Stochastic modeling of composting processes with batch operation by the fokker-planck equation

摘要

Following a simple Marcovian process, a stochastic model was developed for batch-type composting, wherein the state variables vary stochastically with each unit increment of concentration ε. The master equation, a balance equation of the probability distribution of the state, was derived first. Next, it was converted into the Fokker-Planck equation, a continuous-type master equation. Through numerical solution of the Fokker-Planck equation, probability densities and standard deviations of the state variables were calculated and compared with earlier experimental results. Calculated results from the present model generally agreed well with the experimental results. Provided that the value of ε was known in advance, this model would be appropriate to predict the expected values and standard deviations of the state variables at the end of the first stage of the composting process.