A Frame work for Stochastic Modelling and Optimisation of Che mical Engineering

Processes

Usman Abubakar, Srinivas Sriramula and Neill C. Renton
Lloyd's Register Foundation (LRF) Centre for Safety & Reliability Engineering, University of
Aberdeen, UK.
This paper presents a new framework, termed “Stochastic Process Performance Modelling Framework (SPPMF)”, which combines traditional deterministic process simulation, response surface modelling techniques and advanced structural reliability analysis method s to facilitate efficient performance modelling and optimisation of chemical process systems under uncertainties. Stochastic constraints have been added to the conventional process
optimisation formulation as indicated below:

;

where , , and are the vectors of state variables, equipment sizes/dimension specifications, control variables and uncertain parameters respectively. While the joint
probability density function (pdf) is represented by ; is the objective function, and

are the vectors of equality and inequality constraints respectively. Each of the parametric ranges is characterised by a pdf while is the probability value.
Both First Order Reliability Method (FORM) and Monte Carlo Simulation (MCS) are then applied to gain a wide range of performance measures. A number of other Structural Reliability Analysis (SRA) concepts have been adopted and cross-applied to chemical engineering processes. For example, while SRA is mainly concerned with the effects of
random forces and mechanical properties on structural performance, Process Reliability Analysis is focused on random process conditions (e.g. changes in pH, reaction rates, etc) and their effects on both product quantity and quality. Finally, SPPMF has been successfully applied to model stochastic properties of a range of typical process systems. The results show that the new framework can be efficiently implemented in process engineering with significant benefits over the traditional methods.