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1

Steady state characteristics of a three-phase fluidizedbed bioreactor with partial biomass recirculation

Skoneczny Szymon, Tabiś Bolesław

Chemical and Process Engineering

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2019

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Vol. 40, nr 1

77-–86

EN

The paper presents modeling and simulation results of the operation of a three-phase fluidized bedbioreactorwith partial recirculation of biomass. The proposed quantitative description of the bioreactortakes into account biomass growth on inert carriers, microorganisms decay and interphase biomasstransfer. Stationary characteristicsof the bioreactorand local stability of steady-states were determined.The influence of microbiological growth kinetics on the multiplicity of steady-states was discussed.The relationship between biofilm growth and boundaries of fluidized bed existence was shown

2

Dynamical and technological consequences of multiple isolas of steady states in a catalytic fluidised-bed reactor

Bizon K.

Chemical and Process Engineering

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2017

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Vol. 38, nr 3

411--422

EN

Steady-state characteristics of a catalytic fluidised bed reactor and its dynamical consequences are analyzed. The occurrence of an untypical steady-state structure manifesting in a form of multiple isolas is described. A two-phase bubbling bed model is used for a quantitative description of the bed of catalyst. The influence of heat exchange intensity and a fluidisation ratio onto the generation of isolated solution branches is presented for two kinetic schemes. Dynamical consequences of the coexistence of such untypical branches of steady states are presented. The impact of linear growth of the fluidisation ratio and step change of the cooling medium temperature onto the desired product yield is analyzed. The results presented in this study confirm that the identification of a region of the occurrence of multiple isolas is important due to their strong impact both on the process start-up and its control.

3

Nonlinear Dynamics of a Controlled Stirred Tank Bioreactor With Predator-Prey Relationship

Tabiś B., Skoneczny S., Stryjewski W. S.

Chemical and Process Engineering

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2014

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Vol. 35, nr 3

349--360

EN

The paper presents the dynamic characteristics of a continuous tank bioreactor for microbiological process, with a developed predator-prey food chain. The presence of the predator microorganism considerably influences the position and stability character of steady-states. There appears to exist a wide range of unstable steady-states and high-amplitude oscillations of state variables. Without automatic control, the system can operate only in unsteady conditions. From technological point of view, this circumstance is unfavorable. It was shown that oscillations can be removed by employing automatic control with continuous P or PI controllers. Moreover, the use of a controller with integrating element causes removal of the predator from the bioreactor. The paper discusses an application of this phenomenon for practical purposes.

4

Model matematyczny zespołu transformatorowego z trapezoidalnym zakresem regulacji przekładni zespolonej do analiz ustalonych i quasi-ustalonych stanów pracy symetrycznych fazowo

Ziemianek S.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 6

143--151

PL

Przedstawiono metodę budowy modelu matematycznego dla jednego z częściej stosowanych (przy sprzęganiu sieci o różnych napięciach znamionowych) zespołu transformatorowego (składającego się z trzech jednostek) z regulacją przekładni zespolonej w trapezoidalnym zakresie.

EN

The purpose of this paper is to give a method of creating mathematical model for commonly known (in the two voltage networks coupling) three units transformer set with complex ratio control (in the trapezium form).

5

Model matematyczny uninapięciowego przesuwnika fazowego (z symetrycznym napięciem dodawczym) do analiz ustalonych i quasi-ustalonych stanów pracy symetrycznych fazowo

Ziemianek S.

Przegląd Elektrotechniczny

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2013

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R. 89, nr 8

16--22

PL

Przedstawiono metodę budowy modelu matematycznego dla jednego z częściej stosowanych (w sieciach o pojedynczym napięciu znamionowym) wykonań przesuwnika fazowego (z symetrycznym napięciem dodawczym) do analiz ustalonych i quasi-ustalonych stanów pracy symetrycznych fazowo.

EN

The purpose of this paper is to give a method of creating mathematical model for commonly known indirect (two-core design), symmetrical phase shifting transformer.

6

Mathematical modelling and stationary characteristics of a two - phase fluidised - bed bioreactor with external aeration

Tabiś B., Stryjewski W.

