Metabolic Process Modeling of Metal Resources Based on System Dynamics—A Case Study for Steel in Mainland China

Abstract

Rapid urbanization has promoted the development in human production and living standards, and the metabolic rhythm of metal resources has accelerated. Grasping the metabolic processes of metal resources and predicting their future development trends can help the country refine the formulation and adaptability of metal resource production and the recycling strategies for sustainable development. In this study, from the perspective of the entire life cycle of steel resources as an example, a system dynamics-based metal resource metabolism prediction model was established to predict the steel resources in the three stages, including production, in-use and end-of-life recycling. The trend in changes in steel resources production, in-use stock, end-of-life and recycling in mainland China from 1990 to 2020 were also analyzed. The results show that the volume of all stages of steel resource metabolism in mainland China from 1990 to 2020 has shown an increasing trend, and will reach a peak around 2040 and then remain stable. The steel resources in all the metabolism stages in mainland China were predominantly distributed in buildings. In mainland China, steel resource production efficiency reached above 0.9 and the steel resource outflow rate was 0.079, within which the domestic scrap rate reached 0.022 and the recycling rate reached above 0.8.

1. Introduction

With the continuous improvement in China’s technological level and modernization, the level of urban production and construction and the level of human consumption has gradually increased. The macro demand and production volume of metal resources such as iron, copper and aluminum have continued to increase. However, the non-strategic expansion of metal resource production efforts is highly likely to cause structural contradictions of overcapacity and supply exceeding demand for metals. This has led to an excess of end-of-life products and scrap metals, which has resulted in a considerable impact on, and threats to, the current metal recycling system. This can lead to low recycling efficiency, few recycling nodes and relatively limited recycling coverage. Therefore, a series of social problems such as heavy metal pollution, land resource occupation, and wastage of metal resources has occurred [1]. Steel is the most in-demand metal resource and plays a crucial role in economic development. It is vital for the sustainable growth of the metal industry to systematically grasp the metabolic processes and predict future development trends of steel resources.

Compared with the developed countries in the West, there are still substantial disparities between China’s recycling efforts and urban waste resource efficiency. European Union countries have always been in the lead in the context of waste recycling. In 2020, the average recycling rate of urban scrap for the European Union countries was 48%, and the amount of urban scrap recovered for recycling has increased by almost 80% since 2000 [2]. European steel manufacturers were able to achieve a recycling rate of up to 95% in 2019, which includes both on-site recycling as well as external companies’ residual utilization [3]. However, China can recover but not recycle renewable resources worth up to CNY 30–35 billion each year, with approximately 5 million tons (Mt) of scrap steel, and more than 200,000 tons of waste non-ferrous metals. Therefore, the external dependence on China’s resources is relatively high, which is highly unfavorable in the context of sustainable development [4]. Recycling scrap metal resources has become an important trend for solving the problem of international dependence on China’s resources. However, most existing enterprises have a relatively low capacity for recycling and processing scrap resources. For steel, the development rate of China’s steel recycling industry depends mainly on the economic development of the metal industry, government policies, and the technology level of the scrap industry [5]. This study aims to provide a systematic understanding of the current status and future possibilities of the steel cycle for the government, the metal industry, and the recycling industry, which can reveal the potential for steel resource utilization and sustainable development.

Industrial metabolism is a detailed representation of all the physical processes involved in transforming raw materials and energy into finished products and waste [6]. Sun et al. developed a conceptual model based on the industrial metabolism approach. The generic model can be used to analyze the energy flows for the iron and steel industry [7]. The metabolic process of metal resources includes three stages, that is, production, use, and end-of-life recycling. Currently, there are three main methods for modeling and predicting the metabolic process of metal resources, namely, the material flow analysis, the average lifetime method, and the regression analysis method.

The material flow analysis method is an effective tool for industrial metabolic studies of a specific substance on the country or regional scale, which can demonstrate the flow pattern and the flow intensity of a resource in the region [8]. Material flow stock analysis [9,10,11,12] has been widely used to assess social in-use stocks in metal resource end products on steel [13,14], copper [15,16], and aluminum [17,18]. Material flow stock analysis could be divided into top-down and bottom-up methods [19]. The top-down material flow stock analysis method is used to calculate the in-use stock of system resources by adding and summing the volume of resources entering and leaving the boundary of an object system over the years, which encompasses the inflow and outflow of resources and reflects the difference between these two. This approach is predominantly used on the national and provincial scales, because the total resource inflows and outflows at the national and provincial levels are relatively easy ways to count accurate resource inventory results [20,21]. In contrast, resource inventory data on the urban and suburban scale systems are difficult to obtain, so the bottom-up approach is generally utilized for urban-level material stock studies. The bottom-up material flow stock analysis method relies on determining the internal structure and used intensity of the metal end products in the regional system. It can be used to calculate the metal resource in-use stock by determining the number and intensity of structural units, and then accumulating them layer by layer from the individual end product to the regional system. The steel in-use stock estimation model constructed in this study belongs to the bottom-up strategy [22,23].

