A FINITE-STATE MARKOV-CHAIN MODEL FOR AXIAL MIXING OF SOLIDS IN A FLUIDIZED-BED

The aim of this paper is to propose a discrete-time Markov chain model for axial mixing of solids in a fluidized bed and to verify the results with the available experimental data. The type of representation shown is commonly known as a directed graph of states. It is useful in modelling birth and death processes in a physical system. In each step a particle or an object can move from its own state (j) to one of the adjoining states (i or k). Commonly the transition from a particular state to its right is known as a birth process and a transition to the left is regarded as death. The arrows denote the transition probabilities (Pij's) from one state to another. Pij's are known as one-step stationary transition probabilities. This implies that the transition probabilities do not change in time. The possible delays in a state are usually marked on a directed graph of states using an arrow (loop) directed from the state into itself. Such probabilities (Pjj for state j) may be evaluated from the transition probabilities by simple probability balance.