This thesis has made two significant contributions to the field of reactive crystallisation. First, new data from batch cooling crystallisation and semi-batch reactive crystallisation experiments of mono-ammonium phosphate (MAP) were obtained to describe the key factors that influence crystal nucleation and growth rates, crystal size distribution (CSD), and crystal shape. The second contribution is the development of a numerical scheme for solving the population balance equations, which can be used to describe the evolution of CSD during the crystallisation process. This scheme combines the finite difference method with a wavelet method, and is the first reported application of this approach for crystallisation modelling and simulation. / Experiments into the batch cooling crystallisation of MAP were conducted both with and without seed crystals. The effects of key factors such as cooling rate, initial level of supersaturation and seeding technique, including seed concentration and seed size, on the real time supersaturation, final CSD, crystal yield and crystal shape were investigated. It was found that a seed concentration of 20-30% effectively suppressed nucleation. The growth and nucleation rate were estimated by using an isothermal seeded batch approach and their parameters were calculated by non-linear optimisation techniques. / The second series of experiments involved the semi-batch reactive crystallisation of MAP. Both single-feed and dual-feed systems were investigated. In the single-feed arrangement, an ammonia solution was fed into a charge of phosphoric acid. In the dual-feed system, phosphoric acid and ammonia solution were fed into a charge of saturated MAP solution. The molar ratio of the reactants, initial supersaturation, presence or absence of seed crystals, initial MAP concentration, reactants’ flow rate, feeding time and stirring speed were varied, and the effects upon the real time supersaturation, final CSD, crystal yield, crystal shape and solution temperature were measured. X-ray diffraction analysis showed that MAP can be produced in both the single-feed and dual-feed arrangements. For the single feed system, the N/P mole ratio controlled the degree of reaction and the CSD of the product. Di-ammonium phosphate (DAP) was not be observed in the single-feed system due to its high solubility. In the dual-feed system, a seeded solution with slow feed addition, moderate stirring speed and a low initial supersaturation provided the most favourable conditions for generating a desirable supersaturation profile, and thus obtaining a product with good CSD and crystal shape. / A comparative numerical study was undertaken in order to evaluate the existing numerical schemes for solving the population balance equations (PBE) that describe crystallisation. Several analytical solutions to the PBE were used to benchmark the following numerical schemes: Upwind Finite Difference, Biased Upwind Finite Difference, Orthogonal Collocation with Finite Elements, and Wavelet Orthogonal Collocation. The Wavelet Finite Difference (WFD) method has been applied here for the first time for solving PBE problems. The WFD scheme was adapted to solve the batch cooling and the semi-batch reactive crystallisation models, and the solutions were validated against experimental data that we obtained. / In summary, the experimental data provide an improved understanding of MAPreaction and crystallisation mechanisms. The adaptability of the WFD method has beendemonstrated validating the two crystallisation systems, and this should help extendthe application of wavelet-based solutions beyond crystallisation processes and intomore diverse areas of chemical engineering.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho o processo não linear de transmissão de calor condução-radiação é abordado num contexto bidimensional plano e simulado com o uso de um esquema linear em diferenças finitas. O problema original é tratado como o limite de uma sequencia de problemas lineares, do tipo condução-convecção. Este limite, cuja existência é comprovada, é facilmente obtido a partir de procedimentos básicos, accessíveis a qualquer estudante de engenharia, permitindo assim o emprego de hipóteses mais realistas, já que não se tem o limitante matemático para a abordagem numérica de uma equação diferencial parcial elíptica. Neste trabalho foi resolvido o problema de condução de calor em regime permanente em uma placa com condições de contorno convectivas e radioativas utilizando-se o software MatLab, vale ressaltar, que a mesma metodologia é aplicável para geometrias mais complexas. / In this work the nonlinear conduction-radiation heat transfer process is considered under a plane two dimensional assumption and simulated by means of a finite difference linear scheme. The original problem is regarded as the limit (which always exists) of a sequence of linear problems like the conduction-convection ones. Such a limit is reached in an easy way by means of standard procedures, available for any undergraduate engineering student, allowing the employment of more realistic hypotheses, since the mathematical complexities are not a constraint for simulating the elliptic partial differential equation. This work solved the problem of heat conduction in steady state conditions on a plate with convective and radioactive contour using MatLab software, it is noteworthy that the same methodology is applicable to more complex geometries.