The average life method estimates the scrap volume of metal resources in end-of-life products by using the in-use stock and life probability distribution of various metal products [24,25,26]. The method requires the fine-scale distinction between the production year and the length of service for different metal products, while relying on subjective experience or expert knowledge to determine numerous complex model parameters. However, the wide variety and rapid renewal of metal end products in the current society usually lead to considerable uncertain deviations between the prediction results of the average life method and the actual situation.

The regression analysis method usually uses regression modeling such as autoregression or multiple regression to quantitatively fit the relationship between the socioeconomic variables and the metabolic stage volume of metal resources [27,28]. However, because of the spatiotemporal heterogeneity and stage dependence among metal resource metabolic processes, it is hard to characterize the relationship between the metal resource volume of different stages and the real metabolic process by simple linear regression, whose prediction result is relatively brittle and ostensible.

In summary, the existing methods have several challenges. Firstly, they need a large amount of complete high-quality data support to ensure the reliability and robustness of the estimation results, which is hard to obtain from the general cost for the public. Secondly, most existing methods focus on the single-stage model of metal resources, ignoring the transferred constraints and regular links between different metal stages. On this basis, the existing methods are weak at modeling the transfer relationship between the metal stages and the volume; thus, there is a need to rely on a large number of prior manual assumptions to simulate the current situation and forecast the future situation, which is usually subjective and unconvincing.

System dynamics was established in 1956 by Forrester [29,30,31], and takes the entire system as the study object, modeling the dynamic influence feedback among each internal portions of the entire system. The transfer constraints among internal elements can be solved by fitting the real system situation variation. Furthermore, the transfer constraints among internal elements can be controlled to simulate the unknown system situation in different scenarios. This means that system dynamics is an effective strategy to provide decision support about system or internal portions management [32]. Several studies used system dynamics to simulate resource volume variations and system evolution [33,34,35]. Unfortunately, the system dynamics-based metal metabolic process model is currently lacking. Faced with these challenges, this study proposed a system dynamics-based model for simulating the steel metabolic process to investigate and analyze the entire resource evolution.

2. Materials and Methods

In this paper, we utilize system dynamics to construct the steel metabolic process from production to complete disposal, based on the principle of conservation of matter [36]. Section 2.1 describes the steel metabolic process models based on system dynamics. The estimation of stage volume and transfer rates in the steel metabolic process model is elaborated in Section 2.2.

2.1. System Dynamics-Based Modeling of Steel Resource Metabolic Processes

The metabolic process of steel resources comprises three stages, that is, the production and processing of metal minerals, putting the metal products into use, and recycling end-of-life metals. Among them, the process of mining natural minerals, processing, purification and other industrial processes involved in becoming metal products is known as the production stage. The metal products produced at this stage provide services to people in the form of social products, that is, the use stage, until the metal products can no longer meet the needs of people. Finally, all types of end-of-life metal products start by entering the recycling site, until they are re-refined or directly discarded. During the end-of-life recycling stage, the successfully recycled metals re-enter the production stage as raw materials and then continue to participate in the metabolic cycle of metal resources. For the entire metabolic system, the resource metabolism process is in accordance with the law of conservation of matter. Therefore, for steel, the transformation relationship between the volume of resources in different metabolic stages, which is demonstrated by Figure 1, is derived according to the law of conservation of matter, as follows.

$$D\left(t+1\right)\ast \gamma =C\left(t+1\right)-S\left(t+1\right)$$

(1)

$$P\left(t+1\right)=C\left(t+1\right)\ast \omega$$

(2)

$$M\left(t+1\right)=M\left(t\right)-M\left(t\right)\ast \alpha +I\left(t+1\right)+P\left(t+1\right)$$

(3)

$$U\left(t+1\right)=U\left(t\right)-U\left(t\right)\ast \beta +M\left(t\right)\ast \alpha$$

(4)

$$D\left(t+1\right)=U\left(t\right)\ast \theta$$

(5)

where S(t), C(t), M(t), U(t), D(t), I(t), and P(t) are the stage volumes of the steel metabolic process in system dynamics. S(t) represents pig iron production; C(t) is crude steel production; M(t) is steel material volume; U(t) is steel in-use stock; D(t) is scrap; I(t) is net imports, and P(t) is steel production in the study region at the beginning of period t. α, β, θ, γ and ω are transfer rates of the steel metabolic process in system dynamics. α is the steel production rate, which represents the ratio of the amount of steel in social products processed and manufactured per unit time to the total amount of steel. β is the outflow rate of steel, which represents the ratio between the volume of steel social products outflowing the area and the steel social products existing in the study area per unit time. θ is the steel scrap rate, which is the ratio of the amount of steel in social products scrapped per unit time to the amount of steel in all existing steel social products. γ is the steel recycling rate, which represents the ratio of the amount of steel successfully extracted from scrapped social products to the amount of all scrapped steel per unit of time. ω is the steel manufacturing rate, indicating the ratio of the amount of crude steel processed and manufactured into steel per unit time to the total amount of all crude steel.

