Erik Esche

An algorithm for the identification and estimation of relevant parameters for optimization under uncertainty

Abstract Models are prone to errors, often due to uncertain parameters. For optimization under uncertainty, the larger the amount of uncertain parameters, the higher the computational effort and the possibility of obtaining unrealistic results. In this contribution it is assumed that not all uncertain parameters need to be regarded and focus should be laid on a subset. As a first step in the algorithm, a parameter estimation is carried out to determine expected values, followed by a linear-dependency analysis and a ranking of the uncertain parameters. Parameters with a high linear-dependency are fixed, while others are left uncertain. This is followed by a subset selection regarding the sensitivity of the parameters toward the model and toward a user-defined objective function. Thus, only parameters with the largest sensitivities are selected as uncertain parameters and considered for optimization under uncertainty. A case study is presented in which the algorithm is applied.

Optimal Operation of a Membrane Reactor Network

In this work, a two-dimensional model for a conventional packed-bed membrane reactor (CPBMR) is developed for the oxidative coupling of methane, which uses a nonselective porous membrane to continuously feed oxygen to the catalytic bed. The model incorporates radial diffusion and thermal conduction and assumes convective transport for the axial direction. In addition, two 10 cm long cooling segments for the CPBMR were implemented based on the idea of a fixed cooling temperature outside the reactor shell. The resulting model is discretized using two-dimensional orthogonal collocation on finite elements with a combination of Hermite polynomials for the radial and Lagrangian polynomials for the axial coordinate. The simulation study shows that it is necessary to make all transport coefficients dependent on local temperatures and compositions. This leads to a simulation with roughly 130,000 variables, which is then used to generate initial points for the optimization of the CPBMR stand-alone operation. In addition, inequality constraints and variable bounds are introduced so as to avoid potentially hazardous mixtures of methane and oxygen in both shell and tube as well as to keep the temperatures below levels stressing reactor materials (< 1,100 °C). Moreover, membrane thickness, feed compositions, temperatures at the reactor inlet and for the cooling segments, diameters of tube and shell, and finally the amount of inert packing in the reactor are considered as decision variables. The optimization procedure uses IPOPT as a solver. Afterwards, the 2D model is integrated into a membrane reactor network (MRN) proposed by H. Godin, 2010 which is simulated. Finally, attempts are made to optimize its operation.

Taylor-Made Modeling and Solution of Novel Process Units by Modular CAPE-OPEN-based Flowsheeting

Abstract This contribution deals with the integration of custom unit operations into flowsheeting software. By sketching the workflow of designing novel processes in a conventional simulation software and introducing a respective modeling scenario some challenges regarding collaboration and model-solution are named: the exchange of models, the definition of initial values, and the ordering of equations. A strategy to overcome these challenges is presented and applied in case studies using a collaborative modeling and code generation tool and a CAPE OPEN-compliant unit operation framework. These examples show not only the advantages of the CAPE-OPEN standard for interoperability in process science but also the advantages of automatic code generation based on mathematical analysis of the equation systems.

Dynamic Chance-Constrained Optimization under Uncertainty on Reduced Parameter Sets

Abstract Uncertainty is a crucial topic for the decision making process in almost every scientific field. Therefore, the correct implementation into optimization problems is vital. Herein, the chance-constrained optimization approach is applied and compared with a standard Monte Carlo optimization on a CSTR model. The two approaches are expanded by limiting the number of uncertain parameters in the system with according subset selection strategies from parameter estimation studies. The idea here is that a high number of uncertain parameters does not add to a better description of a system. The uncertainty can be represented by a subset of uncertain parameters, which suffice to describe the system behavior. In this contribution, it is shown that the results, both for the chance constrained and Monte Carlo optimization approaches, are improved regarding result stability and control action indication. Additionally, it is discussed how the chance-constrained approach yields even better results regarding the objective function of the optimization problem and it is shown that the solution time is drastically reduced.

