Academic literature on the topic 'Distillation apparatus – Mathematical models'

Conditions of sharp distillation were considered for zeotropic quaternary system (two pairs of components are characterized by relative volatility close to 1) and systems with one (with minimum or maximum boiling point) and two (with minimum and maximum boiling point) binary azeotropes. Regions of compositions for which sharp distillation is effective (distillate and bottom flows don't contain common components) were determined on the basis of analyzing diagrams of unit manifolds of distribution coefficients (distribution coefficients of two components are higher than one, and those of another two components - lower than one). This kind of separation can be recommended if it doesn’t cause an increase in the number of apparatuses in the separation flowsheet. If the system contains azeotropes of saddle type that can generate separatric manifolds, the possibility and expedience of sharp separation decreases. The conclusions were confirmed by simulation of the distillation process in AspenPlus V.10.0 for real and industrially important quaternary systems: ethyl acetate - benzene - toluene - butyl acetate; acetone - methanol - ethanol - propanol-2; methyl acetate - methanol - acetic acid - acetic anhydride and cyclohexene - cyclohexane - cyclohexanone - phenol. Mathematical modeling was carried out using local compositions models Wilson and NRTL-HOC. The relative error of vapor-liquid equilibrium description is less than 4%. The vapor-liquid equilibrium was simulated, a phase diagram was constructed and analyzed, the parameters of sharp distillation column operation (the number of stages, the feed-stage and reflux ratio) were determined for all systems. The effectiveness of using sharp distillation for the system with phenol was confirmed for a wide range of compositions.

Summary The interactions of heavy oil and injected steam in the mature steamflood at the Kern River Field have been extensively studied to gain insight into the effect of steam on compositional changes of oil during the recovery process and to provide input for compositional thermal simulation. Steam distillation behavior of this 13°API California oil between 300 and 467°F under a variety of process conditions, along with extensive analysis of distilled hydrocarbons were incorporated to give a more in-depth description of what is happening to the oil and what changes are occurring in the distillates or produced oil. This information was further integrated with analysis of the field distillate, "casing blow," to infer what is happening in the field. The results show that steam distillation is temperature dependent and more important than originally thought. The data developed in this study are a basis for improvement of numerical thermal models with potential for better designed steamfloods and reservoir management. The results may also impact certain logging techniques used in steamfloods and possible heavy oil upgrading techniques. Kern River oil is more than 10% distillable at 300°F and 15% distillable at 400°F in dynamic laboratory steam distillation tests at steam throughputs of four times the initial volume of oil. Distillate physical properties of density, viscosity, molecular weight, and hydrocarbon composition of the distillates changed significantly. Distillate properties increased in value with increasing steam throughput, and at higher temperatures. This information is important in the tuning of equations of state, including hydrocarbon-water interaction parameters for compositional thermal simulation. Analysis of the field distillate, "casing blow," showed properties similar to laboratory distillates at low steam throughputs. The observation of a light field distillate production in a mature steamflood compared to laboratory measurements implies that the casing system temperature is a major controlling factor in "casing blow" composition and quantity. Background The phase equilibrium behavior of reservoir fluids is an important phenomenon in petroleum production, particularly in enhanced oil recovery processes. However, phase behavior for heavy oils (<15°API) under steamflood has generally been felt to be unimportant or a minimal effect to be neglected.1 A major question exists about whether the phases and fluids in a steamflood are in equilibrium or not. Proper modeling of a reservoir production process would be expected to include knowledge of the phases and their equilibrium compositions. In heavy oil, devoid of significant C1 to C6 composition, it has been sufficient to treat the oil as a dead oil or a nonvolatile phase for steamflood modeling purposes. A history match numerical study2 of steamflood performance in the Kern River Field treated the oil as nonvolatile, and was conducted without the inclusion of hydrocarbon compositional effects. Through the classic works of Willman et al.,3 Volek and Pryor,4 and Closmann and Seba,5 steam distillation has been shown to be an important component mechanism in the overall steamflooding process.6–10 The practical limit of how much of a reservoir fluid can be distilled, is obtained in dynamic steam distillation experiments developed by Brown and Wu,11,12 extended by Hseuh, Hong, and Duerksen,13,14 and refined by Wu and co-workers.15,16 This body of work demonstrates that steam distillation is an operative mechanism in laboratory models, but it has been difficult to translate this to a quantitative contribution to the field recovery process of steamflooding. Laboratory steam distillation experiments have generally been conducted as dynamic tests, that may or may not be near equilibrium. Experiments near equilibrium with extensive analysis of the phases will yield values for the vapor-liquid equilibrium (VLE) ratios (K values), another way of assessing the importance of compositional changes in steamflooding. A major recent steam distillation study by Northrup and Venkatesan17 has been completed on the South Belridge oil. Compositional data from simple distillation and laboratory steamfloods of oils in the range 13 to 33°API, including Kern River oil, has recently been reported.18 The current report is an extension of that work to include analyses of produced field samples for the Kern River steamflood. Compositional reservoir simulators demand greater emphasis on obtaining more crude oil compositional data, which would be used as input into an equation of state (EOS) or to calculate equilibrium ratios, K values. An appreciable amount of incremental oil19,20 could be recovered by steamflooding due to steam distillation depending on the composition of the crude oil. The present work establishes laboratory data to facilitate such efforts. The EOS approach and table look-up for two-phase K values are applied in thermal numerical simulation models, even though they do not fully represent three-phase separation (steam distillation). A three-component system approximation was used by Coats and Smart21 to incorporate steam distillation effects by adding water as a component in the vapor phase. The compositional variations due to steam distillation cannot be fully described by Coats' model. A difficulty in this model is the lack of three-phase laboratory steam distillation data for high-temperature and high-pressure conditions. A future goal of this research is to obtain three-phase laboratory steam distillation data to better understand the effects of water and its vapor on the hydrocarbon separation processes at high-temperature and high-pressure conditions. This includes the investigation on both the pure hydrocarbon component/water systems and crude oil/water systems. The three-phase equilibrium ratios or K values determined from these laboratory investigations are necessary to accurately describe the effects of steam distillation in mathematical reservoir simulation. Experiment Steam Distillation Cell and Procedures. In order to describe the existing laboratory procedures, Fig. 1 is presented. This experimental setup is used to perform three different types of tests:Static system pressure test (SPT).Dynamic distillation test (DDT).Stagewise isochoric distillation test (SWID). The experimental apparatus is composed of the injection assembly (Ruska pumps and the gas bottles), the distillation cell assembly, the withdrawal assembly (condenser, separator) and the automation/data acquisition assembly. The steam distillation apparatus has been extensively described elsewhere.22

