Low-Carbon Optimization Design for Low-Temperature Granary Roof Insulation in Different Ecological Grain Storage Zones in China

Abstract

The optimization design of buildings is very important to the energy consumption, carbon emissions, and sustainable development of buildings. The low-temperature granary has a low grain storage temperature and high energy consumption indexes. The design scheme of the roof insulation for a low-temperature granary should be determined in actual building design processes by considering the costs, carbon emissions, and outdoor climate, comprehensively. In this paper, a new low-carbon optimization design method is proposed for the roof insulation in the low-temperature granary. The low-carbon optimization design method can respond to the cost issue, emission reduction issue, and outdoor climate issue, simultaneously. Moreover, the low-temperature granary roof insulation of different ecological grain storage zones in China is optimized in terms of carbon reduction by using the proposed low-carbon optimization design method. The application results of the optimization design method in different ecological grain storage zones in China indicate that the outdoor climate has significant impacts on the economic performance and carbon reduction effect of roof insulation. The cost considerations related to carbon emissions can apparently increase the economic efficiency of roof insulation. The optimal economic thicknesses of expanded polystyrene (EPS) in the cities of Urumqi, Harbin, Zhengzhou, Changsha, Guiyang, and Haikou are 0.025 m, 0.037 m, 0.085 m, 0.097 m, 0.072 m, and 0.148 m, respectively. The different outdoor climates of the seven ecological grain storage areas in China have important influences on the comprehensive economic performances of low-temperature granary roof insulation. The design of the low-temperature granary roof insulation in Haikou city has the best economic performance among the seven ecological grain storage zones in China.

1. Introduction

The building industry has become one of the most energy-intensive industries in modern society. The production of building materials belongs to a highly energy-intensive production process. The reason for the high energy consumption of buildings is the lack of scientific design and construction of buildings [1]. On the other hand, the lack of energy-waste solutions also leads to high building energy consumption of buildings [2]. The design and application of insulation in building envelope structures, including the roof, floor, and exterior walls, is a commonly used energy-saving method for buildings [3]. The low-temperature granary has a low grain storage temperature and high energy consumption indexes. The low-temperature granary uses low-temperature storage environments to prevent and control the occurrence of grain loss phenomena due to pests and mold and to ensure the quality of stored grains. The grain storage temperature is below 15 °C in the low-temperature granary, and the large temperature difference between indoor and outdoor air can lead to high energy consumption for low-temperature grain storage [4]. The study of energy-saving and emission-reducing techniques with low-temperature granaries has important practical significance and high engineering application value.

The energy-saving and emission-reducing methods related to buildings are critical to the sustainability of buildings [5,6], the environment [7], and human society [8,9]. Zhang et al. [1] analyzed the evolution rules of the three parties’ behavior strategies and evolution stabilization strategies and found the key factors influencing the equilibrium using Mitchell’s score-based approach and the system dynamics model. Zhao et al. [3] presented a BIM-based, low-carbon building design optimization framework. An improved genetic algorithm was utilized to trade off the low-carbon energy savings of buildings and the daylighting performance. Andrade et al. [10] carried out studies on the carbon reduction potential of ultra-low-energy buildings in severely cold regions of China using an optimization method combining meta-models. Yang et al. [11] investigated seven driving factors of carbon emission evolution, encompassing energy, population, and income, and assessed the historical reduction in CO₂ emissions from residential buildings in Henan Province in China using the Kaya–LMDI decomposition method. Yang et al. [12] systematically examined the value, potential, challenges, and improvement path of China’s green hydrogen industry. Liu et al. [13] investigated the retrofitting of existing residential buildings in China’s hot summer–cold winter climate region to improve energy performance and move toward low-energy building goals. Wei et al. [14] measured the life cycle carbon emissions of buildings and decomposed the drivers of carbon emissions in the materialization stage and operation stage of buildings. The optimized design is very helpful in improving energy efficiency and reducing the carbon emissions of buildings. Building design optimization is a multi-objective optimization process involving cost issues, low-carbon issues, and environmental protection issues [15].

A literature review shows that few previous studies consider both economic performance and the carbon reduction effect of building insulation simultaneously in solving the problem of building design [16,17]. This is not conducive to achieving the comprehensive optimization of economic performance and carbon reduction effects in building insulation design. So, the comprehensive optimization of economic performance and the carbon reduction effect of building insulation are taken into account in this study. In this paper, the low-temperature granary roof insulation of different ecological grain storage zones in China is optimized in terms of carbon reduction using a new low-carbon optimization design method. The structure of this paper is as follows: Section 2 proposes a novel low-carbon optimization design approach for building roof insulation; Section 3 depicts the application results in the low-temperature granary roof insulation of different ecological grain storage zones in China; Section 4 proposes the results and discussions of this study; and Section 5 presents the research conclusions, shortcomings, and future research prospects.

