Numerical Methods for Mathematical Models of Heterogeneous Catalytic Fixed Bed Chemical Reactors

2012 ◽  
Vol 11 (1) ◽  
pp. 49-64
Author(s):  
P. D. Devika ◽  
P. A. Dinesh ◽  
G. Padmavathi ◽  
Rama Krishna Prasad
Keyword(s):  
Numerical Methods ◽  
Mathematical Models ◽  
Fixed Bed ◽  
Differential Algebraic Equations ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Chemical Reactors ◽  
Catalytic Systems ◽  
Heterogeneous Catalytic ◽  
Catalytic Material

Mathematical modeling of chemical reactors is of immense interest and of enormous use in the chemical industries. The detailed modeling of heterogeneous catalytic systems is challenging because of the unknown nature of new catalytic material and also the transient behavior of such catalytic systems. The solution of mathematical models can be used to understand the interested physical systems. In addition, the solution can also be used to predict the unknown values which would have been otherwise obtained by conducting the actual experiments. Such solutions of the mathematical models involving ordinary/partial, linear/non-linear, differential/algebraic equations can be determined by using suitable analytical or numerical methods. The present work involves the development of mathematical methods and models to increase the understanding between the model parameters and also to decrease the number of laboratory experiments. In view of this, a detailed modeling of heterogeneous catalytic chemical reactor systems has been considered for the present study.

Numerical methods for differential algebraic equations

Acta Numerica ◽  
1992 ◽  
Vol 1 ◽  
pp. 141-198 ◽  
Author(s):  
Roswitha März
Keyword(s):  
Numerical Methods ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Image Position

Differential algebraic equations (DAE) are special implicit ordinary differential equations (ODE)where the partial Jacobian f′y(y, x, t) is singular for all values of its arguments.

A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock

2021 ◽  
Author(s):  
Laura D’Orsi ◽  
Luciano Curcio ◽  
Fabio Cibella ◽  
Alessandro Borri ◽  
Lilach Gavish ◽  
...  
Keyword(s):  
Heart Rate ◽  
Cardiac Output ◽  
Arterial Pressure ◽  
Hemorrhagic Shock ◽  
Time Course ◽  
Differential Algebraic Equations ◽  
Model Parameters ◽  
Algebraic Equations ◽  
Cardiovascular Dynamics ◽  
Compensation Mechanisms

Abstract A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

Advances in fixed-bed reactor modeling using particle-resolved computational fluid dynamics (CFD)

2019 ◽  
Vol 35 (2) ◽  
pp. 139-190 ◽  
Author(s):  
Nico Jurtz ◽  
Matthias Kraume ◽  
Gregor D. Wehinger
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Fixed Bed ◽  
Review Article ◽  
Catalyst Design ◽  
Fixed Bed Reactor ◽  
Reactor Modeling ◽  
Catalytic Systems ◽  
Heterogeneous Catalytic ◽  
Computational Fluid Dynamics Cfd

Abstract In 2006, Dixon et al. published the comprehensive review article entitled “Packed tubular reactor modeling and catalyst design using computational fluid dynamics.” More than one decade later, many researchers have contributed to novel insights, as well as a deeper understanding of the topic. Likewise, complexity has grown and new issues have arisen, for example, by coupling microkinetics with computational fluid dynamics (CFD). In this review article, the latest advances are summarized in the field of modeling fixed-bed reactors with particle-resolved CFD, i.e. a geometric resolution of every pellet in the bed. The current challenges of the detailed modeling are described, i.e. packing generation, meshing, and solving with an emphasis on coupling microkinetics with CFD. Applications of this detailed approach are discussed, i.e. fluid dynamics and pressure drop, dispersion, heat and mass transfer, as well as heterogeneous catalytic systems. Finally, conclusions and future prospects are presented.

A Geometric Derivation of the Equations of Motion for Mechanical Systems With Scleronomic Constraints

2015 ◽  
Author(s):  
Sotirios Natsiavas ◽  
Elias Paraskevopoulos
Keyword(s):  
Numerical Methods ◽  
Lagrange Multipliers ◽  
Equations Of Motion ◽  
Mechanical Systems ◽  
Main Idea ◽  
Constraint Equation ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Motion Constraints ◽  
Stiffness Properties

A new set of equations of motion is presented for a class of mechanical systems subjected to equality motion constraints. Specifically, the systems examined satisfy a set of holonomic and/or nonholonomic scleronomic constraints. The main idea is to consider the equations describing the action of the constraints as an integral part of the overall process leading to the equations of motion. The constraints are incorporated one by one, in a process analogous to that used for setting up the equations of motion. This proves to be equivalent to assigning appropriate inertia, damping and stiffness properties to each constraint equation and leads to a system of second order ordinary differential equations for both the coordinates and the Lagrange multipliers associated to the motion constraints automatically. This brings considerable advantages, avoiding problems related to systems of differential-algebraic equations or penalty formulations. Apart from its theoretical value, this set of equations is well-suited for developing new robust and accurate numerical methods.

Numerical Methods for Parameter Estimation in Nonlinear Differential Algebraic Equations

2007 ◽  
Vol 30 (2) ◽  
pp. 376-408 ◽  
Author(s):  
Hans Georg Bock ◽  
Ekaterina Kostina ◽  
Johannes P. Schlöder
Keyword(s):  
Parameter Estimation ◽  
Numerical Methods ◽  
Differential Algebraic Equations ◽  
Algebraic Equations
Sign in / Sign up

Export Citation Format

Share Document