949 resultados para Mathematical modelling
Resumo:
La seguridad y fiabilidad de los procesos industriales son la principal preocupación de los ingenieros encargados de las plantas industriales. Por lo tanto, desde un punto de vista económico, el objetivo principal es reducir el costo del mantenimiento, el tiempo de inactividad y las pérdidas causadas por los fallos. Por otra parte, la seguridad de los operadores, que afecta a los aspectos sociales y económicos, es el factor más relevante a considerar en cualquier sistema Debido a esto, el diagnóstico de fallos se ha convertido en un foco importante de interés para los investigadores de todo el mundo e ingenieros en la industria. Los principales trabajos enfocados en detección de fallos se basan en modelos de los procesos. Existen diferentes técnicas para el modelado de procesos industriales tales como máquinas de estado, árboles de decisión y Redes de Petri (RdP). Por lo tanto, esta tesis se centra en el modelado de procesos utilizando redes de petri interpretadas. Redes de Petri es una herramienta usada en el modelado gráfico y matemático con la habilidad para describir información de los sistemas de una manera concurrente, paralela, asincrona, distribuida y no determinística o estocástica. RdP son también una herramienta de comunicación visual gráfica útil como lo son las cartas de flujo o diagramas de bloques. Adicionalmente, las marcas de las RdP simulan la dinámica y concurrencia de los sistemas. Finalmente, ellas tienen la capacidad de definir ecuaciones de estado específicas, ecuaciones algebraicas y otros modelos que representan el comportamiento común de los sistemas. Entre los diferentes tipos de redes de petri (Interpretadas, Coloreadas, etc.), este trabajo de investigación trata con redes de petri interpretadas principalmente debido a características tales como sincronización, lugares temporizados, aparte de su capacidad para procesamiento de datos. Esta investigación comienza con el proceso para diseñar y construir el modelo y diagnosticador para detectar fallos definitivos, posteriormente, la dinámica temporal fue adicionada para detectar fallos intermitentes. Dos procesos industriales, concretamente un HVAC (Calefacción, Ventilación y Aire Acondicionado) y un Proceso de Envasado de Líquidos fueron usados como banco de pruebas para implementar la herramienta de diagnóstico de fallos (FD) creada. Finalmente, su capacidad de diagnóstico fue ampliada en orden a detectar fallos en sistemas híbridos. Finalmente, un pequeño helicóptero no tripulado fue elegido como ejemplo de sistema donde la seguridad es un desafío, y las técnicas de detección de fallos desarrolladas en esta tesis llevan a ser una herramienta valorada, desde que los accidentes de las aeronaves no tripuladas (UAVs) envuelven un alto costo económico y son la principal razón para introducir restricciones de volar sobre áreas pobladas. Así, este trabajo introduce un proceso sistemático para construir un Diagnosticador de Fallos del sistema mencionado basado en RdR Esta novedosa herramienta es capaz de detectar fallos definitivos e intermitentes. El trabajo realizado es discutido desde un punto de vista teórico y práctico. El procedimiento comienza con la división del sistema en subsistemas para seguido integrar en una RdP diagnosticadora global que es capaz de monitorear el sistema completo y mostrar las variables críticas al operador en orden a determinar la salud del UAV, para de esta manera prevenir accidentes. Un Sistema de Adquisición de Datos (DAQ) ha sido también diseñado para recoger datos durante los vuelos y alimentar la RdP diagnosticadora. Vuelos reales realizados bajo condiciones normales y de fallo han sido requeridos para llevar a cabo la configuración del diagnosticador y verificar su comportamiento. Vale la pena señalar que un alto riesgo fue asumido en la generación de fallos durante los vuelos, a pesar de eso esto permitió recoger datos básicos para desarrollar el diagnóstico de fallos, técnicas de aislamiento, protocolos de mantenimiento, modelos de comportamiento, etc. Finalmente, un resumen de la validación de resultados obtenidos durante las pruebas de vuelo es también incluido. Un extensivo uso de esta herramienta mejorará los protocolos de mantenimiento para UAVs (especialmente helicópteros) y permite establecer recomendaciones en regulaciones. El uso del diagnosticador usando redes de petri es considerado un novedoso enfoque. ABSTRACT Safety and reliability of industrial processes are the main concern of the engineers in charge of industrial plants. Thus, from an economic point of view, the main goal is to reduce the maintenance downtime cost and the losses caused by failures. Moreover, the safety of the operators, which affects to social and economic aspects, is the most relevant factor to consider in any system. Due to this, fault diagnosis has become a relevant focus of interest for worldwide researchers and engineers in the industry. The main works focused on failure detection are based on models of the processes. There are different techniques for modelling industrial