Advances in Mathematical Modeling of Gas-Phase Olefin Polymerization

Mathematical modeling of olefin polymerization processes has advanced significantly, driven by factors such as the need for higher-quality end products and more environmentally-friendly processes. The modeling studies have had a wide scope, from reactant and catalyst characterization and polymer synthesis to model validation with plant data. This article reviews mathematical models developed for olefin polymerization processes. Coordination and free-radical mechanisms occurring in different types of reactors, such as fluidized bed reactor (FBR), horizontal-stirred-bed reactor (HSBR), vertical-stirred-bed reactor (VSBR), and tubular reactor are reviewed. A guideline for the development of mathematical models of gas-phase olefin polymerization processes is presented.

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OPTIMISATION OF GRADE TRANSITIONS IN AN INDUSTRIAL GAS-PHASE OLEFIN POLYMERIZATION FLUIDIZED BED REACTOR VIA NCO TRACKING

IFAC Proceedings Volumes ◽

10.3182/20050703-6-cz-1902.01581 ◽

2005 ◽

Vol 38 (1) ◽

pp. 33-38 ◽

Cited By ~ 3

Author(s):

Christos Chatzidoukas ◽

Costas Kiparissides ◽

Bala Srinivasan ◽

Dominique Bonvin

Keyword(s):

Gas Phase ◽

Fluidized Bed ◽

Olefin Polymerization ◽

Fluidized Bed Reactor

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Optimal grade transition and selection of closed-loop controllers in a gas-phase olefin polymerization fluidized bed reactor

Chemical Engineering Science ◽

10.1016/s0009-2509(03)00223-9 ◽

2003 ◽

Vol 58 (16) ◽

pp. 3643-3658 ◽

Cited By ~ 80

Author(s):

C. Chatzidoukas ◽

J.D. Perkins ◽

E.N. Pistikopoulos ◽

C. Kiparissides

Keyword(s):

Gas Phase ◽

Fluidized Bed ◽

Closed Loop ◽

Olefin Polymerization ◽

Fluidized Bed Reactor ◽

Grade Transition ◽

Selection Of

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An algebraic approach to N-soft sets with application in decision-making using TOPSIS

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202717 ◽

2021 ◽

pp. 1-21

Author(s):

Muhammad Shabir ◽

Rimsha Mushtaq ◽

Munazza Naz

Keyword(s):

Decision Making ◽

Mathematical Models ◽

Real World ◽

Algebraic Approach ◽

Multi Criteria Decision Making ◽

Commutative Monoids ◽

Soft Sets ◽

Algebraic Properties ◽

Different Types ◽

Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

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A Tool for the Analysis and Characterization of School Mathematical Models

Mathematics ◽

10.3390/math9131569 ◽

2021 ◽

Vol 9 (13) ◽

pp. 1569

Author(s):

Jesús Montejo-Gámez ◽

Elvira Fernández-Ahumada ◽

Natividad Adamuz-Povedano

Keyword(s):

Mathematical Modeling ◽

Mathematical Models ◽

Educational Research ◽

Analysis Procedure ◽

Real System ◽

The Real ◽

School Model ◽

Corresponding Analysis ◽

Three Components

This paper shows a tool for the analysis of written productions that allows for the characterization of the mathematical models that students develop when solving modeling tasks. For this purpose, different conceptualizations of mathematical models in education are discussed, paying special attention to the evidence that characterizes a school model. The discussion leads to the consideration of three components, which constitute the main categories of the proposed tool: the real system to be modeled, its mathematization and the representations used to express both. These categories and the corresponding analysis procedure are explained and illustrated through two working examples, which expose the value of the tool in establishing the foci of analysis when investigating school models, and thus, suggest modeling skills. The connection of this tool with other approaches to educational research on mathematical modeling is also discussed.

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Development of a tubular continuous flow reactor for the investigation of improved gas–solid interaction in photocatalytic CO2 reduction on TiO2

Photochemical & Photobiological Sciences ◽

10.1039/c8pp00518d ◽

2019 ◽

Vol 18 (2) ◽

pp. 314-318 ◽

Cited By ~ 5

Author(s):

Martin Dilla ◽

Ahmet E. Becerikli ◽

Alina Jakubowski ◽

Robert Schlögl ◽

Simon Ristig

Keyword(s):

Gas Phase ◽

Continuous Flow ◽

Flow Reactor ◽

Tubular Reactor ◽

Co2 Reduction ◽

Continuous Flow Reactor ◽

Reactor Geometry

Newly developed tubular reactor geometry allows intensive gas–solid interaction in photocatalytic gas-phase CO2 reduction.

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Optimization of operating parameters for gas-phase photocatalytic splitting of H2S by novel vermiculate packed tubular reactor

Journal of Environmental Management ◽

10.1016/j.jenvman.2016.08.039 ◽

2016 ◽

Vol 181 ◽

pp. 674-680 ◽

Cited By ~ 4

Author(s):

V. Preethi ◽

S. Kanmani

Keyword(s):

Gas Phase ◽

Tubular Reactor ◽

Operating Parameters

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Call for Manuscripts for the 2015 Focus Issue: Mathematical Modeling

Mathematics Teaching in the Middle School ◽

10.5951/mathteacmiddscho.18.9.0571 ◽

2013 ◽

Vol 18 (9) ◽

pp. 571

Keyword(s):

Mathematical Modeling ◽

Mathematical Models ◽

Real World ◽

The Real

This call for manuscripts is requesting articles that address how to use mathematical models to analyze, predict, and resolve issues arising in the real world.

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RELIABILITY ASSESSMENT OF AXIALLY COMPRESSED COMPOSITE CYLINDRICAL SHELLS WITH RANDOM IMPERFECTIONS

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455411004063 ◽

2011 ◽

Vol 11 (02) ◽

pp. 215-236 ◽

Cited By ~ 9

Author(s):

MATTEO BROGGI ◽

ADRIANO CALVI ◽

GERHART I. SCHUËLLER

Keyword(s):

Mathematical Models ◽

Axial Compression ◽

Cylindrical Shells ◽

Reliability Assessment ◽

Buckling Analysis ◽

Buckling Load ◽

Experimental Results ◽

Drastic Decrease ◽

Different Types ◽

Probability And Statistics

Cylindrical shells under axial compression are susceptible to buckling and hence require the development of enhanced underlying mathematical models in order to accurately predict the buckling load. Imperfections of the geometry of the cylinders may cause a drastic decrease of the buckling load and give rise to the need of advanced techniques in order to consider these imperfections in a buckling analysis. A deterministic buckling analysis is based on the use of the so-called knockdown factors, which specifies the reduction of the buckling load of the perfect shell in order to account for the inherent uncertainties in the geometry. In this paper, it is shown that these knockdown factors are overly conservative and that the fields of probability and statistics provide a mathematical vehicle for realistically modeling the imperfections. Furthermore, the influence of different types of imperfection on the buckling load are examined and validated with experimental results.

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