Stage-to-stage calculations of distillation columns by fixed-point iteration and application of the Banach fixed-point theorem

Hoffmann, Anna; Bortz, Michael; Welke, Richard J.; Burger, J.; Küfer, Karl‐Heinz; Hasse, Hans

doi:10.1016/j.ces.2017.02.006

Cited by 9 publications

(7 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Results were obtained from mathematical modeling using a nonlinear model of the rectification process of the binary methanol-water mixture. Calculation of static characteristic lies in solving systems of a multidimensional nonlinear algebraic equation, known as MESH-equations [17], which describe each contact device separately.…”

Section: Methods For Optimizing the Rectification Process Using Mobilementioning

confidence: 99%

Optimization of Rectification Process Using Mobile Control Action With Account for Criterion of Maximizing Separation Quality

Sheikus¹,

Кovalenko²,

Kotok³

et al. 2020

Eureka: PE

View full text Add to dashboard Cite

The use of mobile control action allows the improvement of technical-economical characteristics of the rectification process and allows for operation regimes that can’t be achieved with traditional control approaches. Mobility lies in the ability to choose the movement law of compound source and energy in the spatial region of apparatus. Mobile control over the rectification process can be realized by changing the column feed point. An optimal number of feed trays must be determined with consideration of cost and output performance, and also the quality of the target product. The work aimed to develop a method for calculating optimal control action, including mobile ones, on the rectification process with additional account for the criterion of maximizing quality of target product, and also, comparison of static column profiles that are optimal by different criteria. Mathematical modeling of the rectification column for separation of water-methanol mixture revealed that increasing quality requirements to target products decreases the number of the optimal feed tray. A method was described for process optimization by the normalized criterion that accounts for separation quality and power consumption. The method was used to determine optimal values of traditional (flows of heat into the column's cube and phlegm) and mobile (feed tray number) control actions that provide the best technical-economical parameters of the rectification column. A proof is presented for the existence and uniqueness of solutions for this optimization problem and the effectiveness of using mobile actions for different requirements to target. The optimal temperature profile of the culms was studied and their characteristic features that correspond to different specific and normalized optimization criteria were found

show abstract

Section: Methods For Optimizing the Rectification Process Using Mobilementioning

confidence: 99%

Optimization of Rectification Process Using Mobile Control Action With Account for Criterion of Maximizing Separation Quality

Sheikus¹,

Кovalenko²,

Kotok³

et al. 2020

Eureka: PE

View full text Add to dashboard Cite

show abstract

“…This means that the equations must be solved reliably and fast. For a conventional distillation column it was previously shown that this can be done by stage-to-stage calculations based on fixed point iterations (see Hoffmann et al 2017). In the following we will show how stage-to-stage caluclations can be used here to obtain all process variables describing a column section.…”

Section: Calculation Of All Process Variables Using a Stage-tostage Proceduresmentioning

confidence: 99%

“…The right choice depends on the considered operating unit. Hoffmann et al 2017 presented a routine for a conventional distillation column. By Seidel et al 2020 this was extended to the interconnection of multiple distillation columns.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous simulation and optimization of multiple dividing wall columns

Seidel

Ränger

Grützner

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

In this work we present a new approach that we use to simulate and optimize multiple dividing wall columns at the same time. Instead of considering all model equations as constraints and all process variables as optimization variables in a large and highly nonlinear optimization problem we only incorporate a subset of the model equations as constraints and a subset of the process variables as optimization variables. The remaining process variables are calculated from this subset by a robust and fast calculation procedure. This calculation procedure also ensures that the remaining model equations are satisfied. A comparison with the commercial process simulator Aspen Plus shows that with the new approach multiple dividing wall columns can be optimized more stable and better solutions are found. Moreover the time needed to find an optimal design decreases significantly.

show abstract

“…The mathematical basis of this network is a fixed-point iteration method [27]. The fixed-point iterative method is usually used for numerical fitting of nonlinear models [28,29].…”

Section: Overall Description Of Masa and Implementation Detailsmentioning

confidence: 99%

“…The function G(sin(θ),cos(φ))=(g1,g2)T is a contraction map and the value of the function belongs to the range of the argument. According to the fix-point iteration theorem [28], the iterative equation has a fixed point, which is the solution of Equation (17). The iteration error satisfies the following expression:||εm||1≤Lm1−L||ε1||1. where ε represents the iteration error, and the subscript represents the number of iterations.…”

Section: Overall Description Of Masa and Implementation Detailsmentioning

confidence: 99%

Self-Calibration of Nonlinear Signal Model for Angular Position Sensors by Model-Based Automatic Search Algorithm

Gao

Zhou

Hou

et al. 2019

Sensors

View full text Add to dashboard Cite

This study proposes a novel model-based automatic search algorithm to realize the self-calibration of nonlinear signal model for angular position sensors. In some high-precision angular position sensors, nonlinearity of the signal model is the main source of errors and cannot be handled effectively. By constructing a signal flow network framework and by embedding a modeling search network, the parameters of the nonlinear signal model can be searched, and the calibration signal can be obtained. The convergence of the network search process was analyzed. The relationship between the optimization threshold and the convergence accuracy was also studied in simulations. Compared with the maximum angular error reduction to 47.42% after the calibration with simplified model that ignores signal nonlinearities, the proposed scheme was able to reduce this error to 0.0025% in simulations. By implementing the technique in a capacitive angular position sensor, the experimental results showed that the maximum angular error was reduced to 1.63% compared to a reduction of 86.02% achieved with the simplified model calibration. The effects of the search network order and layer number on the calibration accuracy were also analyzed, and the optimal parameters under experimental conditions were obtained. Correspondingly, the proposed scheme is able to handle calibration of nonlinear signal model and further improve sensor accuracy.

show abstract

Stage-to-stage calculations of distillation columns by fixed-point iteration and application of the Banach fixed-point theorem

Cited by 9 publications

References 33 publications

Optimization of Rectification Process Using Mobile Control Action With Account for Criterion of Maximizing Separation Quality

Optimization of Rectification Process Using Mobile Control Action With Account for Criterion of Maximizing Separation Quality

Simultaneous simulation and optimization of multiple dividing wall columns

Self-Calibration of Nonlinear Signal Model for Angular Position Sensors by Model-Based Automatic Search Algorithm

Contact Info

Product

Resources

About