processes such as state machines, decision trees and Petri Nets (PN). Thus, this Thesis is focused on modelling processes by using Interpreted Petri Nets. Petri Nets is a tool used in the graphic and mathematical modelling with ability to describe information of the systems in a concurrent, parallel, asynchronous, distributed and not deterministic or stochastic manner. PNs are also useful graphical visual communication tools as flow chart or block diagram. Additionally, the marks of the PN simulate the dynamics and concurrence of the systems. Finally, they are able to define specific state equations, algebraic equations and other models that represent the common behaviour of systems. Among the different types of PN (Interpreted, Coloured, etc.), this research work deals with the interpreted Petri Nets mainly due to features such as synchronization capabilities, timed places, apart from their capability for processing data. This Research begins with the process for designing and building the model and diagnoser to detect permanent faults, subsequently, the temporal dynamic was added for detecting intermittent faults. Two industrial processes, namely HVAC (Heating, Ventilation and Air Condition) and Liquids Packaging Process were used as testbed for implementing the Fault Diagnosis (FD) tool created. Finally, its diagnostic capability was enhanced in order to detect faults in hybrid systems. Finally, a small unmanned helicopter was chosen as example of system where safety is a challenge and fault detection techniques developed in this Thesis turn out to be a valuable tool since UAVs accidents involve high economic cost and are the main reason for setting restrictions to fly over populated areas. Thus, this work introduces a systematic process for building a Fault Diagnoser of the mentioned system based on Petri Nets. This novel tool is able to detect both intermittent and permanent faults. The work carried out is discussed from theoretical and practical point of view. The procedure begins with a division of the system into subsystems for further integration into a global PN diagnoser that is able to monitor the whole system and show critical variables to the operator in order to determine the UAV health, preventing accidents in this manner. A Data Acquisition System (DAQ) has been also designed for collecting data during the flights and feed PN Diagnoser. Real flights carried out under nominal and failure conditions have been required to perform the diagnoser setup and verify its performance. It is worth noting that a high risk was assumed in the generation of faults during the flights, nevertheless this allowed collecting basic data so as to develop fault diagnosis, isolations techniques, maintenance protocols, behaviour models, etc. Finally, a summary of the validation results obtained during real flight tests is also included. An extensive use of this tool will improve preventive maintenance protocols for UAVs (especially helicopters) and allow establishing recommendations in regulations. The use of the diagnoser by using Petri Nets is considered as novel approach.
Resumo:
Dentre os insetos que causam prejuízo a produção de soja, os percevejos fitófagos destacam-se como o principal grupo de pragas, sendo Euschistus heros (Fabricius, 1798), atualmente, a principal espécie de praga da cultura, que está distribuída em todas as regiões brasileiras de cultivo da leguminosa. Para o controle das populações destes insetos, o método mais utilizado é o controle químico. No entanto, as exigências tem sido crescentes no que diz respeito à redução do uso de agroquímicos. Dentre as alternativas, o uso dos parasitoides de ovos Telenomus podisi Ashmead, 1881 e Trissolcus basalis Wollaston, 1858 emerge com bom potencial para programas de controle biológico. O uso desses agentes de controle deve ser baseado em estudos que assegurem a eficiência dos insetos no manejo da população da praga. O presente estudo combina experimentação laboratorial e de campo com modelagem matemática para investigar o potencial dos parasitoides como controladores do percevejo da soja. Foram realizados estudos relacionados aos parâmetros biológicos e potenciais reprodutivos de T. podisi e T. basalis através de tabelas de vida de fertilidade. Foram determinadas as exigências térmicas de ambos os parasitoides de ovos e observou-se o efeito da idade dos ovos de E. heros no parasitismo por T. podisi e T. basalis. Foi também avaliada a interação entre as duas espécies de parasitóides e determinado o número ideal de cada espécie de parasitoide a ser liberado de acordo com a densidade de ovos do hospedeiro. Finalmente um modelo matemático foi proposto visando simular interações e liberações em parasitoides, para o controle de E. heros. Com a combinação entre os experimentos e a implementação de metodologia analítica através de modelagem ecológica espera-se incrementar estratégias de controle da praga, para fundamentar a recomendação do uso do parasitoide mais eficiente para controlar E. heros, ou mesmo a melhor forma de combinar o o uso das espécies de inimigos naturais.