La ferrite résiduelle δ est présente dans les microstructures de coulée des aciers inoxydables austénitiques. Elle résulte de la transformation incomplète δ→γ ayant lieu l'étape de solidification. Sa présence peut nuire à la forgeabilité à chaud des aciers inoxydables et peut conduire à la formation de criques de rives et de pailles en J lors du laminage à chaud des brames. Ce travail de thèse a pour but de comprendre les mécanismes de la transformation δ→γ à haute température dans les aciers inoxydables austénitiques via une modélisation expérimentale et numérique. La transformation a été étudié dans un alliage ternaire Fe-Cr-Ni coulé par lingot et de composition proche de celle des alliages industriels. Trois morphologies de ferrite ont été mises en évidence à l'état brut de solidification: lattes au bord du lingot, vermiculaire et lattes au centre. Leur cinétique de dissolution est étudiée à des températures allant de 1140°C à 1340°C et caractérisée en termes de fraction de ferrite et profils de composition du Cr et du Ni. La dissolution de la ferrite vermiculaire comprend trois étapes : une croissance initiale transitoire suivie par deux régimes de dissolution à haute puis à faible taux de transformation. D'un autre côté, il a été possible d'étudier la dissolution de la ferrite dans des microstructures multicouches élaborées par l'empilement de plaques de ferrite et d'austénite du système Fe-Cr-Ni et soudées à l'état solide par Compression Isostatique à Chaud puis réduits en épaisseurs par laminages successifs. L'étude et la caractérisation de la cinétique de dissolution de la ferrite est plus facile dans ces microstructures étant donnée la planéité initiale des interfaces δ/γ. L'analyse des résultats expérimentaux a été menée via le développement d'un modèle numérique, à interface mobile, de la transformation de phases δ→γ pilotée par la diffusion. La diffusion peut être traitée dans les géométries plane, cylindrique et sphérique. En guise de validation, le modèle a été utilisé pour analyser la dissolution de la ferrite dans les microstructures multicouches. Par la suite il a été appliqué au cas de la ferrite vermiculaire en usant d'une approche novatrice où la morphologie des dendrites est approximée par une combinaison de cylindres et de sphères. Malgré la simplicité des hypothèse sous-jacentes, le modèle a permis d'expliquer les mécanismes de croissance initiale et de changement de régime de dissolution. D'autre part, via une étude paramétrique, l'effet des données d'entrée a été étudié et les plus pertinentes d'entre eux en termes de prédiction quantitative ont été mises en avant, en particulier la description thermodynamique du digramme Fe-Cr-Ni, le gradient initial et la distribution des rayons des particules de ferrite. / Residual δ-ferrite is widely encountered in the as-cast microstructure of austenitic stainless steels. It stems from the incomplete high temperature solid-state δ→γ transformation occurring upon the solidification stage. Its presence has a detrimental effect the hot workability of stainless steels, leading to the formation of edge cracks and sliver defects during slabs hot rolling. This PhD work aims at bringing more understanding of the kinetics of high temperature δ→γ transformation in austenitic stainless steels via experimental and numerical modeling. The transformation was studied in a ternary Fe-Cr-Ni ingot-cast alloy with composition close to the industrial alloys. Three ferrite morphologies were identified: lathy at the edge of the ingot, vermicular and lathy at the center. Their dissolution kinetics were established at temperatures ranging from 1140°C to 1340°C and characterized in terms of ferrite fraction and Cr and Ni diffusion. The vermicular ferrite undergoes a transient growth followed by a high then a low rate dissolution regimes. On the other hand, ferrite dissolution was also studied in the multilayered microstructures. such microstructures were elaborated by alternating ferrite and austenite sheets of the Fe-Cr-Ni system, diffusion-bonded by Hot isostatic Pressing and reduced in thickness by successive rollings. Dissolution is easier to handle in such microstructures thanks to the initial planar δ/γ interfaces. Analysis of the experimental results were carried out with a numerical moving-boundary model of diffusion-controlled δ→γ transformation. Diffusion can be treated in the planar, cylindrical and spherical geometries. As a preliminary validation, the model was used to analyze kinetics of ferrite dissolution in the multilayered microstructures. It was then applied to the cast alloy using an original descriptive approach combining spheres and cylinders as equivalent morphology of dendritic ferrite. Although based on simplifying assumptions, the model was able to reproduce experimental results with satisfactory agreement. Mechanisms underlying the initial growth of vermicular ferrite and the transition in dissolution regimes were outlined. The effect of a wide range of input parameters has been considered and relevant parameters for quantitative calculations were brought to light, such as thermodynamical descriptions of the Fe-Cr-Ni system, composition gradients and distribution of ferrite's radii.