2. Materials and Methods

2.1. Accounting for Building Roof Insulation Optimization Design Method

The optimization design of building roof insulation refers to minimizing the sum of the roof energy consumption cost, roof construction cost, and carbon emission cost in the entire life cycle of the roof insulation. The carbon emissions of building insulation are determined in this paper using the popular carbon emission factor method and process analysis method in the whole life cycle period [7]. The emission trading scheme (ETS) and carbon tax (CT) are used to establish the relationship between carbon emissions and the economic performance of roof insulation [18]. The carbon emission costs of roof insulation can be calculated based on the life cycle carbon emissions and the carbon tax rate (or carbon trading price). The traditional P₁–P₂ economic analysis model for building insulation is modified to consider the carbon emission costs of roof insulation. The balanced index of the carbon reduction effect is used to search for the best roof insulation design scheme candidate. The best roof insulation low-carbon design scheme is obtained when the balanced index of the carbon reduction effect is the lowest. Figure 1 provides a flowchart for determining the best roof insulation design scheme.

2.2. Carbon Emissions of Low-Temperature Granary Roof Insulation

2.2.1. Basic Concepts and Carbon Exchange Ways

Carbon emission is the general term or abbreviation for all greenhouse gas (GHG) emissions. According to the United Nations Framework Convention on Climate Change (UNFCCC), GHGs include the following six main categories [19]: (1) CO₂; (2) CH₄; (3) N₂O; (4) HFCs, e.g., CHF₃; (5) SF₆, halogenated ethers, NF₃, etc.; and (6) PFCs, e.g., CF₄ and C_nF_2n + 2. According to the definition of global warming potential (GWP), the overall effect of GHGs is assessed using equivalent values for each type of GHG according to its greenhouse effect and its correspondence with the mass of CO₂ of the same effect, using equivalent conversions. Among them, the equivalent CO₂ emissions (CO₂e) are often used as a measure of GHG emissions. In addition, other GHGs are usually ignored in general studies due to various considerations such as the specificity of the emission sources, the cumulative effect, and the feasibility and validity of the data statistics [20].

In the construction processes and the use processes of buildings, there are many forms of carbon exchange, which in general can be summarized as follows: (1) carbon emissions generated during the use of fossil energy; (2) carbon emissions or bio-carbon sequestration from industrial production, such as fossil energy extraction [21]; (3) carbon emissions from agricultural production, such as grain cultivation and nitrogen fertilizer application; (4) carbon emissions from composting, landfilling, or incineration of waste; (5) indirect carbon reduction through the use of clean energy instead of traditional energy sources; and (6) carbon storage through CO₂ capture and storage technology [22].

2.2.2. Method to Determine Carbon Emissions of Roof Insulation

The calculation of the carbon emissions of the whole building process is the research focus of the low-carbon building evaluation system. At present, the process analysis method [23] is a common method for carbon emission chemical analysis in the international community. This method splits the production process according to the process flow; it uses the product of the measured carbon emission coefficient and the corresponding carbon emission source activity data to express the carbon emissions generated by each process and then calculates the total carbon emissions of the whole process according to the carbon emissions of each process.

$$E={\displaystyle \sum (\epsilon \times Q)}$$

(1)

where $Q$ and $\epsilon$ are the activity data and emission factors of each process, respectively.

If there is an interaction of energy or raw materials in the process flow, it is calculated in a cycle according to Equation (1). The technology matrix is defined as $\tilde{A}=\left|{\tilde{a}}_{ij}\right|$, where ${\tilde{a}}_{ij}$ is the quantity of the ith product consumed or produced by process j. The relationship between the net production $\tilde{y}$ and the duration of each process $\tilde{x}$ is as follows:

$$\tilde{A}\cdot \tilde{x}=\tilde{y}$$

(2)

The net output column vector of the product is further defined as ${\tilde{Q}}_{net}=\left|{\tilde{Q}}_{net,j}\right|$, and the carbon emission factor row vector is defined as $\tilde{\epsilon }=\left|{\tilde{\epsilon }}_j\right|$, where ${\tilde{\epsilon }}_j$ is the carbon emission generated by process j per unit time; assuming that $\tilde{A}$ is a non-singular matrix, the total carbon emissions can be expressed as follows:

$$E=\tilde{\epsilon }\cdot {\tilde{A}}^{-1}\cdot {\tilde{Q}}_{net}$$

(3)

2.2.3. Building Life Cycle Assessment

Life cycle assessment (LCA) is the only reasonable means of selecting materials, equipment, and components [24]. This paper divides the system’s boundaries and establishes a quantitative model for the life cycle of a roof insulation system based on the LCA theory and describes the greenhouse gas emission reduction policy. A building’s life cycle can be divided into four stages: part production, construction, building operation and maintenance renewal, and building demolition and disposal [25]. Among them, the production of building parts can be divided into the production process of building materials and equipment. All four stages must use energy; that is, the production process involves the use of energy, while the transportation of building parts and energy transmission and distribution connect these parts to form a whole [26], as shown in Figure 2.