Resumo:
Ser eficiente é um requisito para a sustentabilidade das empresas concessionárias de distribuição de energia elétrica no Brasil. A busca pela eficiência deve estar em harmonia com a melhoria contínua da qualidade, da segurança e da satisfação dos consumidores e das partes envolvidas. O desafio de atender múltiplos objetivos requer que as empresas do setor desenvolvam soluções inovadoras, com a mudança de processos, tecnologia, estrutura e a capacitação das pessoas. Desenvolver um modelo operacional eficiente e uma gestão rigorosa dos custos são fatores-chave para o sucesso das empresas, considerando o contexto regulatório de revisão tarifária que incentiva a melhoria do desempenho. O modelo operacional é definido a partir da organização logística dos recursos para atendimento da demanda de serviços, que define também os custos fixos e variáveis de pessoal (salário, horas extras, refeições), infraestrutura (manutenção de prédios, ferramentas e equipamentos) e deslocamentos (manutenção de veículos, combustível), por exemplo. A melhor alocação e o melhor dimensionamento de bases operacionais possibilitam a redução dos custos com deslocamento e infraestrutura, favorecendo o aproveitamento da força de trabalho em campo, a melhoria do atendimento dos clientes e da segurança dos colaboradores. Este trabalho apresenta uma metodologia de otimização de custos através da alocação de bases e equipes operacionais, com o modelamento matemático dos objetivos e restrições do negócio e a aplicação de algoritmo evolutivo para busca das melhores soluções, sendo uma aplicação de Pesquisa Operacional, no campo da Localização de Instalações, em distribuição de energia elétrica. O modelo de otimização desenvolvido possibilita a busca pelo ponto de equilíbrio ótimo que minimiza o custo total formado pelos custos de infraestrutura, frota (veículos e deslocamentos) e pessoal. O algoritmo evolutivo aplicado no modelo oferece soluções otimizadas pelo melhoramento de conjuntos de variáveis binárias com base em conceitos da evolução genética. O modelo de otimização fornece o detalhamento de toda a estrutura operacional e de custos para uma determinada solução do problema, utilizando premissas de produtividade e deslocamentos (velocidades e distâncias) para definir as abrangências de atuação das bases operacionais, recursos (equipes, pessoas, veículos) necessários para atendimento da demanda de serviços, e projetar todos os custos fixos e variáveis associados. A metodologia desenvolvida neste trabalho considera também a projeção de demanda futura para a aplicação no estudo de caso, que evidenciou a efetividade da metodologia como ferramenta para a melhoria da eficiência operacional em empresas de distribuição de energia elétrica.
Resumo:
La gran mayoría de modelos matemáticos propuestos hasta la fecha para simular la propagación del malware están basados en el uso de ecuaciones diferenciales. Dichos modelos son analizados de manera crítica en este trabajo, determinando las principales deficiencias que presentan y planteando distintas alternativas para su subsanación. En este sentido, se estudia el uso de los autómatas celulares como nuevo paradigma en el que basar los modelos epidemiológicos, proponiendo una alternativa explícita basada en ellos a un reciente modelo continuo.
Resumo:
Mathematical morphology addresses the problem of describing shapes in an n-dimensional space using the concepts of set theory. A series of standardized morphological operations are defined, and they are applied to the shapes to transform them using another shape called the structuring element. In an industrial environment, the process of manufacturing a piece is based on the manipulation of a primitive object via contact with a tool that transforms the object progressively to obtain the desired design. The analogy with the morphological operation of erosion is obvious. Nevertheless, few references about the relation between the morphological operations and the process of design and manufacturing can be found. The non-deterministic nature of classic mathematical morphology makes it very difficult to adapt their basic operations to the dynamics of concepts such as the ordered trajectory. A new geometric model is presented, inspired by the classic morphological paradigm, which can define objects and apply morphological operations that transform these objects. The model specializes in classic morphological operations, providing them with the determinism inherent in dynamic processes that require an order of application, as is the case for designing and manufacturing objects in professional computer-aided design and manufacturing (CAD/CAM) environments. The operators are boundary-based so that only the points in the frontier are handled. As a consequence, the process is more efficient and more suitable for use in CAD/CAM systems.
