Model based on Microalgae Carbon Sequestration

Technology and Water Purification Technology

Abstract

At present, the climate and water ecological environment are increasingly tense. It is of great significance to seek better means of water purification and carbon sequestration to promote the realization of dual carbon goal.In this context, our team intends to build a mathematical model, according to the efficient carbon sequestration and water purification of Phaeodactylum tricornutum Bohlin and various needs of this project, to provide theoretical basis for breeding the algae filament and carrying out the project.

First of all, we established evaluation model of coastal water quality in Fujian Province based on TOPSIS synthesis.To identify corresponding changes in water quality and provide corresponding preparation for subsequent water purification project of Phaeodactylum tricornutum Bohlin, we analyzes the water quality data of Fujian Province in recent years(the nitrogen content was analyzed emphatically). But we find that the evaluation score of coastal water quality in Fujian Province is decreasing year by year and Longjiang River has the worst water quality in Fujian Province.

Next, we built water quality prediction model of Longjiang River based on time series.Through the analysis, we know that the current water quality of Longjiang River is poor.In order to further analyze the future changes of water quality, we predict the future water pollutant content whose trend is consistent with the characteristics of "low in summer and high in winter" by time series model. We found that the water quality indexes such as dissolved oxygen, ammonia nitrogen, chemical oxygen demand and total phosphorus in Longjiang River will show a slight downward trend in the future.

Thirdly, we established a microalgae water purification system based on cellular automata.In order to assist project experiment and break through the complex factors in large water systems which traditional biological experiments are difficult to simulate, we use computer technology to simulate and compare contaminant dispersal in the process of microalgae intervene.Through two simulation analyses, we found that the microalgae could absorb and reduce the pollutant contents in water system.

The fourth, we build optimization model of microalgae plant location to maximize carbon sequestration efficiency. To promote application prospect of this project, we need to analyze the project of microalgae plant location by considering different regional illumination time, temperature and carbon sequestration rate of microalgae in different regions.As a result, we found that the eastern coastal area is more suitable for microalgae plant location because of its high carbon sequestration rate.

Our model can further develop the microalgae's function of carbon sequestration and water purification, and provide reference for carbon peak and carbon neutral, improve eutrophication of fresh or sea water, reduce the cost of biomass energy and promote new bio-energy sources.We integrate disciplines of Computer Science and Synthetic Biology, and provide more feasible new ideas for microalgae water purification project by computer technology and machine learning algorithms.

Model 1: Water Quality Assessment Model

1.1 The Data Source

All raw data comes from the file of Fujian Provincial Department of Ecology and Environment Official Website and adopt Information Disclosure Table of seagoing river section monitoring in Fujian province from January 2018 to May 2022. The region including Jiaoxi Saiqi section, Badu section of Huotong Stream, Aojiang Heshan ferry section, Min 'an section of Minjiang River, Diluxi River mouth bridge section,Long Jiang Haikou Bridge Cross Section, Sanjiangkou Crossing of Mulan River, Jinjiang Sturmpu Crossing, Jiulong River estuary cross-section, Zhangjiang River, Yunxiao Gautang Ferry Crossing and Dongxi Daoan Aozitou Crossing. The survey sites for above studies are all in the coastal areas of Fujian, and give a general picture of the pollution in Fujian waters.

1.2 Data pre-processing
1.2.1 Cross-sectional flow rate calculation

The scope of water quality monitoring mainly includes unpolluted water and vulnerable to pollution.In the actual monitoring, it is necessary to use scientific verification methods, analyze the main influencing factors, and control monitoring intensity.The main polluted water bodies in China are surface waters, which are seriously damaged by the discharge of ammonia nitrogen wastewater.The main purpose of water quality monitoring is to determine the level of pollutants in the water body, reflecting the water quality in the region, the main monitoring objects are suspended solids, electrolytes, chemical and biochemical oxygen demand, even the water body of mercury, lead, arsenic and organic pesticides should also be monitored in place.

As the data in Table 1-1 are the average flow velocity of the river at each section, in order to obtain the average concentration of nitrogen at the entire Fujian seaward section, it is necessary to determine the weight of each section according to its average flow velocity[1].