The scope of this paper’s study of the life cycle of roof insulation systems considers the six phases of building production, transportation, construction, operation, demolition, and disposal, which can reduce the energy consumption and carbon emissions of building equipment (for example, heating equipment, ventilation equipment, and air conditioners) can be reduced with the roof insulation [27]. Because there are almost no greenhouse gas emissions in the operation stage of the insulation materials, the carbon emissions from insulation materials in the operation stage can be ignored. The cost consideration of carbon emissions of insulation during the operational phase does not impact the capital investment in roof insulation.

2.2.4. Life Cycle Carbon Emission Evaluation Model

The life cycle carbon emissions of roof insulation ($C_{tot})$ can be determined through the sum of the carbon emissions in the six stages of the entire life cycle of the roof insulation.

$$C_{tot}=C_{pro}+C_{tra}+C_{con}+C_{ope}+C_{dem}+C_{dis}$$

(4)

where $C_{pro}$ represents the carbon emissions from insulation in the production stage, kgCO₂e. $C_{tra}$ represents the carbon emissions from insulation in the transportation stage, kgCO₂e. $C_{con}$ represents the carbon emissions from insulation in the construction stage, kgCO₂e. $C_{ope}$ represents the carbon emissions from insulation in the operation stage, kgCO₂e. $C_{dem}$ represents the carbon emissions from insulation in the demolition stage of insulation, and kgCO₂e. $C_{dis}$ represents the carbon emissions from insulation in the disposal stage, kgCO₂e.

Because there are almost no greenhouse gas emissions in the operation stage of insulation materials, the carbon emissions from insulation materials in the operation stage can be ignored. If building retrofitting occurs, the carbon emissions from the building retrofitting can be calculated using Equation (5). The following is the calculation formula for the carbon emissions in the other five stages of the entire life cycle of roof insulation:

$$C_{pro}={\displaystyle \sum _{i=1}^m{M}_i}\cdot (1+{\epsilon }_i)\cdot F_i+C_{pro,mac}={\displaystyle \sum _{i=1}^l{T}_{mac,i}}\cdot F_{mac,i}$$

(5)

$$C_{tra}={\displaystyle \sum _{i=1}^{n}M{A}_i}\cdot D_i\cdot k_i\cdot \psi$$

(6)

$$C_{con}={\displaystyle \sum _{i=1}^n{T}_{con,i}}\cdot b_i+C_{con,tem}$$

(7)

$$C_{dem}={\displaystyle \sum _{i=1}^p{E}_{dem,i}}\cdot F_{dem,i}$$

(8)

$$C_{dis}=C_{dis,tra}+C_{dis,rec}$$

(9)

where $C_{pro,mat}$ represents the carbon emissions from the raw materials in the production process, kgCO₂e. ${\epsilon }_i$ is a loss ratio of the ith material in the production process. The loss ratio (${\epsilon }_i$) refers to the proportion of loss and waste of the ith raw material in the production process. $M_i$ is the consumption for the ith material, m³. $m$ is the total number of various building insulation materials. $F_i$ is the carbon emission factor of the ith material, kgCO₂e/m³. $T_{mac,i}$ is the running time of the ith production equipment, h. $F_{mac,i}$ is the carbon emission factor for the ith production equipment, kgCO₂e/h. $l$ is the total amount of relevant equipment in the production process. $M{A}_i$ represents the consumption of the ith insulation material, m³. $D_i$ represents the transportation distance of the ith insulation material, km. $k_i^{}$ represents the carbon emission factor of the ith insulation material in the transportation processes, kgCO₂e/km $\psi$ represents the empty return rate of transportation vehicle. $C_{con,tem}$ represents the carbon emission of temporary measures at the construction site during the construction phase, kgCO₂e. These temporary measures include the temporary work shed, equipment shed, material room, etc. $T_{con,i}$ represents the running time of the ith construction equipment, h. $b_i$ represents the carbon emission factor of the ith construction equipment, kgCO₂e/h. $n$ represents the amount of construction machinery. $C_{dem}$ represents the carbon emissions from the insulation in the demolition process, kgCO₂e. $E_{dem,i}$ represents engineering quantity, m². $F_{dem,i}$ represents the carbon emission factor of the ith procedure, kgCO₂e/m². $p$ represents the total number of demolition procedures. $C_{dis,tra}$ represents the carbon emissions of the waste transportation, kgCO₂e. $C_{dis,rec}$ represents the carbon emissions of the insulation recycling, kgCO₂e.