Resumo:
The aim of the conference is to bring together academia and industry to discuss the safety of food packaging as well as the development of new food packaging materials, including active, intelligent and nano concepts. Bio-based materials will be also discussed due to be a growing area of food packaging. Topics: Food Safety & Quality (Physical and chemical hazards: measurement and assessment; Biological hazards: risk and prevention; Mathematical modelling of risk assessment; Evaluation of food spoilage, food quality and shelf life; Food packaging laws and regulations; Food package interactions: migration measurement methods, models and food safety risk assessment; Food Packaging innovation (Active and intelligent packaging; Nano-packaging; New packaging materials and material development; Bio based and edible packaging; Food package testing; Sustainable food contact materials; Recycling and Life Cycle Assessment).
Resumo:
The development of solutions that prevent dehydration or promote adequate re-hydration play a vital role in preventing fatigue during exercise, however, the methods commonly used to assess the hydration ability of such solutions are invasive and often assess the components of absorption separately. This paper describes using a non-invasive deuterium tracer technique that assesses gastric emptying and intestinal absorption simultaneously to evaluate the uptake of water during rest and exercise. The kinetics of absorption are further examined by mathematical modelling of the data generated. For the rest group, 0.05 g/kg of body weight of deuterium, contained in gelatine capsules, was ingested with ordinary tap water and saliva samples were collected every 5 min for one hour while the subject remained seated. The deuterium was administered as above for the exercise group but sample collection was during one hour of exercise on a treadmill at 55% of the subject's maximum heart rate. The enrichment data for each subject were mathematically modelled and the parameters obtained were compared across groups using an independent samples t-test. Compared with the rest condition, the exercise group showed delayed absorption of water as indicated by significant differences for the modelling parameters t(2), t(1/2), maximum absorption rate and solution absorption amount at t(1). Labelling with a deuterium tracer is a good measure of the relative rate ingested fluids are absorbed by the body. Mathematical modelling of the data generates rates of maximum absorption and allows calculation of the percentage of the solution that is absorbed at any given time during the testing period. Copyright (C) 2004 John Wiley Sons, Ltd.
Resumo:
Cystic echinococcosis, caused by Echinococcus grantilosus, is highly endemic in North Africa and the Middle East. This paper examines the abundance and prevalence of infection of E. granulosus in camels in Tunisia. No cysts were found in 103 camels from Kebili, whilst 19 of 188 camels from Benguerden (10.1%) were infected. Of the cysts found 95% were considered fertile with the presence of protoscolices and 80% of protoscolices were considered viable by their ability to exclude aqueous eosin. Molecular techniques were used on cyst material from camels and this demonstrated that the study animals were infected with the G1 sheep strain of E. granulosus. Observed data were fitted to a mathematical model by maximum likelihood techniques to define the parameters and their confidence limits and the negative binomial distribution was used to define the error variance in the observed data. The infection pressure to camels was somewhat lower in comparison to sheep reported in an earlier study. However, because camels are much longer-lived animals, the results of the model fit suggested that older camels have a relatively high prevalence rate, reaching a most likely value of 32% at age 15 years. This could represent an important source of transmission to dogs and hence indirectly to man of this zonotic strain. In common with similar studies on other species, there was no evidence of parasite-induced immunity in camels. (C) 2004 Elsevier B.V. All rights reserved.
Resumo:
The mathematical modelling underlying passive air sampling theory can be based on mass transfer coefficients or rate constants. Generally, these models have not been inter-related. Starting with basic models, the exchange of chemicals between the gaseous phase and the sampler is developed using mass transfer coefficients and rate constants. Importantly, the inter-relationships between the approaches are demonstrated by relating uptake rate constants and loss rate constants to mass transfer coefficients when either sampler-side or air-side resistance is dominating chemical exchange. The influence of sampler area and sampler volume on chemical exchange is discussed in general terms and as they relate to frequently used parameters such as sampling rates and time to equilibrium. Where air-side or sampler-side resistance dominates, an increase in the surface area of the sampler will increase sampling rates. Sampling rates are not related to the sampler/air partition coefficient (K-SV) when air-side resistance dominates and increase with K-SV when sampler-side resistance dominates.
Resumo:
Data envelopment analysis (DEA) is defined based on observed units and by finding the distance of each unit to the border of estimated production possibility set (PPS). The convexity is one of the underlying assumptions of the PPS. This paper shows some difficulties of using standard DEA models in the presence of input-ratios and/or output-ratios. The paper defines a new convexity assumption when data includes a ratio variable. Then it proposes a series of modified DEA models which are capable to rectify this problem.
