Anaerobic digestion gas production analysis method based on Mathematica

Abstract

The invention belongs to the technical field of anaerobic digestion analysis, and particularly relates to a Mathematica-based anaerobic digestion gas production analysis method, which comprises the following steps of: drawing a two-dimensional curve graph of a Logistic model and a modified Gompertz model in Mathematica software, fitting a scatter diagram of actual experimental numerical values with the two two-dimensional curve graphs, and finally obtaining a fitted gas production dynamic formula. According to the invention, conditions can be changed according to actual conditions, various small-sized experiments can be scaled, and necessary technical parameters are provided for biogas engineering.

Description

Technical Field

[0001] The invention belongs to the technical field of anaerobic digestion analysis, and particularly relates to an anaerobic digestion gas production analysis method based on Mathematica. Background Art

[0002] In recent years, the production of food waste in my country has increased rapidly. Efficiently treat food waste and realize the recycling of resources. Anaerobic digestion is an effective method for food waste treatment. It is a complex microbiological process that includes microbial growth, substrate degradation, and metabolite generation. The kinetics of anaerobic digestion aims to characterize the microbial growth rate, substrate degradation rate, and metabolite generation rate in this process through mathematical models, thereby solving the complexity of the reaction rate in the anaerobic fermentation process. Establishing the kinetic mathematical model of the anaerobic fermentation process is important for understanding the reaction law, designing and controlling the reactor.

[0003] ADM1 is the only widely recognized general model launched by the International Water Quality Association. It can more accurately describe the anaerobic digestion process by using a set of differential algebraic equations. Compared with previous models, ADM1 is particularly significant in terms of structural characteristics. Compared with the hydrolysis kinetic model, ADM1 more accurately describes the seven types of microorganisms, three gas-liquid mass transfers and nineteen biochemical kinetic models involved in the anaerobic digestion process. For this purpose, the corresponding kinetic equations are established, and the reaction rate expressions for each process are proposed, thus realizing the quantifiable anaerobic digestion process. In addition to being affected by the hydrolysis rate, biogas production is also closely related to the number of microorganisms. In the analysis of methane production kinetics, population growth models are widely used, among which the Logistic model and the modified Gompertz model are the most representative.

[0004] However, the existing anaerobic dynamics calculation methods are usually cumbersome, time-consuming and laborious, so there is an urgent need for a more convenient and practical calculation method. Mathematica is a software specifically used for mathematical modeling, which can intuitively display formulas and conveniently perform calculations. Summary of the invention

[0005] In order to solve the above technical problems, the present invention provides an anaerobic digestion gas production analysis method based on Mathematica, which can change the conditions according to the actual situation, can scale up various small experiments, and provide necessary technical parameters for biogas projects.

[0006] The present invention is implemented by providing a method for analyzing gas production in anaerobic digestion based on Mathematica, comprising the following steps:

[0007] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0008]

[0009] The formula of the modified Gompertz model is as follows:

[0010]

[0011] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0012] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process into Mathematica software and draw a scatter plot;

[0013] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1 to obtain the P, R, and λ values ​​of the two models after fitting respectively;

[0014] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula to obtain the fitted anaerobic digestion gas production kinetics formula;

[0015] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 If the fitting is satisfied, the two fitted anaerobic digestion gas production kinetic formulas are used to analyze the gas production in the anaerobic digestion process.

[0016] Preferably, in step 1, sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model are added in Mathematica software.

[0017] Preferably, in step 5, R 2 The calculation formula is:

[0018]

[0019] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

[0020] Preferably, the analysis method is a method for analyzing gas production from anaerobic digestion of kitchen waste.

