Advances in Optimization and its Applications in Process Industries

1. Advances in Optimization and its Applications in Process Industries Lorenz T Biegler Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA 15213 July , 2012  http://capd.cheme.cmu.edu

2. Chemical Engineering Department Pittsburgh, PA Carnegie Mellon Campus

3. Center for Advanced Process Decision-making (CAPD) Faculty and Researchers Jeff Siirola Erik Ydstie Ignacio Grossmann Nick Sahinidis Larry Biegler PhD Students: 28 MS Students: 11 Post Docs: 7 Visitors: 10

4. Long term goal: from molecular to enterprise level CAPD Goals • Provide intellectual leadership on complex modeling, design and operational problems faced by process industries • Promote and Enhance PSE Science Base: optimization, control, computer science, systems engineering, business Basic methodologies Process modeling Mathematical programming Systems Engineering Process control Advanced computing Areas of application Process and product synthesis Energy Systems Supply chain optimization Molecular Design Systems Biology

5. L. T. Biegler Nonlinear Programming and Parameter Estimation Optimization of Differential Algebraic Systems Nonlinear Optimization-based Control I. E. Grossmann Mixed Integer Nonlinear Programming for Process Synthesis Planning and Scheduling of Batch and Continuous Processes Design under Uncertainty N. Sahinidis Global Optimization Algorithms, and Software Modeling of metabolic and signaling pathways Design of environmentally benign chemicals J. J. Siirola Process Synthesis of Advanced Energy Systems Synthesis of Nonideal Separation Systems Product and Process Design B. E. Ydstie Adaptive and Robust Control Strategies Thermodynamic Approaches to Process Control Discrete Events and Scheduling  Solar Cell Modeling CAPD Principal Investigators

6. Optimal Design of Responsive Process Supply Chains Ignacio Grossmann Max: Net present value Max: Responsiveness (Expected Lead Time) Supply chain: an integrated network of business units for the supply, production, distribution and consumption of the products.

7. Supply Chain Case Study • Problem Size MINLP: • # of Discrete Variables: 215 • # of Continuous Variables: 8126 • # of Constraints: 14617 • Solution Time: • Solver: GAMS/BARON • Direct Solution: > 2 weeks • Proposed Algorithm: ~ 4 hours

8. Decisions: Number and capacity of TLP/FPSO facilities Installation schedule for facilities Number of sub-sea/TLP wells to drill Oil production profile over time Optimal Development Planning under Uncertainty • Offshore oilfield having several reservoirs under uncertainty • Maximize the expected net present value (ENPV) of the project Tarhan, Grossmann (2009) facilities TLP FPSO Reservoirs wells Uncertainty: • Initial productivity per well • Size of reservoirs • Water breakthrough time for reservoirs

9. Distribution of Net Present Value Oilfield Planning Deterministic Mean Value = $4.38 x 109 Multistage Stoch Progr = $4.92 x 109 => 12% higher, more robust Computation: Algorithm 1: 120 hrs; Algorithm 2: 5.2 hrs Nonconvex MINLP: 1400 discrete vars, 970 cont vars, 8090 Constraints

10. Simulation-based Optimization Nick Sahinidis • Goals: • Efficient optimization of complex chemical processes • Accurate solutions using function evaluations from high fidelity simulators • Challenges and solutions: • Lack of an algebraic model → Build surrogate models • Computationally costly simulations → Selectively choose a minimal data set • Often noisy function evaluations → Use regression surrogate models • Scarcity of fully robust simulations → Disaggregate the process Process simulation Optimization model Function evaluation

11. Automated Learning of Algebraic Models for Optimization Process Simulation Disaggregation and modeling Optimization Block 1 Model 1 Block 2 Model 2 Surrogate model generation using ALAMO Algebraic optimization Block 3 Model 3 True vs. Empirical Error Ideal Model New Model Build simple and accurate models with a functional form tailored for an optimization framework Locate model error Data points Complexity New point Error maximization Rebuild model Combine surrogate models along with design specs, heat/mass balances, logical constraints, etc. to formulate an algebraic optimization model Iterative design of experiments Model functional form

12. CO2 Capture Case Study Outlet gas Solid feed Minimize the increased cost of electricity Maximize %CO2 removal ( ) Cooling water CO2 rich gas CO2 rich solid outlet Surrogate model Simulation Tradeoff: Cost vs. Environmental impact Generate a low-complexity surrogate model of %CO2 removal as a function of reactor bed depth and cooling water flow from Aspen Custom Model runs 2. Surrogate model generation 3. Results: Pareto Analysis 1. Optimize a CO2 fluidized bed reactor