2.2. Model Solving

The main goal of solving the steel resource metabolic model constructed in this study is an estimation of the transfer rates, that is, steel production rate α, steel outflow rate β, steel recycling rate γ, steel manufacturing rate ω, and steel scrap rate θ in the model. The solving process relies on the several known stage volumes, such as C, S, P, I and D that can be obtained from available statistical data, which will be described in Section 3.2. In addition, steel in-use stock U needs to be obtained from the steel resource in-use stock estimation model. This means that the steel in-use stock U should be estimated before the transfer rates are solved.

2.2.1. Steel In-Use Stock U Solving

The in-use stock estimation model of steel resources constructed in this study used the bottom-up method. The bottom-up method calculates the in-use stock of metals in use in the entire economic system by summing the product of the number of products contained in each system in the economy and the intensity of metal used in the products, as follows:

$$U={{\displaystyle \sum }}_i{K}_i\times N_i$$

(6)

where U denotes the steel in-use stock, K_i denotes the quantity of the ith product, that is, the number of structural units, and N_i denotes the steel use intensity, that is, the steel content of the ith product.

This study estimated the in-use stock of steel from 1990 to 2020, and the estimation unit was each province of the country. Considering that the steel in-use stock estimated in this study was to provide data support for steel resource recovery, products with long life cycles and low obsolescence rates were excluded from consideration. According to the study of Song et al. [27] and Zhang et al. [28], we divided the entire socioeconomic system into the infrastructure system, architecture system, transportation facility system, consumer durables system, and machinery equipment system. The end products involved in each system are shown in Figure 2, which contains 69 kinds of products.

2.2.2. Model Parameter Solving

The steel resource metabolic dynamics model consists of a set of differential equations. Solving the steel resource metabolic dynamics model means solving the parameters α, β, γ, ω, and θ in the model. The genetic algorithm and simulated annealing algorithm [37] are both typical computer evolutionary optimization algorithms used to solve infinite enumeration problems. The genetic algorithm uses the population climbing method to search for the optimal value. However, its climbing performance is poor, and it is easy to mistake the local optimal solution for the global optimal solution, therefore, causing inaccuracy in the solution results. In contrast, simulated annealing starts from a higher initial temperature, and along with the decreasing temperature parameter, it combines certain probabilistic jump characteristics to randomly search for the global optimal solution of the objective function in the solution space. The local optimal solution can probabilistically jump out and eventually converge to the global optimal. Compared with the genetic algorithm, it has a faster convergence speed, and can jump out of local optimum until the global optimum is found. It is very suitable for solving combinatorial optimization problems. This method is not only simple, robust and flexible, but also has a performance of approximately global optimum. Therefore, the simulated annealing algorithm is used to solve the metabolic kinetic model of the steel resources in this study. Therefore, in this study, the simulated annealing algorithm was used to solve the steel resource metabolism dynamics model.

We use the simulated annealing algorithm to search a set of key parameters in the parameter space (steel production rate α, outflow rate β), so that the analytical results of the model can best reflect the transmission process of the steel metabolic volume, and the search parameter solution has the asymptotic optimal convergence characteristics. The simulated annealing algorithm includes the probabilistic sudden jump property to find the global optimal solution of the objective function randomly in the solution space. It then determines whether to accept the new solution during the solution process based on the Metropolis criterion, which is shown below:

$$P=\left\{\begin{array}{c} 1 E_{t+1}<E_t\\ e^{\frac{-\left(E_{t+1}-E_t\right)}{kT}} E_{t+1}\ge E_t\end{array} \right.$$

(7)

where, E_t is the objective function of the solving system. The flow chart of the simulated annealing algorithm is shown in Figure 3. The specific experimental steps are as follows:

(1)

Select initial temperature T for the annealing solution, generate a random initial solution X_t for steel production rate α and outflow rate β, and then obtain the value of the objective function E(X_t) corresponding to the initial solution.

(2)

Set the rate of temperature decrease k, where k takes a value between 0 and 1.

(3)

Perturbation is implemented on the current solution to form a new solution X_t+1 for steel production rate α and outflow rate β, and the corresponding objective function value E(X_t+1) is then obtained and calculated:

$$\Delta E=E_{t+1}-E_t$$

(8)

(4)

If ΔE < 0, then accept the new solution as the current sister, otherwise judge whether to accept the new solution based on the Metropolis criterion.

(5)

Repeat the perturbation and acceptance process L times at temperature T, i.e., perform Steps 3 and 4.

(6)

Determine whether the temperature reaches the termination temperature level. If yes, the algorithm is terminated to obtain the final optimal solution. Otherwise, return to Step 2 to cool down and continue the perturbation solution.

Figure 3. Simulated annealing algorithm flow chart.