1.2.2 Calculation of Nitrogen-related Pollutant Concentrations

Nitrogen pollution refers to the environmental pollution caused by nitrogen compound, and the nitrogen compounds that cause atmospheric pollution are mainly nitrogen oxides.Its anthropogenic source is mainly the burning of fossil fuels, which produces emissions of nitric acid, nitrogen fertilizer, gunpowder and other emissions.NOx is the starting reactant for photochemical smog reactions, and it catalyze the breakdown of ozone in the stratosphere with nitrous oxide, so they are both ozone-destroying.Nitrogen in water bodies comes mainly from metabolism and decay of organisms, loss of nitrogen fertilizer, and discharge from industrial wastewater and domestic waste water. The data in Table 1-2 are the average concentrations of nitrogen-related pollutants in the waters around Fujian Sea for each year after adopting the model with weighting calculation.


1.2.3 Calculation of Nitrate Nitrogen, Nitrite Nitrogen and Organic Nitrogen Concentration

Nitrogen exists in the following forms: organic nitrogen, ammonia nitrogen, nitrate nitrogen, nitrite nitrogen and nitrogen gas. Ammonia nitrogen and organic nitrogen are collectively referred to as Total Kjeldahl Nitrogen (TKN).Total nitrogen is the sum of organic nitrogen and inorganic nitrogen (including ammonia nitrogen, nitrite nitrogen, nitrate nitrogen), and its concentration in water should be higher than any kind of nitrogen,.Total nitrogen should include organic nitrogen and inorganic nitrogen, from the strict formulation of standards, its concentration limit and the principle of setting the category of water bodies should be greater than the sum of three nitrogen. The reason is that three nitrogen test only belongs to the inorganic nitrogen part, and the content of organic nitrogen in the water body is relatively high, this part of test need to go through the organic nitrogen into inorganic nitrogen decomposition process (UV decomposition or high temperature decomposition method), the total nitrogen tester can only quickly determine the total nitrogen concentration.(TKN)

Since nitrate and nitrite contain nitrate and nitrite ions, the nitrate and nitrite nitrogen concentrations were calculated according to the proportion of nitrogen. Since the total nitrogen mainly contains ammonia nitrogen, nitrate nitrogen, nitrite nitrogen and organic nitrogen, the concentration of organic nitrogen can be calculated according to the relationship between the four, which can be seen in Table 1-3.


After we process the raw data, line graphs were plotted for ammonia, nitrate, nitrite, organic nitrogen and total nitrogen by time series, which can be seen in Picture 1-2-2.


Figure 1-1 Monthly data line graph for each type of nitrogen content

From Figure 1-1, we can conclude that

①Organic nitrogen accounts for the most nitrogen in seawater

②Nitrite nitrogen accounts for a very small amount of nitrogen in seawater.

③The relationship between organic nitrogen and total nitrogen over time is almost the same, which again indicates that most of the total nitrogen is organic nitrogen

④The trend line of total nitrogen is increasing, indicating that the average nitrogen content in seawater is increasing

1.3 Model Building


1.3.1 Topsis Model Background[2]

Topsis can be translated as Approximating Ideal Solution Ranking Method, which is abbreviated as Superior-Inferior Solution Distance Method in China.This method is a commonly used comprehensive evaluation method, which can make full use of the information from the original data, and its results can accurately reflect the gaps among each evaluation programs.It avoids the subjectivity of data, does not need the objective function, does not need to pass the test, and can well portray the combined impact strength of multiple impact indicators; there is no strict restriction on the data distribution and sample size, the number of indicators, and it is suitable for both small sample data and large systems with multiple evaluation units and indicators, which is so flexible and convenient that the model can be applied to the study of this paper.

Calculation process of Topsis:

①Indicator Positivization

• Since ammonia nitrogen, nitrate nitrogen, nitrite nitrogen, and organic nitrogen are all negative indicators, they should first be normalized.

• For each column of data, the positivization is performed as follows.

