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20 pages, 1888 KiB

Open AccessFeature PaperArticle

Rapid Multi-Objective Optimization of Periodically Operated Processes Based on the Computer-Aided Nonlinear Frequency Response Method

by Luka A. Živković, Viktor Milić, Tanja Vidaković-Koch and Menka Petkovska

Processes 2020, 8(11), 1357; https://doi.org/10.3390/pr8111357 - 27 Oct 2020

Cited by 8 | Viewed by 1899

Abstract

The dynamic optimization of promising forced periodic processes has always been limited by time-consuming and expensive numerical calculations. The Nonlinear Frequency Response (NFR) method removes these limitations by providing excellent estimates of any process performance criteria of interest. Recently, the NFR method evolved [...] Read more.

The dynamic optimization of promising forced periodic processes has always been limited by time-consuming and expensive numerical calculations. The Nonlinear Frequency Response (NFR) method removes these limitations by providing excellent estimates of any process performance criteria of interest. Recently, the NFR method evolved to the computer-aided NFR method (cNFR) through a user-friendly software application for the automatic derivation of the functions necessary to estimate process improvement. By combining the cNFR method with standard multi-objective optimization (MOO) techniques, we developed a unique cNFR–MOO methodology for the optimization of periodic operations in the frequency domain. Since the objective functions are defined with entirely algebraic expressions, the dynamic optimization of forced periodic operations is extraordinarily fast. All optimization parameters, i.e., the steady-state point and the forcing parameters (frequency, amplitudes, and phase difference), are determined rapidly in one step. This gives the ability to find an optimal periodic operation around a sub-optimal steady-state point. The cNFR–MOO methodology was applied to two examples and is shown as an efficient and powerful tool for finding the best forced periodic operation. In both examples, the cNFR–MOO methodology gave conditions that could greatly enhance a process that is normally operated in a steady state. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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24 pages, 8986 KiB

Open AccessFeature PaperArticle

Computer-Aided Nonlinear Frequency Response Method for Investigating the Dynamics of Chemical Engineering Systems

by Luka A. Živković, Tanja Vidaković-Koch and Menka Petkovska

Processes 2020, 8(11), 1354; https://doi.org/10.3390/pr8111354 - 26 Oct 2020

Cited by 11 | Viewed by 2492

Abstract

The Nonlinear Frequency Response (NFR) method is a useful Process Systems Engineering tool for developing experimental techniques and periodic processes that exploit the system nonlinearity. The basic and most time-consuming step of the NFR method is the derivation of frequency response functions (FRFs). [...] Read more.

The Nonlinear Frequency Response (NFR) method is a useful Process Systems Engineering tool for developing experimental techniques and periodic processes that exploit the system nonlinearity. The basic and most time-consuming step of the NFR method is the derivation of frequency response functions (FRFs). The computer-aided Nonlinear Frequency Response (cNFR) method, presented in this work, uses a software application for automatic derivation of the FRFs, thus making the NFR analysis much simpler, even for systems with complex dynamics. The cNFR application uses an Excel user-friendly interface for defining the model equations and variables, and MATLAB code which performs analytical derivations. As a result, the cNFR application generates MATLAB files containing the derived FRFs in a symbolic and algebraic vector form. In this paper, the software is explained in detail and illustrated through: (1) analysis of periodic operation of an isothermal continuous stirred-tank reactor with a simple reaction mechanism, and (2) experimental identification of electrochemical oxygen reduction reaction. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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16 pages, 1255 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Linear Analysis of a Continuous Crystallization Process for Enantiomer Separation

by Michael Mangold, Nadiia Huskova, Jonathan Gänsch and Andreas Seidel-Morgenstern

Processes 2020, 8(11), 1337; https://doi.org/10.3390/pr8111337 - 23 Oct 2020

Cited by 1 | Viewed by 2921

Abstract

Continuous preferential crystallization is an innovative approach to the separation of chiral substances. The process considered in this work takes place in a gently agitated fluidized bed located in a tubular crystallizer. The feasibility of the process has been shown in previous work, [...] Read more.

