In the modelling section, we built a total of three models. We build a stagnant growth model based on the relationship between the growth quantity and growth trend of microalgae to study the growth curve of microalgae to analyse the optimal culture environment for Phaeodactylum tricornutum. After that, we collected data on the cultivation cost, time cost and labour cost of the plant and built a target planning model to predict the optimal microalgae cultivation time and the corresponding production of the plant. To microalgae effectively reduce the total cost of plant production and provide some support for the economic viability of microalgae production of biodiesel, we explored the best site for urban cultivation of microalgae through the DEA model, fully considering environmental factors affecting the growth of microalgae such as rainfall, wastewater volume and sunlight, and studied economic factors such as transportation costs and land costs, and conducted an in-depth study of the most suitable cultivation sites in 31 Chinese provinces. Microalgae are grown in the most suitable areas in 31 provinces in China.
In order to explore the public's perception of GM microalgae as a new energy source and their needs, we also collected 600 domestic questionnaires and 20 foreign questionnaires based on online research. The model is based on the CRITIC weighting method. Based on the user needs model, we analyse the acceptance of users and use the K-means clustering analysis method to explore the potential users and their individual characteristics.
Microalgal Growth Model
Phaeodactylum tricornutum is a marine eukaryotic unicellular algae with fast growth rate, high lipid content and easy to culture. By analyzing the growth of Fucus triangularis at different ascorbic acid concentrations with cell density, lipid density and luteolin content as evaluation indexes, we studied the growth of Fucus triangularis and analyzed the optimal culture environment and the maximum growth rate of Fucus triangularis, and its maximum production at the corresponding time.
In this experiment, one blank experimental group and five other groups were designed to add 80mg/L, 160mg/L, 200mg/L, 250mg/L and 300mg/L of ascorbic acid respectively to collect data on the density of microalgae under six experimental situations.
The Nile Red stain is a lipid-soluble hydrophobic stain that binds to intracellular lipids and emits orange fluorescence when excited by monochromatic light at a specific wavelength, and there is a clear correspondence between fluorescence intensity and lipid content to obtain lipid density data. 
Model Assumptions and Notation
Model AssumptionsHypothesis 1: Microalgae are not disturbed by other uncontrollable environmental factors during growth and cultivation.
Specific growth rate of Phaeodactylum tricornutum under different culture conditionsThe maximum specific growth rate of Phaeodactylum tricornutum μ/d under different ascorbic acid concentration conditions is calculated by cell density. The specific growth rate calculation formula is:
The effect of ascorbic acid concentration on the growth of Phaeodactylum tricornutumThe change in the cell density content of Phaeodactylum tricornutum as the incubation time varied is shown in the graph.
The growth pattern of Phaeodactylum tricornutum can be found as follows: Phaeodactylum tricornutum grows in a J-shaped curve in the first 8 days, which is due to sufficient nutrients in the medium and low resistance to growth. 8-10 days, the density of the algal bloom increases, the resistance to growth becomes greater and the growth trend gradually slows down. On day 11 the maximum holding capacity is reached and thereafter the growth curve fluctuates above and below the maximum holding capacity. There is no significant senescence during a growth cycle.
By observing the trend of microalgae growth, we found that the growth rate tends to decrease when the microalgae grow to a certain number. Based on this phenomenon, we set up a logistic stagnant growth model to study the growth curve of microalgae.
Model SolvingSolving the above process through MATLAB software, you can get the fitted curve as shown in Figure 2.
Based on the curves, the maximum production, the maximum growth rate and the corresponding time for the algae in the six environments were analysed as shown in Table 2, which also corresponds to the growth habit of the algae.
According to the actual growth curve of microalgae and the model fitting curve, it is easy to find that the cultivation environment of 250 mg/L ascorbic acid not only can make the Phaeodactylum tricornutum grow better and extract more oil, but also facilitate the accumulation of lithophanin. Meanwhile, the optimal incubation time for microalgae was 13 days, and the maximum density that could be achieved was 8230600 cells/ml.
Factory Cost Objective Programming Model
With the booming global population growth, humans are facing increasing demand for food and energy and declining fossil fuel reserves, and the use of untapped organisms to support sustainable development is a very hot research direction at present. Microalgae, as a biological resource with high photosynthetic efficiency and adaptability to the environment,  have great potential to address carbon emissions and provide new energy sources, but the commercial application of microalgae is seriously hampered by their high production cost, and it is a serious practical problem to reduce the production cost of microalgae so that they can play their role in the new energy era.
Therefore, by studying the main factors affecting the cost of microalgae production, we establish a target planning model based on the plant's cultivation cost, time cost, and find a balance between the minimum value of cost and the maximum value of production to arrive at the optimal algae cultivation time and the corresponding production and cost.