(1)

②Matrix Standardization

• Assume that there are n objects to be evaluated and m evaluation indicators (which have been normalized) constitute the normalization matrix as follows:

(2)

•Then, the normalized matrix is denoted as X, and each element in X:

(3)

• To determine whether there are negative numbers in the Z matrix, if so, the matrix X needs to be normalized once using another normalization method to obtain the 2 matrix, and the formula for its normalization is:

(4)

③Entropy weight method to calculate the weights [3]

• Suppose there are n objects to be evaluated, m evaluation indicators, and the non-negative matrix obtained from the previous step is:

(5)

• We calculate the probability matrix P,where each element p in P is calculated as follows:

(6)

• Difference Factor Calculation:

(7)

• Calculation of indicator weights:

(8)

④Comprehensive score calculation

• The formula for calculating the composite score of the i-th evaluation object is as follows:

(9)
1.3.2 Results of comprehensive scoring of nitrogen concentration in rivers entering the sea in Fujian

It can be seen in Tables 1-4, the nitrogen concentration score of the rivers entering the sea in Fujian decreases year by year from January 2018 to May 2022, and the lower nitrogen concentration score represents the higher nitrogen concentration and the more serious eutrophication in cross section.

1.3.3Analysis of Nitrogen Concentration Composite Score Result

Figure 1-2 Time series of nitrogen concentration scores in the sea near Fujian

As we can see in Figures 1-3, the nitrogen content scores fluctuate in the range of 0.025-0.005 for the last three years, but annual measurement scores show a linearly decreasing distribution. It indicates that the nitrogen content in the sea area is increasing year by year, and the eutrophication of the water body is gradually increasing, which is consistent with the conclusion derived from the time series plot of total nitrogen obtained above.

1.4 Evaluation of the Monthly Average of each Water Quality index at each Cross Section

1.4.1 Statistical Results of Pollutant Concentration at each Cross Section

Water eutrophication refers to the phenomenon of water pollution caused by excessive content of N, P and other nutrients in water bodies, mainly from unprocessed or incompletely treated industrial wastewater, domestic waste water organic waste ,livestock manure and agricultural fertilizers, the largest source of which is a large amount of chemical fertilizers from farmland.

It is obviously not very objective to judge the eutrophication level of rivers only in terms of nitrogen concentration, therefore, this paper also needs to calculate the total score and evaluate the pollution level of rivers by choosing total phosphorus concentration and chemical oxygen demand together with ammonia nitrogen and total nitrogen concentration separately.


Figure 1-3 Water quality index content of each section


Figure 1-4Histogram of pollutant concentration integrated score at river cross-sections into the sea

1.4.2 Analysis of the Results

In the five histograms in Figs. 1-4, it is easy to find that Longjiang region occupies the top of the list in each index, which proves that among 11 geographical areas in Fujian Province, Longjiang region has the lowest comprehensive score of pollutant concentration in the river cross section into the sea, and is the most serious area of eutrophication as well as pollution at present, so it is reasonable to choose Longjiang as our experimental subject.

1.5 The Evaluation of Pollutant Index in Long River

1.5.1 Statistical Results of [ollutant Concentration in Long River

Figure 1-5 Longjiang various pollutants change curve

1.5.2 Analysis of Results

Water quality testing is of great importance to control water pollution, water resource protection and water health. Using theories and methods of environmental science, while making better use of natural resources, we can gain a deeper understanding of the root causes and hazards of damage to the environment, protect the environment in a planned manner, prevent the deterioration of environmental quality, control environmental pollution, promote the harmonious development of human beings and environment, improve the quality of human life, and protect human health.

Government departments highly emphasize that focusing on regular water quality testing is one of the important means to ensure water quality safety, and relevant testing agencies or enterprises should be highly alert and take up the relevant responsibilities. From January 2018 to May 2022 the water quality of Longjiang River is gradually being improved, its data floating in the standard value of II water quality, but still far from enough, must accelerate the innovation of water purification methods.

1.6 Conclusion Analysis

Longjiang River is the largest river in Fuqing, which originates from Dayang Township in Putian, flows through five towns of Fuqing, namely Dongzhang, Honglu, Yixi, Rongcheng and Haikou, and is injected into Fuqing Bay, and its main tributaries are Taicheng Creek, Dabei Creek, Hu Creek and Guan Creek. The average annual runoff is 400 million cubic meters, which is an important river integrating power generation, flood control, irrigation, sightseeing and urban water supply and drainage, and plays an inestimable role in the economic development of Fuqing City.

