scholarly journals Study of a mathematical model of gasoline catalytic reforming by sensitivity analysis methods

2020 ◽  
pp. 440-451
Author(s):  
Л.Ф. Сафиуллина ◽  
К.Ф. Коледина ◽  
И.М. Губайдуллин ◽  
Р.З. Зайнуллин
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Kinetic Model ◽  
Point Of View ◽  
Oil Refining ◽  
Chemical Transformations ◽  
Catalytic Reforming ◽  
Analysis Methods ◽  
Realistic Description ◽  
General Dynamics

Для изучения одного из важнейших процессов нефтепереработки — каталитического риформинга, требуется детализированная кинетическая модель. При разработке кинетической модели возникает сложность в связи с большим количеством компонентов реакционной смеси и большим количеством стадий химических превращений. Альтернативой могут быть сокращенные механизмы реакций, которые применимы для решения задачи и обеспечивают реалистичное описание процесса. В данной работе для анализа кинетической модели и получения сокращенного механизма реакции используются методы анализа чувствительности математической модели. Применение указанной методики позволяет выявить стадии каталитического риформинга бензина, наименее влияющие на общую динамику изменения концентраций значимых веществ реакции. Исследовано влияние исключения данных стадий на кинетику процесса с химической точки зрения. Предложена редуцированная схема каталитического риформинга бензина с исключением данных стадий. Редуцированная схема обеспечивает вполне удовлетворительное согласие как по профилям температуры, так и по профилям концентраций значимых веществ реакции. A detailed kinetic model is required to study one of the most important oil refining processes known as catalytic reforming. The difficulty arises in connection with a large number of components of the reaction mixture and a large number of stages of chemical transformations in developing the kinetic model. An alternative may be reduced reaction mechanisms that are applicable to solve the problem and provide a realistic description of the process. In this paper, to analyze the kinetic model and to obtain an abbreviated reaction mechanism, the sensitivity analysis methods of the mathematical model are used. The least influential stages of catalytic reforming of gasoline, which do not affect the general dynamics of changes in the concentrations of significant reaction substances are identified using this technique. The effect of eliminating these stages on the kinetics of the process from the chemical point of view is analyzed. A reduced scheme for catalytic reforming of gasoline by excluding these stages is proposed. A reduced scheme provides a quite satisfactory agreement both in temperature profiles and in concentration profiles of significant substances.

scholarly journals Sensitivity analysis of the mathematical model of catalytic reforming of gasoline

2019 ◽  
Vol 3 (2) ◽  
pp. 43-53
Author(s):  
L. F. Safiullina ◽  
◽  
I. M. Gubaydullin ◽  
K. F. Koledina ◽  
R. Z. Zaynullin ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Catalytic Reforming ◽  
The Mathematical Model

On the displacements of the contours of the optic-electronic space images. Mathematical modeling of displacement

2017 ◽  
Vol 992 (4) ◽  
pp. 32-38 ◽  
Author(s):  
E.G. Voronin
Keyword(s):  
Mathematical Modeling ◽  
Remote Sensing ◽  
Mathematical Model ◽  
Point Of View ◽  
Design Features ◽  
Space Images ◽  
Electronic Imaging ◽  
Measuring Accuracy ◽  
Physical Laws

The article opens a cycle of three consecutive publications dedicated to the phenomenon of the displacement of the same points in overlapping scans obtained adjacent CCD matrices with opto-electronic imagery. This phenomenon was noticed by other authors, but the proposed explanation for the origin of displacements and the resulting estimates are insufficient, and developed their solutions seem controversial from the point of view of recovery of the measuring accuracy of opticalelectronic space images, determined by the physical laws of their formation. In the first article the mathematical modeling of the expected displacements based on the design features of a scanning opto-electronic imaging equipment. It is shown that actual bias cannot be forecast, because they include additional terms, which may be gross, systematic and random values. The proposed algorithm for computing the most probable values of the additional displacement and ways to address some of the systematic components of these displacements in a mathematical model of optical-electronic remote sensing.

scholarly journals Comparing sensitivity analysis methods to advance lumped watershed model identification and evaluation

2007 ◽  
Vol 11 (2) ◽  
pp. 793-817 ◽  
Author(s):  
Y. Tang ◽  
P. Reed ◽  
T. Wagener ◽  
K. van Werkhoven
Keyword(s):  
Sensitivity Analysis ◽  
Model Identification ◽  
Local Analysis ◽  
Time Interval ◽  
Watershed Model ◽  
Soil Moisture Accounting ◽  
Analysis Methods ◽  
Accounting Model ◽  
Sobol’S Method ◽  
Comparative Results