Figure 3. Simulated annealing algorithm flow chart.

A key point of the simulated annealing algorithm is the need for an evaluation function that can evaluate the goodness of the solution results, that is, the objective function in the simulated annealing algorithm. In this study, the Hill disequilibrium coefficient [38] as the objective function is as follows:

$$Loss=\frac{\sqrt{{{\displaystyle \sum }}_{t=1}^T\left[{\left(M_t-e{M}_t\right)}^2+{\left(U_t-e{U}_t\right)}^2\right]}}{\sqrt{{{\displaystyle \sum }}_{t=1}^T\left[M_t{}^2+e{M}_t{}^2\right]}+\sqrt{{{\displaystyle \sum }}_{t=1}^T\left[U_t{}^2+e{U}_t{}^2\right]}}$$

(9)

where, M_t and U_t denote the actual value of the steel resource material and in-use stock at time t, respectively. eM_t and eU_t denote the forecast value of the steel resource material and in-use stock at time t, respectively.

3. System Boundary and Data Source

3.1. System Boundary

The entire metabolic process of steel from pig iron to waste recycling was selected as the resource metabolic system boundary in this study. This included processing and manufacturing, in-use, and end-of-life recycling and reprocessing, as shown in Figure 4. Specifically, in this paper, since the initial product of iron and steel metabolism is pig iron, the steel resource metabolism model we constructed does not need to include the import and export of iron ore. In addition, the import and export of the steel terminal products are indirectly reflected by the difference between the steel outflow rate β and scrap rate θ in the metabolic process. The spatial boundaries considered in this study were each province in mainland China, and the time range was 1990–2020.

3.2. Data Sources and Presentation

The data included in this study were predominantly divided into textual data and spatial data. The spatial data mainly included vector boundaries of provincial and municipal scales in China, which come from the public free Geospatial Data Cloud Platform [39]. The textual data include statistics from the available China Statistical Yearbook [40], the Provincial Statistical Yearbook (e.g., Hunan Statistical Yearbook [41]), and the China Steel Yearbook [42]. Based on these extensive data sources, the data links provided in this paper show the standardized data in detail, collated in this study.

The original data needed for the model were obtained from the national statistical yearbooks, steel industry yearbooks, and the relevant literature from 1990 to 2020. Based on this, how to use the original research data to solve the model is described as follows, in detail. Firstly, this study uses the end product volume from the China Statistical Yearbook [40] and steel content according to Wang et al. [43] and some steel industry standards [44,45] to estimate the steel in-use stock U by the in-use stock estimation model mentioned in Section 2.2.1. Then, the standardized data of crude steel production C, pig iron production S, steel production P, steel material quantity M and steel scrap quantity D and some intermediate volume data (steel import and export volume and steel inventory at the beginning of the year) can be obtained from the China Steel Yearbook [42]. Steel net imports I are obtained by adding the steel import and export volume addition and calculation. On this basis, the above known stage volume data are input into the metabolic model of steel resources proposed in this paper, and the simulated annealing algorithm is utilized to estimate the unknown steel manufacturing rate ω, steel productivity rate α, outflow rate β, scrap rate θ, and recycling rate γ, by fitting the above stage volume. Through the above process, this paper can construct the whole steel metabolic process from production, in-use and scrapping to recycling, and estimate the transfer rates and future steel metabolic stage volume.

4. Results

4.1. Analysis of Steel In-Use Stock Estimation Results

In this study, the in-use stock of steel resources was estimated on the national and provincial scale, spanning 1990–2020. The estimation result of the steel in-use stock in this study corresponds to that in the current literature and reports [12,20,27], which reveal the rationality and availability of the steel in-use stock U. More detailed comparison results are shown in Appendix A. From the results of the steel in-use stock estimation, mainland China’s steel in-use stock has shown an increasing trend since 1990, especially since 2010. The growth rate has accelerated significantly, and the national steel resource in-use stock was as high as 9 Gt by 2020 (Figure 5). On the provincial scale, except for Ningxia, Qinghai, and Hainan, where there was no significant change in the in-use stock, all other provinces showed an increasing trend, with Shandong, Guangdong and Jiangsu showing a particularly significant increase (Figure 6). In terms of the annual change in steel in-use stock, the steel in-use stock in infrastructure showed a pronounced upward trend. The growth trend was particularly pronounced after 2010 (Figure 7). The steel resources in-use stock in transportation facilities systems also increased. Meanwhile, the steel stock in machinery and equipment and durable goods facilities did not change significantly compared with other subsystems. According to the estimation results from each subsystem, the steel in-use stock was mainly distributed in the construction and infrastructure systems, accounting for up to 54% of the architecture system and approximately 25% of the infrastructure system in 2020. Meanwhile, the other systems accounted for a relatively small amount (Figure 8). This has highlighted that the steel recycling system can focus on construction steel recycling to improve recycling efficiency.

