Cement dynamic material flow model based on flow driving

Abstract

The invention relates to a cement dynamic material flow model, in particular to a cement dynamic material flow model based on flow driving. The method aims at solving the problems that an existing material flow model cannot represent large-scale dynamic characteristics, an uncertainty analysis framework cannot be embedded, and details of the whole life cycle cannot be covered. The method comprises the following steps: step 1, obtaining the apparent consumption of cement according to the production quantity of cement, inlet and outlet flows and the cement flows of inlet and outlet cement products; 2, calculating the amount of cement flowing into each use department every year according to the market share of the cement flowing into each terminal use department; step 3, based on the cement survival function and the actual cement inflow condition of each terminal use department, calculating the in-use inventory and the scrap outflow volume of the cement; and 4, performing uncertainty analysis on the cement dynamic material flow model by applying a Monte Carlo simulation algorithm. The invention belongs to the technical field of sustainable management and cyclic utilization of cement resources.

Description

Technical Field

[0001] The invention relates to a cement dynamic material flow model, belonging to the technical field of sustainable management and recycling of cement resources. Background Art

[0002] As a core material in the modern construction industry, cement's material flows throughout its life cycle are closely linked to resource and environmental issues. However, existing material flow models suffer from significant limitations in terms of dynamics, systematicity, and reliability, making them difficult to support refined management and sustainable development decisions for the industry. Traditional models often employ static analytical frameworks, relying primarily on macro-statistical data such as annual production and consumption to construct material balance relationships. While these models provide basic insights at the aggregate level, they ignore dynamic characteristics such as the annual evolution of production and consumption, as well as market supply and demand, resulting in a lack of responsiveness to temporal fluctuations and emergencies. Furthermore, traditional models generally assume a direct correlation between cement consumption and production, incorporating import and export data as adjustment factors. These models typically fail to account for the flow and distribution of cement across different end-use sectors. For example, cement demand may vary between sectors such as construction, infrastructure development, and industrial applications, and traditional models often simplify or ignore these differences. Consequently, these models fail to fully reflect the flow and actual consumption of cement. This is particularly true when new urbanization drives a surge in residential construction demand, or when major infrastructure projects trigger fluctuations in demand for civil engineering materials. The rigid allocation mechanisms of traditional models can distort flow analysis.

[0003] At the material life cycle management level, existing research generally lacks a description of the dynamic characteristics of cement during its service life. As a typical long-life building material, the actual service life of cement products is affected by multiple factors such as building type, environmental conditions, and maintenance level, ranging from decades for residential buildings to centuries for infrastructure. Traditional models use linear decay or fixed scrap rates to estimate inventory and outflow. They neither establish a survival function that conforms to engineering reality nor ignore the temporal and spatial differences in cement scrap volume under different usage scenarios, resulting in a distortion of the relationship between inventory dynamics and flow in material flow accounting. This simplification directly affects the assessment of resource recovery potential and the accurate measurement of environmental impacts during the waste stage. In particular, in the context of accelerated urban renewal and a sharp increase in building demolition, model errors may be significantly amplified.

[0004] In addition, the model's insufficient ability to analyze system uncertainties restricts the effectiveness of decision support. The accuracy of the cement material flow model is affected by many factors, especially the fluctuations in key data such as production volume, import and export data, and the average service life of cement products. Traditional deterministic models find it difficult to quantify the impact of the interaction of these variables on the system. Although probabilistic methods such as Monte Carlo simulation are becoming increasingly mature in environmental system analysis, a complete uncertainty analysis framework has not yet been formed in the cement field, resulting in the lack of a risk assessment dimension for the model output results. Therefore, constructing a new material flow model that can characterize large-scale dynamic characteristics, embed an uncertainty analysis framework, and cover details of the entire life cycle has become an urgent need to improve the efficiency of resource and environmental management in the industry. Summary of the Invention

[0005] In order to solve the problems that existing material flow models are unable to characterize large-scale dynamic characteristics, embed uncertainty analysis frameworks, and cover details of the entire life cycle, the present invention proposes a flow-driven cement dynamic material flow model.