The operation of the primary oil refining unit is considered. An analysis of the operation of the operating column K-1 showed that there are noticeable fluctuations in the operating mode of the apparatus in the summer and cold season, as a result, a change in the temperature of the column top and a deterioration in the clarity of fraction rectification were observed. To study the methods of adjusting the parameters of the K-1 topping column, a computational experiment was carried out using the UniSim Design modeling system, in which the models of the apparatus and the installation model as a whole were formed. The Peng-Robinson method was used as a mathematical package for calculating the thermodynamic properties of the mixture components. Comparison of the calculated performance of the two options for the equipment of the column K-1. According to the first version, the operation of the K-1 column was simulated, in which the raw material enters the 19 tray, the hot stream is fed to the bottom of the column to the 24 tray, oil reflux to the 5 tray, acute irrigation and a partial condenser are used. Unstable technological regimes of the column top were observed in this variant in industrial conditions. To assess the fundamental possibility of changing the hardware design of the K-1 column, another option was chosen, in which there is no acute irrigation and oil irrigation, at the same time, upper circulating irrigation was introduced from the 5th to the 1st tray with cooling the flow and the technological scheme of forming and feeding the hot jet was preserved. Comparison of the fractional compositions of the topped oil showed that for the considered options, there are practically similar calculated estimates, while the use of upper circulating irrigation allows not only to unload the upper part of the distillation column from the heat load, but also to use a significant heat flow of the cooler of the upper circulating irrigation for preheating oil , which will also reduce the consumption of liquid fuel for furnaces.

<p class="R-AbstractKeywords"><span lang="EN-US">In present paper we consider the complete statements of initial-boundary problems for the modelling of various aspects of aqueous systems in Latvia. All the proposed models are the evolutionary models: all they are nonstationary and continuous qualitative models having the dynamic parameters and aimed at analysis, evaluation and forecast of aqueous systems (reservoirs, lakes and seas). In constructing these mathematical models as research tools classic apparatus of differential equations (both ODE and PDE) as well as apparatus of mathematical physics were used</span><span lang="EN-US">. </span></p>

This article presents mathematical model of evaporation of aqueous solutions of mineral salts on apparatus with mechanical recompression of water vapor and process intensification upon vacuuming. The developed mathematical model is an engineering prediction where all calculations are associated with technological flowchart of evaporator. Predictions according to the mathematical model for evaporator are exemplified for the case of 2% aqueous solution of sodium chloride evaporated to 15 wt % at distillation capacity of 30 kg/h. Engineering predictions were performed consecutively in 5 stages including material calculation of evaporator; estimation of evaporator temperature mode; hydrodynamic and thermal predictions; estimation of heat transfer coefficient. The developed mathematical model was applied to stationary direct flow evaporation using Mathcad Prime software. In order to perform high quality analysis and to verify adequacy of the mathematical model, 12 criteria were selected characterizing evaporation efficiency in evaporator. Advantages of the developed mathematical model were highlighted and substantiated, practical recommendations on its application were given upon efficiency estimation of vacuum evaporation with mechanical recompression of water vapor.

This study presents a mathematical model for the musculo-skeletal system of the locomotor apparatus. Muscle forces and joint reactions are calculated for the static problem of leaning and squatting and for the dynamic problem of walking on a level surface. Muscle forces thus calculated are compared with electromyographic (EMG) patterns. The model follows previous statically indeterminate mathematical models, from which it differs chiefly in introducing intermediate constraints (in addition to the points of insertion) for the muscles, and in setting bounds on muscle tensile stress depending on system geometry, kinematics, and loading.

There are so many energy-efficient distillation processes that it is difficult to select the best distillation process and achieve optimal design for a mixture of separation. Studying on different energy-efficient distillation processes, and we finally extracted 30 typical energy-efficient distillation processes, and established mathematical models of these processes to optimize and design. The characters and applicable conditions of every flow were obtained. According to the summary, we build a knowledge base for the expert systems. This was main content of the knowledge base of the system software. This expert system software ，based on windows XP system, was installed with Prolog and. Net.

Aerosol particle deposition rates on surfaces inside a clean room are predicted by a model developed to account for particle convection, diffusion and sedimentation. External forces acting on the particle also influence the rate of deposition. Both electrical charge build up on product surfaces and temperature gradients in the air near the product surface are known to effect the rate of deposition. A description of an electrostatic and thermophoretic force on the particle is thus included in the model. The equations governing the particle deposition process and the approach used in obtaining a solution to these equations are both described. A finite element numerical solution is detailed, followed by a description of the electrostatic force models. Finally, predictions of the model are presented with a comparison to data experimentally obtained by other researchers.

Orientador: Sandra Augusta Santos<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-10T15:15:17Z (GMT). No. of bitstreams: 1 Piasson_Diego_M.pdf: 2885536 bytes, checksum: dca4487172738420af3b139864a437bd (MD5) Previous issue date: 2008<br>Resumo: Este trabalho aborda a otimizacao de um processo de destilacao de uma mistura binaria em uma coluna de pratos, motivado pela destilacao do metanol no processo de produção do biodiesel. Mais especificamente, considera a minimização de uma função custo energetico envolvendo o calor do refervedor e a temperatura fornecida a carga de alimentação sujeita a restrições de equilibrio e canalizações. Esse problema foi formulado baseado no artigo de More A collection of Nonlinear Model Problems. Para a solução foi utilizada a metodologia dos multiplicadores de Lagrange delineada no Teorema de Karush-Kuhn-Tucker para otimização de problemas com restrições mistas. Os softwares Maxima e MatLab foram utilizados para a investigação numerica da solução do problema. Uma explanação do funcionamento da coluna tambem e feita, bem como a apresentação dos principais resultados envolvendo otimização, desde problemas irrestritos ate problemas com varias restrições mistas<br>Abstract: This work tackles the optimization of a distillation process of a binary mixture in a column with plates, which came from the methanol distillation in the production process of the biodiesel. More specifically, it considers the minimization of a cost objective function that encompass the heat rate supplied to the reboiler and the feed temperature, subject to equilibrium constraints and simple bounds. This problem was formulated based on Mor'e¿s article A collection of Nonlinear Model Problems. The Lagrange multiplier methodology was used for solve it, outlined in the Karush-Kuhn-Tucker Theorem for optimization problems with mixed constraints. The softwares Maxima and MatLab were employed for the numerical investigation of the problem solution. An explanation about the operation of the column is also included, together with the presentation of the main results encompassing optimization, from unconstrained to mixed constrained problems<br>Mestrado<br>Otimização<br>Mestre em Matemática