2.3. Comprehensive Economic Analysis Model for Roof Insulation

2.3.1. Carbon Reduction Policies and Life Cycle Carbon Costs

To combat global warming, many countries have adopted diverse policy measures [28]. There are many classifications of GHG emission reduction policies related to the building sector; these can be broadly classified into mandatory systems, incentive policies, and GHG-pricing-based emission reduction policies. Among them, GHG-pricing-based abatement policies are those that aim to reduce GHG emissions by pricing and charging for them. There are two basic forms of GHG pricing-based abatement policies: the carbon trading scheme (CTS) and the carbon tax (CT). The emission trading scheme is a scheme in which the government sets the total amount of GHG emissions, and the sum of emission permits issued for companies or individuals cannot exceed the upper limit of GHG emissions. The government can issue GHG emission permits in the form of free permits or auctioned permits [29]. There are various carbon emission trading mechanisms, such as the cap-and-trade, voluntary, and baseline credit models; the basic principles of their operation [30] are shown in Figure 3.

When there is great uncertainty in the marginal cost of GHG emission reduction, the effect of the carbon emission trading mechanism on controlling GHG emissions is better than carbon tax, and the government can accurately control the total amount of GHG emissions within the predicted range using this mechanism. However, it is more difficult for the government to design a carbon emission trading mechanism than a carbon tax, and it also requires higher management and transaction costs. If the allocation of GHG emission allowances lacks public transparency or leaves more room for manipulation by powerful capital groups, it may lead to rent-seeking behaviors by interested parties [31].

The carbon tax refers to the setting of a tax rate by the government on GHG emissions and using the price of GHG emissions to further drive producers or consumers to determine the total GHG emissions of firms or individuals [29]. The basic principle of carbon tax operation is shown in Figure 4. Garbaccio et al. [32] analyzed the potential impact of carbon tax on China’s economic development based on a general equilibrium model, and the results showed that the government’s carbon tax is beneficial to the reduction in carbon emissions while it can promote the long-term growth of China’s economy. Compared to other policy instruments, carbon taxes have lower administrative and transaction costs and can reconfigure the types of taxes while improving the rationality of the taxation mechanism [33]. The fiscal revenue obtained by the government through the carbon tax can be used to implement supporting incentive policies to further influence people’s perceptions and behaviors regarding carbon emission reduction [34], thus forming a virtuous cycle.

At present, with the existing level of carbon emission reduction technology in China, it is important to use the carbon emission reduction policy for the promotion of low-carbon technologies in buildings. In order to further elaborate the implementation effect of GHG emission reduction tools, the following four coordinate systems are established. Among them, the vertical and horizontal coordinates are the GHG emission intensity and the construction cost per unit area, respectively; the curve indicates the inverse relationship between the horizontal and vertical coordinates, and the circle indicates the overall construction site. As shown in Figure 5a, when the government has no intervention, the GHG emission intensity of construction has no upper limit, which is not conducive to the low-carbon development of China’s construction industry.

As shown in Figure 5b, when the government introduces mandatory laws and regulations on carbon emission reduction, the GHG emission intensity of construction enterprises is required to not exceed the specified standard. As shown in Figure 5c, when the government adopts incentive policies to guide construction enterprises to adopt green and low-GHG-emitting materials, the enterprises can put the government subsidies into the construction, which correspondingly reduces the construction cost of the enterprises, and the construction cost curve is thus shifted. However, the incentive policy requires high-cost investment and cannot be widely promoted. So, most enterprises still keep their low-cost and high-emission production methods unchanged. As shown in Figure 5d, when the government adopts the GHG-pricing-based abatement policy tool, the cost of GHG emissions generated by buildings is internalized as a part of the cost of the enterprises. During the implementation of the policy, the government will give a certain amount of GHG quotas to enterprises free of charge, and if the enterprises generate more GHGs than the total amount of their quotas, they will need to buy GHG quotas on the market. Meanwhile, enterprises that produce less than their GHG quotas can sell their excess quotas on the market, thus stimulating their carbon emission reduction behavior and changing the production cost curve at the same time.

The previous two policy tools are easy to implement but have limitations in terms of carbon emission reduction effects. The GHG-pricing-based policy tools are more efficient, do not require higher cost investments by the government, and can be promoted vigorously throughout the society, which is beneficial for the promotion of GHG emission reduction in the construction industry and for the optimization and upgrading of the industrial structure.

2.3.2. Carbon Emission Costs of Roof Thermal Insulation

Energy conservation, economic performance, carbon reduction, and the other influential factors should be considered in the optimization design of roof insulation. These three main influencing factors will interact with each other. Energy conservation due to roof insulation will reduce the electricity consumption cost caused by building roofs. Energy conservation due to roof insulation will also reduce carbon emissions because of the electricity consumption reduction. Currently, there are still no quantitative methods with which to determine the impact of carbon reduction on the economic performance of roof insulation.