[0021] Compared with the prior art, the advantages of the present invention are:

[0022] The present invention provides a method for analyzing gas production in anaerobic digestion based on Mathematica: a suitable anaerobic digestion gas production kinetic model is selected, run in Mathematica, and a two-dimensional curve is drawn; then when analyzing data, the curve can be directly fitted in Mathematica to obtain a kinetic equation. Since the analysis of anaerobic digestion kinetics only needs to be run in Mathematica and can be intuitively displayed, the existing analysis method is greatly facilitated. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a two-dimensional graph of the Logistic model running in Mathematica software;

[0024] Figure 2 This is a two-dimensional graph of the modified Gompertz model running in Mathematica software;

[0025] Figure 3 This is a scatter plot of the experimental time and cumulative methane production during the actual anaerobic digestion process of Example 1;

[0026] Figure 4 The kinetic formula curve of anaerobic digestion gas production of the Logistic model after fitting in Example 1;

[0027] Figure 5 It is the modified Gompertz model anaerobic digestion gas production kinetic formula curve after fitting in Example 1;

[0028] Figure 6 This is a scatter plot of the experimental time and cumulative methane production during the actual anaerobic digestion process of Example 2;

[0029] Figure 7 The kinetic formula curve of anaerobic digestion gas production of the Logistic model after fitting in Example 2;

[0030] Figure 8 It is the modified Gompertz model anaerobic digestion gas production kinetic formula curve after fitting in Example 2;

[0031] Fig. 9The scatter plot is a graph of the experimental time and cumulative methane production during the actual anaerobic digestion process in Example 3;

[0032] Fig.10 The kinetic formula curve of anaerobic digestion gas production of the Logistic model after fitting in Example 3;

[0033] Fig.11 It is the modified Gompertz model anaerobic digestion gas production kinetic formula curve after fitting in Example 3;

[0034] Fig.12 This is a scatter plot of the experimental time and cumulative methane production during the actual anaerobic digestion process of Example 4;

[0035] Fig.13 The kinetic formula curve of anaerobic digestion gas production of the Logistic model after fitting in Example 4;

[0036] Fig.14 It is the modified Gompertz model anaerobic digestion gas production kinetic formula curve after fitting in Example 4;

[0037] Fig.15 This is a scatter plot of the experimental time and cumulative methane production during the actual anaerobic digestion process of Example 5;

[0038] Fig.16 The kinetic formula curve of anaerobic digestion gas production of the Logistic model after fitting in Example 5;

[0039] Fig.17 It is the modified Gompertz model anaerobic digestion gas production kinetic formula curve after fitting in Example 5;

[0040] Fig.18 This is a scatter plot of the experimental time and cumulative methane production during the actual anaerobic digestion process of Example 6;

[0041] Fig.19 The kinetic formula curve of anaerobic digestion gas production of the Logistic model after fitting in Example 6;

[0042] Fig. 20 This is the modified Gompertz model anaerobic digestion gas production kinetic formula curve after fitting in Example 6. DETAILED DESCRIPTION

[0043] The present invention is further described below in conjunction with specific embodiments, but the protection scope of the present invention is not limited thereto.

[0044] Example 1: Kinetic simulation analysis of sequencing batch anaerobic digestion of food waste Example 1: Constant temperature and no human intervention in pH adjustment (SH group).

[0045] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0046]

[0047] The formula of the modified Gompertz model is as follows:

[0048]

[0049] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0050] Add sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model in Mathematica software, refer to Figure 1 , Figure 2 ;

[0051] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process of the SH group into Mathematica software and draw a scatter plot. Figure 3 ;

[0052] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1, and obtain the P, R, and λ values ​​of the two models after fitting: 1973.06, 139.962, -5.36633 and 1977.3, 176.228, -3.81391 respectively;

[0053] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula, that is, slide the sliders of the three parameters P, R, and λ to the corresponding positions to obtain the fitted anaerobic digestion gas production kinetics formula curve, refer to Figure 4 and Figure 5 ;

[0054] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2, are 0.998875 and 0.999076 respectively, both close to 1, which satisfies the fitting. The two fitted anaerobic digestion gas production kinetic formulas can be used to analyze the gas production in the anaerobic digestion process. 2 The calculation formula is:

[0055]

[0056] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

[0057] Example 2: Kinetic simulation analysis of sequencing batch anaerobic digestion of food waste Example 2: Constant temperature and human intervention pH adjustment (NA group).