Orientador: Sandra Augusta Santos<br>Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-10T20:13:19Z (GMT). No. of bitstreams: 1 Padua_SuzanGrazielleBenettide_M.pdf: 4591824 bytes, checksum: 5cf7309d863c45d2b4a0f5c266f4a12b (MD5) Previous issue date: 2008<br>Resumo: Este trabalho se inicia com um breve resgate histórico da abordagem de Fermat para encontrar máximos e mínimos sem o uso de derivadas. Em termos teóricos, trás uma discussão sobre máximos e mínimos de funções em Rn, com um estudo detalhado sobre a otimizacao sem restrições, destacando a regra de Fermat e a classificacao dos pontos críticos. Trata também da otimização com restrições, por meio dos Teoremas dos Mul-tiplicadores de Lagrange para restrições de igualdade e desigualdade, e para restrições mistas, o Teorema de Karush-Kuhn-Tucker (KKT). Do ponto de vista prático, apresenta uma aplicacao envolvendo uma coluna de destilacao do metanol vinculada 'a produção do biodiesel, com a otimização da proporção de metanol destilado<br>Abstract: This work begins with a brief historical overview of Fermat¿s method to find maxima and minima without derivatives. In theoretical terms, the elements concerning maximum and minimum of functions of n variables are discussed, together with a detailed study of unconstrained optimization, focusing on the Fermat¿s rule and the classification of critical points. Constrained optimization is also analyzed, by means of the Lagrange Multilplier Theorem for equality constrained problems, and the Karush-Kuhn-Tucker (KKT) Theorem for mixed constrained optimization. In practical terms, an application concerning a distillation column of methanol associated to the biodiesel production is presented, with the optimization of the proportion of methanol in the amount of material that is removed from the top of the column<br>Mestrado<br>Otimização<br>Mestre em Matemática

Orientadores: Rubens Maciel Filho, Maria Regina Wolf Maciel<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Quimica<br>Made available in DSpace on 2018-08-15T16:03:08Z (GMT). No. of bitstreams: 1 Junqueira_TassiaLopes_M.pdf: 2287179 bytes, checksum: 791ea76c4ab924d80d0233add3519b5b (MD5) Previous issue date: 2010<br>Resumo: No Brasil, o bioetanol é usado para substituir a gasolina, compondo uma porcentagem desta ou sendo usado como combustível alternativo. Esta tendência de substituição dos combustíveis fósseis vem se fortalecendo em âmbito global, sendo necessárias, portanto, alternativas e propostas que viabilizem o aumento da produção de forma economicamente e ambientalmente sustentável. Neste contexto, a otimização energética do processo de separação do bioetanol visa à disponibilização de bagaço de cana-de-açúcar, usado como combustível na geração de vapor de processo, para a produção de bioetanol através do processo de hidrólise. Para tanto, inovações ao processo são essenciais e melhoramento na representação de modelos torna-se necessário para estudos e avaliações. Neste trabalho, simulações da etapa de destilação para a produção de álcool hidratado assim como da etapa de desidratação do bioetanol foram realizadas utilizando o simulador Aspen Plus®. Visando um estudo dentro de um cenário mais realista, a modelagem de estágios de não equilíbrio foi utilizada para prever o comportamento das colunas de destilação envolvidas. Além disso, o uso da correlação de Barros e Wolf para a determinação de eficiência na modelagem de estágios de equilíbrio em colunas de destilação foi avaliado. A comparação entre as modelagens de estágios de equilíbrio e não equilíbrio para as destilações convencional e extrativa indicou que a associação da correlação de eficiência de Barros e Wolf à modelagem de estágios de equilíbrio fornece predições satisfatórias tendo como referência a modelagem de estágios de não-equilíbrio. Para a destilação azeotrópica, o estudo de formação de duas fases líquidas na coluna foi realizado, indicando que os parâmetros de processo, como posição de alimentação, possuem influência significativa. O estudo da fermentação extrativa a vácuo, como configuração alternativa às etapas de fermentação e concentração, revelou seu potencial para redução do consumo de energia na etapa de destilação subseqüente, sendo uma alternativa viável para intensificação de processos<br>Abstract: In Brazil, bioethanol is used to replace gasoline, being a percentage of this or used as an alternative fuel. This trend of replacing fossil fuels has gained strength globally, necessitating, therefore, alternatives and proposals to enable the increase of production in an economically and environmentally sustainable way. In this context, the energy optimization of the bioethanol separation aims the provision of sugarcane bagasse, used as fuel in process steam generation, for bioethanol production through the hydrolysis process. Consequently, innovations to the process are essential and improvement in the representation of models is required for studies and evaluations. In this work, simulations of the distillation step for the production of hydrous bioethanol and the bioethanol dehydration were performed using the simulator Aspen Plus®. In order to study a more realistic scenario, nonequilibrium stage model was used to predict the behavior of the involved distillation columns. Furthermore, the use of Barros and Wolf correlation for the determination of efficiency in equilibrium stage model for distillation columns was evaluated. The comparison between equilibrium and nonequilibrium stage models for conventional and extractive distillation processes indicated that the association between Barros and Wolf efficiency correlation and equilibrium stage model provides satisfactory predictions considering the nonequilibrium stage model as reference. For azeotropic distillation, formation of two liquid phases inside the column was studied, indicating that process parameters, such as feed position, have significant influence. The study of vacuum extractive fermentation, as an alternative configuration to fermentation and concentration steps, showed its potential for reducing energy consumption in the subsequent distillation step, and it seems a viable alternative to process intensification<br>Mestrado<br>Desenvolvimento de Processos Químicos<br>Mestre em Engenharia Química

