Y. Adachi: Tetsu-to-Hagane´ 91 (2005) 179–183. 10) T. E. Graedel, M. Vertram, K. Fuse, R. B. Gordon, R. Lifset, H. Rechberger and S. Spatari: Ecological Economics 42 (2002) 9–26. 11) D. Vexler, M. Bertram, A. Kapur, S. Spatari and T. E. Graedel: Resour. Conserv. Recycle. 41 (2004) 23–46. 12) Road transport bureau Ministry of Land, Infrastructure and Transport, 1958–2004: Jidosha Hoyu Sharyosu 1-31 (Automobile Inspection & Registration Association, Tokyo). 13) K. Kakudate, Y. Adachi and T. Suzuki: Sci. Technol. Adv. Mater. 1 (2000) 105. 14) Committee on iron and steel statistics, The Japan Iron and Steel Federation (JISF): Handbook for Iron and Steel statistics (1971–2003), (JISF, Tokyo, 1971–2003). 15) Committee on iron and steel statistics, JISF: Futsuko Chiikibetsu Juchu

578

I. Daigo, Y. Matsuno and Y. Adachi

Tokeihyo (1971–2003), (JISF, Tokyo, 1971–2003). 16) Y. Komatsu: Journal of Archit. Plann. Environ. Engng, AIJ 439 (1992) 91–99. 17) A. Toi and J. Sato: Energy and Resources 18 (1999) 271–277. 18) Japan technical information service: Private communication. 19) The Japan ferrous raw materials association, Year book of ferrous raw materials 2004, (Tokyo, 2004) pp. 15, 19. 20) Japan automobile research institute: Kodo Gijutsu Shuyakugata Sangyoto Kenkyu Kaihatsu Chosa (Haisha Saishigenka, Haikibutu

Taisaku Suishin Chosa) Hokokusho (Tokyo, 2003) 13. 21) Japan steel can recycling association: http://www.steelcan.jp/recycle/ report/rate2004.html, Status 2005/06/08. 22) K. Nakajima, W. Tamaki, D. Fujimaki and I. Daigo: Tetsu-to-Hagane´ 91 (2005) 150–153. 23) Japan technical information service: Dobokubumon niokeru Tetsu scrap Hasseisuikei, (Japanese society of steel construction, Tokyo, 2003) p. 39.