(537g) Modeling Hierarchical Control Strategies, Header Balances and Tiered Pricing for Real-Time Optimization of Industrial Processes | AIChE

(537g) Modeling Hierarchical Control Strategies, Header Balances and Tiered Pricing for Real-Time Optimization of Industrial Processes


Real-time optimization of steady-state models representing industrial processes is performed by tuning process models with plant data followed by constrained economic optimization that includes updated process constraints and economic prices. First principle fundamental models for various unit operations along with splitters and mixers are used to represent industrial processes. Global optimization is ensured by reformulating the nonconvexities from bilinear equations that arise due to sharp separations for component mass balances in splitters, mixers and other unit operations. Flows can take values of zero thereby resulting in singularities that introduce nonconvexities that are hard to converge using conventional nonlinear programming methods. These nonconvexities need to be addressed for the models to ensure numerical stability thereby creating higher sustainable value in operating plants.

Researchers have studied global optimization of flowsheets consisting of splitters, mixers and other process models that have bilinear equations. A review of bilinear programming has been provided by Al-Khayyal (1992). Wehe and Westerberg (1987) proposed the enumeration of the different separation sequences using splitters with bilinear equations and dropping nonconvex equations. Kocis and Grossmann (1989) have modeled process networks with multicomponent streams in terms of individual component flows to avoid the nonconvex bilinear terms for the component mass balances. Quesada and Grossmann (1995) have proposed a reformulation-linearization technique for global optimization of networks consisting of splitter, mixers and linear process units that involve multicomponent streams. Watson et. al. (2017) have proposed a nonsmooth algorithm to address nonconvexities for handling both two-phase and single-phase flash when a phase may disappear out of the two-phase flash based on process conditions.

Nonconvexities arise in an industrial process flowsheet to model hierarchical control strategies, header balances and tiered pricing for real-time optimization. Hierarchical control strategies are widely used in plants to ensure safety, operational and logistic priorities while maintaining good control of plant operations. These hierarchical control strategies have sharp separations for mass balances that can result in a local optima for plant optimization problems. Header balances for utilities, raw materials and products require the calculation of makeup or excess to ensure steady-state mass balances for the header. Nonconvexities arise to ensure switching between makeup and excess for global optimization. Modeling tiered pricing strategies for product or raw material flows results in numerical singularity due to discontinuity for the jacobian evaluation at the tier limit. These singularities cause nonconvexities that can prevent the global optimization due to the inability to cross tier boundaries even for monotonically increasing or decreasing objective function.

In this work, modeling choices and approximations have been made in flowsheeting modeling to address the nonconvexities for the following typical industrial scenarios:

1) Hierarchical Control Strategies,

2) Header Balances, and

3) Tiered Pricing

Simple prototypical problems are illustrated with mathematical formulations and results that exhibit global optimization for each of the above scenarios with nonconvexities. The modeling approximations for above three industrial plant scenarios have been applied successfully for multiple real-time optimization applications in Dow to achieve the true global optima thereby creating higher sustainable value.


  1. Al-Khayyal, 1992, Generalized bilinear programming - Part I. Models, applications and linear programming relaxation, European Journal of Operational Research, 60, pp 306-314
  2. Wehe and Westerberg, 1987, An algorithmic procedure for the synthesis of distillation sequences with bypass, Computers and Chemical Engineering, Vol. 11, No. 6, pp 619-627
  3. Kocis and Grossmann, 1989, A Modelling and Decomposition Strategy for the MINLP Optimization of Process Flowsheets, Computers and Chemical Engineering, Vol. 13, No. 7, pp 797-819
  4. Quesada and Grossmann, 1995, Global Optimization of Bilinear Process Networks with Multicomponent Flows, Computers and Chemical Engineering, Vol. 19, No. 12, pp 1219-12422
  5. Watson, Vikse, Gundersen, and Barton, 2017, Reliable Flash Calculations: Part 1. Nonsmooth Inside-Out Algorithms, Industrial and Engineering Chemistry Research, Vol. 56, pp 960-973


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