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Unit-operation nonlinear modeling for planning and scheduling applications

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Abstract

The focus of this paper is to detail the quantity and quality modeling aspects of production flowsheets found in all process industries. Production flowsheets are typically at a higher-level than process flowsheets given that in many cases more direct business or economic related decisions are being made such as maximizing profit and performance for the overall plant and/or for several integrated plants together with shared resources. These decisions are usually planning and scheduling related, often referred to as production control, which require a larger spatial and temporal scope compared to more myopic process flowsheets which detail the steady or unsteady-state material, energy and momentum balances of a particular process unit-operation over a relatively short time horizon. This implies that simpler but still representative mathematical models of the individual processes are necessary in order to solve the multi time-period nonlinear system using nonlinear optimizers such as successive linear programming and sequential quadratic programming. In this paper we describe six types of unit-operation models which can be used as fundamental building blocks or objects to formulate large production flowsheets. In addition, we articulate the differences between continuous and batch processes while also discussing several other important implementation issues regarding the use of these unit-operation models within a decision-making system. It is useful to also note that the quantity and quality modeling system described in this paper complements the quantity and logic modeling used to describe production and inventory systems outlined in Zyngier and Kelly (Optimization and logistics challenges in the enterprise, Springer, New York 61–95, 2009).

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References

  • Alattas AM, Grossman IE, Palou-Rivera I (2011) Integration of nonlinear crude distillation unit models in refinery planning optimization. Ind Eng Chem Res 50:6860–6870

    Article  Google Scholar 

  • Andersen ED, Andersen KD (1995) Presolving in linear programming. Math Program 71:221–245

    MathSciNet  MATH  Google Scholar 

  • Anonymous (2002) HYSYS 3.1: dynamic modeling, Hyprotech Inc., Houston

  • Bodington CE (ed) (1995) Planning, scheduling and control integration in the process industries. McGraw-Hill Inc., San Francisco

    Google Scholar 

  • Chinneck JW (2008) Feasibility and infeasibility in optimization: algorithms and computational methods. Springer Science, New York

    MATH  Google Scholar 

  • Eckert E, Vanek T (2009) Improvements in the selection of real components forming a substitute mixture for petroleum fractions. Chem Pap 63:399–405

    Article  Google Scholar 

  • Floudas CA (1995) Nonlinear and mixed-integer optimization: fundamentals and applications. Oxford University Press, New York, pp 284–285

    MATH  Google Scholar 

  • Forbes JF, Marlin TE (1994) Modeling accuracy for economic optimizing controllers: the bias update case. Ind Eng Chem Res 33:1919–1929

    Article  Google Scholar 

  • Gary HJ, Handwerk GE (1994) Petroleum refining technology and economics, 3rd edn. Marcel Dekker, New York

    Google Scholar 

  • Geoffrion AM (1972) Generalized benders decomposition. J Optim Theory Appl 10(4):237–260

    Article  MathSciNet  MATH  Google Scholar 

  • Greenberg HJ (1995) Analyzing the pooling problem. ORSA J Comput 7(2):205–217

    Article  MATH  Google Scholar 

  • Grossmann IE (ed) (1996) Global optimization in engineering design. Kluwer Academic Publishers, Boston

    MATH  Google Scholar 

  • Healy WC, Maassen CW, Peterson RT, (1959) A new approach to blending octanes, API Refining Division, Midyear Meeting, May

  • Henley EJ, Seader JD (1981) Equilibrium-stage separation operations in chemical engineering. Wiley, New York

    Google Scholar 

  • Hines AL, Maddox RN (1985) Mass transfer: fundamentals and applications. Prentice-Hall Inc., New Jersey

    Google Scholar 

  • Karuppiah R, Grossmann IE (2008) A Lagrangean based branch-and-cut algorithm for global optimization of nonconvex mixed-integer nonlinear programs with decomposable structures. J Glob Optim 41:163–186

    Article  MathSciNet  MATH  Google Scholar 

  • Kelly JD (1998a) Tuning digital PI controllers for minimal variance in manipulated input moves applied to imbalanced systems with delay. Can J Chem Eng 76:967–974

    Article  Google Scholar 

  • Kelly JD (1998b) A regularization approach to the reconciliation of constrained data sets. Comput Chem Eng 22:1771–1788

    Article  Google Scholar 

  • Kelly JD (2004a) Formulating production planning models. Chem Eng Prog 100:43–50

    Article  Google Scholar 

  • Kelly JD (2004b) Production modeling for multimodal operations. Chem Eng Prog 100(2):44–46

    Google Scholar 

  • Kelly JD (2004c) Formulating large-scale quantity-quality bilinear data reconciliation problems. Comput Chem Eng 28(3):357–366

    Article  MathSciNet  Google Scholar 

  • Kelly JD (2005) Modeling production-chain information”. Chem Eng Prog 101(2):28–31

    MathSciNet  Google Scholar 

  • Kelly JD (2006) Logistics: the missing link in blend scheduling optimization. Hydrocarb Process 85(6):45–51

    Google Scholar 

  • Kelly JD, Mann JL (2003) Crude-oil blend scheduling optimization: an application with multi-million dollar benefits. Hydrocarb Process 82(6):47–53

    Google Scholar 

  • Kelly JD, Zyngier D (2007) An improved MILP modeling of sequence-dependent switchovers for discrete-time scheduling problems. Ind Eng Chem Res 46:4964–4973

    Article  Google Scholar 

  • Kelly JD, Zyngier D (2008a) Continuously improve the performance of planning and scheduling models with parameter feedback. In: Proceedings of the foundations of computer-aided process operations (FOCAPO), Boston, Massachusetts, July