From the spatial visualization results (Figure 9), the in-use stock of steel in 1990 was below 30 Mt in most regions. Only Shandong and Liaoning provinces exceeded 50 Mt. The in-use stock of steel resources in Hebei, Jiangsu, Zhejiang, and Guangdong provinces was between 30 and 50 Mt. In 2000, the coastal provinces had a steel in-use stock of more than 70 Mt. Of this, up to 160 Mt was accounted for by the central region growth trend, which reached more than 30 Mt. By 2010, except for the western region and the Ningxia Hui Autonomous Region, the steel in-use stock in other provinces exceeded 70 Mt. Guangdong Province had the highest steel in-use stock, with up to 380 Mt. In 2020, except for the Tibet Autonomous Region, Ningxia Hui Autonomous Region, Qinghai Province, and Hainan Province, the steel in-use stock in other provinces was more than 70 Mt. More than 68% of the provinces had more than 100 Mt of steel in-use stock.

From the perspective of temporal variation, the steel in-use stock in mainland China significantly increased, from tens of million tons in 1990 to hundreds of million tons in 2020. This indicated that mainland China’s rapid industrial development during these three decades, and the volume of steel manufacturing in the process of human production and life has been greatly improved. In terms of spatial variation, steel in-use stock from the coastal areas gradually followed the trend of central region development. This was particularly the case in Guangdong Province, which has always been in the top two in the country since 2000. This is closely related to the national policy guidance.

4.2. Solution Analysis of Steel Resource Metabolism Kinetic Model

4.2.1. National-Scale Steel Resource Metabolism Kinetic Model Solving

The steel resource metabolic dynamics model was solved based on the results of the steel resource in-use stock estimation and relevant statistics. On the national scale, the time scale of this study is 2005–2020. The results from solving the transfer rates in the steel metabolic kinetic model are shown in

Table 1. Solving results of transfer rates in steel metabolic kinetic model on the national scale.

Description	Steel Production Rate α	Steel Manufacturing Rate ω	Steel Outflow Rate β	Steel Scrap Rate θ	Steel Recycling Rate γ
Solution of the value	0.955	1.12	0.079	0.022	0.809
R2	0.95	0.665	0.96	0.756	0.81

, and are in line with the reality report [46].

In Table 1, the value of R² indicates the degree of fit during the solution of recycling rate γ, steel manufacturing rate ω, steel outflow rate β, production rate α, and scrap rate θ. The closer the value is to 1, the higher the degree of fit and the more accurate the solution value. The steel manufacturing rate ω is the relationship between the national annual crude steel production and steel production measured in this study (Figure 10a). The reason why it is greater than 1 is that crude steel is made into steel by adding other alloy products to the process of manufacturing. There is double counting when aggregating the total national steel production in real life. Therefore, the steel production in the statistical yearbook is greater than the crude steel production. The reason why the steel outflow rate β is larger than the steel scrap rate is that the country will trade internationally each year for steel end products. This therefore resulted in the change in steel in-use stock being larger than the amount of steel scrap in domestic production life, which is shown in Figure 10b.

The model fit variables were obtained by introducing the solved parameters into the model and comparing them with the real data of the variables. The goodness of fit R² between the predicted and true values of the steel material volume M and the steel in-use stock U (Figure 10c,d), calculated using the production rate α and scrap rate β parameters of the steel resource metabolic dynamics model solved by the simulated annealing algorithm, was as high as 0.95 and 0.96. This indicated that the model solution results were highly reliable.

The time series changes in the steel material volume and steel scrap volume on the national scale in the subsystems were estimated from the estimation results of the steel in-use stock model and related statistical data (Figure 11). In terms of time series changes, the national steel material volume and steel scrap volume increased from 2005 to 2020. The steel material volume increased slowly from 2013. The growth rate was relatively slow in 2017 and accelerated after 2017. Meanwhile, the scrap volume of steel resources maintained a steady growth trend. In terms of subsystem distribution, the subsystem that occupied the major steel in the steel material volume and scrap volume was still the architecture system, followed by the machinery and transportation systems.

4.2.2. Kinetic Model Solving for the Provincial-Scale Metal Resource Metabolism

On the provincial scale, the time scale of this study is 2010–2020. The results from solving the model parameters are shown in

Table 2. Solving results of transfer rates in steel metabolic kinetic model on the provincial scale.

