scholarly journals Modelling of optimum cascade of ideal mixing reactors

2017 ◽  
Vol 2 (20) ◽  
pp. 149-160
Author(s):  
German Efremov ◽  
Julia Geller
Keyword(s):  
Dynamic Programming ◽  
Residence Time ◽  
Order Reaction ◽  
Dynamic Programming Method ◽  
Minimum Volume ◽  
Single Application ◽  
First Order ◽  
Ideal Mixing ◽  
Minimum Residence Time ◽  
Method Of Dynamic Programming

It is discussed the using of dynamic programming method to optimize the parameters of the cascade of ideal mixing reactors, which is held isothermal first order reaction. It is found, that the minimum volume of the cascade of reactors corresponds to the minimum residence time of substance in this cascade. The optimum value of residence time for all reactors are equal and all ratio of input and output concentrations are equal, hence, and all volumes of reactors are also equal. A total volume of the cascade of reactors is less than the amount single. Application of the method of dynamic programming is illustrated with an example of the calculation of the polymerization in a cascade of four reactors according to the literature experimental data.

Development of Torrefaction Kinetics for British Columbia Softwoods

2012 ◽  
Vol 10 (1) ◽  
Author(s):  
Jianghong Peng ◽  
Xiaotao T. Bi ◽  
Jim Lim ◽  
Shabab Sokhansanj
Keyword(s):  
British Columbia ◽  
Weight Loss ◽  
Kinetic Model ◽  
Residence Time ◽  
Order Reaction ◽  
First Order Reaction ◽  
Chemical Components ◽  
First Order ◽  
One Step ◽  
Kinetics Of

Torrefaction is a thermal treatment without air or oxygen in the temperature range of 473-573 K. The pyrolysis kinetics of three chemical components (cellulose, hemicelluloses, and lignin) and wood at low temperatures of relevance to torrefaction conditions have been reviewed. A series of thermogravimetric (TG) experiments have been carried out to study the intrinsic torrefaction kinetics of major chemical components and British Columbia (BC) softwoods. The weight loss during BC softwood torrefaction was found to be mainly associated with the decomposition of hemicelluloses, although there was also certain degree of decomposition of cellulose and lignin. The weight loss of the BC softwoods during torrefaction could be approximately estimated from the chemical composition of wood species and the weight loss data for torrefaction of pure cellulose, hemicelluloses, and lignin, respectively. Based on the fitting of the TG curves of BC softwoods and three chemical components, two different torrefaciton models were proposed. The simple one-step (single-stage) kinetic model with the first order reaction can predict the reaction data reasonably well over the long residence time, with the final sample weight being strongly related to the torrefaction temperature. A two-component and one-step first order reaction kinetic model, on the other hand, gave improved agreement with data over short residence time, and can be used to guide the design and optimization of torrefaction reactors over the weight loss range of 0 to 40% at the temperature range of 533-573 K, which covers the typical range of industrially relevant operations.

scholarly journals ALGORITHMS FOR FINDING OPTIMAL POLICY FOR INTELLIGENT AGENTS BASED ON MARKOV DECISION-MAKING PROCESSES

2018 ◽  
pp. 29-32
Author(s):  
A. V. Lachikhin
Keyword(s):  
Decision Making ◽  
Dynamic Programming ◽  
Optimal Policy ◽  
Intelligent Agents ◽  
Dynamic Programming Method ◽  
Multi Agent Systems ◽  
Markov Decision ◽  
Decision Making Processes ◽  
Multi Agent ◽  
Method Of Dynamic Programming

Currently, the paradigm of intelligent agents and multi-agent systems is actively developing. The policy of agents ‘ actions can be represented as a Markov decision-making process. Such agents need methods to develop optimal policies. The purpose of this study is to review existing techniques, determine the possibility and conditions of their application. The main approaches based on linear and dynamic programming are considered. The specific algorithms used to find the extreme value of utility are given. The method of linear programming - simplex method, and the method of dynamic programming method-iteration of values are considered. The equations necessary to find the optimal policy of intelligent agent actions are given. Restrictions of application of various algorithms are considered. Conclusions the most suitable method for finding the optimal policy is the iteration of values.