Continuous preferential crystallization is an innovative approach to the separation of chiral substances. The process considered in this work takes place in a gently agitated fluidized bed located in a tubular crystallizer. The feasibility of the process has been shown in previous work, but it also turned out that choosing suitable operation conditions is quite delicate. Hence, a model based process design is desirable. Existing models of the process are rather complicated and require long computational times. In this work, a simple linear dynamic model is suggested, which captures the main properties of the process. The model is distributed in space and in a property coordinate. Using the method of characteristics, a semi-analytical solution of the linear model is derived. As a challenge to the solution, there is a recycle loop in the process that causes a feedback and couples the boundary conditions at different boundaries of the computational domain. In order to deal with this, a numerical scheme is suggested. The semi-analytical solution provides a deeper insight into the process dynamics. A comparison with a more detailed mathematical model of the process and with experiments shows strengths and limitations of the linear model. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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19 pages, 3492 KiB

Open AccessFeature PaperArticle

Efficient Simulation of Chromatographic Processes Using the Conservation Element/Solution Element Method

by Valentin Plamenov Chernev, Alain Vande Wouwer and Achim Kienle

Processes 2020, 8(10), 1316; https://doi.org/10.3390/pr8101316 - 20 Oct 2020

Cited by 3 | Viewed by 3057

Abstract

Chromatographic separation processes need efficient simulation methods, especially for nonlinear adsorption isotherms such as the Langmuir isotherms which imply the formation of concentration shocks. The focus of this paper is on the space–time conservation element/solution element (CE/SE) method. This is an explicit method [...] Read more.

Chromatographic separation processes need efficient simulation methods, especially for nonlinear adsorption isotherms such as the Langmuir isotherms which imply the formation of concentration shocks. The focus of this paper is on the space–time conservation element/solution element (CE/SE) method. This is an explicit method for the solution of systems of partial differential equations. Numerical stability of this method is guaranteed when the Courant–Friedrichs–Lewy condition is satisfied. To investigate the accuracy and efficiency of this method, it is compared with the classical cell model, which corresponds to a first-order finite volume discretization using a method of lines approach (MOL). The evaluation is done for different models, including the ideal equilibrium model and a mass transfer model for different adsorption isotherms—including linear and nonlinear Langmuir isotherms—and for different chromatographic processes from single-column operation to more sophisticated simulated moving bed (SMB) processes for the separation of binary and ternary mixtures. The results clearly show that CE/SE outperforms MOL in terms of computational times for all considered cases, ranging from 11-fold for the case with linear isotherm to 350-fold for the most complicated case with ternary center-cut eight-zone SMB with Langmuir isotherms, and it could be successfully applied for the optimization and control studies of such processes. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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15 pages, 5123 KiB

Open AccessArticle

Study of Blockage Diagnosis for Hydrocyclone Using Vibration-Based Technique Based on Wavelet Denoising and Discrete-Time Fourier Transform Method

by Guanghui Wang, Qun Liu, Chuanzhen Wang, Lulu Dong, Dan Dai and Liang Shen

Processes 2020, 8(4), 440; https://doi.org/10.3390/pr8040440 - 08 Apr 2020

Cited by 9 | Viewed by 2717

Abstract

Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate the blockage diagnosis for a [...] Read more.

Hydrocyclones are extensively known as important separation devices which are used in many industrial fields. However, the general method to estimate device performance is time-consuming and has a high cost. The aim of this paper was to investigate the blockage diagnosis for a lab-scale hydrocyclone using a vibration-based technique based on wavelet denoising and the discrete-time Fourier transform method. The results indicate that the farther away the installation location from feed inlet the more regular the frequency is, which reveals that the installation plane near to the spigot generated the regular frequency distribution. Furthermore, the acceleration amplitude under blockage degrees 0%, 50% and 100% fluctuates as a sine shape with increasing time, meanwhile the vibration frequency of the hydrocyclone rises with increasing throughput. Moreover, the distribution of four dimensional and five non-dimensional parameters for the time domain shows that the standard deviation, compared to the others, reduced gradually with increases in blockage degree. Thus, the standard deviation was used to evaluate the online diagnosis of the blockage. The frequency domain distribution under different throughput reveals that the characteristic peaks consisting of the faulty frequency and multiple frequency were produced by the faulty blockage and the feed pump, respectively. Hence, the faulty peak of 16–17 Hz was adopted to judge the real-time blockage of the hydrocyclone, i.e., the presence of the characteristic peak marks the blockage, and its value is proportional to the blockage degree. The application of the online monitoring system demonstrates that the combination of the time domain and the frequency domain could admirably detect the running state and rapidly recognize blockage faults. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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21 pages, 548 KiB

Open AccessFeature PaperArticle

Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction

by Moritz Schulze and René Schenkendorf

Processes 2020, 8(2), 190; https://doi.org/10.3390/pr8020190 - 05 Feb 2020

Cited by 4 | Viewed by 3192

Abstract

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing [...] Read more.