Resumo:
A local area network that can support both voice and data packets offers economic advantages due to the use of only a single network for both types of traffic, greater flexibility to changing user demands, and it also enables efficient use to be made of the transmission capacity. The latter aspect is very important in local broadcast networks where the capacity is a scarce resource, for example mobile radio. This research has examined two types of local broadcast network, these being the Ethernet-type bus local area network and a mobile radio network with a central base station. With such contention networks, medium access control (MAC) protocols are required to gain access to the channel. MAC protocols must provide efficient scheduling on the channel between the distributed population of stations who want to transmit. No access scheme can exceed the performance of a single server queue, due to the spatial distribution of the stations. Stations cannot in general form a queue without using part of the channel capacity to exchange protocol information. In this research, several medium access protocols have been examined and developed in order to increase the channel throughput compared to existing protocols. However, the established performance measures of average packet time delay and throughput cannot adequately characterise protocol performance for packet voice. Rather, the percentage of bits delivered within a given time bound becomes the relevant performance measure. Performance evaluation of the protocols has been examined using discrete event simulation and in some cases also by mathematical modelling. All the protocols use either implicit or explicit reservation schemes, with their efficiency dependent on the fact that many voice packets are generated periodically within a talkspurt. Two of the protocols are based on the existing 'Reservation Virtual Time CSMA/CD' protocol, which forms a distributed queue through implicit reservations. This protocol has been improved firstly by utilising two channels, a packet transmission channel and a packet contention channel. Packet contention is then performed in parallel with a packet transmission to increase throughput. The second protocol uses variable length packets to reduce the contention time between transmissions on a single channel. A third protocol developed, is based on contention for explicit reservations. Once a station has achieved a reservation, it maintains this effective queue position for the remainder of the talkspurt and transmits after it has sensed the transmission from the preceeding station within the queue. In the mobile radio environment, adaptions to the protocols were necessary in order that their operation was robust to signal fading. This was achieved through centralised control at a base station, unlike the local area network versions where the control was distributed at the stations. The results show an improvement in throughput compared to some previous protocols. Further work includes subjective testing to validate the protocols' effectiveness.
Resumo:
The use of digital communication systems is increasing very rapidly. This is due to lower system implementation cost compared to analogue transmission and at the same time, the ease with which several types of data sources (data, digitised speech and video, etc.) can be mixed. The emergence of packet broadcast techniques as an efficient type of multiplexing, especially with the use of contention random multiple access protocols, has led to a wide-spread application of these distributed access protocols in local area networks (LANs) and a further extension of them to radio and mobile radio communication applications. In this research, a proposal for a modified version of the distributed access contention protocol which uses the packet broadcast switching technique has been achieved. The carrier sense multiple access with collision avoidance (CSMA/CA) is found to be the most appropriate protocol which has the ability to satisfy equally the operational requirements for local area networks as well as for radio and mobile radio applications. The suggested version of the protocol is designed in a way in which all desirable features of its precedents is maintained. However, all the shortcomings are eliminated and additional features have been added to strengthen its ability to work with radio and mobile radio channels. Operational performance evaluation of the protocol has been carried out for the two types of non-persistent and slotted non-persistent, through mathematical and simulation modelling of the protocol. The results obtained from the two modelling procedures validate the accuracy of both methods, which compares favourably with its precedent protocol CSMA/CD (with collision detection). A further extension of the protocol operation has been suggested to operate with multichannel systems. Two multichannel systems based on the CSMA/CA protocol for medium access are therefore proposed. These are; the dynamic multichannel system, which is based on two types of channel selection, the random choice (RC) and the idle choice (IC), and the sequential multichannel system. The latter has been proposed in order to supress the effect of the hidden terminal, which always represents a major problem with the usage of the contention random multiple access protocols with radio and mobile radio channels. Verification of their operation performance evaluation has been carried out using mathematical modelling for the dynamic system. However, simulation modelling has been chosen for the sequential system. Both systems are found to improve system operation and fault tolerance when compared to single channel operation.