Our data sources are mainly two parts, one is the human practice group's interface with China Fujian Shenliu company to obtain the cost data of the basic fixed assets depreciation, labor cost and fuel consumption consumption of the microalgae plant; on the other hand, it is obtained from the national public information, where the data of tax and insurance are obtained from the National Tax Bureau and the data of land cost are obtained from the national land network data.
Hypothesis 1: Suppose the bottom area of the culture tank is 2500 square meters and the depth of the culture solution is 0.2 meters, then the volume of the culture solution is 500 cubic meters;
Hypothesis 2: The plant has a fixed daily production time and the production time remains constant during the production cycle of the microalgae；
Model Establishment and Solution
By observing the growth curve of microalgae, we can find that the cultivation time required to reach the maximum density of microalgae is not necessarily the time required to maximize the benefits of the plant, because it often takes longer to cultivate the algae to reach the maximum density, and there is a certain cost for the daily operation of the plant. Therefore, it is also important to balance the relationship between microalgae density and time cost. In this paper, we use a goal planning model to calculate the cultivation time required to maximize benefits as well as to analyze the effect of various additives on microalgae production, which further affects the profitability of the plant.
This model is used to calculate the cost and revenue of a culture tank, assuming that the profit generated by 1g of microalgae is a, the daily labor cost of the plant's algae culture staff is c, and the rest of the plant's daily operating costs are shown in the table above. Let the production on day Xi be mi(g), then the following 0-1 planning model for calculating the profit is obtained.
MATLAB was used to solve the solution and the results were analyzed as follows, where i denotes the optimal number of days of cultivation and c denotes the daily labor cost.
（1）No additives added：
（2）Add 80mg/L ascorbic acid：
The results showed that when labor costs ranged from $20.22 to $40.44, the best incubation time was day 8, when time costs had less effect on profits and yield played a decisive role. The expected variation in profit ranged from $130.09 to $28.98. The maximum average daily profit available was $18.58.
（3）Add 200mg/L ascorbic acid：
The results showed that when labor costs ranged from $20.22 to $40.44, the optimal incubation time was all on day 7, and the expected variation in profit ranged from $112.59 to $11.49. The maximum average profit obtainable per day was $16.08.
（4）Add 250mg/L ascorbic acid：
The results showed that the optimal incubation time should be day 10 when the labor cost was between $20.22 and $35.15, and day 4 when the labor cost was between $33.16 and $40.44, with an expected profit variation range of $216.27 to $39.59. The maximum average daily profit available was $21.63.
（5）Add 300mg/L ascorbic acid：
The results showed that when the labor cost was between $20.22 and $40.44, the optimal cultivation time would be day 3 and the expected variation in profit would range from $-3.73 to $-23.95. At this point, instead of increasing the density of algae growth, the addition greatly reduces the amount of algae produced and may cause the plant to lose money.
In order to observe the variation of profit with cost more intuitively, the curves of cost and profit of various additives were plotted in this paper, as shown in the following figure, it can be found that a maximum point exists in the addition of 250 mg/L L-ascorbic acid, i.e. the maximum value of profit can be reached in the addition of 250 mg/L L-ascorbic acid.
Based on these results, it is clear that the addition of 250 mg/L of L-ascorbic acid to f/2 standard medium can effectively increase the biomass of algae, thus improving the economic efficiency of the plant. The profit is expected to increase by 15.7% year-on-year compared to not adding any additive. By observing the production curve of microalgae, it was also found that the addition could effectively increase the growth rate of microalgae. Therefore, the addition of 250 mg/L L-ascorbic acid can effectively promote the profit growth of the plant and improve the economic efficiency. The other additions did not promote the growth of microalgae and produced lower economic benefits than those without any additive.
Further sensitivity analysis of the experimental results for the addition of 250 mg/L of L-ascorbic acid versus the blank control without any addition shows that when the labor cost is less than $36.06, the profits obtained from the addition of 250 mg/L of L-ascorbic acid are greater than the profits without any addition. And when the labor cost is greater than $36.06, the profit may be lower than the profit without adding any additives. This is because the microalgae with 250 mg/L L-ascorbic acid addition reached the maximum cell density on the 10th day, while the microalgae without any additive reached the maximum cell density on the 7th day. When the labor cost is larger, the time cost of production is also larger at this time, so there will be a situation that the profit of 250 mg/L L-ascorbic acid addition is lower than the profit without any additive. However, on the whole, as long as the labor cost is controlled and the production scale is expanded, this ascorbic acid addition can still effectively increase the profit of the plant by increasing the production of microalgae.