  • Kelly JD, Zyngier D (2008b) A new and improved MILP formulation to optimize observability, redundancy and precision for sensor network problems. AIChE J 54:1282–1291

    Article  Google Scholar 

  • Kelly JD, Zyngier D (2008c) Hierarchical decomposition heuristic for scheduling: coordinated reasoning for decentralized and distributed decision-making problems. Comput Chem Eng 32:2684–2705

    Article  Google Scholar 

  • Levenspiel O (1998) Chemical reaction engineering. Wiley, New York

    Google Scholar 

  • Lodwick WA (1992) Preprocessing nonlinear functional constraints with application to the pooling problem. ORSA J Comput 4(2):119–131

    Article  MathSciNet  MATH  Google Scholar 

  • Martins JRRA, Sturdza P, Alonso JJ (2003) Complex-step derivative approximation. ACM Trans Math Softw 29:245–262

    Article  MathSciNet  MATH  Google Scholar 

  • Misener R, Floudas CA (2009) Advances for the pooling problem: modeling, global optimization, and computational studies. Appl Comput Math 8(1):3–22

    MathSciNet  MATH  Google Scholar 

  • Morris WE (1975) The interaction approach to gasoline blending, NPRA 73rd annual meeting, March, San Antonio, Texas

  • Neiro SMS, Pinto JM (2004) A general modeling framework for the operational planning of petroleum supply chains. Comput Chem Eng 28:871–896

    Article  Google Scholar 

  • Palmer K, Realff M (2002) Metamodeling approach to optimization of steady-state flowsheet simulators: model generation. Chem Eng Res Des 80:7

    Google Scholar 

  • Pantelides CC, Renfro JG (2011) The online use of first-principles models in process operations: review, current status & future needs. In: Proceedings of the chemical process control VIII conference, Savannah, Georgia, January

  • Phismister JR, Seider WD (2001) Bridge the gap with semi-continuous distillation. Chem Eng Prog 97:72–78

    Google Scholar 

  • Ponton JW (1982) The numerical evaluation of analytical derivatives. Comput Chem Eng 6:331–333

    Article  Google Scholar 

  • Quesada I, Grossmann IE (1995) Global optimization of bilinear process networks with multicomponent flows. Comput Chem Eng 19(2):1219–1242

    Article  Google Scholar 

  • Renfro, J.G., Personal communication, 2010

  • Renfro JG, Morshedi AM, Asbjornsen OA (1987) “Simultaneous optimization and solution of systems described by differential/algebraic equations. Comput Chem Eng 11:503–517

    Article  Google Scholar 

  • Robertson DG, Lee JH, Rawlings JB (1996) A moving-horizon based approach to least-squares estimation. AIChE J 42:2209–2224

    Article  Google Scholar 

  • Rusin MH, Chung HS, Marshall JF (1981) A transformation method for calculating the research and motor octane numbers of gasoline blends. Ind Eng Chem Fundam 20:195–204

    Article  Google Scholar 

  • Slaback DD (2004) A surrogate model of refinery-wide optimization. PhD dissertation, Texas Tech University

  • Smith JC, Harriott P, Harriot P, McCabe WL (2000) Unit operations of chemical engineering. McGraw-Hill Book Company, New York

    Google Scholar 

  • Squire W, Trapp G (1998) Using complex variables to estimate derivatives of real functions. SIAM Rev 40:110–112

    Article  MathSciNet  MATH  Google Scholar 

  • Strigle RF (1987) Random packings and packed towers: design and applications. Gulf Publishing Co., Houston

    Google Scholar 

  • Tawarmalani M, Sahinidis NV (2002) Convexification and global optimization in continuous and mixed-integer nonlinear programming. Kluwer Academic Publishers, London

    Book  MATH  Google Scholar 

  • Taylor R, Krishna R (1993) Multicomponent mass transfer. Wiley, New York

    Google Scholar 

  • Towler G, Sinnott R (2008) Chemical engineering design: principles, practice and economics of plant process design. Elesvier, London

    Google Scholar 

  • Worstell JH (2001) Don’t act like a novice about reaction engineering. Chem Eng Prog 97:68–72

    Google Scholar 

  • Zhang J, Kim N-H, Lasdon L (1985) An improved successive linear programming algorithm. Manag Sci 31:1312–1331

    Article  MathSciNet  MATH  Google Scholar 

  • Zyngier D, Kelly JD (2009) Multi-product inventory logistics modeling in the process industries. In: Wanpracha Chaovalitwongse, Kevin C. Furman, Panos M. Pardalos (Eds.) Optimization and logistics challenges in the enterprise. Springer optimization and its applications, 30, Part 1, pp 61–95. doi:10.1007/978-0-387-88617-6_2

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Authors and Affiliations

  1. Industrial Algorithms, 15 St. Andrews Road, Toronto, ON, M1P 4C3, Canada

    Jeffrey D. Kelly

  2. Hatch, 4342 Queen Street, Niagara Falls, L2E 7J7, Canada

    Danielle Zyngier

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  1. Jeffrey D. Kelly
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  2. Danielle Zyngier
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Correspondence to Jeffrey D. Kelly.

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Kelly, J.D., Zyngier, D. Unit-operation nonlinear modeling for planning and scheduling applications. Optim Eng 18, 133–154 (2017). https://doi.org/10.1007/s11081-016-9312-7

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  • DOI: https://doi.org/10.1007/s11081-016-9312-7

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