Superstructure Optimization: Reaction Yield Dependent CO2 Removal from OCM Product Gas

The oxidative coupling of methane presents an alternative for the production of ethene as opposed to the standard steam cracking of crude oil. A drawback of the reaction is the byproduct creation of CO2. Due to economic reasons, CO2 needs to be removed from the product gas efficiently, while keeping the ethene loss below 5%. Therefore, an overall assessment of the reaction and gas purification section of an OCM process is required. In the past, experiments have shown that a combination of various gas separation membranes with an absorption-desorption process leads to efficient hybrid separation processes. In this contribution, superstructure optimization of the separation section is performed combining various gas separation membranes (in type and number) with an absorption-desorption process and using different input values of CO2 and ethene concentrations leading to a significant energy reduction compared to standard absorption processes.

MOSAIC: An Online Modeling Platform Supporting Automatic Discretization of Partial Differential Equation Systems

Abstract Partial differential algebraic equation systems (PDAE) frequently appear in chemical engineering and their discretization is most often an issue when preparing a simulation wherein they appear. In this contribution, an algorithm is presented and implemented facilitating the general analysis of PDAE systems appearing often in chemical engineering problems and their discretization via orthogonal collocation on finite elements. The recognition of differentiating variables, the application of varying boundary conditions, and the subdivision into independent PDAE systems as well as the implementation of the actual discretization is discussed.

Improving Convergence Behavior of Nonlinear Equation Systems in Intensified Process Models by Decomposition Methods

Abstract The two decomposition methods Dulmage-Mendelsohn (DM) decomposition and bordered block transformation (BBTF) have been examined on their capabilities to eliminate convergence problems during the iteration of large, nonlinear equation systems as they occur frequently in process modeling. They both divide the overall system into lower dimensional subsystems, which can be solved separately in sequence. Exemplarily these methods were applied on the model of a reactive distillation column, where the decomposed systems show a higher robustness with respect to systematically selected initial points compared to the original system. Nevertheless, the improvement in DM seems small since a large subsystem with 576 of the 664 model equations remains. The convergence result from the iteration of the BBTF decomposed system depends a lot on the initial values for certain strongly coupled variables called tearing variables. In future, methods will be investigated and may also be developed to further reduce the dimension of the subsystems in DM and provide accurate initial values for the tearing variables in BBTF.

Sequential Flowsheet Optimization: Maximizing the Exergy Efficiency of a High-Pressure Water Scrubbing Process for Biogas Upgrade

Abstract Biogas is an important renewable energy source and potential raw material for the chemical industry. Its utilization frequently requires a treatment and/or upgrade step. The aim here is to maximize the exergy efficiency of a high-pressure water scrubbing process for upgrading biogas into biomethane by coupling a sequential modular simulation flowsheet with different optimization algorithms. By setting adequate operating pressures, and reducing cycle water and stripping air flowrates, an exergy efficiency of 92.4% is reached.

Support of Education in Process Simulation and Optimization via Language Independent Modelling and Versatile Code Generation

Abstract Numerous types of software exist for simulation and optimization of processes in chemical engineering. This is a special challenge towards education in computer-aided chemical engineering, where the focus should rather be on understanding the features of different algorithms than on the code implementation of a model in a certain environment/language. In this contribution, a workflow in the desktop application MOSAIC is presented, which separates modeling and simulation or optimization. This workflow has been tested in a semester accompanying task of a process optimization class as well as in several workshops. Both the task as well as the reaction of the students towards it are documented here.

Linking Process Simulation and Automatic 3D Design for Chemical Plants

Abstract In this contribution, the automatic creation of 3D models for Modular Process Units (MPUs) of chemical plants is presented. A prototype is successfully implemented within the PlantDesign Feature of the modeling environment MOSAIC. It enables the automatic source code generation for detailed 3D models. The constructive design of the MPU models includes norm-compliant equipment components, internal installations, platforms and ladders, structural elements, supports, and close piping including measurement and control devices. The design of the MPUs is individually adaptable to the process data, operating conditions, material selection and constructive design requirements. Besides the spatial information, also process and meta information like process variables, process conditions, constructive user specifications, heuristic information, and calculated design parameters are stored within the 3D data model. The automatically generated source code of the process unit can be imported into 3D CAD tools e.g. E3D/PDMS of AVEVA®. The PlantDesign library includes rectification columns and associated apparatuses.