Help me solving this Biofilter model in matlab

[raj_nitr]

initial cg is known.. i need to find cg Vrs. t

complete model is given in attachment.. please help me out


The model equations were derived form the assumptions and the model structure. The main mass balances in each phase are described by the following equations, where j refers to the vertical segment along the height of the biotrickling filter, numbered form bottom of the reactor, and I refers to the segment depth in the biofilm numbered form the interface.

Gas Phase:

Vg dCg[j] = Fg(Cg[j-1]-Cg[j])-kg1Aw(Cg[j]-Cgi1[j])-kg2Anw(Cg[j]-Cgi2[j] ---------------(1)
dt



Liquid Phase:
VL dCL[j] = FL(CL[j+1]-CL[j])-kg1Aw(Cg[j]-Cgi1[j])-kg2Aw(CL[j]-CLi2[j] ---------------(2)
dt
The mass balance for most wetted biofilm segments is expressed by Equation 3, except for the last layers which bear boundary constraints. The equation for the first biofilm layer near the interface takes the form of Equation r, while that of last layer before the substratum is represented by Equation 5. In a similar manner, pollutant mass balances for the non-wetted biofilm segments described by Equations 6-8.

Wetted Biofilm Phase:
dCwb[j] =D/(FT)2 (Cwb[i-1,j]-2Cwb[i,j]+Cwb[i+1,j]-Rwb[i,j] ---------------(3)
dt


dCwb[1,j] =D/(FT)2 (CL[j]-2Cwb[1,j]+Cwb[2,j]-Rwb[1,j] ---------------(4)
dt


dCwb[N,j] =D/(FT)2 (Cwb[N-1,j]-Cwb[N,j]-Rwb[N,j] ---------------(5)
dt



Non-wetted biofilm segments:

dCnwb[i,j] =D/(FT)2 (Cnwb[i-1,j]-2Cnwb[i,j]+Cnwb[i+1,j]-Rnwb[i,j] ---------------(6)
dt




dCnwb[1,j] =D/(FT)2 (Cg[j]/H-2Cnwb[1,j]+Cnwb[2,j]-Rnwb[1,j] ---------------(7)
dt

dCnwb[N,j] =D/(FT)2 (Cnwb[N-1,j]-Cnwb[N,j]-Rnwb[N,j] --------------(8)
dt


Reaction rates:
For Wetted biofilm:


Rwb[i,j] = Rmax Cwb[i,j]
Ks+Cwb[i,j]



For Non-Wetted Biofilm

Rnwb[i,j] = Rmax Cnwb[i,j]
Ks+Cnwb[i,j]

 

[mmwave]

To find the center of gravity (CG) versus time (t), you will need to solve these equations numerically using a computer program such as MATLAB or Python. First, you will need to define the initial conditions, such as the initial concentrations of gas and liquid phases, and the initial thickness of the biofilm. You will also need to input the values for the parameters such as F, k, and Rmax. Then, using a numerical solver, you can calculate the concentrations of each phase at different time points, and use these values to calculate the location of the CG using the following equation:

CG = (sum of (concentration * distance)) / sum of concentrations

You can repeat this calculation for different time points and plot the CG versus time to see how it changes over time. This will give you an understanding of how the CG shifts as the biofilm grows and changes. You can also use this model to predict how the CG will change under different operating conditions, such as changes in flow rate or pollutant concentration.

 

[tacman]

To solve this model in MATLAB, you can use the built-in ODE solvers such as ode45 or ode15s. You will need to define all the necessary parameters, initial conditions, and functions for the equations. You can also use the "fsolve" function to find the steady-state solution for Cg[j] and CL[j] at each time step. Once you have defined all the necessary components, you can run the solver and plot the results for Cg[j] and CL[j] versus time to visualize the concentration profiles.