Resumo:
The objective of this work was to design, construct and commission a new ablative pyrolysis reactor and a high efficiency product collection system. The reactor was to have a nominal throughput of 10 kg/11r of dry biomass and be inherently scalable up to an industrial scale application of 10 tones/hr. The whole process consists of a bladed ablative pyrolysis reactor, two high efficiency cyclones for char removal and a disk and doughnut quench column combined with a wet walled electrostatic precipitator, which is directly mounted on top, for liquids collection. In order to aid design and scale-up calculations, detailed mathematical modelling was undertaken of the reaction system enabling sizes, efficiencies and operating conditions to be determined. Specifically, a modular approach was taken due to the iterative nature of some of the design methodologies, with the output from one module being the input to the next. Separate modules were developed for the determination of the biomass ablation rate, specification of the reactor capacity, cyclone design, quench column design and electrostatic precipitator design. These models enabled a rigorous design protocol to be developed capable of specifying the required reactor and product collection system size for specified biomass throughputs, operating conditions and collection efficiencies. The reactor proved capable of generating an ablation rate of 0.63 mm/s for pine wood at a temperature of 525 'DC with a relative velocity between the heated surface and reacting biomass particle of 12.1 m/s. The reactor achieved a maximum throughput of 2.3 kg/hr, which was the maximum the biomass feeder could supply. The reactor is capable of being operated at a far higher throughput but this would require a new feeder and drive motor to be purchased. Modelling showed that the reactor is capable of achieving a reactor throughput of approximately 30 kg/hr. This is an area that should be considered for the future as the reactor is currently operating well below its theoretical maximum. Calculations show that the current product collection system could operate efficiently up to a maximum feed rate of 10 kg/Fir, provided the inert gas supply was adjusted accordingly to keep the vapour residence time in the electrostatic precipitator above one second. Operation above 10 kg/hr would require some modifications to the product collection system. Eight experimental runs were documented and considered successful, more were attempted but due to equipment failure had to be abandoned. This does not detract from the fact that the reactor and product collection system design was extremely efficient. The maximum total liquid yield was 64.9 % liquid yields on a dry wood fed basis. It is considered that the liquid yield would have been higher had there been sufficient development time to overcome certain operational difficulties and if longer operating runs had been attempted to offset product losses occurring due to the difficulties in collecting all available product from a large scale collection unit. The liquids collection system was highly efficient and modeling determined a liquid collection efficiency of above 99% on a mass basis. This was validated due to the fact that a dry ice/acetone condenser and a cotton wool filter downstream of the collection unit enabled mass measurements of the amount of condensable product exiting the product collection unit. This showed that the collection efficiency was in excess of 99% on a mass basis.
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The objective of this work has been to investigate the principle of combined bioreaction and separation in a simulated counter-current chromatographic bioreactor-separator system (SCCR-S). The SCCR-S system consisted of twelve 5.4cm i.d x 75cm long columns packed with calcium charged cross-linked polystyrene resin. Three bioreactions, namely the saccharification of modified starch to maltose and dextrin using the enzyme maltogenase, the hydrolysis of lactose to galactose and glucose in the presence of the enzyme lactase and the biosynthesis of dextran from sucrose using the enzyme dextransucrase. Combined bioreaction and separation has been successfully carried out in the SCCR-S system for the saccharification of modified starch to maltose and dextrin. The effects of the operating parameters (switch time, eluent flowrate, feed concentration and enzyme activity) on the performance of the SCCR-S system were investigated. By using an eluent of dilute enzyme solution, starch conversions of up to 60% were achieved using lower amounts of enzyme than the theoretical amount required by a conventional bioreactor to produce the same amount of maltose over the same time period. Comparing the SCCR-S system to a continuous annular chromatograph (CRAC) for the saccharification of modified starch showed that the SCCR-S system required only 34.6-47.3% of the amount of enzyme required by the CRAC. The SCCR-S system was operated in the batch and continuous modes as a bioreactor-separator for the hydrolysis of lactose to galactose and glucose. By operating the system in the continuous mode, the operating parameters were further investigated. During these experiments the eluent was deionised water and the enzyme was introduced into the system through the same port as the feed. The galactose produced was retarded and moved with the stationary phase to be purge as the galactose rich product (GalRP) while the glucose moved with the mobile phase and was collected as the glucose rich product (GRP). By operating at up to 30%w/v lactose feed concentrations, complete conversions were achieved using only 48% of the theoretical amount of enzyme required by a conventional bioreactor to hydrolyse the same amount of glucose over the same time period. The main operating parameters affecting the performance of the SCCR-S system operating in the batch mode were investigated and the results compared to those of the continuous operation of the SCCR-S system. . During the biosynthesis of dextran in the SCCR-S system, a method of on-line regeneration of the resin was required to operate the system continuously. Complete conversion was achieved at sucrose feed concentrations of 5%w/v with fructose rich. products (FRP) of up to 100% obtained. The dextran rich products were contaninated by small amounts of glucose and levan formed during the bioreaction. Mathematical modelling and computer simulation of the SCCR-S. system operating in the continuous mode for the hydrolysis of lactose has been carried out. .