Submitted by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-10-25T17:23:14Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Geovanne_Furriel - 2016.pdf: 10594556 bytes, checksum: e02146f1c9d65005e1bc2e584ca3d281 (MD5)<br>Approved for entry into archive by Cláudia Bueno (claudiamoura18@gmail.com) on 2016-10-25T17:24:42Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Geovanne_Furriel - 2016.pdf: 10594556 bytes, checksum: e02146f1c9d65005e1bc2e584ca3d281 (MD5)<br>Made available in DSpace on 2016-10-25T17:24:42Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Dissertação_Geovanne_Furriel - 2016.pdf: 10594556 bytes, checksum: e02146f1c9d65005e1bc2e584ca3d281 (MD5) Previous issue date: 2016-08-16<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The purpose of this work is to present the development of automatic instrument for measuring soil compaction through penetration resistance. Commonly, this measurement is performed by load cells. In the proposed methodology and apparatus, the penetration resistance is directly measured by the current applied to the motor that performs penetration of the rod into the soil, thus replacing the load cell. The collected data are stored in Datalogger and further processed in order to enable analysis and the generation of maps of the surface with soil compaction values up to a certain depth. The presented results indicate greater precision and control of the fundamental parameters of data acquisition<br>O objetivo deste trabalho é apresentar o desenvolvimento de aparelho automático para medição da compactação do solo através da resistência a penetração. Comumente, esta aferição é realizada por células de carga. Na metodologia e aparelho proposto, a resistência à penetração será medida diretamente pela corrente aplicada ao motor que realiza a penetração da haste no solo, em substituição da célula de carga. Os dados coletados são armazenados em Datalogger e posteriormente tratados de forma que possibilite a análise e a geração de mapas do terreno com valores da compactação do solo até determinada profundidade. Os resultados apresentados indicam maior precisão em relação ao método utilizado e controle sobre os parâmetros fundamentais da coleta de dados.

Submitted by Erika Demachki (erikademachki@gmail.com) on 2017-01-02T20:08:50Z No. of bitstreams: 2 Dissertação - Geovanne Pereira Furriel - 2016.pdf: 10594556 bytes, checksum: e02146f1c9d65005e1bc2e584ca3d281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-01-03T09:57:56Z (GMT) No. of bitstreams: 2 Dissertação - Geovanne Pereira Furriel - 2016.pdf: 10594556 bytes, checksum: e02146f1c9d65005e1bc2e584ca3d281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Made available in DSpace on 2017-01-03T09:57:56Z (GMT). No. of bitstreams: 2 Dissertação - Geovanne Pereira Furriel - 2016.pdf: 10594556 bytes, checksum: e02146f1c9d65005e1bc2e584ca3d281 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-08-16<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The purpose of this work is to present the development of automatic instrument for measuring soil compaction through penetration resistance. Commonly, this measurement is performed by load cells. In the proposed methodology and apparatus, the penetration resistance is directly measured by the current applied to the motor that performs penetration of the rod into the soil, thus replacing the load cell. The collected data are stored in Datalogger and further processed in order to enable analysis and the generation of maps of the surface with soil compaction values up to a certain depth. The presented results indicate greater precision and control of the fundamental parameters of data acquisition.<br>O objetivo deste trabalho é apresentar o desenvolvimento de aparelho automático para medição da compactação do solo através da resistência a penetração. Comumente, esta aferição é realizada por células de carga. Na metodologia e aparelho proposto, a resistência à penetração será medida diretamente pela corrente aplicada ao motor que realiza a penetração da haste no solo, em substituição da célula de carga. Os dados coletados são armazenados em Datalogger e posteriormente tratados de forma que possibilite a análise e a geração de mapas do terreno com valores da compactação do solo até determinada profundidade. Os resultados apresentados indicam maior precisão em relação ao método utilizado e controle sobre os parâmetros fundamentais da coleta de dados.

Two basic approaches to reduce computational requirements for solving distillation problems have been studied: simplifications of the model based on physical approximations and order reduction techniques based on numerical approximations. Several problems have been studied using full and reduced-order techniques along with the following distillation models: Constant Molar Overflow, Constant Molar Holdup and Time-Dependent Molar Holdup. Steady-state results show excellent agreement in the profiles obtained using orthogonal collocation and demonstrate that with an order reduction of up to 54%, reduced-order models yield better results than physically simpler models. Step responses demonstrate that with a reduction in computing time of the order of 60% the method still provides better dynamic simulations than those obtained using physical simplifications. Frequency response data obtained from pulse tests has been used to verify that reduced-order solutions preserve the dynamic characteristics of the original full-order system while physical simplifications do not. The orthogonal collocation technique is also applied to a coupled columns scheme with good results.<br>Graduation date: 1992

Bibliography: leaves 222-230<br>xiv, 230 leaves : ill ; 30 cm.<br>Title page, contents and abstract only. The complete thesis in print form is available from the University Library.<br>Thesis (Ph.D.)--University of Adelaide, Dept. of Electrical and Electronic Engineering, 1992