The cost consideration of the carbon emissions of building insulation can be determined by carbon trading price [18], carbon tax price [35], and the other potential economic quantitative determination methods. The relationship between carbon emissions and economic performance of roof insulation can be established using the carbon trading scheme and carbon tax. The cost consideration of the carbon emissions can be included in the economic analysis models of roof insulation. The following is the calculation formula for the carbon emission costs:

$$C_{ins}=\frac{0.001S_{tot}\cdot q_{tax,car}}{V}$$

(10)

where $C_{ins}$ is the carbon emission cost of the roof insulation, USD/m³. $S_{tot}$ is the total carbon emission of the roof insulation, tCO₂e. $q_{tax,car}$ is the carbon emission price, USD/tCO₂e. $V$ is the amount of the consumed insulation material, m³.

2.3.3. Comprehensive Economic Analysis Model for Roof Insulation

The carbon emission costs will influence the economic indexes for insulation in the low-temperature granary roof. The traditional P₁–P₂ economic analysis model has been applied in the evaluation of economic performances of building insulation [36]. In this paper, the carbon emission costs will be included in the P₁–P₂ economic analysis model, which can comprehensively evaluate the economic performance of insulation. When the life-cycle investment cost of insulation ($LC{T}_{in}$) is the minimum or the life-cycle saving of insulation ($LC{S}_{in}$) is the maximum, the insulation layer thickness is optimal. The improved P₁–P₂ economic analysis model for insulation is given as follows:

$$LC{T}_{in}=P_1\cdot E{C}_{co}+P_2(G_i\cdot \lambda +C_{ins}\cdot \lambda +IC)$$

(11)

$$LC{S}_{in}=P_1\cdot (E{C}_{sa}+E{C}_t)-P_2(G_i\cdot \lambda +IC)$$

(12)

$$P_1=PWF(L_c,r,z)=\left\{\begin{array}{l}\frac{1}{r-z}{\left[1-\frac{1+z}{1+r}\right]}^{L_c},r\ne z\\ \frac{L_c}{1+r},r=z\end{array}\right.$$

(13)

$$P_2=DP+(1-DP)\frac{PWF(N_{\min },0,z)}{PWF(N_m,0,c)}+P_1\cdot M-\frac{R}{{(1+z)}^{L_c}}$$

(14)

$$Lp=\left\{\begin{array}{c}\begin{array}{cc}\frac{\ln \left[1-\frac{P_2(G_i\cdot \lambda +C_c)(r-w)}{\Delta E_c}\right]}{\ln (\frac{1+w}{1+r})},& r\ne z\end{array}\\ \begin{array}{cc}\frac{P_2(G_i\cdot \lambda +C_c)(z-r)}{\Delta E_c},& r=z\end{array}\end{array}\right.$$

(15)

where $P_1$ is the ratio of the first year’s energy consumption cost to the total energy consumption cost. $P_2$ is the life cycle investment cost to the initial investment cost in the building insulation. $E{C}_{co}$ is the energy consumption capital investment, USD/m². $E{C}_{sa}$ is the decrease in energy consumption capital investment due to the roof insulation, USD/m². $E{C}_t$ is the decrease in carbon emission capital investment due to the roof insulation, USD/m². $G_i$ is the price of the insulation material, USD/m³. $IC$ is the comprehensive capital investment in insulation, USD/m². $\lambda$ is the insulation layer thickness, m. $PWF$ is the present worth factor. $r$ is the market rate, $r$ = 1% [37]. $z$ is the inflation rate, $z$ = 5% [38]. $L_c$ is the time period of the entire lifecycle, year. $DP$ is the ratio of the deposit cost to the capital investment cost, $DP=100\%$ [39]. $M$ is the proportion of installment payments relative to the total investment in roof insulation. $N_m$ is the loan period, $N_{\min }=\min (L_c,N_m)$. $c$ is the loan interest rate. $R$ is the proportion of the resale price relative to the total investment cost, $R=0$. $Lp$ is the discounted payback period, year.

2.4. Balanced Index of Carbon Emission Reduction Effect

Assessment indexes of carbon emissions can be used to assess different control measures for the carbon emissions of buildings. The conventional index [40], load index [34], and balanced index [41] are three common types of assessment indexes of carbon emissions. In this paper, the balanced index of the carbon emission reduction effect can be used to comprehensively investigate the carbon emission factor and the additional capital consumption factor [42]. The balanced index of the carbon emission reduction effect ($Bi$) can be calculated using Equation (16). The value of the balanced index of the carbon emission reduction effect decreases with the increase in the investment return rate for carbon emission reduction measures. The best low-carbon design scheme for roof insulation can be determined when the balanced index of the carbon emission reduction effect is the lowest.

$$Bi=\frac{I_r\cdot E{R}_o}{I_o\cdot E{R}_r}$$

(16)

where $I_o$ is the capital investment without control measures for carbon emissions, USD/m². $E{R}_o$ is the carbon emission without one control measure, kgCO₂e/m². $I_r$ is the capital investment due to the roof insulation, USD/m². $E{R}_r$ represents the carbon emission reduction in the control measures for carbon emissions, kgCO₂e/m².