scholarly journals МЕТОД ДИНАМІЧНОГО ПРОГРАМУВАННЯ ЩОДО СИНТЕЗУ ВХІДНОГО ВИМІРЮВАЛЬНОГО СИГНАЛУ ДЛЯ КОНТРОЛЮ ТЕХНІЧНОГО СТАНУ РАДІОНАВІГАЦІЙНИХ КОМПЛЕКСІВ

2019 ◽  
pp. 57-63
Author(s):  
Олена Анатоліївна Дакі
Keyword(s):  
Dynamic Programming ◽  
Water Transport ◽  
Traffic Control ◽  
Complex Form ◽  
Technical State ◽  
Dynamic Programming Method ◽  
Navigation Systems ◽  
Radio Navigation ◽  
Measuring Signal ◽  
Method Of Dynamic Programming

The article shows that the use of modern navigation systems and complexes for controlling the movement of means of water transport makes it possible to ensure safe navigation. It is substantiated that the proper functioning of the means of navigation support – radio navigation complexes – depends on their technical condition. The work substantiates and investigates mathematical expressions for calculating the parameters of input measuring signals for controlling the technical state of radio navigation complexes. The results of the analysis of methods for determining the technical state of radio electronic devices are presented, based on studies of their dynamic characteristics. It has been shown that inertial units (elements) are used to increase the noise immunity coefficient of radio navigation complexes, which increases the time to control the harmonic signal of a sinus or cosine type. It is possible to avoid this disadvantage by using test signals with a normalized spectrum, representing the sum of a certain number of useful harmonics – test signals of complex form. The purpose of the article is to develop a method of dynamic programming for the synthesis of the input measurement signal for monitoring the state of the radio navigation complexes of the means of water transport. The obtained recurrence ratio can be used to determine the characteristics of a measuring signal in the case of continuous monitoring of the output signal. To do this, you need to replace the integral in the expression for the synthesis criterion with the corresponding integral sum. The method of dynamic programming when using personal computers in comparison with other methods has the advantage since it allows you to use a cyclic program in calculations. However, although in the dynamic programming method at each stage it is necessary to calculate and memorize only one function, with a considerable amount of coordinates (with a significant amount of control parameters and rather complex systems and complexes of navigation and traffic control of sea vessels), the volume of calculations can be very large.

Leaching Kinetics of Atrazine and Inorganic Chemicals in Tilled and Orchard Soils

2014 ◽  
Vol 28 (2) ◽  
pp. 231-237 ◽  
Author(s):  
Lech W. Szajdak ◽  
Jerzy Lipiec ◽  
Anna Siczek ◽  
Artur Nosalewicz ◽  
Urszula Majewska
Keyword(s):  
Reaction Rate ◽  
Inorganic Compounds ◽  
Model Performance ◽  
Order Reaction ◽  
First Order Reaction ◽  
Order Kinetic ◽  
Time Data ◽  
First Order ◽  
Concentration Changes ◽  
Reaction Constants

Abstract The aim of this study was to verify first-order kinetic reaction rate model performance in predicting of leaching of atrazine and inorganic compounds (K+1, Fe+3, Mg+2, Mn+2, NH4 +, NO3 - and PO4 -3) from tilled and orchard silty loam soils. This model provided an excellent fit to the experimental concentration changes of the compounds vs. time data during leaching. Calculated values of the first-order reaction rate constants for the changes of all chemicals were from 3.8 to 19.0 times higher in orchard than in tilled soil. Higher first-order reaction constants for orchard than tilled soil correspond with both higher total porosity and contribution of biological pores in the former. The first order reaction constants for the leaching of chemical compounds enables prediction of the actual compound concentration and the interactions between compound and soil as affected by management system. The study demonstrates the effectiveness of simultaneous chemical and physical analyses as a tool for the understanding of leaching in variously managed soils.

