Greedy algorithm for scheduling batch plants with sequence‐dependent changeovers

This article presents a new algorithm for scheduling multistage batch plants with a large number of orders and sequence‐dependent changeovers. Such problems are either intractable when solved with full‐space approaches or poor solutions result. We use decomposition on the entire set of orders and derive the complete schedule in several iterations, by inserting a couple of orders at a time. The key idea is to allow for partial rescheduling without altering the main decisions in terms of unit assignments and sequencing (linked to the binary variables) so that the combinatorial complexity is kept at a manageable level. The algorithm has been implemented for three alternative continuous‐time mixed integer linear programing models and tested through the solution of 10 example problems for different decomposition settings. The results show that an industrial‐size scheduling problem with 50 orders, 17 units distributed over six stages can effectively be solved in roughly 6 min of computational time. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

A novel MILP formulation for short-term scheduling of multi-stage multi-product batch plants with sequence-dependent constraints

This paper presents a continuous-time mixed-integer linear programming (MILP) model for short-term scheduling of multi-stage multi-product batch plants. The model determines the optimal sequencing and the allocation of customer orders to non-identical processing units by minimizing the earliness and tardiness of order completion. This is a highly combinatorial problem, especially when sequence-dependent relations are considered such as the setup time between consecutive orders. A common approach to this scheduling problem relies on the application of tetra-index binary variables, i.e. (order, order, stage, unit) to represent all the combinations of order sequences and assignments to units in the various stages. This generates a huge number of binary variables and, as a consequence, much time is required for solutions. This paper proposes a novel formulation that replaces the tetra-index binary variables by one set of tri-index binary variables (order, order, stage) without losing the model's generality. By the elimination of the unit index, the new formulation requires considerably fewer binary variables, thus significantly shortening the solution time.     

A pattern matching method for large‐scale multipurpose process scheduling

This article proposes a novel pattern matching method for the large‐scale multipurpose process scheduling with variable or constant processing times. For the commonly used mathematical programming models, large‐scale scheduling with long‐time horizons implies a large number of binary variables and time sequence constraints, which makes the models intractable. Hence, decomposition and cyclic scheduling are often applied to such scheduling. In this work, a long‐time horizon of scheduling is divided into two phases. Phase one is duplicated from a pattern schedule constructed according to the principle that crucial units work continuously, in parallel and/or with full load as possible, exclusive of time‐consuming optimization. Phase two involves a small‐size subproblem that can be optimized easily by a heuristic method. The computational effort of the proposed method does not increase with the problem size. The pattern schedule can be not only used for production/profit maximization but also for makespan estimation and minimization. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

An MILP continuous-time approach to short-term scheduling of resource-constrained multistage flowshop batch facilities

This work presents a new MILP mathematical formulation for the resource-constrained short-term scheduling of flowshop batch facilities with a known topology and limited supplies of discrete resources. The processing structure is composed of multiple stages arranged in series and several units working in parallel at each one. All production orders consist of a single batch and follow the same processing sequence throughout the plant. The proposed MILP approach is based on a continuous time domain representation that relies on the notion of order predecessor and accounts for sequence-dependent setup times. Assignment and sequencing decisions are independently handled through separate sets of binary variables. A proper formulation of the sequencing constraints provides a substantial saving in sequencing variables and constraints. By postulating a pair of conditions for the simultaneous execution of processing tasks, rather simple resource constraints requiring a few extra binary variables are derived. The proposed MILP scheduling approach shows a remarkable computational efficiency when applied to real-world problems.     

Regulation of trans‐1,4‐polyisoprene crystallinity and mechanical properties of styrene‐butadiene rubber/trans‐1,4‐polyisoprene vulcanizate

The effects of processing temperature and bis‐[γ‐(triethoxysilyl)‐propyl]‐tetrasulfide (Si69) on crystallization, morphology, and mechanical properties of styrene‐butadiene rubber (SBR)/trans‐1,4‐polyisoprene (TPI) vulcanizate are investigated. The crystallinity and crystalline melting temperature (T_m) of TPI in the vulcanizates with TPI/silica/(Si69) pre‐mixed at 150 °C are much lower than that pre‐mixed at 80 °C. At the same pre‐mixing temperature, the presence of 1 phr Si69 leads to a decreased crystallinity and T_m. The TPI domains with phase size of about 1 μm and silica are well dispersed in the vulcanizate, and TPI crystals get smaller in size and less in amount by pre‐mixing TPI, silica and Si69 at 150 °C. The vulcanizates with TPI/silica/(Si69) pre‐mixed at 150 °C have decreased tensile strength and modulus at a given extension than that pre‐mixed at 80 °C. At the same pre‐mixing temperature, the tensile strength and modulus of the vulcanizate increase with the addition of 1 phr Si69. The crystallinity of TPI component in SBR/TPI vulcanizate is effectively controlled by changing processing temperature and adding Si69, which is important for theoretical research and practical application of TPI. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44395.     