3. Application of Optimization Design Method in Low-Temperature Granary Roof

3.1. Typical Cities in China and Buildings Considered

The low-temperature granary is used as an object in this study because its indoor air temperature (below 15 °C) is lower than that of other building types. China has a wide area and large differences in climate from one place to another [43]. Climate conditions are one of the most important external influencing factors that must be considered for the low-carbon design of the low-temperature granary. The roof insulation optimization design method was applied to the low-temperature granary roofs in seven ecological grain storage areas in China. Seven typical cities were selected from the seven ecological grain storage zones in China. These seven typical cities are Xining city (with typical Qinghai–Tibet Plateau grain storage climate characteristics); Urumqi city (with typical Mengxin grain storage climate characteristics); Harbin city (with typical northeast grain storage climate characteristics); Zhengzhou city (with typical North China grain storage climate characteristics); Changsha city (with typical Central China grain storage climate characteristics); Guiyang city (with typical southwest grain storage climate characteristics); and Haikou city (with typical South China grain storage climate characteristics).

The typical roof structure of the low-temperature granary was used to analyze the economic performances of roof insulation in seven ecological grain storage zones in China, as shown in Figure 6.

Table 1. Performance parameters of roof elements.

Layers	Material Name	Thermal Conductivity (W/m·K)	Density (kg/m3)	Specific Heat Capacity (J/kg·K)	Thickness (mm)
1	Waterproof layer	0.23	900	1620	5
2	Cement mortar	0.93	1800	1050	20
3	EPS	0.039	25	1380	30
4	Cement mortar	0.93	1800	1050	20
5	Cement slag	0.26	900	920	100
6	Reinforced concrete	1.74	2500	920	120
7	Cement mortar	0.93	1800	1050	25

shows the performance parameters of the roof elements for the typical roof structure of a low-temperature granary. The indoor air temperature in the low-temperature granary was set at 15 °C. The grain storage temperature in the low-temperature granary was maintained at 15 °C using air-conditioners with a 2.3 energy efficiency ratio. The life cycle of the insulation materials was set at 20 years.

3.2. Life Cycle Carbon Emissions of Roof Insulation

COMSOL software and the EnergyPlus software were utilized to forecast the energy consumption of low-temperature granary roofs, respectively. To ensure the accuracy of the prediction results, the simulation results were mutually verified with each other. The total annual cooling load of the low-temperature granary roof was obtained through summing the hour-by-hour heat transfer per unit area of the roof. The low-temperature storage environment is beneficial to maintaining grain quality and inhibiting the growth of grain pests. The lower the temperature of grain storage, the safer the storage of grain in the granary. Therefore, the heating periods were not considered in the simulation studies.

Table 2. Roof cooling load.

Typical City	Number of Days for Average Temperature > 5 °C	Cooling Load without Insulation (MW/m2)	Cooling Load with Insulation (MW/m2)
Xining	0–30	-	-
Urumqi	112–194	211.514328	64.965168
Harbin	55–122	186.863112	58.068504
Zhengzhou	143–192	496.436294	149.47992
Changsha	121–253	518.710788	158.03532
Guiyang	173–224	399.005784	122.57575
Haikou	289–352	1017.59494	312.38114

shows the roof cooling loads for the low-temperature granary roofs with an EPS insulation layer thickness of 30 mm in the seven typical cities. For example, Figure 7 shows the annual roof cooling loads for different insulation layer thicknesses in the low-temperature granary roofs in Zhengzhou city. The annual roof cooling load decreases with the increase in the roof insulation layer thickness. However, the reduction rate of the annual roof cooling load decreases with the increase in the roof insulation layer thickness. Xining city is a typical representative city of the Qinghai–Tibet Plateau grain storage climate characteristics. It should be noted that the number of months with an outdoor air average temperature > 15 °C is 0. Therefore, the low-temperature granary in Xining city does not require mechanical cooling to maintain the lower grain storage temperatures. Xining city will not be involved in the economic performance analysis of granary roof insulation.

Four types of common insulation materials in granary roofs were discussed in this study. These four types of common insulation materials were rock wool (RW), extruded polystyrene (XPS), polyurethane (PU), and expanded polystyrene (EPS). The carbon emissions and the corresponding carbon emission costs for the above four types of insulation materials were calculated using the methods presented in Section 2.3, as shown in

Table 3. Carbon emission costs of roof insulation.

