Team:CIEI-China/Model
Food waste, which comes from citizens’ daily production and consumption, includes leftovers from restaurants, canteens, and residents’ homes. It consists of rice, flour, vegetables, plant or animal oil, meat, bones, and so on, and therefore, contains high percentages of organic substances, mainly starch, protein, cellulose, and lipids. Specific Groups in food waste may vary in different regions due to their size, function, life level, and citizens’ habits; yet in China, food waste generally has a higher level of starch and lipids, with a lower level of protein and cellulose. Because of the amount of organic substances and moisture in food waste, which is considerably larger than in other solid waste, food waste is easy to decay at high temperature, produce repulsive smell, breed bacteria and pathogens, and thus lead to tremendous harms and pollution to the surrounding areas.
Osmosis pressure plays an important role in microbes’ life. Their living environment must have a relatively equal osmosis pressure as in their cells; if the surrounding osmosis pressure goes beyond the limits or changes all of a sudden, microbes may not be able to conduct normal activities or even die. In hypertonic solution, the cells dehydrate, protoplasma contracts, and the cell plasma becomes viscous, leading to plasmolysis. In hypotonic solution, water moves in to the cell, and cells expand or even burst. In isotonic solution, microbes metabolize the best, and the cells neither contract nor expand – they keep their original form. Normal saline (0.85% NaCl solution) is one kind of isotonic solution.
The influence of salinity on microbes mainly includes:
Since water naturally move from lower concentration to higher concentration, if the outside environment contains excessive salt, water inside the microbes will get lost through osmosis, resulting in the change of inner biochemical environment. The microbes will unable to perform metabolic reactions and die of dehydration.
Generally, cells absorb beneficial substances, a process influenced by outside solution concentration directly. Too much salinity will interfere or even halt the absorption, and repress microbes’ metabolism.
Salt may get inside of the microbes and destroy their inner biochemical reaction processes; some may react with cell membrane and change its protective/absorption characteristics (for example, heavy metal salt).
During our research, we discovered that high salinity influences anaerobic composting in the following aspects: 1. Active sludge: longer adjusting period, lower growing speed in logarithm growth period, longer decelerating period; 2. Stronger microbe respiration and cell lysis; 3. Lower organic biodegradable degree; 4. Lower composting efficiency.
In the following article, we will discuss the influence of hypertonicity and high salinity on microbes in food waste anaerobic composting through dynamic models.
Hypertonicity and high salinity reduce the microbe survivability in food waste disposal, and it is a negative factor in the anaerobic fermentation, which decreases the effectiveness and efficiency of the microbes.
Anaerobic fermentation, known as anaerobic composting or biogas fermentation, refers to the process of transforming organic crop straw, livestock manure, organic waste from industrial and domestic waste water into CH4 and CO2.
The essence of anaerobic fermentation is the transforming process of microbial metabolism and energy conversion. The microbes utilize a small part of organic matter for microorganism’s own metabolism, and the remaining part are used for biogas production.
Anaerobic fermentation can reduce the amount of waste, achieve the purpose of reduction, decrease environmental pollution, and produce available energy to obtain green resources. The main components of biogas are CH4 and CO2 and, 60% of which is CH4, 40% is CO2, and a small amount of etc. Different fermentation substrate produces slightly different biogas. At the same time, biogas residue and slurry produced by anaerobic fermentation can also be used as fertilizer and other agricultural purposes.
Anaerobic composting is a process involving many stages and various microbes. People's understanding of this complex reaction process has developed through the Two-Stage Theory in the 1930s to the Three Stage Theory and the Four Stage Theory. According to the differences in microbes’ biological chemical process, Two Stage Theory divided the microbes into two groups: fermentation bacteria which produce methane and bacteria which do not produce methane, and the anaerobic composting was divided into acid and methane production stages. The acid production stage is the process through which the microbes decompose the complex organic matter into fatty acid, alcohol, and so on through hydrolysis, and the stage of methane production further transforms the substance into CH4 and CO2. This theory gives a brief description of anaerobic composting, and guide the production practice of anaerobic fermentation in the last century; however, this theory did not fully reflect the essence of anaerobic composting, and there are still some questions remaining for further researches.