[0058] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0059]

[0060] The formula of the modified Gompertz model is as follows:

[0061]

[0062] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0063] Add sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model in Mathematica software, refer to Figure 1 , Figure 2 ;

[0064] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process of the NA group into Mathematica software and draw a scatter plot. Figure 6 ;

[0065] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1, and obtain the P, R, and λ values ​​of the two models after fitting: 2208.08, 114.915, -6.1354 and 2223.84, 135.561, -4.76986 respectively;

[0066] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula, that is, slide the sliders of the three parameters P, R, and λ to the corresponding positions to obtain the fitted anaerobic digestion gas production kinetics formula curve, refer to Figure 7 and Figure 8 ;

[0067] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 , are 0.999408 and 0.999529 respectively, both close to 1, which satisfies the fitting. The two fitted anaerobic digestion gas production kinetic formulas can be used to analyze the gas production in the anaerobic digestion process. 2 The calculation formula is:

[0068]

[0069] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

[0070] Example 3: Kinetic simulation analysis of sequencing batch anaerobic digestion of food waste Example 3: Variable temperature and no human intervention in pH adjustment (TF group).

[0071] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0072]

[0073] The formula of the modified Gompertz model is as follows:

[0074]

[0075] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0076] Add sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model in Mathematica software, refer to Figure 1 , Figure 2 ;

[0077] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process of the NA group into Mathematica software and draw a scatter plot. Fig. 9 ;

[0078] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1, and obtain the P, R, and λ values ​​of the two models after fitting: 1839.93, 98.3.64, -6.5485 and 1848.4, 119.324, -4.92556 respectively;

[0079] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula, that is, slide the sliders of the three parameters P, R, and λ to the corresponding positions to obtain the fitted anaerobic digestion gas production kinetics formula curve, refer to Fig.10 and Fig.11 ;

[0080] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 , are 0.999599 and 0.999674 respectively, both close to 1, which satisfies the fitting. The two fitted anaerobic digestion gas production kinetic formulas can be used to analyze the gas production in the anaerobic digestion process. 2 The calculation formula is:

[0081]

[0082] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

[0083] Example 4: Kinetic simulation analysis of sequencing batch anaerobic digestion of food waste Example 4: Variable temperature and human intervention pH adjustment (TF-SH group).

[0084] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0085]

[0086] The formula of the modified Gompertz model is as follows:

[0087]

[0088] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0089] Add sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model in Mathematica software, refer to Figure 1 , Figure 2 ;

[0090] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process of the NA group into Mathematica software and draw a scatter plot. Fig.12 ;

[0091] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1, and obtain the P, R, and λ values ​​of the two models after fitting: 2093.56, 114.874, -5.22076 and 2109.11, 133.323, -4.12451 respectively;

[0092] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula, that is, slide the sliders of the three parameters P, R, and λ to the corresponding positions to obtain the fitted anaerobic digestion gas production kinetics formula curve, refer to Fig.13 and Fig.14 ;

[0093] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 , are 0.999243 and 0.999269 respectively, both close to 1, which satisfies the fitting. The two fitted anaerobic digestion gas production kinetic formulas can be used to analyze the gas production in the anaerobic digestion process. 2 The calculation formula is:

[0094]

[0095] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

[0096] Example 5: Kinetic simulation analysis of continuous anaerobic digestion of food waste with solar-assisted heating:

[0097] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0098]

[0099] The formula of the modified Gompertz model is as follows:

[0100]

[0101] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0102] Add sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model in Mathematica software, refer to Figure 1 , Figure 2 ;

[0103] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process of solar-assisted food waste into Mathematica software and draw a scatter plot. Fig.15 ;