With the rapid development of urban and rural economy and society, the problem of water pollution in Longjiang River is becoming more and more serious, with some sections of the river showing black odor for a long time, which is one of the most seriously polluted water systems among the 12 major water systems in the province and has seriously restricted the economic development of Fuqing City. In addition, the Longjiang River basin in Fuqing City is seriously lagging behind in the construction of urban infrastructure, and there is excessive exploitation of water resources, excessive discharge of pollutants, river siltation, beach occupation and other ecological damage, resulting in the deterioration of the quality of the water environment in the Longjiang River basin. Therefore, the control of pollution to protect the Longjiang water resources has become an urgent task.

We propose to strengthen livestock breeding, industrial pollution source control, improve the construction of urban environmental protection infrastructure, ecological water replenishment, the implementation of comprehensive river improvement, ecological restoration projects and other comprehensive remediation measures. We propose to intervene by means of science and technology, using machinery and equipment to improve the ability of microorganisms or plants to fix nitrogen and purify water bodies. The government should issue some relevant regulations to explicitly prohibit chemical plants from discharging pollutants directly into water, and each plant should establish standard water purification equipment; strengthen publicity and education to improve the quality of citizens; add a reward and punishment mechanism to reward plants that discharge in accordance with the regulations, and propose to suspend factories that do not rectify repeated violations of the regulations. The proposal to suspend operation of factories that do not rectify the situation.


Model 2:Water Quality Prediction Model

2.1 Simple Seasonal Model

Import the processed data into SPSS software, and feed back into a simple seasonal model by using the expert modeler [4]. According to the definition of the simple seasonal model, we can get the following three equations:

① Horizontal smoothing equation:

(10)

② Seasonal smoothing equation:

(11)

③ Prediction equation:

(12)

in the formula:

2.2 Data Processing And Modeling Ideas

Use SPSS to fill in the missing values of chemical oxygen demand, nitrate, nitrite, and undetected data as series averages, form new variables, perform subsequent index analysis, and forecast separately by month. Therefore, a time prediction model is used for the pollutant data of Longjiang in the past four years to predict the changes of each pollutant in the next two years and realize visualization.

2.3 Prediction Effect

The prediction results show the predicted changes in the concentrations of dissolved oxygen, ammonia, nitrogen, chemical oxygen demand, total nitrogen, total phosphorus, nitrate, and nitrite at the Longjiang River into the sea from 2018 to 2024.

Stationary R-square:Refers to the goodness of fit, which is the degree of fit of the regression line to the observations. The higher the R-squared value, the greater the change in fund performance due to changes in the performance benchmark. If the R-squared value equals 35, 35% of the fund's return can be attributed to changes in the performance benchmark.

RMSE:Root Mean Square Error, For example, RMSE=10, it can be considered that the regression effect is 10 different from the real value on average.

MAPE: It is a statistical index to measure the prediction accuracy, and it is a percentage value. It is generally believed that when the MAPE is less than 10, the prediction accuracy is higher. If MAPE is 5, it means that the predicted results deviate from the real results by an average of 5%.

MAE:Mean Absolute Error,It represents the mean of the absolute error between the predicted value and the observed value.

NormalizationBIC:The BIC value represents the interpretation of the model to the data. The smaller the BIC value, the stronger the interpretation of the model.

2.3.1 Dissolved Oxygen Index Analysis

(1)The stationary R-square and R-square of the simple seasonal model are 0.702 and 0.417, respectively, that is, the model has a goodness of fit of 70.2%.

RMSE=1.238, it can be considered that the regression effect is not much different from the actual value on average.

MAE=0.942, which means that the mean of the absolute error between the predicted value and the observed value is 0.942.

BIC=0.576, the model is more powerful in explaining the data.

(2) The significance (P value) of the " Yang-Box Q(18)" statistic=0.498, which is greater than 0.05 (the significance (P value)> 0.05 here is the expected result), then accept the null hypothesis and consider this The residuals of the series conform to the random series distribution, and there are no outliers, which also reflects that the fitting effect of the simple seasonal model data is acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good. Figure 2-1 Dissolved oxygen residual ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.


Figure 2-1 Dissolved oxygen residual ACF and PACF diagram



Figure 2-2 Predicted dissolved oxygen value

2.3.2 Ammonia Nitrogen Index Analysis

(1)The stable R-square, RMSE, MAE, and BIC values of the ammonia nitrogen index all represent the stronger the model's ability to interpret the data.