[0006] The technical solution adopted by the present invention to solve the above problems is: the steps of the present invention include:

[0007] Step 1: Obtain the apparent cement consumption by calculating the cement production, import and export flows, and cement flows of imported and exported cement products;

[0008] Step 2: Calculate the amount of cement flowing into each end-use sector each year based on the market share of cement flowing into each end-use sector;

[0009] Step 3: Based on the cement survival function and the actual cement inflow of each end-use sector, calculate the cement in-use inventory and scrap outflow;

[0010] Step 4: Use the Monte Carlo simulation algorithm to perform uncertainty analysis on the cement dynamic material flow model.

[0011] Furthermore, the calculation process of the apparent consumption of cement in step 1 is:

[0012] P Cement,tn =C Prod,tn +C Imp,tn -C Exp,tn +C Eq,i,tn -C Eq,e,tn (1),

[0013] In formula (1), P Cement,tn Indicates the tth n Annual apparent cement consumption, C Prod,tn Indicates the tth n Annual cement production, C Imp,tn Indicates the tth nAnnual cement import volume, C Exp,tn Indicates the tth n Annual cement export volume, C Eq,i,tn Indicates the tth n Equivalent cement volume of annual imported cement products, C Eq,e,tn Indicates the tth n Equivalent cement volume of annual exported cement products;

[0014] C Eq,i,tn =C Prod,i,tn ×R i (2),

[0015] In formula (2), C Prod,i,tn Indicates the tth n Annual cement product import volume, R i It indicates the ratio of imported cement products converted into equivalent cement, that is, the cement content of imported cement products;

[0016] C Eq,e,tn =C Prod,e,tn ×R e (3),

[0017] In formula (3), C Prod,e,tn Indicates the tth n Annual cement product export volume, R e It indicates the ratio of exported cement products converted into equivalent cement, that is, the cement content of exported cement products.

[0018] Furthermore, the calculation process of cement inflow to each end-use sector in step 2 is as follows:

[0019] I j,tn =P Cement,tn ×R j (4),

[0020] In formula (4), I j,tn Indicates the tth n The amount of cement flowing into end-use sector j in a year, R j represents the cement market share of end-use sector j, that is, the proportion of cement flowing into each end-use sector.

[0021] Furthermore, the calculation process of cement inventory in use of each terminal use department in step 3 is as follows:

[0022]

[0023] In formula (5), Indicates the tth n The amount of cement in use in the end-use sector j in year t, that is, considering the service life of cement, n The cumulative stock of cement in the sector as of year;

[0024] S j (t,t n ) represents the cement survival function in the end-use sector j, i.e., the product entering at time t is n There is a probability of use;

[0025] S j (t,t n )=1-F j (t,t n ) (6),

[0026] In formula (6), F j (t,t n ) represents the cement life distribution function in the end-use sector j.

[0027] Furthermore, the calculation process of cement scrap outflow of each terminal use department in step 3 is as follows:

[0028]

[0029] In formula (7), Indicates the tth n The outflow of cement scrap in end-use sector j in year t n The amount of cement scrapped after reaching the end of its service life in this department in year.

[0030] The beneficial effects of the present invention are:

[0031] 1. This invention adopts a flow-driven approach, taking into account the dynamic relationship between cement production, import and export, and end-use sectors, and can accurately reflect cement flow and inventory changes. Compared with traditional static models, it can provide more accurate cement material flow analysis results;

[0032] 2. By introducing the cement survival function and the probability distribution of cement service life (such as Weibull distribution), the present invention can accurately calculate the in-use inventory and scrap outflow of cement, comprehensively considering the life cycle effect of cement, and making the calculation of material flow more consistent with actual conditions;

[0033] 3. The present invention uses the Monte Carlo simulation algorithm to perform uncertainty analysis on the model, which can effectively evaluate the model prediction error caused by the uncertainty of the input data, thereby enhancing the robustness and reliability of the model;

