Team:WHU-China/Model
Overview
This year we attempt to establish a comprehensive mathematical model to describe the sewage treatment process and help us understand our system better. We take the primary constituents in influent wastewater into consideration and focus on “growth-decay-hydrolysis” process of main kinds of organisms. By doing so, we determine 24 parameters and 9 components in influent water involved in the whole circular process. According to the principle of mass conservation, each part of the process follows the equation:
Input- output+ product newly generated=Accumulation
To establish the relationship among these elements, we obtain the typical values from literature review along with field research data in sewage treatment plant. Referring to several articles, we successfully put forward a new model describing the change of essential variables in the system, such as the concentration of halides and the birth rate of the bacteria.
But at first, we did a pre-experiment to measure the growth condition of natural B. megaterium under different organohalide concentrations.
Pre-experiment
In the pre-experiment, 3,5-dichloro-2-hydroxybenzoic acid (A) and 3,5-dibromo-2-hydroxybenzoicacid (B) are chosen as representatives for organohalides in wastewater for their relative high toxicity and potential harm to B. megaterium. And OD578 is used as an indication of B. megaterium’s growth condition. Every group has the same volume but different concentrations of organohalides. We hope to find out B. megaterium’s bearable growth conditions to estimate our project’s practicality in model.
One thing should be mentioned is that, although we’ve considered expression of RdhANP may have impact on its growth condition in wastewater and we’ve tried our best to make it in expressing RdhANP, we still didn’t have enough time for those statistics. So our model here just takes the growth condition of natural B. megaterium into consideration. And if time permits, we would modify our model with this factor. We did this pre-experiments twice and finally got a pleasant result.
From the figures above, we can determine that the proper surviving interval for B. megateium ranges from 0M to 1000Um (for both A and B). Over 1000uM, severe reduction can be detected. By doing literature review, we know that RdhANP has high activity and efficiency in that interval. In this case, we confirmed that our engineering bacterium is truly suitable for our sewage disposing system.
Parameters and componentsm
We divide the bacteria existing in our bioreactor into 3 groups: aerobic halide bacteria, other aerobic organisms and anaerobic heterotrophic bacteria (as follows). They take up different sources and play different roles in the system.
| Elements for their growth | Elements for their hydrolysis | Task | |
| Aerobic halide bacteria | C, N, lg, P, O | C, N, P, lg | Intake halide and break it down, hydrolyze particulate substances |
| Other aerobic bacteria | O,N,P | C,N,P | Hydrolyze particulate substances |
| Anaerobic heterotrophic bacteria | C,N,P | C,N,P | Hydrolyze particulate substances |
Table 1. Bacteria in bioreactor(lg represent for organohalide)
Figure 1. Relationships in bioreactor
In the picture, every rectangle indicates a reaction, every circle represents one kind of components. Minor sign means decreasing whiles plus sign means increasing.
The specific meaning of the abbreviations can be found in the following tables.
Parameters:
| Symbol | Name | Unit | |
| 1 | a | Birth coefficient for organisms | 1/D |
| 2 | b | Nutrient coefficient for organisms | 1/D |
| 3 | c | Halide coefficient for halide bacterium | 1/D |
| 4 | iHA | Competition coefficient(from H to A) | / |
| 5 | iAH | Competition coefficient(from A to H) | / |
| 6 | iAN | Competition coefficient(from A to N) | / |
| 7 | iNA | Competition coefficient(from N to A) | / |
| 8 | iHN | Competition coefficient(from H to N) | / |
| 9 | iNH | Competition coefficient(from N to H) | / |
| 10 | KH0 | Carrying capacity for halide | / |
| 11 | KA0 | Carrying capacity for aerobic organisms | / |
| 12 | KN0 | Carrying capacity for anaerobic bacterium | / |
| 13 | ixs | Mass of carbon per mass of COD in biomass | g(C)/g(COD) |
| 14 | ixlg | Mass of halide per mass of COD in biomass | g(lg)/g(COD) |
| 15 | ixn | Mass of nitrogen per mass of COD in biomass | g(N)/g(COD) |
| 16 | ixp | Mass of phosphorus per mass of COD in biomass | g(P)/g(COD) |
| 17 | fp | Fraction of biomass leading to particulate products | |
| 18 | C0 | Concentration of oxygen in bioreactor | Mg/mL |
| 19 | u | Velocity of wastewater | L/s |
| 20 | Cs | Concentration of nutrient in bioreactor | Mg/mL |
| 21 | C1 | Concentration of halide in bioreactor | Mg/mL |
| 22 | V | Volume of bioreactor | L |
| 23 | Cl0 | Concentration of halide in influent water | Mg/mL |
| 24 | Cs0 | Concentration of nutrient in influent water | Mg/mL |
Components:
| Symbol | Name |
| Ss | Soluble carbon in influent wastewater |
| Slg | Soluble halide in influent wastewater |
| So | Dissolved oxygen in influent wastewater |
| Sno | Soluble nitrogen in influent wastewater |
| Sp | Soluble phosphorus in influent wastewater |
| XA | Active biomass for aerobic organisms |
| XH | Active biomass for heterotrophic halide bacterium |
| XN | Active biomass for heterotrophic bacterium |
| X | Particulate substances in bioreactor |
Assumptions
Based on our classification, the relationship among three groups and sources in the environment are depicted as following:
When a wastewater treatment system is to be modelled, a certain number of simplifications and assumptions must be made in order to make the model tractable. Some of these are associated with physical system itself, whereas others concern the mathematical model.