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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18 pages, 1220 KiB

Open AccessFeature PaperArticle

A Modular Framework for the Modelling and Optimization of Advanced Chromatographic Processes

by Johannes Schmölder and Malte Kaspereit

Processes 2020, 8(1), 65; https://doi.org/10.3390/pr8010065 - 03 Jan 2020

Cited by 10 | Viewed by 4494

Abstract

A framework is introduced for the systematic development of preparative chromatographic processes. It is intended for the optimal design of conventional and advanced concepts that exploit strategies, such as recycling, side streams, bypasses, using single or multiple columns, and combinations thereof. The Python-based [...] Read more.

A framework is introduced for the systematic development of preparative chromatographic processes. It is intended for the optimal design of conventional and advanced concepts that exploit strategies, such as recycling, side streams, bypasses, using single or multiple columns, and combinations thereof. The Python-based platform simplifies the implementation of new processes and design problems by decoupling design tasks into individual modules for modelling, simulation, assertion of cyclic stationarity, product fractionation, and optimization. Interfaces to external libraries provide flexibility regarding the choice of column model, solver, and optimizer. The current implementation, named CADET-Process, uses the software CADET for solving the model equations. The structure of the framework is discussed and its application for optimal design of existing and identification of new chromatographic operating concepts is demonstrated by case studies. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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21 pages, 1074 KiB

Open AccessFeature PaperArticle

Optimisation of the Autothermal NH₃ Production Process for Power-to-Ammonia

by Izzat Iqbal Cheema and Ulrike Krewer

Processes 2020, 8(1), 38; https://doi.org/10.3390/pr8010038 - 30 Dec 2019

Cited by 14 | Viewed by 7663

Abstract

The power-to-ammonia process requires flexible operation due to intermittent renewable energy supply. In this work, we analyse three-bed autothermal reactor systems for design and off-design performance for power-to-ammonia application. The five reactor systems differ in terms of inter-stage cooling methods, i.e., direct cooling [...] Read more.

The power-to-ammonia process requires flexible operation due to intermittent renewable energy supply. In this work, we analyse three-bed autothermal reactor systems for design and off-design performance for power-to-ammonia application. The five reactor systems differ in terms of inter-stage cooling methods, i.e., direct cooling by quenching (2Q), combination of indirect and direct cooling (HQ and QH) and indirect cooling (2H) with variations. At optimum nominal operation conditions, the inter-stage indirect cooling (2H) reactor systems result in the highest NH₃ production. For off-design performance analysis, NH₃ production is minimised or maximised by varying one of the following process variables at a time: inert gas, feed flow rate or H₂-to-N₂ ratio. For each variation, the effect on H₂ intake, recycle stream load and recycle-to-feed ratio is also analysed. Among the three process variables, the H₂-to-N₂ ratio provided ca. 70% lower NH₃ production and 70% lower H₂ intake than at nominal operation for all five reactor systems. Operation of autothermal reactor systems at significantly lower H₂ intake makes them reliable for power-to-ammonia application; as during energy outage period, shutdown can be delayed. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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20 pages, 391 KiB

Open AccessFeature PaperArticle

Systematic Selection of Green Solvents and Process Optimization for the Hydroformylation of Long-Chain Olefines

by Tobias Keßler, Christian Kunde, Steffen Linke, Kevin McBride, Kai Sundmacher and Achim Kienle

Processes 2019, 7(12), 882; https://doi.org/10.3390/pr7120882 - 26 Nov 2019

Cited by 8 | Viewed by 2858

Abstract

Including ecologic and environmental aspects in chemical engineering requires new methods for process design and optimization. In this work, a hydroformylation process of long-chain olefines is investigated. A thermomorphic multiphase system is employed that is homogeneous at reaction conditions and biphasic at lower [...] Read more.