Province	Steel Production Rate α	Steel Manufacturing Rate ω	Steel Outflow Rate β	Steel Scrap Rate θ	Steel Recycling Rate γ	Loss
Beijing	0.76217	1.3843	0.015	0.02388	0.69265	0.009
Tianjin	0.96004	2.6887	0.60916	0.02071	0.44051	0.05
Hebei	0.99247	1.2184	0.80102	0.01665	0.78521	0.01
Shanxi	0.95075	0.9936	0.27596	0.02157	0.93014	0.03
Inner Mongolia	0.97968	0.9914	0.06684	0.02292	0.93534	0.01
Liaoning	0.97221	1.0583	0.27376	0.02089	0.99232	0.01
Jilin	0.95820	1.1153	0.15747	0.02030	0.76493	0.02
Heilongjiang	0.93069	0.8892	0.00850	0.02164	0.96935	0.01
Shanghai	0.94702	1.1538	0.10713	0.01554	0.96555	0.006
Jiangsu	0.98409	1.3260	0.23475	0.02019	0.66627	0.01
Zhejiang	0.93343	2.5243	0.07094	0.02032	0.39380	0.02
Anhui	0.96783	1.2384	0.11391	0.01797	0.68887	0.004
Fujian	0.97479	1.6209	0.12355	0.02471	0.68829	0.012
Jiangxi	0.97711	1.1039	0.17170	0.02095	0.84622	0.007
Shandong	0.98358	1.2904	0.16221	0.02077	0.78528	0.008
Henan	0.95826	1.4394	0.12406	0.01646	0.66669	0.009
Hubei	0.95787	1.1792	0.10971	0.02393	0.72683	0.02
Hunan	0.97931	1.0581	0.05327	0.01521	0.98861	0.02
Guangdong	0.93608	1.8789	0.06703	0.01861	0.35664	0.01
Guangxi	0.98009	1.5430	0.19023	0.01811	0.69393	0.03
Hainan	0.84607	0.0003	0.00030	0.01702	0.47892	0.12
Chongqing	0.96486	1.8376	0.09733	0.01780	0.47678	0.004
Sichuan	0.98493	1.3101	0.05964	0.01902	0.72196	0.02
Guizhou	0.97393	1.0295	0.00106	0.01856	0.78082	0.04
Yunnan	0.96640	1.0641	0.10823	0.02256	0.96446	0.01
Shaanxi	0.95688	1.4774	0.09364	0.01914	0.58563	0.01
Gansu	0.90719	1.0503	0.05460	0.01862	0.82213	0.01
Qinghai	0.95249	0.9777	0.00038	0.01971	0.96967	0.09
Ningxia	0.94025	1.0743	0.00075	0.02218	0.50731	0.04
Xinjiang	0.96346	1.1783	0.08511	0.02459	0.82474	0.01

. The reliability of the provincial solution results is shown in Appendix B.

Table 2 shows that the steel production rate of most provinces is above 0.9. Hebei province was the highest, reaching 0.99. This is in line with Hebei province being the largest steel-producing province in China. It is also the province with the largest steel production in China, followed by Beijing with a steel production rate of 0.76. This is relatively low compared to other provinces, because as the capital of China, Beijing hardly carries out any industrial production. Its steel demand is predominantly derived from imports from outside the province rather than from its own production. The steel manufacturing rate of Shanxi, Inner Mongolia Autonomous Region, Hainan, and the Qinghai provinces is less than 1. This is because the region has less steel production and there is no duplication in the steel production statistics from the data. Shanxi, the Inner Mongolia Autonomous Region, and Qinghai provinces are able to produce and sell their own steel resources. Meanwhile, the steel manufacturing rate of Hainan province is 0.0003. This indicates that Hainan’s steel resources are heavily dependent on those outside the province. The steel scrap rate for each province fluctuates by approximately 0.02. This is comparable to the steel scrap on the national scale, because the base of steel in-use stock is the largest among the variables in the metabolic model. Therefore, the efficiency values do not substantially change. Based on the physical importance of the steel outflow rate and the steel scrap rate, if the steel outflow rate in a region is greater than the steel scrap rate, then there is a net export (exports are greater than imports) for steel resources in that region, and vice versa, indicating a net import.

From the model solution results, Beijing, Heilongjiang, Hainan, Guizhou, Qinghai, and Ningxia Hui Autonomous Regions depend on steel resources imported from other provinces. Meanwhile, Hebei Province has a large export of steel resources, and its steel outflow rate is much larger than the steel scrap rate compared to other provinces. The results from the solutions to the provincial steel resource metabolic dynamics model all correspond to a loss value below 0.05. The predicted values of the model plotted for steel resource material volume, steel resource in-use stock, and scrap volume in Shandong province fit the true values (Figure 12). The difference between the predicted and true values is relatively small. In addition, the goodness of fit of the predicted values of the steel resource metabolic process volume obtained by substituting the solved parameters into the model with the true values is approximately 0.9. This indicates that the solved results are reliable. In addition, Appendix B reveals the reliability of fit between the statistical value and the predicted value of other provinces.

From the spatial distribution (Figure 13), in the steel resource metabolism process, the steel production rate in most provinces was above 0.9, except for in the Hainan, Ningxia, and Qinghai provinces. According to the information query, steel production in these provinces is relatively low. The provinces are also not steel-production provinces. The steel outflow rate was predominantly less than 0.19. The outflow rate peak regional distribution in North China and Jiangsu Province in coastal areas, and the central China steel outflow rate was mainly in the 0.09–0.019 range. The steel scrap rate distribution in the eastern coastal provinces and the economic development at the forefront of the regional scrap rate was higher. This is consistent with the high efficiency of the production-and-life phenomenon. The more efficient the production and life, the more developed the economy, and the higher the rate of product use and the scrap rate. However, in the western region of Tibet, the scrap rate was relatively high. The reason for the high scrap rate in Tibet, which is in the western region, was the small base of steel in use. The regions with high recycling rates were concentrated in the southern region and some first-tier cities.