La transduction électrostatique est utilisée depuis plusieurs décennies dans les fréquences du domaine audible, principalement sous la forme de microphones membranaires. La transposition du même principe de transduction, mais dans un domaine de fréquence au-dessus du MHz, et par l’utilisation de dispositifs micro-usinés, c'est-à-dire produits à l’aide de technologies de photolithographie, a été proposée à partir de la fin des années 1990. Ces transducteurs, désignés sous l’acronyme cMUT (capacitive micromachine ultrasonic transducers), se composent d’un assemblage de transducteurs élémentaires, chacun possédant une partie mobile conventionnellement appelée diaphragme ou membrane, actionnée par la pression électrostatique. Cette thèse s’inscrit dans le développement de transducteurs de ce type destinés au domaine de l’imagerie médicale ultrasonore. Ce secteur d’application utilise actuellement des transducteurs basés sur des céramiques (ou, dans certains cas précis, des polymères) piézoélectriques. Le cMUT est intéressant dans certains sous-domaines d’application des ultrasons médicaux en raison de sa bonne adaptation à une production en grande série, de son intégration plus facile avec des éléments électroniques, de son faible échauffement et de l’absence de matériaux toxiques dans son processus de fabrication. La partie théorique de cette thèse repose sur une approche de modélisation par différences finies. Un modèle basé sur la théorie des plaques minces est développé pour prendre en compte la mécanique du transducteur élémentaire cMUT (c'est-à-dire d’un seul diaphragme). Ce modèle est ensuite complété par l’intégration de l’effet d’un chargement acoustique par un fluide. De façon à modéliser un transducteur entier, il est nécessaire de prendre en compte le couplage acoustique existant entre les différentes membranes. Pour rendre cela possible, un circuit équivalent, permettant de réduire chaque membrane à un système à un seul degré de liberté, est développé. Il est validé en le comparant au modèle de différences finies dans des cas où celui-ci peut être utilisé. Les travaux expérimentaux ont fait appel principalement aux deux techniques de caractérisation suivantes : les mesures d’impédance électrique, et les mesures de déplacement effectuées par interférométrie laser. Ces mesures ont été utilisées dans une double optique. D’une part, dans un objectif de caractérisation, ils ont permis de vérifier la fonctionnalité des dispositifs fabriqués et d’évaluer leurs performances. D’autre part, en comparant différentes configurations entre elles, ils ont rendu possible une validation expérimentale du modèle qui a été mis au point. / Electro-acoustic transduction based on electrostatic force has a long history in the range of audible frequencies, mainly as membrane-based microphones. Starting in the late 1990’s, it has been proposed to use the same principle in the multi-MHz frequency domain, thanks to micro-machined devices – meaning they’re produced through lithography technology. Such transducers, known as cMUT for capacitive micromachine ultrasonic transducers, are made of an assembly of elementary vertically mobile cells, usually designated as membranes, driven by electrostatic force. This PhD work is part of the development of this kind of transducers designed for medical imaging applications. This area currently uses transducers based on piezoelectric ceramics (or piezoelectric polymers for some peculiar cases). CMUT is an interesting alternative for some subdomains of medical ultrasound applications, due to its volume production ability, its easier integration with electronic elements, its low heat dissipation and the absence of toxic materials.