A novel adaptive surrogate modeling‐based algorithm for simultaneous optimization of sequential batch process scheduling and dynamic operations

A novel adaptive surrogate modeling‐based algorithm is proposed to solve the integrated scheduling and dynamic optimization problem for sequential batch processes. The integrated optimization problem is formulated as a large scale mixed‐integer nonlinear programming (MINLP) problem. To overcome the computational challenge of solving the integrated MINLP problem, an efficient solution algorithm based on the bilevel structure of the integrated problem is proposed. Because processing times and costs of each batch are the only linking variables between the scheduling and dynamic optimization problems, surrogate models based on piece‐wise linear functions are built for the dynamic optimization problems of each batch. These surrogate models are then updated adaptively, either by adding a new sampling point based on the solution of the previous iteration, or by doubling the upper bound of total processing time for the current surrogate model. The performance of the proposed method is demonstrated through the optimization of a multiproduct sequential batch process with seven units and up to five tasks. The results show that the proposed algorithm leads to a 31% higher profit than the sequential method. The proposed method also outperforms the full space simultaneous method by reducing the computational time by more than four orders of magnitude and returning a 9.59% higher profit. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4191–4209, 2015     

A Bayesian regime‐switching time‐series model

This article provides a new Bayesian approach for AR(2) time‐series models with multiple regime‐switching points. Our formulation of the regime‐switching model involves a binary discrete variable that indicates the regime change. This variable is specified to be detected by data in each regime. The model is estimated using Stochastic approximation Monte Carlo method proposed by Liang et al. [JASA (2007)]. This methodology is quite useful since it allows for fitting of more complex regime‐switching models without transition constraint. The proposed model is illustrated using simulated and real data such as GNP and US interest rate data.     

Effect of inorganic fillers in binary processing aids on the rheology of a metallocene linear low‐density polyethylene

Inorganic fillers including porous diatomite, flaky talc, and spherical calcium carbonate were blended with polyethylene glycol (PEG) to prepare binary processing aids, and the effect of varied binary processing aids on the melt flow properties and extrudates distortion of a metallocene linear low‐density polyethylene (mLLDPE) was studied. It was found that the binary processing aids exhibit better effect on viscosity reduction of mLLDPE than that obtained when PEG was added alone. The morphology of inorganic fillers influences the effect of binary processing aids. The diatomite/PEG binary processing aid shows the most noticeable effect, followed by the talc/PEG binary processing aid, and then the calcium carbonate/PEG binary processing aid. The influence of particle size of the diatomite on the effectiveness of the diatomite/PEG binary processing aid was also studied. The mechanism for the improved effect of binary processing aids on reducing viscosity of mLLDPE was proposed. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 96: 1824–1829;2005     

Data‐driven mathematical modeling and global optimization framework for entire petrochemical planning operations

In this work we develop a novel modeling and global optimization‐based planning formulation, which predicts product yields and properties for all of the production units within a highly integrated refinery‐petrochemical complex. Distillation is modeled using swing‐cut theory, while data‐based nonlinear models are developed for other processing units. The parameters of the postulated models are globally optimized based on a large data set of daily production. Property indices in blending units are linearly additive and they are calculated on a weight or volume basis. Binary variables are introduced to denote unit and operation modes selection. The planning model is a large‐scale non‐convex mixed integer nonlinear optimization model, which is solved to ε‐global optimality. Computational results for multiple case studies indicate that we achieve a significant profit increase (37–65%) using the proposed data‐driven global optimization framework. Finally, a user‐friendly interface is presented which enables automated updating of demand, specification, and cost parameters. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3020–3040, 2016     

Prediction of Layer‐Inversion Behavior of Down‐Flow Binary Solid‐Liquid Fluidized Beds

The layer‐inversion behavior of down‐flow binary solid‐liquid fluidized beds is predicted using the property‐averaging approach. The binary pair in this case consists of a larger solid species which is also heavier than its smaller counterpart, while both are lighter than the fluidizing medium. The model is based on using the generalized Richardson‐Zaki correlation for evaluation of the bed void fraction wherein mean values of particle properties are used. However, unlike the maximum bulk density condition for the conventional up‐flow binary solid fluidized bed, the model is based on a minimum bulk density condition for occurrence of layer inversion. This is due to the fact that the volume contraction phenomenon associated with the mixing of unequal solid species leads to a decrease in bulk density of the bed. Model predictions are also compared using the limited data available in the literature. Predictions are consistent with the observed mixing behavior.     