From the spatial and temporal visualization results (Figure 14) from 2010 to 2020, mainland China’s steel material volume showed an upward trend. The national average steel material in 2010 was approximately 26 Mt by 2020. In 2010, only the Hebei and Jiangsu steel material volume reached more than 80 Mt. Of these, Hebei, with 160 Mt of steel resource materials, ranked first. By 2020, the volume of steel materials reached more than 80 Mt by province compared with 2010. There was an increase in Shandong and Guangdong, and Shandong reached 310 Mt. This was followed by a significant increase in the volume of steel materials, by more than 20 Mt, by province. The main development areas were distributed in the southeast.

The spatial and temporal evolution of the scrapped steel scrap is shown in Figure 15. In 2000, the high-value areas for steel scrap were predominantly located in coastal areas, such as Shandong, Jiangsu, Zhejiang and Guangdong, with scrapped steel scrap exceeding 4 Mt. The highest was Guangdong with approximately 7.86 Mt, followed by Liaoning and some central areas belonging to the second tier. However, the steel scrap of Jiangxi was only 1.87 Mt. Meanwhile, that of its neighboring provinces were higher than 2 Mt. This has shown that Jiangxi is lagging behind the development of its neighboring regions. Most of the coastal provinces with steel scrap in 2020 exceeded 8 Mt, up to 10 Mt, followed by most provinces in the country with more than 2 Mt. The remaining provinces had relatively low steel scrap because of population, economic, environmental, and other constraining factors.

4.3. Steel Resource Metabolism Forecast

Based on the results of solving the parameters in the steel metabolic dynamics model on the national and provincial scales, the future steel resource material volume, in-use stock, and scrap volume could be predicted. However, given that human steel resource ownership will not always show an upward trend with time, it will eventually tend to a saturated and stable state. According to Gordon et al. [47], the baseline scenario is defined as the technical level of the steel industry remaining unchanged, and the maximum per capita steel ownership will not exceed the threshold of the living standards of developed countries under the existing technical level, i.e., the per capita steel ownership of each industry are 5.7 t of construction, 2.3 t of transportation, 2.1 t of machinery, 0.6 t of durable consumer goods and another 0.8 t [48]. The projected results for the metabolic process volume of steel resources under this scenario are shown in Figure 16. After 2040, the metabolic process stage volume of steel resources in mainland China was projected to maintain a stable development trend, in which the steel in-use stock reached a threshold value of approximately 16 Gt. The steel end-of-life volume was approximately 380 Mt, and the steel material volume reached a threshold value of 1.6 Gt and fluctuated smoothly in its vicinity. The steel recycling volume followed the changes in the steel end-of-life volume.

The results forecasted for the metabolic process stage volume of steel resources under different systems in the baseline scenario are shown in Figure 17. This shows the metabolic trends of steel material volume, in-use stock, scrap volume, and recycling volume in each subsystem. In terms of subsystems, China’s steel resources mainly accumulated in the architecture system, accounting for approximately 50% of the total resources. After 2025, the growth rate of the metabolic process stage volume of steel resources slows down, reaches a development peak after 2040, and then remains stable.

5. Discussion

5.1. Robustness and Limitations of Our Estimation

We proposed a system dynamics-based metabolic model for the whole life cycle of steel resources, and conducted an experimental analysis in mainland China at the provincial level. We compared the steel in-use stock estimation model results with the current literature and realistic situation reports (see Appendix A), which demonstrated the robustness and reliability of our experimental results of an in-use stock estimation. At the national level, the differences between our steel in-use stock estimation and that of the existing studies are within 6%, and within 30% at the provincial level, which are acceptable for the metal resource estimation. It is worth noting that, although the difference in the comparison results of the Hebei Province is as high as 29.5%, the results of this paper are consistent with the existing research results in the order of magnitude. Hebei Province, as a large steel-producing province in China, has a large amount of steel in-use stock. The reason why the estimation results of Hebei Steel’s in-use stock calculated by Song et al. [12] are larger than our estimation results is that they consider more end products in the infrastructure, such as power stations, cables, etc. In addition, this study measures credibility by calculating the R² between the estimated results from the proposed steel metabolic dynamic model and the survey statistical data from the Statistical Yearbook [40,42], and explores self-consistency by comparing the transfer rates for the provincial average and on the national scale (see Appendix B). The value range of R² is 0–1, and the closer the value is to 1, the better the simulated effect. From the R² between the predicted steel material volume M, steel in-use stock U and steel scrap volume D of the proposed method, we can see that the model solution results are reliable and can indicate well the reality and future development trends. The provincial average is roughly the same as the national scale result (see

Table A3. Comparison between the average value of the provincial scale and national scale of model parameter solution results.