Submitted by Raniere Barreto (raniere.barros@ufvjm.edu.br) on 2018-05-07T19:57:19Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) victor_luiz_batista_aguiar.pdf: 2508647 bytes, checksum: 87d9596e1cf8e04b90b12aa373fa4748 (MD5) / Approved for entry into archive by Rodrigo Martins Cruz (rodrigo.cruz@ufvjm.edu.br) on 2018-05-08T12:30:45Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) victor_luiz_batista_aguiar.pdf: 2508647 bytes, checksum: 87d9596e1cf8e04b90b12aa373fa4748 (MD5) / Made available in DSpace on 2018-05-08T12:30:45Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) victor_luiz_batista_aguiar.pdf: 2508647 bytes, checksum: 87d9596e1cf8e04b90b12aa373fa4748 (MD5) Previous issue date: 2017 / A crescente demanda pela utiliza??o de recursos h?dricos em nossa sociedade faz com que seja necess?ria a amplia??o dos meios de capta??o de ?gua. As ?guas subterr?neas surgem como alternativa ? capta??o convencional, tendo em vista que o armazenamento da ?gua nas camadas inferiores do solo garanta a manuten??o da qualidade deste recurso, uma vez que passam por processos naturais de filtra??o. Nesse sentido, a caracteriza??o dos sistemas aqu?feros por meio de modelagem matem?tica surge como ferramenta de aux?lio na compreens?o do fluxo subterr?neo local. A presente pesquisa tem como principal objetivo analisar o comportamento hidrogeol?gico do munic?pio de Te?filo Otoni - MG, com base em simula??es oriundas de modelos conceituais, pelo m?todo das diferen?as finitas. Por meio de simula??o de propriedades influentes no transporte h?drico como taxa de recarga, vaz?o de bombeamento de po?os e condutividade hidr?ulica, foi poss?vel observar as varia??es nos valores m?ximos e m?nimos de carga hidr?ulica em pontos discretizados nos limites do modelo conceitual proposto, auxiliando assim no entendimento dos resultados obtidos. / Disserta??o (Mestrado Profissional) ? Programa de P?s-Gradua??o em Tecnologia, Sa?de e Sociedade, Universidade Federal dos Vales do Jequitinhonha e Mucuri, 2017. / The growing demand for the use of water resources in our society makes it necessary to expand the means of abstraction of water. Groundwater emerges as an alternative to conventional abstraction, owing to the storage of water in the lower layers of the soil ensures the maintenance of the quality of this resource, since they undergo natural filtration processes. In this sense, the characterization of the aquifer systems through mathematical modeling appears as a tool to aid in the understanding of the local underground flow. The present research has as main objective to analyze the hydrogeological behavior of Te?filo Otoni - MG, based on simulations derived from conceptual models, by the finite difference method. By means of simulation of influent properties in the water transport as recharge rate, well pumping rate and hydraulic conductivity it was possible to observe the variations in the maximum and minimum values of hydraulic head in discretized points within the limits of the proposed conceptual model, thus helping in the understanding of the results obtained.

>Magister Scientiae - MSc / We present various methods of pricing Asian options. The methods include Monte Carlo simulations designed using control and antithetic variates, numerical solution of partial differential equation and using lower bounds.The price of the Asian option is known to be a certain risk-neutral expectation. Using the Feynman-Kac theorem, we deduce that the problem of determining the expectation implies solving a linear parabolic partial differential equation. This partial differential equation does not admit explicit solutions due to the fact that the distribution of a sum of lognormal variables is not explicit. We then solve the partial differential equation numerically using finite difference and Monte Carlo methods.Our Monte Carlo approach is based on the pseudo random numbers and not deterministic sequence of numbers on which Quasi-Monte Carlo methods are designed. To make the Monte Carlo method more effective, two variance reduction techniques are discussed.Under the finite difference method, we consider explicit and the Crank-Nicholson’s schemes. We demonstrate that the explicit method gives rise to extraneous solutions because the stability conditions are difficult to satisfy. On the other hand, the Crank-Nicholson method is unconditionally stable and provides correct solutions. Finally, we apply the pricing methods to a similar problem of determining the price of a European-style arithmetic basket option under the Black-Scholes framework. We find the optimal lower bound, calculate it numerically and compare this with those obtained by the Monte Carlo and Moment Matching methods.Our presentation here includes some of the most recent advances on Asian options, and we contribute in particular by adding detail to the proofs and explanations. We also contribute some novel numerical methods. Most significantly, we include an original contribution on the use of very sharp lower bounds towards pricing European basket options.