(2) As shown in Table 2-2, although the significance (P value) of the "Yang-Box Q(18)" statistic = 0.004, it is less than 0.05 (the significance (P value) > 0.05 here is expected Results), rejecting the null hypothesis, but the residuals of this series conform to the random sequence distribution, and there are no outliers, which also reflect that the fitting effect of the simple seasonal model data is still acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.






Figure 2-3 ACF and PACF diagrams of ammonia nitrogen content residuals


Figure 2-4 Predicted value of ammonia nitrogen content

2.3.3 Chemical Oxygen Demand Analysis

(1) The stable R-square, RMSE, MAE, and BIC values of the COD index all represent the stronger the model's ability to interpret the data.

(2) As shown in Table 2-4, the significance (P value) of the "Yang-Box Q(18)" statistic = 0.248, which is greater than 0.05 (the significance (P value) > 0.05 here is the expected result ), accepting the null hypothesis, the residuals of this series conform to the random series distribution, and there are no outliers, which also reflects that the fitting effect of the simple seasonal model data is acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.





Figure 2-5 Chemical oxygen demand residual ACF and PACF diagrams


Figure 2-6 Predicted value of chemical oxygen demand

2.3.4 Total Nitrogen Analysis

(1) The stable R-square, RMSE, MAE, and BIC values of the total nitrogen index all indicate that the model has a stronger explanatory power for the data.

(2) As shown in Table 2-6, although the significance (P value) of the "Yang-Box Q(18)" statistic = 0.004, it is less than 0.05 (the significance (P value) > 0.05 here is expected to be obtained Results), rejecting the null hypothesis, but the residuals of this series conform to the random sequence distribution, and there are no outliers, which also reflect that the fitting effect of the simple seasonal model data is still acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.






Figure 2-7 Total nitrogen residual ACF and PACF diagram


Figure 2-8 Predicted value of total nitrogen

2.3.5 Analysis of total phosphorus

(1) The stable R-square, RMSE, MAE, and BIC values of the total phosphorus index all indicate that the model has a stronger explanatory power for the data.

(2) As shown in Table 2-8, although the significance (P value) of the "Yang-Box Q(18)" statistic = 0.006, it is less than 0.05 (the significance (P value) > 0.05 here is expected to be obtained Results), rejecting the null hypothesis, but the residuals of this series conform to the random sequence distribution, and there are no outliers, which also reflect that the fitting effect of the simple seasonal model data is still acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.



Figure 2-9 Total phosphorus residual ACF and PACF diagrams


Figure 2-10 Predicted value of total phosphorus

2.3.6 Nitrate Content Analysis

(1) The stable R-square, RMSE, MAE, and BIC values of the nitrate content index all indicate that the model has a stronger explanatory power for the data.

(2) As shown in Table 2-10, although the significance (P value) of the "Yang-Box Q(18)" statistic = 0, it is less than 0.05 (the significance (P value) > 0.05 here is expected Results), rejecting the null hypothesis, but the residuals of this series conform to the random sequence distribution, and there are no outliers, which also reflect that the fitting effect of the simple seasonal model data is still acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.




Figure 2-11 Nitrate residual ACF and PACF plots


Figure 2-12 Nitrate measurement

2.3.7 Analysis Of Nitrite Content

(1) The stable R-square, RMSE, MAE, and BIC values of the nitrate content index all indicate that the model has a stronger explanatory power for the data.

(2) As shown in Table 2-12, the significance (P value) of the "Yang-Box Q(18)" statistic = 0.551, which is greater than 0.05 (the significance (P value) > 0.05 here is the expected result ), accepting the null hypothesis, the residuals of this series conform to the random series distribution, and there are no outliers, which also reflects that the fitting effect of the simple seasonal model data is acceptable.

(3) At the same time, it can be seen from the ACF and PACF diagrams of the residuals that the autocorrelation coefficients and partial correlation coefficients of all lag orders are not significantly different from 0, indicating that the prediction effect is good.




Figure 2-13 Nitrite residual ACF and PACF plots


Figure 2-14 Predicted value of nitrite

2.4 Result Analysis

Whether it is from the seasonal model analyzed by SPSS software or from the time series chart of the forecast results, the pollutant concentration shows a seasonal trend of high in winter and spring and low in summer and autumn. Therefore, the current seasonal factors should be fully considered when sampling.