[0034] 4. Each step in the model of the present invention, such as the calculation of apparent cement consumption, cement inflow to end-use departments, in-use inventory and scrap outflow, can be adjusted and optimized according to different needs to meet analysis requirements at different levels and dimensions. It can also be combined with other prediction models, optimization algorithms, scenario analysis methods, etc. to achieve accurate prediction of future cement material flows. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a diagram of China's apparent cement consumption from 2008 to 2022;

[0036] Figure 2 This is a diagram of China's cement inventory in use from 2008 to 2022;

[0037] Figure 3 This is a comparison chart of China's cement inventory in use in 2022;

[0038] Figure 4 This is a diagram showing the Monte Carlo simulation results of China's cement inventory from 2008 to 2022. DETAILED DESCRIPTION

[0039] Specific implementation method 1: A cement dynamic material flow model based on flow drive, the specific steps include:

[0040] Step 1: Obtain the apparent cement consumption by calculating the cement production, import and export flows, and cement flows of imported and exported cement products;

[0041] The calculation process of apparent cement consumption is:

[0042] P Cement,tn =C Prod,tn +C Imp,tn -C Exp,tn +C Eq,i,tn -C Eq,e,tn (1),

[0043] In formula (1), P Cement,tn Indicates the tth n Annual apparent cement consumption, C Prod,tn Indicates the tth n Annual cement production, C Imp,tn Indicates the tth n Annual cement import volume, C Exp,tn Indicates the tth n Annual cement export volume, C Eq,i,tn Indicates the tth n Equivalent cement volume of annual imported cement products, C Eq,e,tn Indicates the tth n Equivalent cement volume of annual exported cement products;

[0044] C Eq,i,tn =C Prod,i,tn ×R i (2),

[0045] In formula (2), C Prod,i,tn Indicates the tth n Annual cement product import volume, R i It indicates the ratio of imported cement products converted into equivalent cement, that is, the cement content of imported cement products;

[0046] C Eq,e,tn =C Prod,e,tn ×R e (3),

[0047] In formula (3), C Prod,e,tn Indicates the tth n Annual cement product export volume, R e It indicates the ratio of exported cement products converted into equivalent cement, that is, the cement content of exported cement products;

[0048] Step 2: Calculate the amount of cement flowing into each end-use sector each year based on the market share of cement flowing into each end-use sector;

[0049] The calculation process of cement inflow to each end-use sector is as follows:

[0050] I j,tn =P Cement,tn ×R j (4),

[0051] In formula (4), I j,tn Indicates the tth n The amount of cement flowing into end-use sector j in a year, R j represents the cement market share of end-use sector j, that is, the proportion of cement flowing into each end-use sector;

[0052] Step 3: Based on the cement survival function and the actual cement inflow of each end-use sector, calculate the cement in-use inventory and scrap outflow;

[0053] The calculation process of cement inventory in use in each end-use sector is as follows:

[0054]

[0055] In formula (5), Indicates the tth n The amount of cement in use in the end-use sector j in year t, that is, considering the service life of cement, n The cumulative stock of cement in the sector as of year;

[0056] Sj (t,t n ) represents the cement survival function in the end-use sector j, i.e., the product entering at time t is n There is a probability of use;

[0057] S j (t,t n )=1-F j (t,t n ) (6),

[0058] In formula (6), F j (t,t n ) represents the cement life distribution function in the end-use sector j;

[0059] The calculation process of cement scrap outflow of each end-use sector is as follows:

[0060]

[0061] In formula (7), Indicates the tth n The outflow of cement scrap in end-use sector j in year t n The amount of cement scrapped after reaching the end of its service life in the sector in the year;

[0062] Step 4: Use the Monte Carlo simulation algorithm to perform uncertainty analysis on the cement dynamic material flow model.

[0063] Among them, the uncertainty analysis in step 4 needs to consider important data uncertainty factors such as production volume, import and export flows, and the average service life of cement products; the volatility of these data is modeled separately using normal distribution, with different coefficients of variation (CV) used for production and import data of developed and underdeveloped countries, and the uncertainty of trade data and service life is represented by normal distribution; different parameter fluctuation scenarios are simulated through the Monte Carlo simulation algorithm, and 10,000 independent experiments are conducted to capture the impact of the uncertainty of each data source on the output of the cement material flow model.

