Stochastic Sensitivity Analysis Based Design Margin And Margin Evaluation For Chemical Processes

Because there are various uncertainties in actual chemical processes,for avoiding the constraints violation,it is necessary to add the margins for design variables under the precondition of meeting the process constraints and ensuring the optimal economic benefits.Considering the stochastic distribution of uncertain parameters and sensitivity analysis method,an optimal margin design method for chemical processes is presented based on stochastic sensitivity.Through process design optimization,the nominal values of the optimal design point are obtained by setting the nominal values of uncertain parameters.Assuming that the process uncertain parameters are subject to the normal distribution,the means and variances of the constraint variables are determined based on sensitivity analysis,the stochastic optimization problem for the optimal design margins is solved under the condition of guaranteeing low probability constraints violation.Considering dynamic process,the dynamic sensitivity curves are obtained based on step response under the conditions of closed-loop PID control and model predictive control respectively,then the dynamic mean and variance curves of the constraint variables are calculated.The stochastic dynamic optimization problem for the optimal design margins is solved,ensuring that the confidence intervals of constraint variables satisfying certain confidence coefficient will fall in the constraint ranges.Finally,the case studies of CSTR in series and FCCU show the effectiveness of this method.If the margin of each design variable is not enough or excessively consumed,the operating point will move to the process constraints to form the operation bottleneck,so it is necessary to evaluate the design margin and find out which design variable is short of margin.In this paper,the operation optimization is used to identify operation bottlenecks in design variables.The sensitivities of economic benefit to constraints are obtained according to the lagrangian multipliers of steady-state operation optimization,then the sensitivities of economic benefit to design variables are calculated as the basis of margin evaluation.Considering the stochastic disturbances and control system in actual dynamic process,the means and variances of the constraint variables are calculated according to the closed-loop transfer functions.The confidence intervals of constraint variables satisfying certain confidence coefficient are acquired to adjust the constraints and implement the iterative optimization with varying constraints,so the effect of dynamic optimization can be achieved by steady-state optimization,and the achievable economic benefit of dynamic optimization can be used for margin evaluation.Finally,the case study of FCCU shows the effectiveness of this method.