Single and Binary CO2/CH4 Separation of a Zeolitic Imidazolate Framework‐8 Membrane

The performance of a zeolitic imidazolate framework‐8 (ZIF‐8) membrane in single and binary CO₂/CH₄ gas separation was investigated by means of a gas transport model that included generalized Maxwell‐Stefan and binary friction models. The model concerns gas diffusion through the membrane layer, gas flow through membrane intercrystalline pores, and resistance of the support layer. The effective membrane area considering the actual area for the gas permeated through the membrane was also introduced in this model. The selective ZIF‐8 membrane was successfully synthesized using a microwave‐assisted solvothermal method on an α‐alumina support pre‐attached with ZIF‐8 seeds by solvent evaporation. The simulated data agreed well with the experimental data. The model revealed that the membrane intercrystalline pores and its effective area significantly affected the CO₂/CH₄ gas permeation and separation performance.     

Regression‐based analysis of multivariate non‐Gaussian datasets for diagnosing abnormal situations in chemical processes

This article presents a regression‐based monitoring approach for diagnosing abnormal conditions in complex chemical process systems. Such systems typically yield process variables that may be both Gaussian and non‐Gaussian distributed. The proposed approach utilizes the statistical local approach to monitor parametric changes of the latent variable model that is identified by a revised non‐Gaussian regression algorithm. Based on a numerical example and recorded data from a fluidized bed reactor, the article shows that the proposed approach is more sensitive when compared to existing work in this area. A detailed analysis of both application studies highlights that the introduced non‐Gaussian monitoring scheme extracts latent components that provide a better approximation of non‐Gaussian source signal and/or is more sensitive in detecting process abnormities. © 2013 American Institute of Chemical Engineers AIChE J, 60: 148–159, 2014     

Modular‐Based Simulation of Single Process Units

A novel simulation strategy for the modular‐based calculation of models describing single unit operations is proposed. It is based on the functional decomposition of the model with further application of the waveform relaxation approach for data exchange and convergence analysis. Compared to convenient simultaneous calculation of units, the proposed approach leads to higher flexibility during model creation and allow simultaneous usage of several solvers and simulation methods. To illustrate the usability of the developed strategy and analyze its efficiency it has been applied for modeling of a fluidized‐bed spray granulator. Based on the functional decomposition, the granulator model has been decomposed into six separate submodels connected with information streams for data exchange.     

A Control‐oriented Dynamic Model Adapted to Variant Steam‐to‐carbon Ratios for an SOFC with Exhaust Fuel Recirculation

The steam‐to‐carbon ratio (S/C) is a typical disturbance parameter in the operation of solid oxide fuel cell (SOFC) power generation system. A planar SOFC with a pre‐reformer and exhaust fuel recirculation system is investigated in this work. A lumped, nonlinear dynamic model is developed for the SOFC with consideration both of the spatial effect and the variant S/Cs. The dynamic model is deduced based on a fitting function so‐called Exponential Association Function, which is employed to describe the spatial distribution of state variables in SOFC. Three parameters of the fitting function are identified to integrate the spatial effect and S/C effect in the model. The parameters of Exponential Association Function are determined by function fitting on three‐dimensional numerical data at the sample operation points. Carbon formation activity is analysed using the simulation results and thermodynamic data. Dynamic simulation is implemented with the help of software MATLAB/SIMULINK. The results show that the developed model has good performance in predicting the responses of the state variables and catching the changes of S/C.     

Dynamic modeling of a gas pressure control system for a gas‐assisted injection molding process

This study presents the development of dynamic models for gas injection pressure that may be implemented in the design of control systems for gas‐injection units. A nonlinear dynamic model was first derived and then verified by experimental measurements. This was done by using a laboratory‐built, gas‐assisted injection unit. The agreement between the prediction and measurement indicates that the present nonlinear dynamic model adequately predicts the dynamic behavior of gas injection pressure during the process. Although the resulting model is useful for understanding the behavior of the process and the effects of different process variables, its complexity may cause difficulties in a real control application. Therefore, a second‐order model based on the basic characteristics of the nonlinear model was proposed to approximate the gas injection pressure. In order to determine the model parameters, the algorithm of recursive least‐square system identification was employed. A comparison of simulated results of an identified model with experimental data showed that the model accurately predicted the transient behavior of gas injection pressure. Consequently, this low‐order model can be easily implemented into the control system design of a gas‐injection unit.     