Insulation Material	Life Cycle Stage	Carbon Emissions (tCO2e/m3)	Carbon Emission Costs (USD/m3)
EPS	Production	4.5 × 10−1	3.73 × 100
	Transportation	2.1 × 10−5	1.73 × 10−4
	Construction	5.6 × 10−4	4.60 × 10−3
	Demolition	5.0 × 10−4	4.11 × 10−3
	Disposal stage	7.0 × 10−5	5.75 × 10−4
	Total	4.51 × 10−1	3.74 × 100
XPS	Production	6.3 × 10−1	5.22 × 100
	Transportation	2.9 × 10−5	2.39 × 10−4
	Construction	5.6 × 10−4	4.6 × 10−3
	Demolition	5.0 × 10−4	4.11 × 10−3
	Disposal stage	9.7 × 10−5	7.98 × 10−4
	Total	6.31 × 10−1	5.23 × 100
PU	Production	7.5 × 10−1	6.22 × 100
	Transportation	2.9 × 10−5	2.39 × 10−4
	Construction	5.6 × 10−4	4.6 × 10−3
	Demolition	5.0 × 10−4	4.11 × 10−3
	Disposal stage	8.3 × 10−5	6.83 × 10−4
	Total	7.51 × 10−1	6.23 × 100
RW	Production	5.5 × 10−1	4.56 × 100
	Transportation	4.8 × 10−5	3.94 × 10−4
	Construction	4.6 × 10−4	3.78 × 10−3
	Demolition	4.1 × 10−4	3.38 × 10−3
	Disposal stage	1.6 × 10−5	1.31 × 10−4
	Total	5.51 × 10−1	4.57 × 100

. The carbon emission of EPS is 0.451 tCO₂e/m³, which is the lowest carbon emission among the four types of insulation materials. Therefore, EPS was used in this paper as the insulation material in the low-temperature granary roofs in seven ecological grain zones in China. In this paper, the electricity price was set as 0.1027 USD/kWh. The carbon trading price was set at 8.29 USD/tCO₂e according to statistical data [30], and the electricity price was set at 0.0083 USD/kWh [38].

The vast majority of the carbon emissions of insulation material mainly come from the production stage of the insulation material. The carbon emissions of the four types of insulation materials considered are different. The order of carbon emissions of the four insulation materials is EPS < XPS < RW < PU. The main reason for the different carbon emissions of the four types of insulation materials is the different raw materials and production processes used for insulation materials. The carbon emissions of EPS mainly come from the preparation process of the polymer materials and the production process of the EPS insulation board. The preparation process of styrene raw materials and the production process of insulation boards are the two main sources of carbon emissions for XPS. The preparation process of the raw materials and the foaming curing process are the two main sources of the carbon emissions for PU. The preparation and production processes of raw materials are the two main sources of carbon emissions for RW. The carbon emissions of EPS are the lowest carbon emissions among the four types of insulation materials considered.

4. Results and Discussions

4.1. Economic Performance Analysis of Granary Roof Insulation

Figure 8 shows the calculated results of $LCT$ for EPS in the granary roofs with different insulation thicknesses in the six selected typical cities in China. Figure 9 shows the calculated results of $LCS$ for EPS in the granary roofs with different insulation thicknesses in the six selected typical cities in China. There is a minimum point of $LCT$, and this point corresponds to the thickness of the insulation material that is the optimal thickness. When the material thickness is less than or thicker than this economic thickness, all the $LCT$ values increase accordingly. There is a maximum minimum point of $LCS$, and this point also corresponds to the thickness of the insulation material that is the optimal thickness. When the material thickness is less than or thicker than this economic thickness, all $LCS$ values decrease accordingly. The calculated minimum values of $LCT$ in Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city were 13.98 USD/m², 15.94 USD/m², 23.59 USD/m², 25.37 USD/m², 21.40 USD/m², and 33.27 USD/m², respectively. Meanwhile, the $LCS$ values of Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city were 4.01 USD/m², 8.13 USD/m², 40.63 USD/m², 49.85 USD/m², 29.14 USD/m², and 105.76 USD/m², respectively. The ranking of the economic benefits of the six typical cities was Urumqi < Harbin < Guiyang < Zhengzhou < Changsha < Haikou. Therefore, Haikou city achieved the best economic benefits among the six typical cities, followed by Changsha city; Harbin city and Urumqi city had smaller economic benefits. As Harbin city and Urumqi city, with their natural climatic conditions, can meet the requirements of low-temperature grain storage in most cases, the energy consumption saved using low-temperature grain storage technology is less compared to that of the other cities, and thus, the economic benefits it brings are not significant.