Item	Steel Production Rate α	Steel Manufacturing Rate ω	Steel Outflow Rate β	Steel Scrap Rate θ	Steel Recycling Rate γ
China	0.955	1.12	0.079	0.022	0.809
Provincial average	0.951	1.23	0.14	0.02	0.74
Difference	−0.42%	9.8%	77.2%	−0.09%	−8.5%

). It is worth noting that the provincial average steel outflow rate β is different from the national level, which is due to the fact that the steel resource inflows and outflows between provinces differ from the steel resource flows between countries.

Our study has certain limitations that can be further improved in future works. In fact, the steel metabolic transfer rates among different stages should be varied with periodic development. Due to the limitations of data granularity, it is hard to accurately establish the dynamic relationship between transfer rate and times. Therefore, it is expected that, with the improvement in data granularity and prior domain knowledge, the time-dependent transfer rates could be modeled using the policies and the economic factors. Secondly, this paper only takes steel as a study case. The proposed method has potential for other meta resources, such as copper or aluminum, but the stage volume and transfer rate in the metabolic model should be modified in future works.

5.2. Policy Implications for Resource Sustainability

Understanding the spatiotemporal evolution of the whole process of resource metabolism and its future development trend provides intuitive and powerful support for the government to formulate efficient and local recycling decisions. Due to the heterogeneity of population and urbanization, the accumulation of ground resources is diverse in cities. Therefore, the resource intensity and policy preferences in different regions are various. It is necessary to realize policy guidance according to the local resource conditions, so as to promote energy conservation but reduce resource consumption, environmental pollution and recycling costs. It is of great significance to grasp the current situation and future regulation of the steel metabolic system for the goal of sustainable green development.

The proposed method can systematically model the steel metabolism process, and find the bottleneck and optimization points of resource utilization based on transfer rates, which provide insights for promoting the sustainable development of economic and environmental resources from the perspective of regional synergy. The steel production rate α represents the ratio of the amount of steel in the social end product process per unit time to the total amount of steel material. The low α value indicates that the steel end product processed level is inferior to the steel material; thus, the government can promote the steel end product process to enhance the weak urban industry, or outflow steel materials as an industrial city to avoid the accumulation or waste of steel materials. The steel scrap rate θ is the ratio of the amount of steel in social end product scrap per unit time to the amount of steel in all existing steel social end products. The high θ value indicates that the update of steel end products in the region is large, and the government should pay more attention to the vigorous recycling strategy of waste steel resources to conserve resources and execute sustainable development. The steel recycling rate γ represents the ratio of the amount of steel successfully extracted from scrapped steel social end products per unit of time to the amount of all scrapped steel. The relatively lower γ value denotes that the extraction and purification of scrapped steel social end products are inferior to the recycling level of other regions, which encourages the government or industry to strengthen the policy preference or the recycling technological level.

6. Conclusions

This study proposes a system dynamics-based metabolic model for the entire life cycle of steel resources, which contains a bottom-up steel in-use stock estimation model to estimate the steel in-use stock in each province from 1990 to 2020. The spatiotemporal evolution of the metabolic process of steel resources, comprising steel material, in-use stock, and scrap, was analyzed at the national and provincial scales. The experimental results show that the steel resources were predominantly concentrated in the eastern region, from a spatial perspective, which is related to the regional economic development. Meanwhile, the metabolic process of steel resources has shown an overall increasing trend from a temporal perspective. In the metabolic process of steel resources, the production rate could generally reach approximately 0.9, except for in Hainan, Ningxia, and Qinghai, which are non-steel-producing provinces with a relatively low steel product level. The scrap rate relies on the large volume of steel in-use stock and durable steel products, which fluctuates by about 0.02. Comparing the steel outflow rate and the scrap rate can describe the regional external and internal steel demand. The high value of the recycling rate was mainly distributed in South China and North China. However, there was relatively little difference in the steel recycling rate between the provinces, with an average value of about 0.7. According to the system dynamics-based steel resource metabolic model proposed in this study, the metabolic development trend of mainland China’s steel resources under the baseline scenario was predicted. The results show that the metabolic process of mainland China’s steel resources slows down after 2025 and then reaches a peak in 2040, after which it tends to develop steadily.

The steel resource metabolic model based on system dynamics proposed in this paper takes pig iron as the starting stage of steel metabolism, and scrap steel recycling as the end stage of steel metabolism. The proposed method employs the material transfer constraints of the metabolic process to comprehensively and finely simulate the whole process of steel stages and their transformation, which solves the issue of an incomplete monitoring of stage volume changes in the steel metabolic process using industry survey statistics, and realizes the interpretable prediction of the future evolution trend of steel resources. The principle of this method can be applied to other metal resources, and provides data and decision support for China’s renewable-resource utilization industry.