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]