Use of confidence region in the optimal design of a separation process in the presence of uncertainties

A large number of real-world problems nowadays require that decisions be made in the presence of uncertainties. Traditionally, the task of separation systems design neglects the influence of uncertainties. This work, however, explores the optimization strategy of a frequently encountered equilibrium-based distillation system design problem in the face of uncertainties. In particular, uncertainties arising from thermodynamic model parameters, which represent the vapor-liquid equilibrium (VLE) behavior of non-ideal mixtures involved in the system and are germane to the rational design of the separation system, are considered in the work. Joint confidence regions for the key thermodynamic model parameters estimated by the nonlinear least squares method have been incorporated in the analysis of the uncertain regions. We propose a novel two-stage stochastic programming solution scheme utilizing the optimum searching capacity of the simulated annealing algorithm in the first (design) stage and ASPEN Plus flowsheet simulator in the second (operating) stage in which Hammersley sequence sampling scheme has been implemented. A case study that investigates the optimal design of a two-column distillation system in an isopropanol (IPA) process will be demonstrated. Overall, this study provides us with a useful means to scrutinize the uncertainties and to optimize our design by quantifying the impact associated with them.

[1]  Urmila M. Diwekar,et al.  Robust design using an efficient sampling technique , 1996 .

[2]  R. M. Roberts,et al.  Confidence region estimation techniques for nonlinear regression in groundwater flow: Three case studies , 2007 .

[3]  Wallace B. Whiting,et al.  Incorporating uncertainty in chemical process design for environmental risk assessment , 2004 .

[4]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[5]  Marianthi G. Ierapetritou,et al.  Multiobjective framework for modular design generation incorporating demand uncertainty , 2005 .

[6]  Urmila M. Diwekar,et al.  BONUS Algorithm for Large Scale Stochastic Nonlinear Programming Problems , 2015 .

[7]  Lorenz T. Biegler,et al.  Design for model parameter uncertainty using nonlinear confidence regions , 2001 .

[8]  Efstratios N. Pistikopoulos,et al.  Uncertainty in process design and operations , 1995 .

[9]  手塚 集.  Uniform random numbers : theory and practice , 1995 .

[10]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[11]  J. M. Douglas,et al.  Simple, analytical criteria for the sequencing of distillation columns , 1985 .

[12]  Shu Tezuka,et al.  Uniform Random Numbers , 1995 .

[13]  Fernando P. Bernardo,et al.  Integration and Computational Issues in Stochastic Design and Planning Optimization Problems , 1999 .

[14]  Urmila M. Diwekar,et al.  An efficient sampling technique for off-line quality control , 1997 .

[15]  Urmila M. Diwekar,et al.  Synthesis approach to the determination of optimal waste blends under uncertainty , 1999 .

[16]  Sandia Report,et al.  Condence Region Estimation Techniques for Nonlinear Regression: Three Case Studies , 2005 .

[17]  J. Prausnitz,et al.  LOCAL COMPOSITIONS IN THERMODYNAMIC EXCESS FUNCTIONS FOR LIQUID MIXTURES , 1968 .

[18]  Jianjun Cui,et al.  Equidistribution on the Sphere , 1997, SIAM J. Sci. Comput..