Model 3: Simulation Model Of Microalgae Water Purification System Based On Cellular Automata

3.1 Overview

Traditional biological experiments are difficult to simulate the superimposed effects of multiple environmental factors in complex natural water systems. In order to solve this problem, we introduce computer technology to simulate them. Our work breaks through the limitations of traditional biological experiments, realizes interdisciplinary cooperation, and provides new ideas for the development of synthetic biology.

In order to simulate the complex space-time evolution process, we decided to use the cellular automata model, which can decompose the complex system into cells one by one, and simulate its evolution process by defining evolution rules.

3.2 Cellular Automata Model Background Knowledge

The Cellular Automation Model (CA model for short) is a modeling method used to simulate the self-organized evolution process of the system caused by the strong nonlinear interaction between the internal units of a discrete dynamic system. Discretization and regular locality [5]. It was first proposed by von Neumann in the 1950s. At present, it has been successfully used in the simulation of many physical systems and natural phenomena, such as the simulation of the self-replication function of living systems, the simulation of forest fire spread, and the simulation of traffic flow, and has become a very active frontier field in complexity scientific research.

The cellular automata model consists of four parts: cells, states, neighbors and rules [6]. All cells are discrete from each other, forming a cell space. A cell can only have one state at a time, and the state is taken from a finite set; the neighbors are the set of cells that are delimited by a certain shape around the cell, and they affect the state of the cell at the next moment; the cell Rules define the rules for cell state transitions. In this way, each cell scattered in the regular grid takes a finite discrete state, follows the same action rules and updates synchronously according to the determined local rules. A large number of cells form a dynamic evolution system through simple interaction.

The CA model can be described in the language of sets as:S_(t+1)=f(S_t,N). In the formula, S is the finite set, which is the cell state; N is the cell neighbor; t is the time; f is the local transformation rule.


Figure 3-1 Changes in the diffusion of pollutants in the water system

3.3 Model Building

3.3.1 Elemental Diffusion Analysis of Water Pollution Without Microalgae

In this paper, the principle of cellular automata is used to simulate the propagation and diffusion of water pollutants, that is, the water pollution system is regarded as a whole composed of cells. The factors that affect the content of pollutants in a single cell are wind speed, water flow, the content of pollutants in the surrounding cells, the state threshold of the cell and the pollution transfer coefficient [7] . The pollutant transfer coefficient is measured first without considering the wind speed and water flow, and under this premise, the transmission of pollutants in the water satisfies the following formula:

(13)

Among them, M_(i,j)^trepresents the pollutant mass of the i -th row and j -column cells at time t. m is the transmission coefficient of pollutants in the four positive directions. At the same time, the transmission coefficient in the oblique direction should be different from the transmission coefficient in the positive direction, so the original coefficient m needs to be multiplied by d for correction. And the quality of pollutants flowing out of the cell needs to be less than the quality of pollutants in the cell, so m+md≤2.5 is calculated according to the above formula. In the simulation experiment, set m=0.084 and d=0.16.In real life, the situation of no wind and no water flow is difficult to exist, so this paper also considers the influence of wind speed and water flow on the spread of pollutants in the simulation experiment. After considering wind speed and water flow, equation(1)needs to be modified as:

(14)
(15)

`W^f`(k,l) the effect of wind field on pollutants,`W^s`(k,l) is the effect of water flow.

(16)


(17)

δ=B/h ratio of water surface width to depth;νis the average wind speed;β=0.03 is an empirical constant.

(18)

`W^s`(k,l) is the effect of water flow on pollutants

(19)

`V^s`(k,l) is the flow velocity from the k direction to the l direction; V maxis the flow velocity from the k direction to the l direction.

Taking the Cihu River in Ma'anshan City, Anhui Province as an example, this paper simulates the diffusion of pollutants in the water under the action of the southwesterly wind with a velocity of 2.8m/s and the north-south flow with a velocity of 9.78m/s according to the local hydrometeorological data. The other parameters are: The average river width B is 110m, the average water depth h is 10.5m, the pollutants are set to be randomly distributed, and the initial walk radius is 0.01km, The forward diffusion coefficient m=0.084, the oblique diffusion coefficient d=0.16, the wind drift factor α(k,l)=0.032, and the cell state threshold Mth=1g. The distribution of pollutants in the water area is obtained, and the pollutant content maps after the 1st, 5th, 10th, 15th, 20th, 25th, and 30th iterations are listed as follows. After 30 iterations, it gradually becomes stable, and the pollutant content map is as follows It can be seen that the distribution of pollutant content tends to be stable after 25 iterations.

