Optimization of Batch Processes

Transcription

1 Integrated Scheduling and Dynamic Optimization of Batch Processes Yisu Nie and Lorenz T. Biegler Center for Advanced Process Decision-making Department of Chemical Engineering Carnegie Mellon University John M. Wassick The Dow Chemical Company 3/12/2011 1

2 Presentation Outline Introduction Motivating example Integrated formulation Case study Conclusions 3/12/2011 2

3 Introduction Batch chemical process These two problems are nested in nature An integrated decision-making approach merits attention 3/12/2011 3

4 Introduction How do we model dynamics? Differential Algebraic Equations Energy cost Material production Material consumption Material purity 3/12/2011 4

5 Introduction What advantages do dynamic optimization offer? Improvement on economic performance of individual operations A door to optimal production schedule of overall process... Trade-offs in an operation Trade-offs between a group of operations 3/12/2011 5

6 Motivating Example Recipe Flowsheet of a typical batch process 1) React feed material in the batch reactor for 1 hour at constant temperature 385 K 2) Remove the waste component generated by side reaction in the filter for 2 hours 3) Purify the intermediate in the distillation column for 2 hours with reflux ratio = 3 3/12/2011 6

7 Motivating Example Reactor 20 Gantt chart of recipe based model Optimal control profile Reactor temperature Dynamic Recipe 9 8 Optimal control profile Reflux ratio in column Dynamic Recipe Filter Column Reactor 20 Filter Column Time(hr) Gantt chart of integrated model dl Time(hr) Gantt charts Retemp Reflux 6 5 Optimal control profiles /12/2011 7

8 Scheduling Formulation Network-based representation of batch processes State Task Network (STN) (E. Kondili et al. 93) Resource Task Network (RTN) (C.C. Pantelides 94) Is there an alternative perspective? 3/12/2011 8

9 Scheduling Formulation A closed loop representation of chemical processes 3/12/2011 9

10 Scheduling Formulation Mathematical formulation Assignment constraints Material balance Capacity constraints 3/12/

11 Scheduling Formulation Sequencing constraints Operations in the same unit Operations in different units Material quality measurement Mixture composition Purity requirements 3/12/

12 Scheduling Formulation Unit operation Operating state Idle state 3/12/

13 Scheduling Formulation Overall formulation Mixed-Logic Dynamic Optimization (MLDO) Reformulation strategy Mixed-Integer Nonlinear Program (MINLP) Simultaneous collocation DAE Nonlinear algebraic equations Big-M reformulation Disjunctions Relaxed inequalities 3/12/

14 Case Study A state equipment representation of a multiproduct batch process Product recipes 3/12/

15 Case Study Gantt-chart for the case study Heater Heat <80> Heat <45> Heat <24.8> Reactor1 Rct1 <35> Rct2 <35> Rct2 <24.8> Reactor2 Rct1 <34.1> Rct2 <45> Rct2 <45> Filter1 Fil1 <69.1> Filter2 Fil2 <79.2> Fil2 <45.8> Fil2 <24.8> Column Dis1 <60> Dis2 <60> Dis2 <37.2> Line1 Pck1 <14.3> Pck2 <25.1> Line2 Pck1 <40.9> Pck2 <28.8> Pck3 <22.4> Time (hr) 3/12/

16 Case Study Scaled te emperature led temperature 8 6 Optimal temperature profile reactor 2 during slot Processing time (hr) 10 5 Optimal temperature profile reactor 2 during slot 2 Sca Scaled tempera ature Processing time (hr) 10 5 Optimal temperature profile reactor 2 during slot Processing time (hr) 3/12/

17 Case Study 6 Optimal reflux ratio profile of column during slot 3 Reflux ratio Processing time (hr) 6 Optimal reflux ratio profile of column during slot 4 Reflux ratio Processing time (hr) 4 Optimal reflux ratio profile of column during slot 5 Reflux ratio Processing time (hr) 3/12/

18 Conclusions Concluding remarks An integrated framework for short-term scheduling and dynamic real-time optimization of batch processes A reformulation strategy of mixed-logic dynamic optimization problems Future developments Decomposition techniques for practical applications Implementation with fast dynamic models Nonconvex MINLP solution strategies Material transportation and storage, changeovers and order fulfillment in scheduling 3/12/

19 Acknowledgements 3/12/