[0064] Example

[0065] like Figures 1 to 4 As shown,

[0066] Step 1: Obtain China's apparent cement consumption by analyzing China's cement production, import and export flows, and cement flows of imported and exported cement products;

[0067] Specifically include:

[0068] Step 101: First, classify China's cement trade data, directly record the annual cement import and export volumes of each region, and filter out indirect cement trade data for each cement product (e.g., concrete);

[0069] Step 102: converting the equivalent cement amount into the equivalent cement amount by using the equivalent cement ratio coefficient of different cement products;

[0070]

[0071] in, Indicates the tth n Equivalent cement volume of annual imported cement products; Indicates the tth n Annual cement product import volume; R i It indicates the ratio of imported cement products converted into equivalent cement, that is, the cement content of imported cement products;

[0072]

[0073] in, Indicates the tth n Equivalent cement volume of annual exported cement products; Indicates the tth n Annual cement product export volume; R e It indicates the ratio of exported cement products converted into equivalent cement, that is, the cement content of exported cement products;

[0074] Step 103: Substitute China's cement production data and trade data into the following formula to calculate China's apparent cement consumption: Figure 1 is China's apparent cement consumption from 2008 to 2022;

[0075]

[0076] in, Indicates the tth n Annual apparent cement consumption; Indicates the tth n Annual cement production; Indicates the tth n Annual cement import volume; Indicates the tth n Annual cement export volume;

[0077] Step 2: Calculate the annual amount of Chinese cement flowing into each end-use sector based on the market share of Chinese cement flowing into each end-use sector;

[0078] Specifically include:

[0079] Step 201: Cement end-use sectors in China are divided into three categories: residential construction (RES), non-residential construction (NRES), and civil engineering (CE);

[0080] Step 202: Based on China's annual apparent cement consumption and the cement market share of the three major end-use sectors, calculate the amount of cement flowing into each end-use sector;

[0081]

[0082] in, Indicates the tth n The amount of cement flowing into end-use sector j in a year; R j represents the cement market share of end-use sector j, that is, the proportion of cement flowing into each end-use sector, such as residential construction, non-residential construction, civil engineering, etc.;

[0083] Step 3: Based on China's cement survival function and the actual cement inflow into the three major end-use sectors, calculate the cement in-use inventory and scrap outflow;

[0084] Specifically include:

[0085] Step 301: Use Weibull distribution to fit the service life distribution of Chinese cement, and determine the scale parameter and shape parameter of Weibull distribution;

[0086]

[0087] Among them, F j (t,t n ) represents the cement life distribution function in the end-use sector j; λ j is the scale parameter of the Weibull distribution, which represents the characteristic time of cement service life; k j is the shape parameter, which controls the shape of the distribution. j =1, the Weibull distribution degenerates into an exponential distribution, indicating that the service life of cement is a fixed random variable;

[0088] Step 302: Based on the Chinese cement life distribution function, obtain the Chinese cement survival function;

[0089]

[0090] Among them, S j (t,t n ) represents the cement survival function in the end-use sector j. That is, the product entering at time t is n There is a probability of use;

[0091] Step 303: Calculate the in-use inventory and scrap outflow of China's cement through China's cement survival function and the actual cement inflow of the three major end-use sectors. Figure 2 is the amount of cement in use in China from 2008 to 2022. Figure 3 A comparison chart of China's cement inventory in use in 2022;

[0092]

[0093] in, Indicates the tth n The amount of cement in use in the end-use sector j in year t, that is, considering the service life of cement, n The cumulative stock of cement in the sector as of year;

[0094]

[0095] in, Indicates the tth n The outflow of cement scrap in the terminal use sector j in year t is: n The amount of cement scrapped after reaching the end of its service life in the sector in the year;

