Team:Nanjing NFLS/Model

Model

An ordinary differential equation model is established to describe the variation of current density with time in MFC. By changing the model parameters, the power output of MFC under different conditions is predicted.

1. Background

MFC is a device that converts chemical energy to electrical energy by the action of microorganisms. We try to improve the performance of MFCs, especially the electricity output, by overexpression of three genes. However, we only do the analysis of enzymatic activity at present, and a math modeling in dry lab can in some degree make up for the limitation of wet lab.

2. Problem analysis

Power output of MFC depends on the concentration of electrochemical activity substance produced by bacteria. Such electrochemical active substances are related to the growth state of bacteria. Therefore, the current density of MFC will change with time and the amount of nutrients (or organic waste wateretc.) added to the medium. Describing the variation of current density of MFC is helpful to better understand the production process of MFC, and the power output of MFC under different conditions can also be predicted by changing the model parameters. Therefore, we build the ordinary differential equation (ODE) model to describe the variation of current density of MFC with time.

3. Hypothesis

1） We assume that the current density of MFC is proportional to the concentration of the electrochemical active substance.
2） We assume a linear relationship between the concentration of the electrochemical active substance and the concentration of the added nutrient.
3） We assume a linear relationship between the degradation of electrochemical active substances and their concentration.

4. Description of symbols

Cw：Concentration of precursor substances, such as nutrients or organic wastewater, that produces electrochemical activity substances
Ce：Concentration of electrochemical active substances
Kw：The conversion rate from precursors to electrochemical active substances
Ke：Degradation rate of electrochemical active substances
Kc：Parameters of power output efficiency of electrochemical active substances
J：current density
Pulse（A，time）：The amount by which the concentration of a precursor substance is increased after it is added

5. Modeling and solving

We established an ordinary differential equation model to describe the changes of the concentration of precursor substances and electrochemical active substances in MFC as well as the change of MFC electricity generation over time. And The model structure is as follows.

In MFC, the main source of precursor substances is exogenous addition, and the main consumption is converted into electrochemical active substances. The concentration change equation of Cw is as follows.

The main source of electrochemical active substances is produced by precursor substances, and the main consumption is degradation. The concentration change equation is as follows.

Since we assume that the current density of MFC is proportional to the concentration of electrochemical active substances, the equation of current density is as follows.

According to the data in the literature of Yong et al.[1], Berkeley Madonna software is used to fit the differential equations and optimize the values of various parameters. As shown in the figure below, our model can well fit the data in the article.

The fitting parameters are shown in the table below.

ParametersValues
Kw0.15
Ke0.01
Kc0.04
A800

6. Model prediction

Since we overexpress nadE (NAD synthase gene), rhlA (rhamnosyl transferase gene), and phzM (methyltransferase encoding gene) in Pseudomonas aeruginosa in our experiments，it can be considered that the electrical efficiency of the electron donor has been changed. Therefore, we simulated the situation where the Kc value was increased by 1.5 times or 2 times, and the current density-time curve is shown in the figure below.

7. Conclusion

An ordinary differential equation model is established to describe the variation of current density with time in MFC. By changing the model parameters, the power output of MFC under different conditions is predicted. We find that if the parameters of power output efficiency increase, the current density will also increase.

8. The source code

METHOD RK4

STARTTIME = 0
STOPTIME=300
DT = 0.2
d/dt(Cw)=-Kw*Cw+pulse(dose,0,50)-pulse(dose,100,50)+pulse(dose,120,80)
pulse(dose,200,80) +pulse(dose,200,90)
d/dt(Ce)=Kw*Cw-Ke*Ce
init Cw = 0
init Ce = 0
Kw=0.15
Ke = 0.01
Kc=0.04
dose = 800

J_Predicted=Kc*Ce




[1] Yong XY, Yan ZY, Shen HB, Zhou J, Wu XY, Zhang LJ, Zheng T, Jiang M, Wei P, Jia HH, Yong YC. An integrated strategy for performance enhancement of Pseudomonas aeruginosa-inoculated microbial fuel cell. Bioresour Technol.