Derivation of critical and optimal operating conditions for a semibatch reactor under parametric uncertainty based on failure probability indices

Abstract

Derivation of optimal operating policies and runaway boundaries for a semibatch reactor (SBR), when highly exothermic reactions are conducted and hazardous side reactions may occur, is a difficult task because of multiple sources of process uncertainty to be considered (variability in raw materials, catalyst, impurities, model inaccuracies, measurement errors, technological, economic and safety constraints). The present work introduces a new criterion based on failure probability indices related to uncertainty in the runaway boundaries and disturbances of the operating parameters. Such a criterion is used not only to derive more prudent SBR optimal operating policies but also to appreciate rapprochement to critical conditions. An example is provided for an SBR used for conducting the hazardous acetoacetylation of pyrrole with diketene in homogeneous liquid phase catalysis. Both uncertainties in evaluating the runaway boundaries, with a generalized sensitivity criterion, and of the running conditions are used to generate optimal operating strategies, making a satisfactory compromise between the productivity goal and safety requirements.

Derivation of Pareto Optimal Operating Policies Based on Safety Indices for a Catalytic Multi-tubular Reactor Used for Nitrobenzene Hydrogenation

“…Thus, a safety criterion can also be included in the optimization procedure, i.e., minimization of a runaway probability P f (which varies in the range of [0,1]). Following the definition of Maria and Dan 10,14 , this objective function includes the double parametric and safety limit uncertainty in only one cumulative index. The evaluation of the runaway risk probability has been proposed by Maria and Dan 10,14 in the form of:…”

“…5,8,9,[32][33][34][35][36] On the other hand, the plant optimal operating policy should be considered as a trade-off between economic, environmental, and safety objectives. By using a new "safe operation criterion" introduced by Maria and Dan,[10][11][12][13][14] based on the sum of two failure probability indices related to uncertainty in the reactor runaway boundaries and random disturbances in the operating parameters, a multi-objective optimization can be formulated by defining the sustainability by simultaneously considering technological, economic, and safety constraints.…”

“…37 According to Maria and Dan, the thermal runaway risk during reactor operation can be quantified, and included in the multi-criteria optimization function by using an overall failure probability index. [10][11][12][13][14] Briefly, the methodology of Maria and Dan [10][11][12][13][14] to obtain the Pareto-optimal operating policies for a multi-objective optimization problem in the presence of uncertainty in the control variables and runaway boundaries includes: derivation of the process and reactor dynamic model; definition of the technological constraints; evaluation of the safety limits and their confidence band for the control variables in the parametric space by also considering their random fluctuations around the setpoint; 14 approximation of the critical variety with simple algebraic correlations to facilitate further reactor optimization rule; evaluation of the joint failure probability index based on the parametric and safety limit uncertainty, and then formulation of the multi-criteria objective function followed by derivation of the so-called "optimal-Pareto front" solution. Then, a trade-off optimal solution is selected based on several criteria.…”

“…The present study is aiming at exemplifying this reactor operation optimization methodology of Maria and Dan [10][11][12][13][14] to obtain the Pareto-optimal operating policy for the case of an industrial fixed-bed tubular reactor used for the catalytic hydrogenation of nitrobenzene to aniline in vapor-phase in the presence of uncertainty in safety limits of the operating region and uncertainty associated with the random fluctuations of the control variables. The applied model-based methodology to obtain the Pareto-operating policies of the reactor is that of Maria and Dan.…”

“…The applied model-based methodology to obtain the Pareto-operating policies of the reactor is that of Maria and Dan. [10][11][12][13][14] This methodology, described here very briefly, is detailed below in the Theory Section.…”