13. Process Control Research at CMUErik Ydstie Research topics: Solar Energy (Production processes and DSSC) Dynamic modeling and Control of Supply Chains Modeling and Control of Particulate Systems Adaptive Control and Adaptive Optimization Plant wide Simulation and Control Process Automation and Safety Fundamental Control Theory

14. Feed Forward Adaptive Control Applied to Propane Cracker - DOW Chemicals • Control Objectives: • Stabilize pressure (CV) in response to frequent disturbances • Optimally choose cheapest fuel CV: Pressure MV: Low-pressure Flow DV1: Off-gas DV2: Residue DV3: Fuel flow to Propane cracker • PI Control (green) • PI with adaptive optimization (blue) B Erik Ydstie, CMU

15. Plantwide Control Systems? From Sand to Windshields(with Dr Yu Jiao PPG Inc, Glass Technology Research Center) Silicate Sand Soda-ash Iron Oxide ++ 8 flat glass plants 10 windshield lines Accuracy of shape, color, distortion (optical properties) depend on mix, melting conditions in furnace and operation of the tin bath.

16. Results from Trial at Wichita Falls TX Conditioner temperature (KPI) • Yield improved by 3-5% • Excellent operator acceptance • Maintainable and expandable • Implemented on all PPG plants • $30-40M per year saving Defects Measured

17. Large Scale Nonlinear Programming Algorithms: process optimization for design, control and operations Evolution of NLP Solvers: Process OptimizationL. T. Biegler SQP rSQP IPOPT rSQP++ IPOPT 3.x ’80s: Flowsheet optimization over 100 variables and constraints ’90s: Static Real-time optimization (RTO) over 100 000 variables and constraints ’00s: Simultaneous dynamic optimization over 1 000 000 variables and constraints Object Oriented Codes to tailor structure, architecture to problems

18. Grade Transitions - Polymer Processes Large-Scale Optimization (L. T. Biegler) • Periodic Adsorption Process Optimization Simulated Moving Bed - Optimal Operation CPU Time for optimization: 9.03 min 34098 variables, 34013 equations Real-time Dynamic Optimization

19. Dynamic Optimization Problem s.t. t, time z, differential variables y, algebraic variables tf, final time u, control variables p, time independent parameters

20. Collocation on finite Elements Nonlinear Programming Problem (NLP) Discretized variables NonlinearProgrammingFormulation Nonlinear Dynamic Optimization Problem (Piecewise) Continuous profiles

21. Nonlinear Programming Problem s.t. Finite elements, hi, can also be variable to determine break points for u(t). Add hu ≥hi≥ 0, S hi=tf Can add constraints g(h, z, u) ≤ e for approximation error

22. Process Optimization with Dynamic Reactor Models • Optimal Catalyst Distribution in Graded Fixed Bed Reactors (Y. Nie, Dr. Paul Witt, Dr. AnshulAgarwal) • Dynamic Modeling and Recipe Optimization of Polyether Polyol Processes (Y. Nie, Dr. Carlos Villa) • Combined Recipe Optimization and Product Scheduling (YisuNie, Dr. John Wassick) • Characteristics: • Large-scale, nonlinear, (often) exothermic reactive systems • Modeled with simultaneous collocation methods • Need to capture nonlinear, (often) unstable modes and runaways, enable highly efficient and safe operation • Fast solution of optimization problems

23. Optimization of Runaway Reactors

24. Optimization of Runaway Reactors

25. Optimal Catalyst DistributionMultizone Optimization Problem

26. Dynamic Optimization Solution Strategy

27. Dynamic Optimization Results

28. Catalyst Distribution Profiles

29. Recipe Optimization Semi-Batch Polyether Polyol Process (Yisu Nie)

30. Semi-batch polyether polyol process

31. Process Recipe Optimization

32. Polyol Dynamic Process Calibration

33. Polyol Dynamic Optimization Results

34. Special industrial interest group: Enterprise-wide Optimization for Process Industries Multidisciplinary team: Chemical engineers, Operations Research, Industrial Engineering Researchers: Carnegie Mellon: Ignacio Grossmann (ChE) Larry Biegler (ChE) John Hooker (OR) Nicola Secomandi (OR) Lehigh University: Katya Scheinberg (Ind. Eng) Univ. Pittsburgh: Andrew Schaeffer (Ind. Eng.) Overall Goal: • Novel planning and scheduling models, including consideration of uncertainty • Effective integration of Production Planning, Scheduling and Real–time Optimization • Optimization of Entire Supply Chains

35. Hierarchy of Enterprise Wide Optimization • Supply Chain, Planning and Scheduling • Large LP and MILP models • Many Discrete Decisions • Few Nonlinearities • Essential link needed to process models • Decisions need to be feasible at lower levels