Microalgae Factory Location Model
Microalgae have a high potential to contribute to world energy and mass commodity demand as a raw material for the production of energy and other commodities, but have always been inhibited by their production costs. After studying the optimisation of plant production costs for microalgae, we selected the optimal site for microalgae production by using data envelopment analysis methods for the geographical environment and economic situation of 31 provinces and regions in China. Optimising the site for microalgae production can effectively reduce the total cost of plant production and provide some support for the economic viability of microalgae production for biodiesel.
Materials and Methods
The Data Envelopment Network Data Envelopment Analysis (DEA) method uses observed sample information data to evaluate the production effectiveness of decision units or to deal with other multi-objective decision problems. By explicitly considering the application of multiple inputs and the production of multiple outputs, it can be used to compare the efficiency between multiple service units providing similar services, it avoids calculating the standard cost of each service and translates multiple inputs and multiple outputs into The numerator and denominator of the efficiency ratio, the DEA approach to measuring efficiency provides a clear picture of the mix of inputs and outputs. 
Our data is mainly derived from the annual data published in the National Bureau of Statistics for each province and the main data collected are as follows.
Location Model Based on DEA
Quantitative AnalysisMicroalgae culture requires considerable amounts of water, energy and nitrogen dioxide. Determining the best location for microalgae depends on a variety of factors such as the physical environment, economic conditions and policy support, but specifically, the level of production of microalgae depends mainly on environmental factors represented by water, climatic conditions and carbon dioxide, as well as economic factors such as transport and land costs.
A total of nine indicators have been selected for analysis for both environmental and economic factors as follows.
(1) Annual Rainfall (AR):The annual rainfall of a province has a significant impact on water resources, the higher the annual rainfall, the more water is available for the growth of microalgae.
(2) Solar Radiation (SR):The growth process of microalgae requires solar radiation and an ideal environment for microalgae production should have a high level of solar radiation.
(3) Water Resources (WR):Water resources provide the water needed for algae cultivation and have a positive impact on the growth of microalgae.
(4) Average Annual Daily Temperature (DT):Microalgae need hot places to grow rapidly.
(5) Volume of Wastewater (WW):Wastewater is a suitable environment for the growth of microalgae.
(6) Population (PO):In more populated provinces, the microalgae industry can provide a certain number of jobs and has lower labour costs.
(7) Land Cost (LC):Due to the large size of culture ponds, plants should consider local land values when selecting sites, and sites with lower costs can be considered on a limited basis.
(8) Transport Costs (TC):After the microalgae are produced, they need to be transported to refineries to extract biodiesel or made into other algae derivatives by the plant to be transported elsewhere for sale, so sites with lower transport costs can provide a significant reduction in production costs.
（9）Human Development Index (HDI):The Human Development Index is an index representing the welfare and development speed of various provinces. When selecting sites, provinces with lower HDI can be considered, which can inject fresh blood into more underdeveloped provinces.
According to the economic and environmental data of 31 provinces in China, the relationship between input and output indicators is established as shown in Table 5.
Results and Discussion
In the results of the data envelopment analysis, if the optimal solution of the linear programming θ=1,then the decision unit DEA is said to be valid, indicating that the input to output ratio is optimal, if θ < 1，then the decision unit is said to be non-DEA effective, indicating that the input to output ratio is not optimal and, in general, a larger θ indicates better results.
We solved the model by python and obtained the evaluation results for the 31 provinces as shown in Table 6. Therefore, combining the above results, we concluded that the seven provinces of Shanghai, Jilin, Jiangsu, Sichuan, Xinjiang, Guangxi and Shaanxi are the most suitable locations for cultivating microalgae in China, while the provinces of Heilongjiang, Tianjin, Henan and Shandong are not suitable for cultivating microalgae.
In recent years, the production of biodiesel from microalgae has attracted much interest. The advantages of urban cultivation of microalgae are urban wastewater use, oxygen production and employment sustainability, and the commercialisation of biodiesel production from microalgae has been supported by scientific evaluation and practical experience. The selection of a microalgae cultivation site that is suitable for both the environment and the economy can effectively reduce feedstock costs for diesel production. We used the DEA model to identify the most suitable provinces for cultivating microalgae in 31 provinces in China, fully considering environmental factors affecting the growth of microalgae such as rainfall, wastewater volume and sunlight, and studying economic factors such as transportation costs and land costs. The results obtained also validate the validity and feasibility of the DEA model in selecting the best site for microalgae cultivation, and in the next step, we will continue to study in more depth In the next step, we will continue to study the location of microalgae plants in more detail.
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