In this thesis, a mathematical model for HIV and TB co-infection with TB treatment among populations of Ethiopia is developed and analyzed. The TB model includes an age of infection. We compute the basic reproduction numbers RTB and RH for TB and HIV respectively, and the overall repro- duction number R for the system. We find that if R < 1 and R > 1; then the disease-free and the endemic equilibria are locally asymptotically stable, respectively. Otherwise these equilibria are unstable. The TB-only endemic equilibrium is locally asymptotically stable if RTB > 1, and RH < 1. How- ever, the symmetric condition, RTB < 1 and RH > 1, does not necessarily guarantee the stability of the HIV-only equilibrium, but it is possible that TB can coexist with HIV when RH > 1: As a result, we assess the impact of TB treatment on the prevalence of TB and HIV co-infection. To derive and formulate the nonlinear differential equations models for HIV and TB co-infection that accounts for treatment, we formulate and analyze the HIV only sub models, the TB-only sub models and the full models of HIV and TB combined. The TB-only sub model includes both ODEs and PDEs in order to describe the variable infectiousness and e ect of TB treatment during the infectious period. To analyse and solve the three models, we construct robust methods, namely the numerical nonstandard definite difference methods (NSFDMs). Moreover, we improve the order of convergence of these methods in their applications to solve the model of HIV and TB co-infection with TB treatment at the population level in Ethiopia. The methods developed in this thesis work and show convergence, especially for individuals with small tolerance either to the disease free or the endemic equilibria for first order mixed ODE and PDE as we observed in our models. / Mathematical Sciences / Ph. D. (Applied Mathematics)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho o processo não linear de transmissão de calor condução-radiação é abordado num contexto bidimensional plano e simulado com o uso de um esquema linear em diferenças finitas. O problema original é tratado como o limite de uma sequencia de problemas lineares, do tipo condução-convecção. Este limite, cuja existência é comprovada, é facilmente obtido a partir de procedimentos básicos, accessíveis a qualquer estudante de engenharia, permitindo assim o emprego de hipóteses mais realistas, já que não se tem o limitante matemático para a abordagem numérica de uma equação diferencial parcial elíptica. Neste trabalho foi resolvido o problema de condução de calor em regime permanente em uma placa com condições de contorno convectivas e radioativas utilizando-se o software MatLab, vale ressaltar, que a mesma metodologia é aplicável para geometrias mais complexas. / In this work the nonlinear conduction-radiation heat transfer process is considered under a plane two dimensional assumption and simulated by means of a finite difference linear scheme. The original problem is regarded as the limit (which always exists) of a sequence of linear problems like the conduction-convection ones. Such a limit is reached in an easy way by means of standard procedures, available for any undergraduate engineering student, allowing the employment of more realistic hypotheses, since the mathematical complexities are not a constraint for simulating the elliptic partial differential equation. This work solved the problem of heat conduction in steady state conditions on a plate with convective and radioactive contour using MatLab software, it is noteworthy that the same methodology is applicable to more complex geometries.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Apresenta-se uma abordagemnumérica para ummodelo que descreve a formação de padrões por sputtering iônico na superfície de ummaterial. Esse processo é responsável pela formação de padrões inesperadamente organizados, como ondulações, nanopontos e filas hexagonais de nanoburacos. Uma análise numérica de padrões preexistentes é proposta para investigar a dinâmica na superfície, baseada em ummodelo resumido em uma equação anisotrópica amortecida de Kuramoto-Sivashinsky, em uma superfície bidimensional com condições de contorno periódicas. Apesar de determinística, seu caráter altamente não-linear fornece uma rica gama de resultados, sendo possível descrever acuradamente diferentes padrões. Umesquema semi implícito de diferenças finitas com fatoração no tempo é aplicado na discretização da equação governante. Simulações foram realizadas com coeficientes realísticos relacionados aos parâmetros físicos (anisotropias, orientação do feixe, difusão). A estabilidade do esquema numérico foi analisada por testes de passo de tempo e espaçamento de malha, enquanto a verificação do mesmo foi realizada pelo Método das Soluções Manufaturadas. Ondulações e padrões hexagonais foram obtidos a partir de condições iniciais monomodais para determinados valores do coeficiente de amortecimento, enquanto caos espaço-temporal apareceu para valores inferiores. Os efeitos anisotrópicos na formação de padrões foramestudados, variando o ângulo de incidência. / A numerical approach is presented for amodel describing the pattern formation by ion beam sputtering on a material surface. This process is responsible for the appearance of unexpectedly organized patterns, such as ripples, nanodots, and hexagonal arrays of nanoholes. A numerical analysis of preexisting patterns is proposed to investigate surface dynamics, based on a model resumed in an anisotropic damped Kuramoto-Sivashinsky equation, in a two dimensional surface with periodic boundary conditions. While deterministic, its highly nonlinear character gives a rich range of results, making it possible to describe accurately different patterns. A finite-difference semi-implicit time splitting scheme is employed on the discretization of the governing equation. Simulations were conducted with realistic coefficients related to physical parameters (anisotropies, beam orientation, diffusion). The stability of the numerical scheme is analyzed with time step and grid spacing tests for the pattern evolution, and the Method ofManufactured Solutions has been used to verify the scheme. Ripples and hexagonal patterns were obtained from amonomodal initial condition for certain values of the damping coefficient, while spatiotemporal chaos appeared for lower values. The anisotropy effects on pattern formation were studied, varying the angle of incidence.