With further anaerobic composting research, people have developed a deeper understanding of the relationship between microbial populations in anaerobic composting. In 1967, Bryant introduced the Three Stage Theory of anaerobic composting in 1979. The anaerobic composting process was divided into three stages: hydrolysis, acid production and methane production. At the same time, Zeikus et al. proposed the Four Stage Theory of anaerobic composting. The anaerobic composting process was divided into four stages: hydrolysis, acid production, acetic acid production and methane production. The Four Stage Theory has clearly defined the types and roles of microbes at each stage of anaerobic composting and thus received wide acceptance.
On the one hand, the main influencing factors of anaerobic fermentation include total solids concentration, temperature, pH value and inhibition factors. In addition, the number of microorganisms plays a key role in the anaerobic fermentation; however, hypertonicity and high salinity can affect the number of microorganisms, so we, using anaerobic fermentation effect, have to analyze the osmotic pressure and high salinity effects on microorganisms. Therefore, we constructed a model to provide a detailed analysis of our idea.
According to different composition of particulate organic matter and the hydrolysis process, hydrolysis kinetics model of particulate organic matter (POM) is divided into 3 categories: hydrolysis model based on the concentration of POM; hydrolysis model based on particle surface area of POM; hydrolysis model based on the component of POM. Therefore, we also considered the effects of hypertonicity and high salinity on microorganisms in accordance with these three models.
In Contois model, substrate concentration is related to the initial substrate concentration in the anaerobic composting, saturation constant is proportional to the initial substrate concentration. The diffusion in the matrix under high concentration limits the hydrolysis reaction, namely the particle dissolution process is the rate limiting step.
(2-1)In which, Xs is the concentration of dissolved organic substances, mg/L; XH is the concentration of undissolved organic substances, mg/L. kH is the hydrolysis constant; kx is the saturation hydrolysis constant.
The following formula consider influence from the hypertonicity and high salinity:
(2-2)In which, p is the osmosis pressure, s is the salt concentration, α is the constant of the osmosis pressure’s influence on dissolved organic substances,β is the constant of the salinity’s influence on dissolved organic substances.
Contois model was firstly applied in the hydrolysis process of dissolved organic substances in aerobic activated sludge, and was developed in anaerobic fermentation process of POM. Contois model highly fits within the anaerobic fermentation of high concentrated substances.
The hydrolysis of POM is the process of gradually hydrolyzing in descending order. We applied surface area of POM into the traditional first order model in the formula:
（2-3）n which, ks is the constant of POM hydrolysis per unit are,m-2·s-1; A is the surface area of POM at t moment,m2; φ is the constant of the increase in actual surface areas of particles due to the porosity; X is the concentration of undissolved POM at t moment, mg/L.
Uavilin et al. Introduced the hydrolysis model based on different shapes of POM in the two-stage model:
（2-4）In which, r is the hydrolysis rate; k is the hydrolysis rate constant; S, SF are respectively the current and initial concentration of substances; when n is 0 , 1/2, 2/3 , n means respectively the plate-like particle, cylindrical particle, and spherical particle. When n is 0, the formula fits within the zero order kinetics. Hydrolysis constant is the function of the ratio of POM size and bacteria size:
Spherical) （2-5）
(Cylindrical) （2-6）In which, k is the hydrolysis rate; rmis the maximum hydrolysis rate;
px, psare respectively particle and microbe size;δis the hydrolysis level of microbes;d is the size of the current particles.
Considering the influence of hypertonicity and high salinity, the formula can
Be changed as follows:
（2-7）In which, p is the osmosis pressure, s is the salinity, α is the constant of osmosis pressure’s influence on dissolved organic substances,β is constant of salinity’s influence on dissolved organic substances.
Yasui.H et al. studied the changes of gas production rates between primary and secondary sludge in the anaerobic composting process. Instead of considering secondary sludge as a whole, we take it as two kinds of hydrolysis, group 1 and 2 respectively in accordance with the hydrolysis level and Contois hydrolysis model. The fitting effect is good. The primary sludge can be regarded as a mixture of 4 components with different hydrolysis characteristics. Studies have shown that the Yasui.H model has a good fitting effect on the hydrolysis process of POM, such as food waste. Although the specific hydrolysis characteristics of each component in the Yasui.H model are not clear, it is undoubtedly a new approach. The models are shown as follows:
（2-8）In which, Xs1, Xs2 are respectively the concentration of dissolved organic substance in group 1 and 2,mg/L; XH1, XH2 are respectively the concentration of undissolved organic substance in group 1 and 2.
Next is the analysis of the influence osmosis pressure and salinity have on soluble organic substances concentration.
According to formula(2-2), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.