3.3.2 Analysis Of Water Pollution Element Content After Microalgae Intervention

(1) Microalgae growth

Simulating the mass change of microalgae particles is an important condition for predicting the distribution changes of various pollutants under the intervention of microalgae. Therefore, this paper uses differential equations to predict the mass changes of microalgae particles[8]. The mass change of microalgae particles satisfies the following differential equation:

(20)

where mass is the mass of microalgae particles,Kts is the net mortality and net growth rate under the combined effect of salinity and temperature.Kts satisfy:

(21)

Among them,Kt is the mortality rate of microalgae particles under the influence of temperature, and Ks is the mortality rate of microalgae particles under the influence of salinity. Its expression is:

(22)

Note: The parameter description is as follows



Figure 3-2 Changes in pollutant content of microalgae after multiple iterations


Model 4: Site Selection Model of Microalgae Plant based on Carbon Sequestration Rate

4.1 Model Background

Microalgae have a very high carbon sequestration rate. While breeding large-scale microalgae, carbon dioxide in the air as the inorganic carbon source is efficiently converted into high value-added products such as oils, carbohydrates, proteins and pigments. Some studies have shown that the carbon sequestration rate of microalgae is affected by air temperature, light duration and other factors[9]

(23)

x1x2x3Among them, the light intensity, the average temperature, is the sunshine length. Therefore, we plan to study the site selection problem of microalgae, and establish the optimization model with the highest carbon sequestration rate of microalgae, so as to obtain the best site selection city of microalgae plants.

4.2 Study Area and Data Sources

4.2.1 Research Area

According to China's current administrative divisions, prefecture-level administrative regions include prefecture-level cities, regions, autonomous prefectures and leagues, and are under the jurisdiction of provincial administrative regions. In addition, from the perspective of the integrity of administrative divisions and management functions, counties (cities) and counties (cities) directly under provincial jurisdiction are directly managed by provinces or autonomous regions, and should also be studied as independent geographical units. Therefore, we take 371 administrative divisions in China as the research objects, including 293 prefecture-level cities, 7 regions, 30 autonomous prefectures and 3 alliances, including 4 municipalities directly under the Central Government, 2 special administrative regions, 31 counties directly under the jurisdiction of provinces, and Taiwan (provincial administrative regions and municipalities directly under the Central Government).

4.2.2 Data Source and Processing

The monthly average temperature and sunshine duration data of each administrative division are derived from the 2021 China Statistical Yearbook, statistical yearbooks of various provinces, statistical yearbooks of various prefecture-level cities, environmental statistical bulletin and the website of the local Ecology and Environment Bureau. Light intensity data were obtained from the 5th generation reanalysis dataset data released by ECMWF, using the average surface downward shortwave radiation flux therein[10].


As shown in the above table, the collection is the monthly cumulative sunshine duration of each city, while the data we calculate is the daily cumulative duration, so the data needs to be processed first:

(24)

sum(longi)Among them, the cumulative light duration of each month in 2021 is the number of days of each month in 2021.ni


4.3 Model Solution and analysis

By entering the collected monthly data into the model for solution, we defined the microalgae carbon sequestration rate at a negative temperature as 0, considering the case where the carbon sequestration rate caused by the low temperature is negative. The final grid diagram of the carbon sequestration rates in various cities in different months is shown in Figure 4.

We can find that in terms of regional distribution, the rate of carbon sequestration in various cities is high in the eastern coastal area, and the rate is high in summer and autumn and low in winter and spring. This is because the light intensity and average air temperature have a very significant impact on the carbon sequestration potential of microalgae, so the relative carbon sequestration rate is high in summer and autumn. However, the eastern coastal areas and other places are in the climate conditions with relatively high light and temperature all the year round, and the rainy days are not as concentrated as in the northern areas. Therefore, the growth rate of microalgae is relatively high, and the carbon sequestration rate of microalgae is also relatively high.


Figure 4 Carbon fixation rates in cities across the country




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