The Kinetics of Glucose Decomposition with Sulfate Reduction in the Anaerobic Fluidized Bed Reactor

1993 ◽  
Vol 28 (2) ◽  
pp. 135-144 ◽  
Author(s):  
S. Matsui ◽  
R. Ikemoto Yamamoto ◽  
Y. Tsuchiya ◽  
B. Inanc
Keyword(s):  
Sulfate Reduction ◽  
Fluidized Bed ◽  
Kinetic Equations ◽  
Fluidized Bed Reactor ◽  
Order Reaction ◽  
First Order Reaction ◽  
First Order ◽  
Glucose Decomposition ◽  
Reaction Equations ◽  
Kinetics Of

Using a fluidized bed reactor, experiments on glucose decomposition with and without sulfate reduction were conducted. Glucose in the reactor was mainly decomposed into lactate and ethanol. Lactate was mainly decomposed into propionate and acetate, while ethanol was decomposed into propionate, acetate, and hydrogen. Sulfate reduction was not involved in the decomposition of glucose, lactate, and ethanol, but was related to propionate and acetate decomposition. The stepwise reactions were modeled using either a Monod expression or first order reaction kinetics in respect to the reactions. The coefficients of the kinetic equations were determined experimentally. The modified Monod and first order reaction equations were effective at predicting concentrations of glucose, lactate, ethanol, propionate, acetate, and sulfate along the beight of the reactor. With sulfate reduction, propionate was decomposed into acetate, while without sulfate reduction, accumulation of propionate was observed in the reactor. Sulfate reduction accelerated propionate conversion into acetate by decreasing the hydrogen concentration.

Complete monotonicity of entropy production in chemical reaction

1981 ◽  
Vol 46 (2) ◽  
pp. 452-456
Author(s):  
Milan Šolc
Keyword(s):  
Entropy Production ◽  
Equilibrium Constant ◽  
Chemical Reaction ◽  
Relative Entropy ◽  
Order Reaction ◽  
Complete Monotonicity ◽  
First Order Reaction ◽  
First Order ◽  
Completely Monotonic ◽  
Derivatives Of

The successive time derivatives of relative entropy and entropy production for a system with a reversible first-order reaction alternate in sign. It is proved that the relative entropy for reactions with an equilibrium constant smaller than or equal to one is completely monotonic in the whole definition interval, and for reactions with an equilibrium constant larger than one this function is completely monotonic at the beginning of the reaction and near to equilibrium.

Photocolouration of 2,4,4,6-Tetraaryl-4H-pyrans and Their Heteroanalogues: Importance of Hypervalent Photoisomers

1995 ◽  
Vol 60 (10) ◽  
pp. 1621-1633 ◽  
Author(s):  
Stanislav Böhm ◽  
Mojmír Adamec ◽  
Stanislav Nešpůrek ◽  
Josef Kuthan
Keyword(s):  
Reaction Kinetics ◽  
Absorption Spectra ◽  
Electronic Absorption ◽  
Electronic Absorption Spectra ◽  
Theoretical Data ◽  
Order Reaction ◽  
Bleaching Process ◽  
First Order ◽  
Photodegradation Products ◽  
Hypervalent Molecules

Molecular geometries of 2,4,4,6-tetraphenyl-4H-pyran (Ia), 4,4-(biphenyl-2,2e-diyl)-2,6-diphenyl-4H-pyran (Ib) and their heterocyclic isomers II-V were optimized by the PM3 method and used for the calculation of electronic absorption spectra by the CNDO/S-CI procedure. Comparison of the theoretical data with experimental UV-VIS absorption spectra made possible to select hypervalent molecules IIIa, IIIb, IVa and IVb being responsible for the photocolouration of 4H-pyrans Ia, Ib, while compounds Va, Vb, VI and VII come into account as possible photodegradation products. The bleaching process of the UV illuminated compound Ia is analyzed in terms of dispersive first-order reaction kinetics.