[0096] Step 4: Use the Monte Carlo simulation algorithm to perform uncertainty analysis on the cement dynamic material flow model;

[0097] Specifically include:

[0098] Step 401: taking production volume, import and export flow rates, and average service life of cement products as important data uncertainty factors affecting cement material flow estimation;

[0099] Step 402: Set the coefficient of variation (CV) of production and import and export flows of developed and underdeveloped countries to 5% and 10% respectively;

[0100] Cement production and consumption in developed countries are relatively stable, so the uncertainty of their data is low; while in less developed countries, the uncertainty of their data is high due to the greater volatility of production and market environment;

[0101] Step 403: Evaluate the uncertainty of trade data using normal distribution to effectively capture possible fluctuations in trade data, thereby making a more accurate estimate of cement flow;

[0102] Step 404: Based on existing literature and data, the natural fluctuation of the service life of cement products is fully considered. It is assumed that the average service life of each cement used follows a normal distribution, and the coefficient of variation (CV) is set to 10%;

[0103] Step 405: Using the Monte Carlo simulation algorithm, we integrate the uncertainties from different sources and simulate the performance of the cement material flow model in the face of uncertain data through 10,000 independent experiments. Figure 4 The Monte Carlo simulation results of China's cement inventory in use from 2008 to 2022 are as follows;

[0104] In each test, key parameters such as production volume, inlet and outlet flow rates, and service life are randomly sampled and fluctuated according to the set distribution.

[0105] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A cement dynamic material flow model based on flow drive, characterized in that: The specific steps include: Step 1: Obtain the apparent cement consumption by calculating the cement production, import and export flows, and cement flows of imported and exported cement products; Step 2: Calculate the amount of cement flowing into each end-use sector each year based on the market share of cement flowing into each end-use sector; Step 3: Based on the cement survival function and the actual cement inflow of each end-use sector, calculate the cement in-use inventory and scrap outflow; Step 4: Use the Monte Carlo simulation algorithm to perform uncertainty analysis on the cement dynamic material flow model.

2. The cement dynamic material flow model based on flow drive according to claim 1 is characterized in that: The calculation process of apparent cement consumption in step 1 is: In formula (1), Indicates the tth n Annual apparent cement consumption, Indicates the tth n Annual cement production, Indicates the tth n Annual cement import volume, Indicates the tth n Annual cement exports, Indicates the tth n Equivalent cement volume of annual imported cement products, Indicates the tth n Equivalent cement volume of annual exported cement products; In formula (2), Indicates the tth n Annual cement product import volume, R i It indicates the ratio of imported cement products converted into equivalent cement, that is, the cement content of imported cement products; In formula (3), Indicates the tth n Annual cement product export volume, R e It indicates the ratio of exported cement products converted into equivalent cement, that is, the cement content of exported cement products.

3. The cement dynamic material flow model based on flow drive according to claim 1 is characterized in that: The calculation process of cement inflow to each end-use sector in step 2 is: In formula (4), Indicates the tth n The amount of cement flowing into end-use sector j in a year, R j represents the cement market share of end-use sector j, that is, the proportion of cement flowing into each end-use sector.

4. The cement dynamic material flow model based on flow drive according to claim 1 is characterized in that: The calculation process of cement inventory in use of each end-use sector in step 3 is as follows: In formula (5), Indicates the tth n The amount of cement in use in the end-use sector j in year t, that is, considering the service life of cement, n The cumulative stock of cement in the sector as of year; Sj(t,tn) represents the cement survival function in the end-use sector j, that is, the product entering at time t is n There is a probability of use; S j (t,t n )=1-F j (t,t n )(6), In formula (6), F j (t,t n ) represents the cement life distribution function in the end-use sector j.

5. The cement dynamic material flow model based on flow drive according to claim 1 is characterized in that: The calculation process of cement scrap outflow of each end-use sector in step 3 is as follows: In formula (7), Indicates the tth n The outflow of cement scrap in end-use sector j in year t n The amount of cement scrapped after reaching the end of its service life in this department in year.

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