O óxido de etileno (EO) é um agente de esterilização dominante na indústria dos dispositivos médicos, devido à sua efectividade e compatibilidade com a maioria dos materiais. Considerando o crescimento exponencial do mercado de dispositivos médicos sensíveis, complexos e sofisticados, assim como de conjuntos de procedimento customizados (que combinam uma grande diversidade de produtos e gama de polímeros) utilizados em actos médicos e cirúrgicos específicos, o EO emerge como o método de esterilização de eleição. A optimização deste processo constitui um desafio devido ao facto da competitividade do mercado global exigir custo-efectividade, flexibilidade e redução do tempo de ciclo necessário à colocação dos produtos no mercado, sem prejuízo da segurança e assegurando o cumprimento dos requisitos reguladores. A esterilização por EO é um processo multi-paramétrico complexo, que exige uma fase final de arejamento dos materiais. A eficácia destes processos é influenciada por diversas variáveis (e.g. temperatura, humidade, concentração do agente, material alvo), pelo que a sua optimização exige o conhecimento da influência das condições impostas e das suas relações com os produtos. A modelização matemática do processo de esterilização e arejamento permite a definição das condições óptimas para morte microbiana e desgaseificação, respectivamente. Tal permite a redução dos tempos de ciclo e/ou concentração de EO, assim como a comparação de diferentes processos de esterilização. Deste modo é possível contribuir para o desenvolvimento de processos com eficiência e flexibilidade acrescidas e a libertação paramétrica da esterilização surge assim cientificamente apoiada. Nesta dissertação foi estudada a influência das condições de processo na esterilização de dispositivos médicos por EO. Este é um processo implementado na empresa Bastos Viegas, S.A., desde 2005. Foram estudados os efeitos e interacções da temperatura, concentração de óxido de etileno e humidade relativa na inactivação do Bacillus subtilis, var. niger (ATCC 9372), o microrganismo de referência usado no controlo do processo. As experiências foram realizadas em câmaras de esterilização, com uma carga de campos cirúrgicos. Aplicou-se um planeamento experimental factorial 23 para avaliação dos efeitos das três variáveis (de acordo com limites comuns de condições operacionais) na letalidade da esterilização por EO. A inactivação do B. subtilis apresentou um comportamento sigmoidal e um modelo baseado em Gompertz foi ajustado com sucesso aos dados experimentais. Características importantes das curvas, tais como atraso inicial e taxa de inactivação foram considerados parâmetros do modelo. A temperatura e a concentração de óxido de etileno foram as variáveis que afectaram significativamente esses parâmetros, pelo que experiências adicionais foram realizadas de forma a incluir o efeito dessas variáveis do processo. Foi desenvolvido um modelo matemático para previsão da morte de B. subtilis expresso em função da temperatura e concentração de EO. Uma vez que a letalidade demonstrou estar directamente relacionada com a concentração de agente esterilizante, compreender a efectividade da esterilização por EO suscita obter a permeabilidade dos materiais ao gás, assim como o conhecimento sobre a dinâmica deste processo. A análise em tempo real da concentração de EO no espaço-livre do esterilizador tem-se tornado prática comum e o desafio neste momento é prever o seu valor no interior da carga. Foi desenhado, concebido e desenvolvido um equipamento para determinar a difusividade e a solubilidade de EO, e a permeabilidade de diversos materiais ao gás, pela metodologia de tempo de atraso. A operação deste equipamento é baseada no princípio de medição de uma mudança transiente de pressão em condições de volume e temperatura constantes (abordagem pressão-variável) e permite a determinação do tempo de atraso e do fluxo de EO em estado estacionário através de diversos materiais. As experiências foram executadas com um material de campo cirúrgico, a uma temperatura típica de esterilização, i.e. 48 ˚C, e a uma pressão de 3,2x105 Pa. As propriedades de transferência do EO no campo cirúrgico foram usadas para modelizar a sua cinética numa carga industrial do mesmo material. A segunda lei de Fick demonstrou ser adequada na descrição do processo de transferência, o que foi validado pela utilização de dosímetros que integraram a concentração de EO durante o tempo de exposição. A etapa de arejamento é importante para reduzir os resíduos de EO a um nível seguro e neste contexto, prever a desorção do EO é uma importante ferramenta para a optimização global da esterilização por EO. A cinética de desorção de EO de diferentes materiais esterilizados foi avaliada numa gama de temperaturas de arejamento entre 1,5 e 59,0 °C. Os dados experimentais seguiram um processo de difusão Fickiano e as difusividades foram estimadas para dois materiais médicos têxteis e dois poliméricos. Os resultados apresentados nesta dissertação contribuem para uma melhor compreensão da dinâmica do processo de esterilização por EO e por conseguinte, para uma optimização e controlo eficiente deste processo.<br>Ethylene oxide (EO) is a dominant sterilisation agent in medical device industry, due to its effectiveness and compatibility with most materials. Considering the exponential market growth of sensitive, complex and sophisticated medical devices, as well as custom procedure packs (that combine a large diversity of products and range of polymers) for use in specific medical and surgical procedures, EO emerges as the sterilisation method of choice. The process optimisation is a challenge, due to the fact that the global competition market requires cost effectiveness, flexibility and inherent reduction of turnaround time required to get the products to market, without compromising safety and compliance with regulatory requirements. Ethylene oxide sterilisation is a complex multi-parameter process that requires an aeration final step of the materials. The effectiveness of these processes is influenced by several variables (e.g. temperature, humidity, concentration of the agent, target material), so their optimisation requires knowledge of the influence of the conditions imposed and of their relations with the products. Mathematical modelling of the sterilisation and aeration processes allows the definition of optimal microbial inactivation and outgassing conditions, respectively. This allows cycle times and/or EO concentration reduction, as well as the comparison of different sterilisation processes. In this way it is possible to contribute to the development of processes with added efficiency and flexibility and, therefore, the parametric release of the sterilization arises scientifically supported. In this dissertation the influence of process conditions on EO sterilization of medical devices was studied. This is an implemented process in Bastos Viegas, S.A. company, since 2005. The main effects and interactions of temperature, ethylene oxide concentration and relative humidity on the inactivation of the Bacillus subtilis, var. niger (ATCC 9372), the reference microorganism used in the control of the process, were assessed. The experiments were carried out in sterilisation chambers, with a load of surgical drapes. A 23 full factorial experimental design was applied for evaluation of the effects of the three variables (under the common limits of operational conditions) on microbial lethality by EO sterilisation. The B. subtilis inactivation presented a sigmoidal behaviour and a Gompertz based model was successfully applied in experimental data fitting. Important characteristics of the curves, as initial shoulder and inactivation rate were considered model parameters. Temperature and ethylene oxide concentration were the variables that significantly affected those parameters, so additional experiments were carried out to include the effects of those process variables. A mathematical model for B. subtilis death prediction was developed, expressed in terms of temperature and EO concentration. Since the lethality was found to be directly related with the sterilant agent concentration, understanding EO sterilisation effectiveness requires attaining gas permeability of materials, as well as the knowledge of the process dynamics. The on-line analysis of EO concentration in the steriliser head-space is becoming common practice and the challenge now is to predict its value within the load. An apparatus was designed, conceived and developed for determination of EO diffusivity and solubility, and gas permeability of sheet materials, by lag time methodology. The operation of this apparatus is based upon the principle of measuring a transient change in pressure at conditions of constant volume and temperature (variable-pressure approach) and allows determination of lag time and steady state flow of EO through different materials. Experiments were carried out with a surgical drape material at a standard sterilisation temperature, i.e. 48 ˚C, and at a pressure of 3.22x105 Pa. The transport properties of EO through surgical drape were used for modelling its kinetics through an industrial load of the same material. The Fick‟s second law was adequate for describing the transport process, which was validated by the use of dosimeters that integrated EO concentration through exposure time. The aeration step is important for reducing EO residues to a safe level and in this context, prediction of EO desorption is a valuable tool for the overall optimisation of EO sterilisation. The kinetics of EO desorption, from different sterilised materials, was assessed within the range of aeration temperatures from 1.5 to 59.0 °C. The experimental data followed a Fickian diffusion process and diffusivities were estimated for two textile and two polymeric medical materials. The results presented in this dissertation contributes to a better understanding of the full dynamics of EO sterilisation and consequently, for an optimisation and efficient control of this process.