Abstract. This study seeks to identify sensitivity tools that will advance our understanding of lumped hydrologic models for the purposes of model improvement, calibration efficiency and improved measurement schemes. Four sensitivity analysis methods were tested: (1) local analysis using parameter estimation software (PEST), (2) regional sensitivity analysis (RSA), (3) analysis of variance (ANOVA), and (4) Sobol's method. The methods' relative efficiencies and effectiveness have been analyzed and compared. These four sensitivity methods were applied to the lumped Sacramento soil moisture accounting model (SAC-SMA) coupled with SNOW-17. Results from this study characterize model sensitivities for two medium sized watersheds within the Juniata River Basin in Pennsylvania, USA. Comparative results for the 4 sensitivity methods are presented for a 3-year time series with 1 h, 6 h, and 24 h time intervals. The results of this study show that model parameter sensitivities are heavily impacted by the choice of analysis method as well as the model time interval. Differences between the two adjacent watersheds also suggest strong influences of local physical characteristics on the sensitivity methods' results. This study also contributes a comprehensive assessment of the repeatability, robustness, efficiency, and ease-of-implementation of the four sensitivity methods. Overall ANOVA and Sobol's method were shown to be superior to RSA and PEST. Relative to one another, ANOVA has reduced computational requirements and Sobol's method yielded more robust sensitivity rankings.

A note on design-based versus model-based variance estimation in stereology

2002 ◽  
Vol 34 (03) ◽  
pp. 484-490 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Mathematical Model ◽  
Original Problem ◽  
Variance Estimation ◽  
Point Of View ◽  
Systematic Sampling ◽  
Variance Estimator ◽  
Shape Model ◽  
Model Based ◽  
Versus Model ◽  
Special Case

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

Effective Properties of Superconducting and Superfluid Composites

1998 ◽  
Vol 12 (29n31) ◽  
pp. 3063-3073 ◽  
Author(s):  
Leonid Berlyand
Keyword(s):  
Mathematical Model ◽  
Linear Problem ◽  
Effective Properties ◽  
Point Of View ◽  
Periodicity Cell ◽  
Unit Size ◽  
Composite Media ◽  
Homogenization Procedure

We consider a mathematical model which describes an ideal superfluid with a large number of thin insulating rods and an ideal superconductor reinforced by such rods. We suggest a homogenization procedure for calculating effective properties of both composite media. From the numerical point of view the procedure amounts to solving a linear problem in a periodicity cell of unit size.

scholarly journals The Application and Implications of Novel Deterministic Sensitivity Analysis Methods

2020 ◽  
Vol 39 (1) ◽  
pp. 1-17
Author(s):  
Rick A. Vreman ◽  
Joost W. Geenen ◽  
Saskia Knies ◽  
Aukje K. Mantel-Teeuwisse ◽  
Hubert G. M. Leufkens ◽  
...  
Keyword(s):  
Sensitivity Analysis ◽  
Deterministic Sensitivity Analysis ◽  
Analysis Methods

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

A Sensitivity Analysis Based Method for Robot Calibration

1992 ◽  
Author(s):  
S. Kaizerman ◽  
B. Benhabib ◽  
R. G. Fenton ◽  
G. Zak
Keyword(s):  
Sensitivity Analysis ◽  
Kinematic Model ◽  
Calibration Procedure ◽  
Inverse Kinematic ◽  
Model Parameters ◽  
Robot Calibration ◽  
Adjoint Sensitivity ◽  
Analysis Methods ◽  
The Matrix ◽  
Direct Sensitivity

Abstract A new robot kinematic calibration procedure is presented. The parameters of the kinematic model are estimated through a relationship established between the deviations in the joint variables and the deviations in the model parameters. Thus, the new method can be classified as an inverse calibration procedure. Using suitable sensitivity analysis methods, the matrix of the partial derivatives of joint variables with respect to robot parameters is calculated without having explicit expressions of joint variables as a function of task space coordinates (closed inverse kinematic solution). This matrix provides the relationship between the changes in the joint variables and the changes in the parameter values required for the calibration. Two deterministic sensitivity analysis methods are applied, namely the Direct Sensitivity Approach and the Adjoint Sensitivity Method. The new calibration procedure was successfully tested by the simulated calibrations of a two degree of freedom revolute-joint planar manipulator.

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