Chart 3-1 Evaluation of parameter (osmosis pressure)
| Parameter | kH | kx | α | β | s |
| Value(Standard Unit) | 10 | 14 | 0.1 | 0.2 | 20 |
We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.
Fig. 1 The Influence of Osmosis Pressure on the Concentration of Solute
From Fig.1, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.
According to formula(2-2), we then analyze the influence of osmosis pressure on microbes. Here are the parameters.
Chart 3-2 Evaluation of Parameter (Salinity)
| Parameter | kH | kx | α | β | p |
| Value (Standard Unit) | 10 | 14 | 0.1 | 0.1 | 20 |
We choose different values of salinity, and see the change in the concentration of solute. The values of salinity are 5,10,15,20.
Fig. 2 The Influence of Salinity on the Concentration of Solute
From Fig.2, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.
According to formula(2-7), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.
Chart 3-3 Evaluation of Parameters (Osmosis Pressure)
| Parameter | φ | A | Ks | β | α | s |
| Value (Standard Unit) | 0.5 | 2 | 10 | 0.1 | 0.1 | 20 |
We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.
Fig. 3 The Influence of Osmosis Pressure on the Concentration of Solute
From Fig.3, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. If the osmosis pressure is too high, the number of the microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.
According to formula(2-7), we then analyze the influence of salinity on microbes. Here are the parameters.
Chart 3-4 Evaluation of Parameter (Salinity)
| Parameter | φ | A | Ks | β | α | p |
| Value (Standard Unit) | 0.5 | 2 | 10 | 0.1 | 0.1 | 20 |
We choose different values of salinity, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.
Fig. 4 The Influence of Salinity on the Concentration of Solute
From Fig.4, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.
According to formula(2-8), we first analyze the influence of osmosis pressure on microbes. Here are the parameters.
Chart 3-5 Evaluation of Parameter (osmosis pressure)
| Parameter | kH1 | kH2 | Kx1 | kx2 | α | β | s |
| Value (Standard Unit) | 10 | 8 | 14 | 12 | 0.1 | 0.1 | 20 |
We choose different values of osmosis pressure, and see the change in the concentration of solute. The values of osmosis pressure are 5,10,15,20.
Fig 5 The Influence of Osmosis Pressure on the Concentration of Solute in Group 1
Fig. 6 The Influence of Osmosis Pressure on the Concentration of Solute in Group 2
From Fig 5 and 6, we can conclude that hypertonicity will lower the stable value of solute concentration, thus indicating the reduction of microbes’ number in the food waste. Therefore, hypertonicity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.
According to formula(2-8), we then analyze the influence of salinity on microbes. Here are the parameters.
Chart 3-6 Evaluation of Parameter (Salinity)
| Parameter | kH1 | kH2 | Kx1 | kx2 | α | β | p |
| Value (Standard Unit) | 10 | 8 | 14 | 12 | 0.1 | 0.1 | 20 |
We choose different values of salinity, and see the change in the concentration of solute. The values of salinity are 5,10,15,20.
Fig 7. The Influence of Salinity on the Concentration of Solute in Group 1
Fig 8. The Influence of Salinity on the Concentration of Solute in Group 2
From Fig.7 and 8, we can conclude that high salinity will lower the stable value of solute concentration, thus indicating the reduction of microbes number in the food waste. Moreover, if the salinity is too high, the number of microbes will approach 0, meaning that the microbes will all die, and that they are unable to continue anaerobic composting. Therefore, high salinity will lower the numbers of microbes in food waste composting, leading to decreased efficiency.
[1]Zhao, Y,. (2012). Process on High-Solids Anaerobic Fermentation for Converting Food Waste and Excess Sludge to Biogas[D]. Jiangnan University.
[2]Cai, L,. (2002). Garbage Assortment is Necessary to Cope with Pollution and Develop Recycling Economics[J]. Complex Utilization of Chinese Resources, 2002,2:9-13.
[3]Li, J,. (2008). The Preliminary Study on the Interfusion Anaerobic Fermentation of Kitchen Waste and Its Dynamic Model[D], Southwest Jiaotong University.
[4]Qu, Z, Wang, J, &Liu, T,. (2006). The Choice of Chinese Municipal Solid Waste Composting Technology[J]. Environmental Sanitation Engineering. 2006,14(3):58-60.
[5]Sun, Y,. (2005). Research on Municipal Solid Waste Anaerobic Composting[D]. Kunming University of Science and Technology.