In the previous chapter, we developed a set of conceptual and mathematical tools for analyzing the models and experimental data that form the subject matter of nonlinear chemical dynamics. Here, we describe some of the key items of experimental apparatus used to obtain these data so that the reader can better appreciate the results discussed in the following chapters and can learn how to begin his or her own investigations. The first several sections are devoted to measurements of temporal behavior, with emphasis on the techniques used to monitor reactions in time and on the reactors in which these reactions are studied. The final section focuses on the study of spatial patterns and waves in chemical systems. It is possible, by methods that we shall discuss later, to reconstruct the qualitative dynamics of a system from the measurement of only a single variable. However, the more species whose concentrations can be measured, the easier it is to elucidate a mechanism and the more rigorously that mechanism can be tested. The most impressive study of multiple species in a chemical oscillator was carried out by Vidal et al. (1980), who were able, by a combination of techniques, to monitor the concentrations of Ce4 + , Ce3+ , Br2, Br-, bromomalonic acid, O2, and CO2 in the BZ reaction. In the following sections, we will look at the most widely employed techniques: spectroscopic and potentiometric methods. In principle, and occasionally in practice, essentially any technique that can be used to detect changes in concentration can be utilized to monitor the systems that we are interested in. Approaches that have been employed to date include polarography, high-pressure liquid chromatography, and calorimetry. If there are absorbing species, ultraviolet and/or visible (UV/vis) spectroscopy offers rapid response time and high sensitivity for monitoring concentrations, particularly if the species of interest have spectra with relatively little overlap. Measurements can be made in a cuvette placed in a standard UV/vis spectrophotometer, but this configuration has several limitations.

Terminology is one of the constituents of the scientific knowledge system. Mastering terminology means to learn the extent and content of notions, and also to use these terms in work. The problems of terminology formation were studied by Bogoyavlensky, Galperin, Talyzina. In the studies of Vygodsky, the inner speech derives from conversational speech in a way of changing its function and consequently its structure. Though there has not been developed complete methodic conception of forming terminology apparatus in children, the chapter is intended to describe a model that forms mathematical terminology apparatus in the process of teaching. The main methods of studies were psychology literature analysis, educational process analysis (teaching mathematics), watching and testing elementary school children in Russia.

This chapter provides an introduction to the basic notions in Mixed-Integer Linear Optimization. Sections 5.1 and 5.2 present the motivation, formulation, and outline of methods. Section 5.3 discusses the key ideas in a branch and bound framework for mixed-integer linear programming problems. A large number of optimization models have continuous and integer variables which appear linearly, and hence separably, in the objective function and constraints. These mathematical models are denoted as Mixed-Integer Linear Programming MILP problems. In many applications of MILP models the integer variables are 0 — 1 variables (i.e., binary variables), and in this chapter we will focus on this sub-class of MILP problems. A wide range of applications can be modeled as mixed-integer linear programming MILP problems. These applications have attracted a lot of attention in the field of Operations Research and include facility location and allocation problems, scheduling problems, and fixed-charge network problems. The excellent books of Nemhauser and Wolsey (1988), and Parker and Rardin (1988) provide not only an exposition to such applications but also very thorough presentation of the theory of discrete optimization. Applications of MILP models in Chemical Engineering have also received significant attention particularly in the areas of Process Synthesis, Design, and Control. These applications include (i) the minimum number of matches in heat exchanger synthesis (Papoulias and Grossmann, 1983; see also chapter 8) (ii) heat integration of sharp distillation sequences (Andrecovich and Westerberg, 1985); (iii) multicomponent multiproduct distillation column synthesis (Floudas and Anastasiadis, 1988); (iv) multiperiod heat exchanger network, and distillation system synthesis (Floudas and Grossmann, 1986; Paules and Floudas, 1988); flexibility analysis of chemical processes (Grossmann and Floudas, 1987); (v) structural properties of control systems (Georgiou and Floudas, 1989, 1990); (vi) scheduling of batch processes (e.g., Rich and Prokapakis, 1986, 1986; Kondili et al., 1993; Shah et al, 1993; Voudouris and Grossmann, 1992, 1993); and (vii) planning and scheduling of batch processes (Shah and Pantelides, 1991, Sahinidis et al, 1989, Sahinidis and Grossmann, 1991). In addition to the above applications, MILP models are employed as subproblems in the mixed-integer nonlinear optimization approaches which we will discuss in the next chapter. In this section, we will present the formulation of Mixed-Integer Linear Programming MILP problems, discuss the complexity issues, and provide a brief overview of the solution methodologies proposed for MILP models.

Molecular mechanisms and targets of cyclic guanosine monophosphate (cGMP) accounting for vascular smooth muscles (VSM) contractility are reviewed. Mathematical models of five published mechanisms are presented, and four novel mechanisms are proposed. cGMP, which is primarily produced by the nitric oxide (NO) dependent soluble guanylate cyclase (sGC), activates cGMP-dependent protein kinase (PKG). The NO/cGMP/PKG signaling pathway targets are the mechanisms that regulate cytosolic calcium ([Ca2+]i) signaling and those implicated in the Ca2+-desensitization of the contractile apparatus. In addition to previous mathematical models of cGMP-mediated molecular mechanisms targeting [Ca2+]i regulation, such as large-conductance Ca2+-activated K+ channels (BKCa), Ca2+-dependent Cl− channels (ClCa), Na+/Ca2+ exchanger (NCX), Na+/K+/Cl− cotransport (NKCC), and Na+/K+-ATPase (NKA), other four novel mechanisms are proposed here based on the existing but perhaps overlooked experimental results. These are the effects of cGMP on the sarco−/endo- plasmic reticulum Ca2+-ATPase (SERCA), the plasma membrane Ca2+-ATPase (PMCA), the inositol 1,4,5-trisphosphate (IP3) receptor channels type 1 (IP3R1), and on the myosin light chain phosphatase (MLCP), which is implicated in the Ca2+-desensitization. Different modeling approaches are presented and discussed, and novel model descriptions are proposed.

