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Abstract: Shortcut design methods can be valuable tools for rapid screening of different separation process alternatives to assess feasibility and determine minimum energy demand. This work presents a variant of the feed angle method (), which applies to single- and double-feed reactive distillation columns. The proposed method relies on pinch point analysis and determines the minimum energy demand from the calculation of a tray at the feed pinch. It is fully algorithmic and insensitive to impurities in product specifications. Its validity and performance is illustrated by a variety of case studies covering multi-component and multi-reaction systems, mixtures with potential liquid–liquid phase split, and double-feed columns. The results show that the method is sufficiently accurate and computationally efficient, even for highly non-ideal systems and complex configurations. [Copyright &y& Elsevier]

Abstract: A new distributed model-predictive control method is introduced, which is based on a novel distributed optimization algorithm, relying on a sensitivity-based coordination mechanism. Coordination and therefore overall optimality is achieved by means of a linear approximation of the objective functions of neighboring controllers within the objective function of each local controller. As for most of the distributed optimization methods, an iterative solution of the distributed optimal control problems is required. An analysis of the method with respect to its convergence properties is provided. For illustration, the sensitivity-driven distributed model-predictive control (S-DMPC) method is applied to a simulated alkylation process. An almost optimal control sequence can be achieved after only one iteration in this case. [Copyright &y& Elsevier]

One approach to solve optimal control problems by direct methods is the so-called sequential approach or single shooting. Only the control variables are discretized resulting in a nonlinear program (NLP) which can be solved with SQP or interior point methods. This paper presents a new methodology to efficiently provide the Hessian of the Lagrangian of that resulting NLP. The algorithm is based on the second-order adjoint method and introduces the novel concept of composite adjoints to reduce the computational effort of a Hessian evaluation. Though this contribution is for the sake of simplicity restricted to single shooting, the same methodology can also be easily applied to multiple shooting. [ABSTRACT FROM AUTHOR]

Abstract: A new formulation of a block-structured model based on the Hammerstein operator is presented for the identification of multi-variate systems with input directionality. In contrast to the existing formulations for multi-variate Hammerstein models, the proposed structure offers the possibility to independently model the dynamic and nonlinear characteristics of the system and at the same time preserves the possibility to use the new efficient algorithms developed for the identification of single input Hammerstein models. Further, the formulation allows for a representation of arbitrary static nonlinear coupling of input variables with a considerably lower amount of parameters compared to existing formulations. The new model structure is applied to the identification of a fluid catalytic cracking (FCC) unit and significantly outperforms all previous multi-variate Hammerstein model structures by reducing the prediction error by over 50%. [Copyright &y& Elsevier]

Abstract: The paper presents the extension of our work on the adaptive steady-state simulation of refinery processes to dynamic problems. The results show that the adaptive algorithm is capable of following the changes in the composition by adapting the composition representation during the course of simulation. The method is based on a continuous model formulation. In principle, each model given in a discrete (or pseudocomponent) formulation can be rewritten by means of continuous distribution functions. This continuous formulation does not yet reduce the model size but comprises the full detailed model. A model reduction is accomplished by applying a discretization scheme to the continuous formulation. Thus, the continuous reformulation allows the usage of modern discretization techniques including grid adaptation (adaptive wavelet-Galerkin discretization) and multigrid methods. In the iterative algorithm suggested, the approximate solution of the dynamic process model is obtained on the full composition grid. In each iteration loop the current iterate is corrected by a correction term, which is determined on a coarse grid for the composition representation. According to the multigrid framework the obtained intermediate solution is prolongated to the full composition detail by means of a linearization of the model equations. Within these iterations, the discretization grid is adapted by exploitation of the particular properties of the employed wavelet basis functions. [Copyright &y& Elsevier]

The established technique for simulation of refinery processes is the use of pseudocomponents. However, in order to increase the economical benefit of plant operation, it seems inevitable to include molecular information in petroleum mixtures characterization. This will lead to a strong increase of problem size. For this new class of models, there currently seems to be no special algorithms available. The classic pseudocomponent approach is compared with a newly developed solution strategy, which is explicitly developed to efficiently solve simulation problems with a high detail in composition representation. The new solution strategy is an adaptive multigrid method based on a wavelet-Galerkin discretization. With the wavelet-Galerkin discretization the model can easily be formulated on various levels of detail. In an iterative procedure the multigrid concept exploits these different formulations to construct correction-term approximations to the true solution. The discretization of these correction-term models is now done with a detail in composition representation that is determined by a residual-based adaptation strategy. The proposed method has been implemented for a simple 9-stage distillation column and tested for a variety of feed mixtures. In all investigated tests the proposed method proved to be superior to the conventional pseudocomponent approach in terms of accuracy and efficiency. [ABSTRACT FROM AUTHOR]

