Stationary states of chemical reactor connected to a separation unit

Stationary states are analyzed of an isothermal chemical reactor connected by direct recycle with a separation unit from which a part of mixture enriched by the initial substances is returned into the reactor. It was found out that recycling can be the cause of the existence of multiple stationary states of system. The effect is discussed of kinetic law of chemical reaction and separation function of separation unit on the number of stationary states and their stability. The method based on the determination of trajectories of pseudostationary states of the initial substance concentrations in phase plane was used for analysis.

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Determination of catastrophic sets of a tubular chemical reactor by two-parameter continuation method

International Journal of Chemical Reactor Engineering ◽

10.1515/ijcre-2020-0135 ◽

2020 ◽

Vol 0 (0) ◽

Author(s):

Marek Berezowski

Keyword(s):

Continuation Method ◽

Extreme Points ◽

Chemical Reactor ◽

Stationary States ◽

Parameter Continuation Method ◽

It Systems ◽

Parametric Continuation ◽

Parameter Continuation ◽

Two Parameter

AbstractThe work relates to development and presentation a two-parameter continuation method for determining catastrophic sets of stationary states of a tubular chemical reactor with mass recycle. The catastrophic set is a set of extreme points occurring in the bifurcation diagrams of the reactor. There are many large IT systems that use the parametric continuation method. The most popular is AUTO’97. However, its use is sometimes not convenient. The method developed in this work allows to eliminate the necessity to use huge IT systems from the calculations. Unlike these systems, it can be inserted into the program as a short subroutine. In addition, this method eliminates time-consuming iterations from the calculations.

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Homotopic Parametric Continuation Method for Determining Stationary States of Chemical Reactors with Dispersion

Symmetry ◽

10.3390/sym13122324 ◽

2021 ◽

Vol 13 (12) ◽

pp. 2324

Author(s):

Marek Berezowski ◽

Marcin Lawnik

Keyword(s):

Mathematical Model ◽

Nonlinear Differential Equations ◽

Continuation Method ◽

Chemical Reactor ◽

Systems Of Nonlinear Equations ◽

Stationary States ◽

Physical Processes ◽

Chemical Reactors ◽

Parametric Continuation

Physical processes occurring in devices with distributed variables and a turbulent tide with a dispersion of mass and heat are often modeled using systems of nonlinear equations. Solving such a system is sometimes impossible in an analytical manner. The iterative methods, such as Newton’s method, are not always sufficiently effective in such cases. In this article, a combination of the homotopy method and the parametric continuation method was proposed to solve the system of nonlinear differential equations. These methods are symmetrical, i.e., the calculations can be made by increasing or decreasing the value of the parameters. Thanks to this approach, the determination of all roots of the system does not require any iterative method. Moreover, when the solutions of the system are close to each other, the proposed method easily determines all of them. As an example of the method use a mathematical model of a non-adiabatic catalytic pseudohomogeneous tubular chemical reactor with longitudinal dispersion was chosen.

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DETERMINATION OF QUALITY OF SURFACE IN HOME CONDITIONS

RUSSIAN ELECTRONIC SCIENTIFIC JOURNAL ◽

10.31563/2308-9644-2020-36-2-93-101 ◽

2020 ◽

Vol 36 (2) ◽

pp. 93-101

Author(s):

G.A. Irgalina ◽

Keyword(s):

Chemical Reaction ◽

Regulatory Document ◽

Organoleptic Evaluation ◽

Organoleptic Characteristics ◽

Small Grains ◽

Sour Cream ◽

Taste And Smell ◽

Home Conditions

The article reflects the assessment of the quality of sour cream at home, and considers methods for determining the quality of sour cream. Organoleptic evaluation was performed for compliance with the requirements of GOST 52092-2003 " Smetana. Technical conditions " in terms of appearance, consistency, color, taste and smell. The consistency of sour cream is determined during its mixing, while evaluating the presence of a glossy appearance of sour cream. Sour cream is considered thick if it slowly drains from the whorl. The smell is determined immediately after mixing. Then we evaluate the taste. When evaluating the quality of the samples under study, it was found that the organoleptic characteristics of the samples fully comply with the requirements of the regulatory document. Analyzing the results of the experiment, we can conclude that in the first experiment, the sour cream purchased on the market was completely dissolved, and the sour cream from the store after dissolution showed small grains. And in the second experiment, the results showed that the color did not change in the sample # 2, but under # 1 it turned blue. The basis of this experiment is a qualitative chemical reaction to starch, which is used as a thickener.

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Thermal Stresses in Chemically Hardening Elastic Media With Application to the Molding Process

Journal of Applied Mechanics ◽

10.1115/1.3423364 ◽

1974 ◽

Vol 41 (3) ◽

pp. 647-651 ◽

Cited By ~ 16

Author(s):

Myron Levitsky ◽

Bernard W. Shaffer

Keyword(s):

Residual Stress ◽

Chemical Reaction ◽

Thermal Stresses ◽

Stress Component ◽

Elastic Solid ◽

Molding Process ◽

Hardening Process ◽

Exothermic Chemical Reaction ◽

Component Parallel

A method has been formulated for the determination of thermal stresses in materials which harden in the presence of an exothermic chemical reaction. Hardening is described by the transformation of the material from an inviscid liquid-like state into an elastic solid, where intermediate states consist of a mixture of the two, in a ratio which is determined by the degree of chemical reaction. The method is illustrated in terms of an infinite slab cast between two rigid mold surfaces. It is found that the stress component normal to the slab surfaces vanishes in the residual state, so that removal of the slab from the mold leaves the remaining residual stress unchanged. On the other hand, the residual stress component parallel to the slab surfaces does not vanish. Its distribution is described as a function of the parameters of the hardening process.

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CFD Simulation of Solid Suspension for a Liquid–Solid Industrial Stirred Reactor

Applied Sciences ◽

10.3390/app11125705 ◽

2021 ◽

Vol 11 (12) ◽

pp. 5705

Author(s):

Adrian Stuparu ◽

Romeo Susan-Resiga ◽

Alin Bosioc

Keyword(s):

Chemical Reaction ◽

Cfd Simulation ◽

Simulation Analysis ◽

Solid Phase ◽

Initial Conditions ◽

Chemical Reactor ◽

Liquid Mixtures ◽

Multiphase Model ◽

Chemical Product ◽

Two Phase

The present study examines the possibility of using an industrial stirred chemical reactor, originally employed for liquid–liquid mixtures, for operating with two-phase liquid–solid suspensions. It is critical when obtaining a high-quality chemical product that the solid phase remains suspended in the liquid phase long enough that the chemical reaction takes place. The impeller was designed for the preparation of a chemical product with a prescribed composition. The present study aims at finding, using a numerical simulation analysis, if the performance of the original impeller is suitable for obtaining a new chemical product with a different composition. The Eulerian multiphase model was employed along with the renormalization (RNG) k-ε turbulence model to simulate liquid–solid flow with a free surface in a stirred tank. A sliding-mesh approach was used to model the impeller rotation with the commercial CFD code, FLUENT. The results obtained underline that 25% to 40% of the solid phase is sedimented on the lower part of the reactor, depending on the initial conditions. It results that the impeller does not perform as needed; hence, the suspension time of the solid phase is not long enough for the chemical reaction to be properly completed.

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