Kinetics and Mechanism of Hexachloroiridate(IV) Oxidation of Arsenic(III) in Acidic Perchlorate Solutions

1992 ◽  
Vol 57 (7) ◽  
pp. 1451-1458 ◽  
Author(s):  
Refat M. Hassan
Keyword(s):  
Ionic Strength ◽  
Fractional Order ◽  
Activation Parameters ◽  
Order Reaction ◽  
First Order Reaction ◽  
Intermediate Complex ◽  
Constant Ionic Strength ◽  
Kinetics Of Oxidation ◽  
First Order ◽  
Kinetics Of

The kinetics of oxidation of arsenic(III) by hexachloroiridate(IV) at lower acid concentrations and at constant ionic strength of 1.0 mol dm-3 have been investigated spectrophotometrically. A first-order reaction in [IrCl62-] and fractional order with respect to arsenic(III) have been observed. A kinetic evidence for the formation of an intermediate complex between the hydrolyzed arsenic(III) species and the oxidant was presented. The results showed that decreasing the [H+] is accompanied by an appreciable acceleration of the rate of oxidation. The activation parameters have been evaluated and a mechanism consistent with the kinetic results was suggested.

The Structure and Photochromism of 2,4,4,6-Tetraphenyl-4H-thiopyran

1992 ◽  
Vol 57 (6) ◽  
pp. 1326-1334 ◽  
Author(s):  
Jaroslav Vojtěchovský ◽  
Jindřich Hašek ◽  
Stanislav Nešpůrek ◽  
Mojmír Adamec
Keyword(s):  
Solid State ◽  
Uv Light ◽  
Order Reaction ◽  
Boat Conformation ◽  
X Rays ◽  
Exponential Time ◽  
First Order ◽  
Double Plane ◽  
The Mean ◽  
Independent Molecules

2,4,4,6-Tetraphenyl-4H-thiopyran, C29H22S, orthorhombic, Pna21, a = 17.980(4), b = 6.956(2), c = 34.562(11) Å, V = 4323(2) Å3, Z = 8, Dx = 1.237 g cm-3, F(000) = 1696, λ(CuKα) = 1.54184 A, μ = 1.372 mm-2, T = 294 K. The final R was 0.050 for the unique set of 3103 observed reflections. The central 4H-thiopyran ring forms a boat conformation for both symmetrically independent molecules with average boat angles 4.4(3) and 6.8(3)° at S and C(sp3), respectively. The mean planes of phenyls at the position 2 and 6 are turned from the double plane of 4H-thiopyran by 42.5(5) and 35.8(3)°, respectively. The investigated material undergoes a photochromic change in the solid state after irradiation with UV light or X-rays. The maximum of the new absorption band is situated at 564 nm. The non-exponential time dependence of photochromic bleaching is analysed in terms of a dispersive first-order reaction.

scholarly journals Single-Manufacturer Multi-Retailer Supply Chain Models with Discrete Stochastic Demand

2021 ◽  
Vol 13 (15) ◽  
pp. 8271
Author(s):  
Yaqing Xu ◽  
Jiang Zhang ◽  
Zihao Chen ◽  
Yihua Wei
Keyword(s):  
Dynamic Programming ◽  
Supply Chain ◽  
Computational Complexity ◽  
Stackelberg Game ◽  
Programming Model ◽  
Dynamic Programming Method ◽  
Game Model ◽  
Chain Model ◽  
Stochastic Demands ◽  
Demand Models

Although there are highly discrete stochastic demands in practical supply chain problems, they are seldom considered in the research on supply chain systems, especially the single-manufacturer multi-retailer supply chain systems. There are no significant differences between continuous and discrete demand supply chain models, but the solutions for discrete random demand models are more challenging and difficult. This paper studies a supply chain system of a single manufacturer and multiple retailers with discrete stochastic demands. Each retailer faces a random discrete demand, and the manufacturer utilizes different wholesale prices to influence each retailer’s ordering decision. Both Make-To-Order and Make-To-Stock scenarios are considered. For each scenario, the corresponding Stackelberg game model is constructed respectively. By proving a series of theorems, we transfer the solution of the game model into non-linear integer programming model, which can be easily solved by a dynamic programming method. However, with the increase in the number of retailers and the production capacity of manufacturers, the computational complexity of dynamic programming drastically increases due to the Dimension Barrier. Therefore, the Fast Fourier Transform (FFT) approach is introduced, which significantly reduces the computational complexity of solving the supply chain model.

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