Chemical and Process Engineering

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2013

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Vol. 34, nr 4

435--448

EN

A mathematical model for a two-phase fluidised bed bioreactor with liquid d recirculation and an external aerator was proposed. A stationary nonlin ear analysis of such a bioreactor for an aerobic process with double-substrate kinetics was carried out. The influences of a volumetric fraction of solid carriers in the liquid phase, the rate of active e biomass transfer from the biofilm to the liquid, the concentration of carbonaceous substrate, the mean residence time of the liquid and the efficiency of the external aerator on the steady state characteristics of the bioreactor were described. A method for determination of the minimal recirculation ratio related to oxygen demand and fluidised bed conditions was presented. On the basis of the obtained results, it is possible to choose reasonable operating conditions of such plants and to determine constraints, while considering acceptable concentrations of a toxic substrate being degraded.

7

Steady states analysis of micro-grids operation

Księżyk K., Parol M.

Przegląd Elektrotechniczny

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2008

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R. 84, nr 11

14-19

EN

Short characteristics of micro-grid and results of computer simulations of exemplary micro-grid operation in steady states have been presented in the paper. Micro-grid operation, for different variants of micro-sources and battery energy storage operation, has been shown. In order to carry out computer simulation of micro-grid operation specialized software has been used. Influence of micro-sources kinds and their locations and battery energy storage operation way on node voltage levels, branch power flows and power losses in micro-grid have been analyzed.

PL

W artykule przedstawiono krótką charakterystykę mikrosieci oraz rezultaty obliczeń symulacyjnych prezentujących działanie przykładowej mikrosieci w stanach ustalonych. Pokazano działanie mikrosieci w różnych wariantach pracy mikroźródeł oraz bateryjnego zasobnika energii. W celu przeprowadzenia obliczeń symulujących działanie mikrosieci zastosowano specjalistyczne oprogramowanie narzędziowe. Przeanalizowano wpływ rodzaju mikroźródeł i ich lokalizacji, a także sposobu działania bateryjnego zasobnika energii na poziomy napięć węzłowych, przepływy w gałęziach i straty mocy w mikrosieci.

8

R. Thomas' Modeling of Biological Regulatory Networks : Introduction of Singular States in the Qualitative Dynamics

Richard A., Comet J-P., Bernot G.

Fundamenta Informaticae

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2005

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Vol. 65, nr 4

373--392

EN

In the field of biological regulation, models extracted from experimental works are usually complex networks comprising intertwined feedback circuits. The overall behavior is difficult to grasp and the development of formal methods is needed in order to model and simulate biological regulatory networks. To model the behavior of such systems, R. Thomas and coworkers developed a qualitative approach in which the dynamics is described by a state transition system. Even if all steady states of the system can be detected in this formalism, some of them, the singular ones, are not formally included in the transition system. Consequently, temporal properties in which singular states have to be described, cannot be checked against the transition system. However, steady singular states play an essential role in the dynamics since they can induce homeostasis or multistationnarity and sometimes are associated to biological phenotypes. These observations motivated our interest for developing an extension of Thomas formalism in which all singular states are represented, allowing us to check temporal properties concerning singular states. We easily demonstrate in our formalism the previously demonstrated theorems giving the conditions for the steadiness of singular states. We also prove that our formalism is coherent with the Thomas one since all paths of the Thomas transition system are preserved in our one, which in addition includes singular states.

9

On application dynamical systems theory to prediction of an agile aircraft post stall behaviour

Dębicka S., Sibilski K.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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2004

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z. 23

111-116

EN

Investigations of post-stall manoeuvres dynamics show the necessity of automation of aircraft and engines control during post-stall manoeuvres, and the necessity of special control system operational modes. This paper describes the implementation of continuation methods and bifurcation analysis in the "global" identification of aircraft's non-linear dynamics. In the examples presented, continuation method is used to determine the steady states of a thrust-vectoring, supersonic combat aircraft with a streaked wing, as functions of the deflections of thrust vector, and bifurcations of these steady states are encountered.

