Parameter estimation and model discrimination of batch solid-liquid reactors

Transcription

1 estimation and model discrimination of batch solid-liquid reactors Yajun Wang, Lorenz T. Biegler Carnegie Mellon University Mukund Patel, John Wassick The Dow Chemical Company Enterprise-wide Optimization Meeting March 2017

2 Batch reactor Solvent and reactant materials Agitator Solvent Vent Solid W Preparation Cooling water inlet jacket Liquid X Solid-liquid Reaction W(s) + X(l) Y(s/l) + Z(s) Unknown reaction mechanism Surface reaction, dissolution, diffusion Different particle shapes and sizes Product effects Cooling water outlet discharge Limited information Lack of concentration measurements An over-parameterized model without enough data 2

3 Reaction Mechanisms Shrinking particle model (SPM) s c l b c l Dissolution model (DM) Assume dissolution is the rate limiting step. Fluid film Reactant reactant Reactant reactant Liquid reactant diffuses onto the particle surface Solid-liquid reaction Solid particles dissolve into solvent Liquid liquid reaction Solid product breaks off from reaction surface. Products precipitate into solid phase. Reaction rate of SPM depends on liquid reactant concentration while DM doesn t. 3

4 Batch Model Total surface area is related to total amount and the shape of particles [1]. SPM DM dn dt dn dt am Ea s s 1/ as 1 1/ as RT s ssr s Ns0 Ns k0e (c l ) sr0 am Ea s s 1/ as 1 1/ as RT ks s Ns0 Ns k0e sr0 am s 1/ a 1 1/ a S Ns0 Ns sr0 s Model indicator F=0 DM F>0 SPM [1] Salmi, Tapio, et al. "New modelling approach to liquid solid reaction kinetics: From ideal particles to real particles." Chemical Engineering Research and Design (2013):

5 Estimability evaluation Estimable? YES Simultaneous estimation quality analysis Small Confidence interval? YES NO Posterior probability share NO Sensitivity coefficient matrix QR transformation with column permutation Rank parameters by their individual variance contribution Reduce parameter set/ Simplify model EVM formulation > WLS formulation Data reconciliation estimation covariance matrix Reduced Hessian confidence region Posterior probability share Bayes theorem Fitting Number of parameters Model Validation Validation by unseen batch data Cross validation 5

6 Solid-liquid batch reactor Batch k k = 1 NS Measured input u kj * Measured output η ki * Normally distributed measurements Jacket temperatures Inlet flowrates weights temperatures Concentrations Estimability evaluation Rank parameters by QRcp of scaled sensitivity matrix rankings at different points are different All parameters are included in the estimation 6

7 Scaled temperature Scaled temperature Simultaneous estimation -- EVM Measured output errors Measured input errors temperature Predict Data EVM does parameter estimation and data reconciliation simultaneously Better output data fitting Accumulated squared errors of EVM is reduced by 44% compared with WLS Intensive computational load EVM has variables and equation constraints temperatures End-point concentrations Jacket temperatures Weights and flowrates WLS Scaled time EVM temperature Scaled time Predict Data 7

8 quality analysis Set C b,x = C s,x Set F = 0 dissolution model Fix parameter U A Linearly temperature-dependent U Posterior probability share 8

9 A results Model Validations New data 9-fold cross validation Estimated value in each iteration Average of 9 estimations Estimated value by all data Unseen data Iteration 9

10 Conclusions & Significance Discussed two potential models for a solid-liquid reaction in a batch reactor Built a uniform dynamic model with an indicating parameter to discriminate two mechanisms Introduced a parameter estimation procedure Applied parameter estimation to the solid-liquid batch reactor model Conducted model validation to examine the model capability of predicting system behaviors Optimal control will be conducted based on estimated model to reduce the batch time Conclusions & Significance 10