Including ecologic and environmental aspects in chemical engineering requires new methods for process design and optimization. In this work, a hydroformylation process of long-chain olefines is investigated. A thermomorphic multiphase system is employed that is homogeneous at reaction conditions and biphasic at lower temperatures for catalyst recycling. In an attempt to replace the toxic polar solvent N,N-dimethylformamide (DMF), ecologically benign alternatives are selected using a screening approach. Economic process optimization is conducted for DMF and two candidate solvents. It is found that one of the green candidates performs similarly well as the standard benchmark solvent DMF, without being toxic. Therefore, the candidate has the potential to replace it. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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22 pages, 742 KiB

Open AccessFeature PaperEditor’s ChoiceArticle

Splitting Triglycerides with a Counter-Current Liquid–Liquid Spray Column: Modeling, Global Sensitivity Analysis, Parameter Estimation and Optimization

by Mark Nicholas Jones, Hector Forero-Hernandez, Alexandr Zubov, Bent Sarup and Gürkan Sin

Processes 2019, 7(12), 881; https://doi.org/10.3390/pr7120881 - 26 Nov 2019

Cited by 3 | Viewed by 8390

Abstract

In this work we present the model of a counter-current spray column in which a triglyceride (tripalmitic triglyceride) is hydrolyzed by water and leads to fatty acid (palmitic acid) and glycerol. A finite volume model (FVM) of the column was developed to describe [...] Read more.

In this work we present the model of a counter-current spray column in which a triglyceride (tripalmitic triglyceride) is hydrolyzed by water and leads to fatty acid (palmitic acid) and glycerol. A finite volume model (FVM) of the column was developed to describe the reactive extraction process with a two-phase system and validated with an analytical model from the literature with the given data set encompassing six experimental runs. Global, variance-based (Sobol) sensitivity analysis allowed assessment of the sensitivity of the sweet water glycerol content in respect to liquid density, overall mass-transfer coefficient, reaction rate coefficient and the equilibrium ratio to rank them accordingly. Furthermore, parameter estimation with a differential evolution (DE) algorithm was performed to obtain among others the mass transfer, backmixing and reaction rate coefficients. The model was used to formulate and solve a process design problem regarding economic and sustainable performance. Multi-criteria optimization was applied via DE to minimize total annual cost (TAC) and the Eco99 indicator by varying the steam inlet flow rate and distribution over the two steam inlets as the independent variables. The model and analysis was implemented in Fortran and Python where the Fortran model can also be embedded in a process simulator such as PRO/II or Aspen. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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19 pages, 1533 KiB

Open AccessArticle

Theoretical Analysis of Forced Segmented Temperature Gradients in Liquid Chromatography

by Adnan Hayat, Xinghai An, Shamsul Qamar, Gerald Warnecke and Andreas Seidel-Morgenstern

Processes 2019, 7(11), 846; https://doi.org/10.3390/pr7110846 - 12 Nov 2019

Cited by 6 | Viewed by 2595

Abstract

An equilibrium model is applied to study the effect of forced temperature gradients introduced through heat exchange via specific segments of the wall of a chromatographic column operating with a liquid mobile phase. For illustration of the principle, the column is divided into [...] Read more.

An equilibrium model is applied to study the effect of forced temperature gradients introduced through heat exchange via specific segments of the wall of a chromatographic column operating with a liquid mobile phase. For illustration of the principle, the column is divided into two segments in such a manner that the first segment is kept at a fixed reference temperature, while the temperature of the second segment can be changed stepwise through fixed heating or cooling over the column wall to modulate the migration speeds of the solute concentration profiles. The method of characteristics is used to obtain the solution trajectories analytically. It is demonstrated that appropriate heating or cooling in the second segment can accelerate or decelerate the specific concentration profiles in order to improve certain performance criteria. The results obtained verify that the proposed analysis is well suited to evaluate the application of forced segmented temperature gradients. The suggested gradient procedure provides the potential to reduce the cycle time and, thus, improving the production rate of the chromatographic separation process compared to conventional isothermal (isocratic) operation. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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16 pages, 349 KiB