PL

Teoria układów dynamicznych pozwala na globalną analizę rozwiązań nieliniowego układu równań różniczkowych. Pierwszym krokiem tej analizy jest ocena stateczności stanów ustalonych. Stany ustalone są wyznaczane poprzez przyrównanie do zera pochodnych i rozwiązaniu układu równań algebraicznych. Twierdzenie Hartmana-Grobmana stanowi, że lokalna stateczność stanu quasi-ustaionego jest zdeterminowana poprzez wartości własne zlinearyzowanego wokół położenia równowagi układu równań różniczkowych, opisujących badany system dynamiczny. W pracy przedstawiono wyniki bifurkacyjnej analizy manewrów wykonywanych na dużych kątach natarcia.

10

Statyczna i dynamiczna struktura stanów stacjonarnych kaskady bioreaktorów dla procesu mikrobiologicznego z podwójnym poziomem troficznym

Grzywacz R., Tabiś B.

Inżynieria Chemiczna i Procesowa

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2002

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T. 23, z. 3

325-339

PL

Dokonano systematycznej, ilościowej analizy właściwości kaskady bioreaktorów z częściową recyrkulacją i zagęszczaniem biomasy. Szczegółowo omówiono zjawisko wielokrotności wtórnej stanów stacjonarnych, które wykryto w bioreaktorach zbiornikowych dla procesów mikrobiologicznych z dwoma poziomami troficznymi typu drapieżca-ofiara, przebiegających w obecności tzw. kryjówek mikrobiologicznych. Określono wpływ stopnia niedostępności ofiar, zagęszczania biomasy oraz rozłożenia objętości reakcyjnych w obiekcie na strukturę i stabilność liniową stanów stacjonarnych. Podjęto próbę wyjaśnienia wpływu mikroorganizmów eukariotycznych i kryjówek mikrobiologicznych na stacjonarne cechy bioreaktorów.

EN

A comprehensive quantitative analysis on the non-linear stationary properties for a cascade of stirred tank bioreactors with partial recirculation and thickening of biomass has been carried out. The phenomenon of secondary multiplicities of the steady states discovered in such bioreactors for processes with two trophic levels was discussed in detail. The process analysed occurs according to the predator-prey scheme at the presence of so-called hiding places for prey. An influence of a degree of inaccessibility of the prey, thickening of biomass and distribution of operative volumes in the object on the structure and linear stability of the steady states has been evaluated. An attempt of explanation of the role of protozoa and hiding places for the prey on stationary properties of the bioreactors was undertaken.

11

Principles of bone remodelling - the limit cycles of bone remodelling

Petrtyl M., Danešová J.

Acta of Bioengineering and Biomechanics

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2001

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Vol. 3, nr 1

75-91

EN

The bone tissue remodelling is a relatively slow process. In physiologically "normal" conditions, it tends towards the state of remodelling equilibrium. In the state of final remodelling equilibrium, the strain energy reaches its minimum. In the life of each human being, the bone tissue passes through the repeating limit cycles of its development, functioning and destruction. The paper presented is aimed at the biomechanochemical processes within one limit cycle of bone remodelling using the stoichiometric equations and kinetic equations. Each limit cycle of the bone tissue remodelling (in its assumed volume element) consists of several stages, in which the biochemical reactions are proceeding in a highly intensive way, and of several periods in which the tissue is in weakly steady states (i.e.. the biochemical reactions are very slow or they almost do not take place). Generally, throughout the life of a human, a bone tissue is several times in the principal weakly steady state, i.e., in such a state in which the long-term remodelling equilibrium is reached. This period lasts for several years (roughly for 6-8 years) in the life of an adult human in his/her productive age, while in the life of a child this period is shorter. Figuratively speaking, the stages of the bone tissue remodelling (during one limit cycle) can be compared to the tissue "childhood and maruraiion" (i.e., n stage of remodelling - apposition of the tissue), and "aging-demise" (I stage of remodelling - resorption). One limit cycle of the bone tissue life (out of the series of the subsequent periodic limit cycles) that is characterized by the bone tissue development, functioning and destruction (in the unit volume element) can be synoptically, and in the real time, described by four stages. The limit cycle is a close trajectory of solution of kinetic equations of bone remodelling. The bone tissue (in its unit volume element) passes through the repeating harmonic limit cycles (i.e., the stable periodic processes) of its development and destruction.