[0104] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1, and obtain the P, R, and λ values ​​of the two models after fitting: 1621.09, 33.4941, 34.0406 and 12707.5, 79.9857, 58.8466 respectively;

[0105] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula, that is, slide the sliders of the three parameters P, R, and λ to the corresponding positions to obtain the fitted anaerobic digestion gas production kinetics formula curve, refer to Fig.16 and Fig.17 ;

[0106] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 , are 0.999399 and 0.999093 respectively, both close to 1, which satisfies the fitting. The two fitted anaerobic digestion gas production kinetic formulas can be used to analyze the gas production in the anaerobic digestion process. 2 The calculation formula is:

[0107]

[0108] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

[0109] Example 6: Kinetic simulation analysis of continuous anaerobic digestion of kitchen waste using electric energy for heating:

[0110] Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows:

[0111]

[0112] The formula of the modified Gompertz model is as follows:

[0113]

[0114] Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time;

[0115] Add sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model in Mathematica software, refer to Figure 1 , Figure 2 ;

[0116] Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process of solar-assisted food waste into Mathematica software and draw a scatter plot. Fig.18 ;

[0117] Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1, and obtain the P, R, and λ values ​​of the two models after fitting: 1682.19, 44.0262, 27.4991 and 2877.03, 41.8117, 26.7868 respectively;

[0118] Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula, that is, slide the sliders of the three parameters P, R, and λ to the corresponding positions to obtain the fitted anaerobic digestion gas production kinetics formula curve, refer to Fig.19 and Fig. 20 ;

[0119] Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 , are 0.99946 and 0.999817 respectively, both close to 1, which satisfies the fitting. The two fitted anaerobic digestion gas production kinetic formulas can be used to analyze the gas production in the anaerobic digestion process. 2 The calculation formula is:

[0120]

[0121] Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

Claims

1. The anaerobic digestion gas production analysis method based on Mathematica is characterized by: The steps include: Step 1: Draw the two-dimensional curve graphs of the Logistic model and the modified Gompertz model in Mathematica software. The formula of the Logistic model is as follows: The formula of the modified Gompertz model is as follows: Among them, L and G are the cumulative methane production at time t in the anaerobic digestion process under the Logistic model and the modified Gompertz model, respectively; P is the maximum methane production potential of the anaerobic digestion process; R is the maximum methane production rate of the anaerobic digestion process; t is the experimental time; and λ is the reaction stagnation time; Step 2: Import the experimental time and cumulative methane production of the actual anaerobic digestion process into Mathematica software and draw a scatter plot; Step 3: Fit the scatter plot in step 2 and the two-dimensional curve graph of the Logistic model in step 1 in Mathematica software, and fit the scatter plot in step 2 and the two-dimensional curve graph of the modified Gompertz model in step 1 to obtain the P, R, and λ values ​​of the two models after fitting respectively; Step 4: Substitute the P, R, and λ values ​​of the two models into the Logistic model and the modified Gompertz model formula to obtain the fitted anaerobic digestion gas production kinetics formula; Step 5: Calculate the R of the two fitted anaerobic digestion gas production kinetics formula curves 2 If the fitting is satisfied, the two fitted anaerobic digestion gas production kinetic formulas are used to analyze the gas production in the anaerobic digestion process.

2. The anaerobic digestion gas production analysis method based on Mathematica according to claim 1, characterized in that: In the step 1, sliders for adjusting the three parameters P, R, and λ of the Logistic model and the modified Gompertz model are added in the Mathematica software.

3. The anaerobic digestion gas production analysis method based on Mathematica according to claim 1, characterized in that: In step 5, R 2 The calculation formula is: Among them, SSE is the residual sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the model predicted values, and SST is the total sum of squares, that is, the sum of squares of the differences between the actual observed values ​​and the mean of the observed values.

4. The anaerobic digestion gas production analysis method based on Mathematica according to claim 1, characterized in that: The analysis method is a method for analyzing gas production by anaerobic digestion of kitchen waste.

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