36. Process Operations Applications • Real-time Optimization and Control • Large, Complex Process Models • Few Discrete Decisions • Nonlinearities and Dynamics • Essential to Link with Logistics and Planning • “Time-limited” on-line optimization • Optimal performance needs to be passed to higher levels

37. Multiscale temporal and spatial integration Multi-site Production Planning Polymer plants (25 grades) Objective: Production Planning and Distribution Model for Batch Polymerization Reactors

38. Production Site: Raw material availability and Raw material costs Storage tanks with associated capacity Transportation costs to each customer Reactors: Materials it can produce batch sizes (lbs) for each material it can produce operating costs ($/hr) for each material Sequence dependent clean out times (hrs per transition for each material pair) Time the reactor is available during a given month (hrs) STORAGE Reaction 1 A F1 INTERMEDIATE STORAGE F2 STORAGE Reaction 2 B F3 STORAGE Reaction 3 C F4 Production Planning and Scheduling • Customers: • Monthly forecasted demands for desired products • Price paid for each product • Materials: • Raw materials, Intermediates, Finished products • Unit ratios (lbs of needed material per lb of material produced)

39. Production Scheduling Coupled with Recipe Optimization

40. Scheduling: State Equipment Network (SEN) Model

41. Mixed-Logic Dynamic Optimization (MLDO)

42. SEN/DAE Case Study

43. Case Results (40% Profit Increase)

44. Real-time Optimization for ASUs • Air Separation Unit, key unit in IGCC-based Power Plants • Need for high purity O2 • Respond quickly to changes in process demand • Large, highly nonlinear dynamic separation (MESH) models • Related work: • Methanol distillation (Diehl, Bock et al., 2005) • 40 trays, 210 DAEs, 19746 discretized equations • Argon Recovery Column • 50 trays, 260 DAEs, 21306 discretized equations • Double Column ASU Case Study • 80 trays, 1520 DAEs, 116,900 discretized equations

45. w Real-time Optimization: Components Plant APC y u RTO c(x, u, p) = 0 DR-PE c(x, u, p) = 0 p • Data reconciliation – identify gross errors and inconsistency in data • Periodic update of process model identification • Usually requires APC loops (MPC, DMC, etc.) • RTO/APC interactions: Assume decomposition of time scales • APC to handle disturbances and fast dynamics • RTO to handle static operations • Typical cycle: 1-2 hours, closed loop • What if steady state and dynamic models are inconsistent?

46. d Plant Dynamic Real-time Optimization (RTO) m PC u y Real-time Optimization Dynamic Models State Estimation Model Updates p • Goal: Integrate On-line Optimization with Advanced Process Control • Requires time-critical calculations • Current optimization makes this available in practice • Links to Decision-making at other scales/levels • Several applications in Chemical Industry • Essential for: • Inherently Dynamic Energy Systems • Handling Uncertainties in prices, supplies and demands • Optimal disturbance rejection

47. NMPC Estimation and Control On-line Optimization: Nonlinear Model Predictive Control (NMPC) • Why NMPC? • Track a profile – evolve from linear dynamic models (MPC) • Severe nonlinear dynamics (e.g, sign changes in gains) • Operate process over wide range (e.g., startup and shutdown) z : differential states y : algebraic states Process d : disturbances u : manipulated variables NMPC Controller ysp : set points Model Updater NMPC Subproblem

48. What about Fast NMPC? • Fast NMPC is not just NMPC with a fast solver (Engell, 2007) • Computational delay – between receipt of process measurement and injection of control, determined by cost of dynamic optimization • Leads to loss of performance and stability(see Findeisen and Allgöwer, 2004; Santos et al., 2001) As larger NLPs are considered for NMPC, can computational delay be overcome?

49. Can we avoid on-line optimization? • Divide Dynamic Optimization Problem: • preparation, feedback response and transition stages • solve complete NLP in background (‘between’ sampling times) as part of preparation and transition stages • solve perturbed problem on-line based on NLP sensitivity • > two orders of magnitude reduction in on-line computation • Based on NLP sensitivity of z0 for dynamic systems • Extended to Collocation approach – Zavala et al. (2008, 2009) • Similar approach for Moving Horizon Estimation – Zavala et al. (2008) • Stability Properties (Zavala et al., 2009) • Nominal stability – no disturbances nor model mismatch • Lyapunov-based analysis for NMPC • Robust stability – some degree of mismatch • Input to State Stability (ISS) from Magni et al. (2005) • Extension to economic objective functions

50. Advanced Step Nonlinear MPC (Zavala, B., 2008) Solve NLP in background (between steps, not on-line) Update using sensitivity on-line x(k) xk+1|k u(k) tk tk+1 tk+2 tk+N Solve NLP(k) in background (between tk and tk+1)