21st European Symposium on Computer Aided Process Engineering – ESCAPE 21 E.N. Pistikopoulos, M.C. Georgiadis and A.C. Kokossis (Editors) © 2011 Elsevier B.V. All rights reserved. Stochastic Monte Carlo Simulations as an Efficient Multi-Scale Modeling Tool for the Prediction of Multi-Variate Distributions Dimitrios Meimaroglou, a,c Costas Kiparissides a,b a Chemical Process Engineering Research Institute, Centre for Research and Technology Hellas, Thessaloniki, Greece 570 01 b Department of Chemical Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece, 60361 c Current Address: Laboratory of Reactions and Process Engineering, Nancy University, LRGP-ENSIC-INPL, 1 rue Grandville, BP 20451, 54000 Nancy, France Abstract In the present work, the role of stochastic Monte Carlo simulations as an efficient computational tool for the simulation of multi-variate physico-chemical systems, within the general framework of population balances, is presented. The applicability of the Monte Carlo method to different length scales of a process is clearly illustrated in two representative examples, namely the prediction of the bi-variate particle size distribution of particulate processes and the calculation of distributed molecular properties of highly-branched polymers on the basis of their exact topological architecture. Keywords: stochastic simulations, Monte Carlo, population balance equation, particle size distribution, highly-branched polymers. 1. Introduction Mathematical modeling and in silico analysis of chemical processes have been widely used for more than 40 years and have contributed to great advances in numerous research areas. Depending on the complexity of the process under study, the mathematical model implemented for its description may contain systems of algebraic, differential or integro-differential equations of different order. Accordingly, a number of advanced numerical methods have been developed to deal with the complex systems of equations a mathematical model may contain. These methods are broadly classified into two general categories, namely the deterministic and stochastic numerical methods. The deterministic approach is based on the principle that events are bound by causality, i.e., any state of the system under study is majorly determined by prior states. This approach is commonly characterized by low computational requirements (for simple systems) and high accuracy and repeatability in the calculated results. On the other hand, its application to multi-dimensional process models is bounded by an increased level of complexity. An alternative approach to the commonly employed deterministic numerical methods is the use of probabilistic tools (i.e., Monte Carlo simulations). The stochastic approach is based on the principle that a system's subsequent state is mainly determined by a random element. Stochastic methods have attracted significant attention over the last