1.The direct interactions between these three kinds of organisms are taken into consideration. Their interdependence is reflected on a competition coefficient i.
2.The aeration tank operates at constant temperature, because lots of parameters are the function of temperature.
3.The aeration tank operates at constant and proper pH value, nearly neutral pH value, the effects of pH value will be discussed later.
4.It is assumed that the concentration of substances in influent water is variant but their components are constant. The reactions between carbon, nitrogen and halide are not taken into consideration. Only B. megaterium is capable of disposing of the halide substances.
5.Ammonification has been ignored because it is not the fundamental process occurring in our reactor.
6.The proportion of all kinds of particulate substances is assumed to be consistent, the saturation coefficient of nitrogen, carbon, phosphorus is nearly analogous.
7.The particulate substances will be hydrolyzed instantaneously. Those non-biodegradable constituents are totally inert.
Results
According to the assumptions, a few calculations can be done.
Details of our calculations can be found as follows.
5.1 Switching function
We introduce switching function to predict whether the process is on or off as environmental conditions are changed.
Take hydrolysis of soluble halide as example. Within our context and through conceptual modeling, this process can only occur under aerobic condition. In that case, if the dissolved oxygen falls to zero, this process is unable to proceed any more. Then we use switching function to describe this change:
Where, S0 means dissolved oxygen, KO.Lg is a constant. It is obvious that the rate of process is nearly constant for moderate change of oxygen concentration but will decrease to zero severely when dissolved oxygen approaches zero.
Consequently, for a specific process, the positive effect for the management is accordant to positive switching function. Conversely, negative effect correlates to minor switching function.
5.2 Environmental carrying capacity
It is assumed that every kind of organisms in our modeling has a population limitation, which means they can’t reach up to infinity. We use symbol K to describe carrying capacity.
5.3. Other functions used when calculating different rates
| Rate of birth |
 |
| Rate of death |
 |
| Rate of growth |
 |
| Rate of nutrient variation |
 |
| Rate for the degradation of halide substances |
 |
Later, in order to explore the realistic effects of our model, we use Runge-Kutta methods with the help of MATLAB. In static and dynamic modeling, we respectively hypothesize that our bioreactor is a closed pond or an open system, we control the properties of influent water by setting up initial value and simulate it on the computer. And the different output is obtained as we adjust the proportion of B. megaterium in the system.
Figure 2. Relative change of halide bacteria and halide
Discussion
Besides aiding our project, our model can also serve as a platform for other teams’ project related to industrial engineering bacterial application. Based on our modeling, each value can be adjusted according to the actual states of specific experiments in their project. Regrettably, due to the limitation of time, we can’t do the verification of our model through our hardware, but we do welcome our model be tested by more and more teams and hope that our model can bring sort of convenience to them.
References
[1] IWA Task Group on Mathematical Modelling for Design and Operation of Biological Wastewater Treatment. Activated sludge models ASM1, ASM2, ASM2d and ASM3[J]. Iwa Scientific Technical Report, 2005, 9.
[2] 沙锦箖. 基于ASM1模型改善城市污水处理厂运行工况与效果的研究[D]. 郑州大学, 2005.
[3] 王志强. PDMS/PS复合中空纤维膜处理含酚废水的研究[D]. 大连理工大学, 2006.
[4] 陈文亮, 吕锡武, 姚重华. 不同进水条件下ASM1模型参数的灵敏度分析[J]. 环境污染与防治, 2013, 35(8):59-63.
[5] 张静, 侯红勋, 王淦,等. 小型一体化污水处理设备工艺研究[J]. 工业用水与废水, 2014, 45(1):60-64.