The mode of operation of induction motors (IMs) affects their performance. In most cases, motors are optimally designed for steady state operation. When operating in other modes, additional attention is required to the problems of energy efficiency. Induction motors are the most common type of electromechanical energy converters, and a significant part of them operate under conditions of periodic changes in the load torque. The work is devoted to solving the problem of increasing the energy efficiency of asynchronous motors of electromechanical systems with a periodic load, including pumping and compressor equipment. The traditional solution to this problem for compressor equipment is the optimal design of an IM under static conditions, as well as the use of flywheels, the use of an IM with an increased slip value and controlled IM with a squirrel-cage rotor and with frequency converters. In this work, the modes of operation of asynchronous motors with periodic loading are investigated. For this, complex mathematical models are developed in the simulation system. Such models are effective in modeling taking into account periodic load changes: repetitive transient processes, their possible asymmetry and non-sinusoidality, increased influence of nonlinearity of electromagnetic parameters. In complex mathematical modeling, the mutual influence of the constituent parts of the electromechanical system is taken into account. Simulation allowed quantifying the deterioration in energy efficiency under intermittent loading, in comparison with static modes. Criteria for evaluating quasi-static modes have been developed and areas of critical decrease in efficiency have been determined. The paper proposes and demonstrates a methodology for solving this problem. For this purpose, tools have been created for the optimal design of asynchronous motors as part of electromechanical systems with periodic loading. These tools include: complex mathematical models of electromechanical systems with asynchronous motors with periodic load, mathematical tools for determining the parameters of quasi-steady-state modes, the methodology of optimal design based on the criterion of the maximum efficiency of processes under quasi-steady-state modes of operation. The possibilities, advantages and prospects of using the developed mathemati-cal apparatus for solving a number of problems to improve the efficiency of electric drives of compressor and pumping equipment are demonstrated. It is shown that by taking into account quasi-static processes, the use of complex mathematical models for the optimal design of asynchronous motors with a periodic load provides an in-crease in efficiency up to 8 ... 10%, relative to the indicators of motors that are de-signed without taking into account the quasi-static modes. The areas of intense quasi-steady-state modes are determined using the devel-oped criterion. In these areas, there is a critical decrease in efficiency compared to continuous load operation. A decrease in efficiency is associated with a decrease in the amount of kinetic energy of the rotating parts compared to the amount of electromagnetic energy. In connection with the development of a frequency-controlled asynchronous drive of mechanisms with a periodic load, the relevance of design taking into account the peculiarities of quasi-static has increased significantly. For example, a variable frequency drive of a refrigerator compressor or a heat pump can increase energy efficiency up to 40%, but at low speeds, due to a decrease in kinetic energy, the efficiency can decrease to 10 ... 15%, unless a special design methodology is applied. This problem can be solved by using the complex mathematical modeling tools developed in the article.

The analysis of multi-criteria techniques showed that at present, methods based on the mechanism of pairwise comparison are widely used. This may be due to the fact that it is easier for experts to compare objects in pairs than, for example, to give them some ordering (ranking). In turn, such methods have a number of disad-vantages, for example, a limitation on the number of elements compared in pairs, the need to evaluate all available elements (objects, alternatives), a high level of con-sistency of expert assessments, etc. A modification of the analytic hierarchy process (AHP) method based on the mathematical apparatus of a mathematical theory of evidence and a theory of plausible and paradoxical reasoning has been considered as approach that allows obtaining more effective results of pairwise comparison, as well as taking into account various forms of interaction of expert judgments expressed on the same set of initial data and factors such as uncertainty, inaccuracy, fuzziness and incompleteness of expert information. As part of solving the problem of ranking group expert assessments, mathematical models of expert judgments (evidence, assessments) have been developed that allow processing the results of an expert survey in order to construct final rank-orderings of group expert assessments under multi-criteria, multi-alternative, uncertainty and conflicting (contradictory) expert judgments. Alternative approaches of evidence combination in the framework of the Dempster-Shafer model are investigated and a method for constructing a final ranking is proposed, which is based on the complex use of the conjunctive consensus evidence combination rules (Dempster’s, Yager’s, Zhang’s, Inagaki’s, Smets’ rules). The proposed technique takes into account the degree of difference and the structure of individual groups of evidence to choose the order of expert judgments combination. This allows to make full use of the original expert information and exclude situations in which part of the expert information may be lost (for example, when trying to combine contradictory evidence). An adaptive algorithm for choosing the optimal combination rule has been proposed. The adaptability of the algorithm lies in the fact that, depending on the formed set of criteria, one of the considered combination rules is selected for each pair of expert judgments that are combined. As criteria for choosing the rules, the following were considered: information about data sources (experts), their competence, the nature of the analyzed data (information about conflicts and consensus; information about the degree of interaction and structure of expert evidence, etc.). A methodology for synthesis of information technology and a generalized structure of information technology for decision-making are proposed for solving the problem of structuring expert assessments under multi-criteria and complex forms of ignorance based on the methods of the theory of evidence and the theory of plausible and paradoxical reasoning. The practical implementation of the proposed information technology synthesis technique for construction of the final rank-ordering of the analyzed objects is considered on the example of solving the problem of choosing a geographic information systems.

The article describes one of the possible models of fuzzy multiparametric assessment of students' competencies. The mathematical apparatus of the model is described, taking into account the requirements of fuzzy logic. The concept of competence indicators as generalized characteristics of competencies and as learning outcomes is specified; their comparability with labor functions and (or) labor actions and with the set of KS (Knowledge skills) is taken into account. This model is considered in the synthesis of the "discipline" - "project" categories in the education system.

The purpose of this study is to establish a new monitoring technique to detect the state of sliding portion and connecting portion, where it is known that some failure often occurs. In this paper, we examined the feasibility of estimation for the state in which the support rigidity of the sliding portion using the vibration characteristics in the experiment for a small experimental equipment and in the eigenvalue analysis based on the mathematical model. To simulate the change of the rigidity for the sliding portion, we employ two kinds of material, carbon and molybdenum steel as the ring bush of the ground support. To obtain the natural frequencies and modes for both the case, the impact tests are carried out for several crank angles in the small experimental apparatus as the vibration characteristics is depend upon the crank angle. Based on the obtained natural frequencies, the parameter identification was carried out. As a result, it showed the possibility of estimating the characteristics of the sliding portion by focusing on the natural vibration characteristics.