[6]Xu, D, Shen, D, Feng, H,. (2011). Discussion on Characteristics and Resource Recycling Technology of Food Residue[J]. Bulletin of Science and Technology. 2011,1:130-135.
[7]Wu, X, Wei, K, Sha, S,. (2011). Present Status and Developing Trend of Kitchen Waste Processing in China and Abroad[J]. Agriculture Equipment & Vehicle Engineering. 2011,12:49-53.
clear
%Model 1
%Osmosis Pressure
k_x=14;
k_h=10;
a=0.1;
b=0.2;
s=20;
p=5;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'b')
hold on
p=10;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'r')
p=15;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'g')
p=20;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘The influence of osmosis pressure on concentration of solute’)
grid on
clear
%Salinity
figure
k_x=14;
k_h=10;
a=0.1;
b=0.1;
p=20;
s=5;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'b')
hold on
s=10;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'r')
s=15;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'g')
s=20;
f=@(t,x)[-k_h*x/(k_x*(1-x)+x)+a*p-b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('s=5','s=10','s=15','s=20')
title(‘The influence of salinity on concentration of solute’)
grid on
clear
%Model 1
%Osmosis pressure
fai=0.5;
A=2;
k_s=10;
a=0.1;
b=0.1;
s=20;
p=5;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'b')
hold on
p=10;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'r')
p=15;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'g')
p=20;
f=@(t,x)[-fai*A*k_s*x-a*p+b*s];
[t,y]=ode23(f,[0 10],0.5);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘The influence of osmosis pressure on concentration of solue’)
grid on
clear
%Salinity
figure
fai=0.5;
A=2;
k_s=10;
a=0.1;
b=0.1;
p=20;
s=5;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'b')
hold on
s=10;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'r')
s=15;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'g')
s=20;
f=@(t,x)[-fai*A*k_s*x+a*p-b*s];
[t,y]=ode23(f,[0 10],0.6);
plot(t,y,'k')
xlabel('time')
ylabel('X_s')
legend('s=5','s=10','s=15','s=20')
title(‘The influence of salinity on concentration of solute’)
grid on
clear
%Model 1
%Osmosis pressure
k_x=14;
k_x2=12;
k_h2=8;
k_h=10;
a=0.1;
b=0.2;
s=20;
p=5;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t1,y1]=ode23(f,[0 10],[0.5,0.4]);
p=10;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t2,y2]=ode23(f,[0 10],[0.5,0.4]);
p=15;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t3,y3]=ode23(f,[0 10],[0.5,0.4]);
p=20;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))-a*p+b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))-a*p+b*s];
[t4,y4]=ode23(f,[0 10],[0.5,0.4]);
hold on
plot(t1,y1(:,1),'b')
plot(t2,y2(:,1),'r')
plot(t3,y3(:,1),'g')
plot(t4,y4(:,1),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 1 on concentration of solute’)
grid on
figure
hold on
plot(t1,y1(:,2),'b')
plot(t2,y2(:,2),'r')
plot(t3,y3(:,2),'g')
plot(t4,y4(:,2),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 2 on concentration of solute’)
grid on
clear
%Salinity
figure
k_x=14;
k_x2=12;
k_h2=8;
k_h=10;
a=0.1;
b=0.1;
p=20;
s=5;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t1,y1]=ode23(f,[0 10],[0.5,0.4]);
s=10;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t2,y2]=ode23(f,[0 10],[0.5,0.4]);
s=15;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t3,y3]=ode23(f,[0 10],[0.5,0.4]);
s=20;
f=@(t,x)[-k_h*x(1)/(k_x*(1-x(1))+x(1))+a*p-b*s;-k_h2*x(2)/(k_x2*(1-x(2))+x(2))+a*p-b*s];
[t4,y4]=ode23(f,[0 10],[0.5,0.4]);
hold on
plot(t1,y1(:,1),'b')
plot(t2,y2(:,1),'r')
plot(t3,y3(:,1),'g')
plot(t4,y4(:,1),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 1 on concentration of solute’)
grid on
figure
hold on
plot(t1,y1(:,2),'b')
plot(t2,y2(:,2),'r')
plot(t3,y3(:,2),'g')
plot(t4,y4(:,2),'k')
xlabel('time')
ylabel('X_s')
legend('p=5','p=10','p=15','p=20')
title(‘ The influence of osmosis pressure of Group 2 on concentration of solute’)
grid on