In this article we address the steady state design of a nonlinear tryptophan biosynthesis model with guaranteed stability of the optimal solution in the presence of parametric uncertainty. The optimization based approach – denoted constructive nonlinear dynamics (CNLD) – is based on constraints that enforce a minimal distance in the space of the uncertain parameters between a stability boundary and the optimal solution. The results obtained with CNLD are compared to results recently presented by Chang and Sahinidis [Chang, Y. J., & Sahinidis, N. V. (2005). Optimization of metabolic pathways under stability considerations. Computers and Chemical Engineering, 29 (3), 467–479], where the optimization of the tryptophan biosynthesis model was addressed by a global optimization algorithm. CNLD takes the nonlinearities of the process exactly into account and satisfies the specified robustness criteria without being overly conservative. [Copyright &y& Elsevier]

This paper treats the solution of nonlinear optimization problems involving discrete decision variables, also known as generalized disjunctive programming (GDP) or mixed-integer nonlinear programming (MINLP) problems, that arise in process engineering. The key idea is to eliminate the discrete decision variables by adding a set of continuous variables and constraints that represent the discrete decision space of the optimization problem. With such a reformulation, we are able to apply solution algorithms for purely continuous nonlinear optimization problems to efficiently calculate local minima of GDP or MINLP problems. In this contribution, we propose different alternatives to reformulate GDP/MINLP problems as continuous optimization problems. We furthermore investigate theoretical properties of the different reformulations with regard to their numerical solution. The proposed formulations are illustrated and analyzed on the basis of optimization problems dealing with process engineering applications involving stationary as well as dynamic process models. [Copyright &y& Elsevier]

Shortcut methods are valuable tools in the early stages of chemical process design, where numerous flowsheet alternatives need to be evaluated to determine the most energy-efficient, feasible flowsheet. Various shortcut methods based on tray-to-tray or pinch point analysis for the inspection of feasibility and the determination of the minimum energy demand (MED) for homogeneous azeotropic distillation have been published. For multicomponent heteroazeotropic distillation, however, no generally applicable shortcut methods are available yet. In this work, various shortcut methods for heteroazeotropic multicomponent distillation are assessed. Two novel thermodynamically sound shortcut methods, the feed pinch method (FPM) and the feed angle method (FAM), are proposed to resolve the limitations of existing methods. In particular, the fully algorithmic FAM is applicable to direct, indirect, and intermediate splits for heterogeneous azeotropic mixtures of any number of components. The novel methods are illustrated by four sample separations involving ternary, quaternary and quinternary heterogeneous mixtures. The performance of the FAM is highlighted by an industrial case study, where the effectiveness of an optimization-based conceptual design of a heteroazeotropic column sequence is demonstrated. The computational efficiency of the FAM allows a numerical optimization of the operating points of flowsheet alternatives in order to determine the most energy-efficient variant. [ABSTRACT FROM AUTHOR]

The targeted quantitative structure–property relationship (TQSPR) method of Brauner et al. [Brauner, N., Stateva, R. P., Cholakov, G. St., & Shacham, M. (2006) and a structurally “targeted” QSPR method for property prediction, Industrial & Engineering Chemistry Research, 45, 8430–8437] is analyzed in this study with respect to its various algorithmic steps. It is shown that accurate QSPRs for predicting the critical temperature can be developed using a training set of 10 compounds that exhibit the highest level of similarity with the target compound (the compound for which a property has to be predicted). Alternative methods to compute the similarity of compounds and to assemble the training set are compared. The potential of a principal component analysis of the molecular descriptor data to improve the TQSPR performance is assessed and a new stopping criterion for QSPR refinement based on the discrepancy principle is introduced. It is shown that collinearity between molecular descriptors and the increase of the number of compounds and descriptors in the database do not have adverse effects on the performance of the TQSPR method. [Copyright &y& Elsevier]

Abstract: In this paper we present a method for the optimization of dynamic systems using problem-adapted discretizations. The method is based on the direct sequential or single-shooting approach, where the optimization problem is converted into a nonlinear programming problem by parameterization of the control profiles. A fully adaptive, problem-dependent parameterization is generated by repetitive solution of increasingly refined finite-dimensional optimization problems. In each step of the proposed algorithm, the adaptation is based on a wavelet analysis of the solution profiles obtained in the previous step. The method is applied to several case study problems to demonstrate that the adaptive parameterization is more efficient and robust compared to a uniform parameterization of comparable accuracy. [Copyright &y& Elsevier]