To model complex structure with numerous components and solids, the condition of contact between two solids must be adequately described. In this investigation, a special apparatus developed to analyze the condition of contact between two solids is presented. With this apparatus, experimental tests can be performed to determine the condition of friction (static and dynamic and the transition from one to the other) and the thermal and electrical contact resistances between two disk shaped rotating samples of different nature at various temperatures (from ambient up to 1000°C) and contact pressures. To determine the evolution of the friction mechanism as a function of the relative displacement between the solids, an inverse mathematical method has been developed and is presented. The results obtained with the apparatus proposed will provide a better understanding of the contact condition and could be easily incorporated in future mathematical models describing the behaviour of complex, multi layered structures.

In the first part of this paper the equations and results for the transient models developed for the SAS components in isolation have been thoroughly explained together with the assumptions made and the limitations that arose subsequently. This second part explains the work carried out to couple the individual components into a single network with the aim of assembling a dynamic model for the whole engine air system. To the authors’ knowledge the models published hitherto are only valid for steady or quasi steady state. It is then the case that the differential equations that govern the fluid movement are not time discretised and thus can be solved in a relatively straightforward fashion. Unlike during transients, the flow is not supposed to reach sonic conditions anywhere within the network and most important, flow reversal cannot be accounted for. This study deals with the mathematical apparatus utilised and the difficulties found to integrate the single components into a network to predict the transient operation of the air system. The flow regime — subsonic or supersonic — and its direction have deemed the choice of the appropriate numerical and physical boundary conditions at the components’ interface for each time step particularly important. The integration is successfully validated against a known numerical benchmark — the De Haller test. A parametric analysis is then carried out to assess the effect of the length of the pipes that connect the system cavities on the pressure evolution in a downstream reservoir. Transient flow through connecting pipes is dependent on the fluid inertia and so it takes a certain time for the information to be transported from one end of the duct to the other. As it would be expected, the system with a longer pipe is found to have a longer settling time. Finally, the work concludes with the analysis of the flow evolution in the secondary air system during a shaft failure event. This work is intended to continue to address the limitations imposed by some of the assumptions made for an extended and more accurate applicability of the tool.

Флагманом современной географии выступает моделирование географических систем и процессов их функционирования, базирующееся на огромных базах данных и алгоритмах многомерного компьютерного моделирования поведения сложных многосвязных систем. Сам процесс моделирования базируется на мощном аппарате математического анализа и статистической обработки базовых параметров объектов, на основе которых производится построение имитационных моделей их функционирования и развития. Речной бассейн является самым распространенным на поверхности суши природным объектом, обладающий отчетливо выраженными границами, структурной организацией, иерархией, относительной замкнутостью потоков вещества и энергии. При описании структуры водосборного бассейна речной системы традиционно применяются порядковые классификации. Порядковая классификация водотоков базируется на основополагающем свойстве речных потоков образовывать при последовательном слиянии древовидную структуру со ступенчатым нарастанием основных параметров системы. Стабильность структуры при этом поддерживается непрерывной деятельностью мощных потоков вещества и энергии. Широкое применение получила нисходящая порядковая классификация Р. Хортона 7, в основу которой легло положение о том, что неразветвленные элементарные водотоки сходны в разных условиях и должны иметь наименьший 1й порядок, образуя при слиянии водоток 2го порядка, в то время как водотоки 2го порядка образуют водоток 3го порядка и т. д. Также Хортоном, на основе анализа структуры речных сетей и их бассейнов были предложены законы соотношения основных характеристик водотоков разных порядков. Позднее порядковая классификация Хортона была доработана Стралером 6, который исключил понятие главной реки , которая на всем своем протяжении имеет максимальный порядок, хотя структурно состоит из множества разнопорядковых сегментов. Данные классификации сейчас принято рассматривать в едином контексте как классификацию ХортонаСтралера. Еще в XIX веке был высказан тезис о том, что водоразделы и тальвеги являются главными структурными линиями рельефа и находятся в тесной взаимосвязи 2, определяя распределение потоков вещества и энергии в водосборном бассейне. С использованием классификации водотоков ХортонаСтралера предложен принцип классификации водоразделов. На основе авторской методики обработки цифровых моделей рельефа (ЦМР) с использованием инструментов ГИС было апробировано использование порядковых характеристик водоразделов для получения детальной информации о вариациях основных характеристик однопорядковых элементов речной сети в зависимости от порядка водораздела в пределах бассейна реки Уссури.The flagship of modern geography is the modeling of geographical systems and the processes of their functioning, based on huge databases and algorithms for multidimensional computer modeling of the behavior of complex multiply connected systems. The modeling process itself is based on a powerful apparatus for mathematical analysis and statistical processing of the basic parameters of objects, based on which simulation models of their functioning and development are built. The river basin is the most widespread natural object on the land surface, which has distinct boundaries, structural organization, hierarchy, and relative isolation of matter and energy flows. In describing the structure of the catchment of a river system, ordinal classifications are traditionally applied. The ordinal classification of watercourses is based on the fundamental property of river flows to form a tree structure with successive merging with a stepwise increase in the main parameters of the system. The stability of the structure is supported by the continuous activity of powerful flows of matter and energy. The descending ordinal classification of R. Horton 7 was widely used, which was based on the proposition that unbranched elementary watercourses are similar under different conditions and should have the smallest 1st order, forming second order watercourses at the time how 2nd order watercourses form a 3rd order watercourse, etc. Also, Horton, based on an analysis of the structure of river networks and their basins, proposed the laws of correlation of the main characteristics of watercourses of different orders. Later, the Horton ordinal classification was finalized by A. Straler 6, who excluded the concept of the main river, which along its entire length has the maximum order, although it structurally consists of many differentorder segments. Classification data is now considered to be considered in a single context as the HortonStrahler classification. As early as the 19th century, the thesis was expressed that watersheds and thalwegs are the main structural lines of the relief and are closely interconnected 2, determining the distribution of matter and energy flows in the catchment. Using the classification of HortonStrahler watercourses, the principle of the classification of watersheds is proposed. Based on the authors methodology for processing digital elevation models (DEM) using GIS tools, the use of ordinal characteristics of watersheds was tested to obtain detailed information on variations of the main characteristics of singleorder elements of the river network depending on the order of the watershed within the Ussuri River Basin.