MASTER EQUATION FORMULATION AND MONTE CARLO SIMULATION OF SOME MULTINOMIAL STOCHASTIC PROCESSES FROM CHEMICAL ENGINEERING

The objective of this work is to formulate and study certain stochastic models for systems of importance in chemical engineering. The work is divided into two main parts. Stochastic modeling of process systems, in general, and master-equation-based models, in particular, are discussed in Part I. Emphasis is placed on modeling entity populations undergoing generic breakage and coalescence phenomena. The complexity of the master equation and the desire to understand the random nature of the evolution of stochastic populations often necessitate the actual simulation of the governing master equation. The basic procedure for performing a Monte Carlo simulation of the master equation is also discussed in Part I. This part of the dissertation concludes with a discussion of time series analysis which can be employed to study the results emanating from a Monte Carlo simulation. Master-equation-based stochastic models for the bubble population in a bubbling fluidized bed, and for coalescence and breakage phenomena are developed and studied in Part II. The master equation for the bubble population in a fluidized bed includes transition rates for coalescence of bubbles, their upward movement, and their entrance at the distributor. Monte Carlo simulation results for the bubble-size distribution are presented and time series representing the total volume and surface area of the bubble phase analyzed. The bubble population behaves quite stochastically due to the random formation of large bubbles by coalescence. The correlation structure of the fluctuations in the total surface area and volume can be modeled by the same univariate Ornstein-Uhlenbeck process.; The master-equation-based model for coalescence and breakage includes transition rates for these processes in addition to terms for their entrance and exit from the system. A novel technique for arriving at an expression for the daughter-size distribution after breakage based on the probabilities assigned to model-independent ordered sets is proposed. Pure-breakage and coalescence-breakage systems are simulated via the Monte Carlo approach. Entity-size distributions and times series analysis of the results for the bivariate time series representing the total volume and surface area of the dispersed phase are given. The relative magnitude of the fluctuations in total surface area and volume are not large for the parameters investigated. The time-correlation structure of the fluctuations in the bivariate time series is characterized by the existence of a single characteristic time constant. Such fluctuations can be successfully modeled as an Ornstein-Uhlenbeck process.