Open AccessFeature PaperArticle

Surrogate Modeling for Liquid–Liquid Equilibria Using a Parameterization of the Binodal Curve

by Christian Kunde, Tobias Keßler, Steffen Linke, Kevin McBride, Kai Sundmacher and Achim Kienle

Processes 2019, 7(10), 753; https://doi.org/10.3390/pr7100753 - 16 Oct 2019

Cited by 7 | Viewed by 3906

Abstract

Computational effort and convergence problems can pose serious challenges when employing advanced thermodynamic models in process simulation and optimization. Data-based surrogate modeling helps to overcome these problems at the cost of additional modeling effort. The present work extends the range of methods for [...] Read more.

Computational effort and convergence problems can pose serious challenges when employing advanced thermodynamic models in process simulation and optimization. Data-based surrogate modeling helps to overcome these problems at the cost of additional modeling effort. The present work extends the range of methods for efficient data-based surrogate modeling of liquid–liquid equilibria. A new model formulation is presented that enables smaller surrogates with box-constrained input domains and reduced input dimensions. Sample data are generated efficiently by using numerical continuation. The new methods are demonstrated for the surrogate modeling and optimization of a process for the hydroformylation of 1-decene in a thermomorphic multiphase system. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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19 pages, 790 KiB

Open AccessFeature PaperArticle

Lethality Calculation of Particulate Liquid Foods during Aseptic Processing

by Mohd Tarmizan Ibrahim, Heiko Briesen, Petra Först and Jörg Zacharias

Processes 2019, 7(9), 587; https://doi.org/10.3390/pr7090587 - 03 Sep 2019

Cited by 4 | Viewed by 4186

Abstract

In the past two decades, aseptic processing has been implemented in the food industry to sterilize particulate liquid food mixtures. To ensure that particulates in the liquid receive sufficient heating, mathematical modeling is employed to evaluate the temperature and lethality level in the [...] Read more.

In the past two decades, aseptic processing has been implemented in the food industry to sterilize particulate liquid food mixtures. To ensure that particulates in the liquid receive sufficient heating, mathematical modeling is employed to evaluate the temperature and lethality level in the particles. We developed a model for the thermal processing of liquid foods containing cubic particles in a continuous laminar pipe flow system, comprising a tubular heat exchanger. In our simplified approach, heat transfer equations for particulate liquid foods were solved analytically and numerically to evaluate the effect of certain process parameters on the time temperature profiles of particles and the lethality value in the products. A comparison of the particles’ lethality values was made between the experiment and simulation for two different particle residence times in a case study, and the model predictions were in good agreement with experimental data. Based on modeling studies, it was found that within the range of parameters studied, an increase in flow rate and particle size resulted in a decrease in the lethality value of the particles, while an increase in particle concentration and holding tube length resulted in the opposite effect. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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Review

Jump to: Research

20 pages, 579 KiB

Open AccessReview

Gray-box Soft Sensors in Process Industry: Current Practice, and Future Prospects in Era of Big Data

by Iftikhar Ahmad, Ahsan Ayub, Manabu Kano and Izzat Iqbal Cheema

Processes 2020, 8(2), 243; https://doi.org/10.3390/pr8020243 - 20 Feb 2020

Cited by 29 | Viewed by 5594

Abstract

Virtual sensors, or soft sensors, have greatly contributed to the evolution of the sensing systems in industry. The soft sensors are process models having three fundamental categories, namely white-box (WB), black-box (BB) and gray-box (GB) models. WB models are based on process knowledge [...] Read more.

Virtual sensors, or soft sensors, have greatly contributed to the evolution of the sensing systems in industry. The soft sensors are process models having three fundamental categories, namely white-box (WB), black-box (BB) and gray-box (GB) models. WB models are based on process knowledge while the BB models are developed using data collected from the process. The GB models integrate the WB and BB models for addressing the concerns, i.e., accuracy and intuitiveness, of industrial operators. In this work, various design aspects of the GB models are discussed followed by their application in the process industry. In addition, the changes in the data-driven part of the GB models in the context of enormous amount of process data collected in Industry 4.0 are elaborated. Full article

(This article belongs to the Special Issue Advanced Methods in Process and Systems Engineering)

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