A study of the three‐dimensional particle size segregation structure in a rotating drum

Three‐dimensional particle size segregation structures of binary mixtures of six different size ratios (SR = 1.42–3.37) in a rotating drum are studied. The formation of two smaller particle satellites around the central smaller‐particle rich band after the band formation core‐thickening mechanism is reported for the first time. The binary mixtures of six SRs show three satellite shapes, including the small bump shape, the axe shape, and the hemisphere shape. Except for the binary mixture of SR = 2.01 with the axe satellite shape, the satellite size increases with the increasing of the SR value at the same bed depth. The degrees of mixing of binary mixtures of six different SRs at different bed depths are analyzed using the Lacey mixing index. The degree of mixing at the bed surface and close to the drum cylindrical wall can be explained by the drift‐diffusional model of Savage (1993). © 2011 American Institute of Chemical Engineers AIChE J, 2012     

Dynamic modeling and collocation‐based model reduction of cryogenic air separation units

High purity distillation columns and multi‐stream heat exchangers (MSHXs) are critical units in cryogenic air separation plants. This article focuses on modeling approaches for the primary section of a super‐staged argon plant. A full‐order stage‐wise model for distillation columns in air separation units (ASUs) that considers key process phenomena is presented, followed by a reduced‐order model using a collocation approach. The extent of model reduction that can be achieved without losing significant prediction accuracy is demonstrated. A novel moving boundary model is proposed to handle MSHXs with phase change. Simulation results demonstrate the capability of the proposed model for tracking the phase change occurrence along the length of the heat exchanger. Dynamic simulation studies of the integrated plant show that the thermal integration between the feed and product streams captured in the primary heat exchanger is critical to accurately capture the behavior of ASUs. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1602–1615, 2016     

Simultaneous solution approach to model‐based experimental design

A model‐based experimental design is formulated and solved as a large‐scale NLP problem. The key idea of the proposed approach is the extension of model equations with sensitivity equations forming an extended sensitivities‐state equation system. The resulting system is then totally discretized and simultaneously solved as constraints of the NLP problem. Thereby, higher derivatives of the parameter sensitivities with respect to the control variables are directly calculated and exact. This is an advantage in comparison with proposed sequential approaches to model‐based experimental design so far, where these derivatives have to be additionally integrated throughout the optimization steps. This can end up in a high‐computational load especially for systems with many control variables. Furthermore, an advanced sampling strategy is proposed which combines the strength of the optimal sampling design and the variation of the collocation element lengths while fully using the entire optimization space of the simultaneous formulation. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4169–4183, 2013     

Continuous production of solid polystyrene in back‐mixed and linear‐flow reactors

A mathematical model has been developed to predict the steady state performance of a continuous bulk styrene polymerization process with catalytic initiation for solid polystyrene. The polymerization section contains one boiling CSTR, followed by multiple linear‐flow reactors. The devolatilization section consists of two polymer pre‐heaters and two high‐solids flashes. The polymer moment equations were solved simultaneously with the reactor modeling equations. The non‐linear algebraic equations were solved by a Newton‐Raphson iteration technique to give the steady‐state styrene monomer weight fraction in a CSTR. The coupled, non‐linear ordinary differential equations were numerically integrated using a single‐step, 4th‐order Runge‐Kutta technique, followed by a multi‐step Adams‐Moulton technique. The resulting computer simulation model is capable of evaluating how the production rate and product quality are affected by feed composition, temperature, initiator type, initiator concentration, and residence time. Several case studies were given for commercially important crystal‐clear and impact‐resistant resins. A binary initiation system gives a good balance of monomer conversion, polymer molecular weights, and rubber grafting compared to a single initiation system. The styrene dimer/trimer occur in low concentrations but can be substantially reduced with a low temperature initiator. The ideal mean residence time is approximately one minute or less in a shell‐and‐tube devolatilization pre‐heater. Low flash chamber vacuum is more effective than high polystyrene melt temperature to reduce the volatile content of the final product. The water injected to the low volatile melt shows promising improvement in the second‐stage polystyrene devolatilization.     

Model‐Based Optimization of a Photocatalytic Reactor with Light‐Emitting Diodes

The complicated interplay between mass and photon transfer within a photocatalytic reactor calls for an integrated design approach. A model‐based optimization approach for LED‐based photocatalytic reactors is presented. First, a model that describes the distribution of reactants and photons within a photocatalytic reactor is developed. Then, several design variables related to the reactor dimensions and light sources are optimized simultaneously using the photocatalytic degradation of toluene as a model system. The results demonstrate how different formulations of the problem can be used to either minimize the reactor cost or to obtain a specified concentration profile within the reactor.