4.2. Roof Insulation Optimal Insulation Layer Thicknesses

When the carbon emission costs of roof insulation were not considered, the optimal insulation layer thicknesses in the low-temperature granaries of Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city were 0.026 m, 0.039 m, 0.088 m, 0.101 m, 0.075 m, and 0.152 m, respectively. When the carbon emission costs of roof insulation were considered, the optimal insulation layer thicknesses in the low-temperature granaries of Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city were 0.025 m, 0.037 m, 0.085 m, 0.097 m, 0.072 m, and 0.148 m, respectively. Therefore, the carbon emission costs because of roof insulation decreased by 3.85~5.13% for the six selected typical cities. After determining the optimal insulation layer thicknesses in the low-temperature granaries, the payback periods of roof insulation were determined using Equation (15). When the carbon emission costs of roof insulation were not considered, the payback periods of roof insulation in the low-temperature granaries of Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city were 2.62 years, 2.55 years, 1.95 years, 1.86 years, 2.17 years, and 1.45 years, respectively. When the carbon emission costs of for roof insulation were considered, the payback periods of roof insulation in the low-temperature granaries of Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city were 2.58 years, 2.43 years, 1.89 years, 1.79 years, 2.09 years, and 1.41 years, respectively. As shown in Figure 10, the carbon emission costs of roof insulation cause the payback periods to be reduced by 1.52~4.71%. The smaller the payback period, the better the economic performance of the insulation material.

4.3. Effect of Carbon Emission Costs on Economic Performance of Roof Insulation

The lifecycle carbon emission costs due to roof insulation can increase the lifecycle total investment of building roof insulation. Figure 11 shows the increased LCT after considering carbon emission costs of the roof insulation. Considering the carbon emission costs, the increase in $LCT$ values for the six typical cities was 0.67% to 1.69%. Figure 12 shows the increased $LCS$ after cost consideration of carbon emission for roof insulation. The energy consumption reduction due to insulation decreases the carbon emissions due to energy consumption. The reduction in carbon emission costs brings about the increase in $LCS$ for roof insulation. The $LCS$ values increased by 1.78 USD/m², 1.55 USD/m², 5.22 USD/m², 5.51 USD/m², 4.06 USD/m², and 11.54 USD/m² for Urumqi city, Harbin city, Zhengzhou city, Changsha city, Guiyang city, and Haikou city, respectively. The increase in $LCS$ after considering carbon emission costs was 12.25~24.06%. It is worth noting that the increase in $LCS$ (12.25~24.06%) is much higher than the increase in $LCT$ (0.67~1.69%). Therefore, considering carbon emission costs can significantly improve the economic benefits of roof insulation in a low-temperature granary.

4.4. Calculated Balanced Indexes for Different Ecological Grain Storage Zones

The balanced indexes of the roof insulation in the low-temperature granaries were calculated using Equation (16). Figure 13 shows the balanced indexes of the roof insulation with and without considering the carbon emission costs for the six typical cities. For each city, the balanced index of roof insulation after considering carbon emission costs was lower than that without consideration carbon emission costs. When the carbon emission costs were considered, the variation values of the balanced indexes of the roof insulation for the six typical cities were 0.066~0.108. The priority order of the balanced indexes of the roof insulation for the six typical cities was Haikou city > Changsha city > Zhengzhou city > Guiyang city > Harbin city > Urumqi city. The economic benefit of the roof insulation in the low-temperature granary for Haikou city was the greatest among the six typical cities in China.

5. Conclusions

Although the carbon trading mechanism, carbon tax, and the other carbon reduction policies and measures are beneficial to urban environmental protection and building sustainable development, the studies on the low-carbon optimization design of buildings are still highly insufficient. In this paper, the low-temperature granary roof insulation for different ecological grain storage zones in China was optimized in terms of carbon reduction. The following conclusions were obtained:

(1)

A novel low-carbon design optimization method of roof insulation is very useful for determining the best insulation design scheme in a low-temperature granary roof;

(2)

The P₁–P₂ economic analysis model was modified to cope with the carbon emissions of roof insulation. The carbon emission costs were found to have certain influences on the economic performance of the low-temperature granary roof insulation;

(3)

The outdoor climates of the different ecological grain storage zones in China have significant impacts on the economic performance and carbon reduction effect of low-temperature granary roof insulation;

(4)

The priority order of the balanced indexes of roof insulation for the six typical cities is Haikou city > Changsha city > Zhengzhou city > Guiyang city > Harbin city > Urumqi city. The economic benefit of roof insulation in the low-temperature granary of Haikou city is the greatest among the six typical cities in China.

This paper only takes the roof insulation materials in buildings as the research object and investigates the low-carbon design optimization of roof insulation. In the future, the research scope can be extended to the low-carbon design optimization of the whole building. Although the carbon trading mechanism, carbon tax, and the other carbon reduction policies and measures are very helpful in reducing carbon emissions in buildings, more low-carbon economic analysis methods and more insulation material types should be studied to achieve the goal of building energy conservation and emission reduction.