Made available in DSpace on 2016-06-02T19:56:56Z (GMT). No. of bitstreams: 1 6271.pdf: 1816121 bytes, checksum: 358e1c3f7d194a552db21ddb44f4761c (MD5) Previous issue date: 2014-08-28 / Financiadora de Estudos e Projetos / In general, the chemical processes can be represented using mathematical models, in the case of lumped systems include ordinary differential equations, or, partial differential equations, when distributed parameter systems using methods is necessary in both cases numerical resolution in these models, with the purpose to simulate, analyze and control the process. The implementation of control systems in chemical processes, brings with it many advantages, among these, the improvement and stability in production rates, ensuring product quality and the possibility of a safe operation of the process. Thus, in the last 30 years, different control methodologies were developed, one of the most used techniques, the Model Predictive Control Based on. Its success is due to the fact that this type of control accepts constraints on input variables and process output, determining the future of this movement, while optimizing an objective function can lead to the output of the process until the desired set point. The objective of this project is to implement the Model Predictive Controller with Nonlinear (CPNL ) for a reactor pulp bleaching by the use of chlorine dioxide, whose mathematical model is comprised of partial differential equations, thus being a model parameter distributed. Implementation of the controller, the plant is discretized by the Finite Difference Method and the process model is solved with the technique of Orthogonal Collocation. The integration of the resulting ordinary differential equations systems is performed by the method of Runge-Kutta. The Predictive Controller was compared with a Controller Proportional-Integral (PI). Studies have shown that CPNL has better performance, with faster response and values of the Integral Absolute Error (IAE) and Integral Square Error (ISE) smaller than those calculated for the PI controller. / Em geral, os processos químicos podem ser representados mediante modelos matemáticos que, no caso dos sistemas de parâmetros concentrados, incluem equações diferenciais ordinárias, ou então, equações diferenciais parciais, quando são sistemas de parâmetros distribuídos, sendo necessário nos dois casos o uso de métodos numéricos na resolução destes modelos, com a finalidade de simular, analisar e controlar o processo. A implementação de sistemas de controle em processos químicos, traz consigo múltiplas vantagens, entre essas, a melhora e a estabilidade nas taxas de produção, a garantia da qualidade do produto e a possibilidade de uma operação segura do processo. Desta forma, nos últimos 30 anos, foram desenvolvidas diferentes metodologias de controle, sendo uma das técnicas mais empregadas, o Controle Preditivo Baseado no Modelo. Seu sucesso se deve ao fato de que este tipo de controle aceita restrições nas variáveis de entrada e saída do processo, determinando os movimentos futuros deste, além de otimizar uma função objetivo para conseguir levar a saída do processo até o Set-Point desejado. Assim, o objetivo deste projeto é implementar o Controlador Preditivo com Modelo Não Linear (CPNL ) para um reator de branqueamento de celulose, mediante o uso de dióxido cloro, cujo modelo matemático está constituído por equações diferenciais parciais, sendo assim, um modelo de parâmetros distribuídos. Na implementação do controlador, a planta é discretizada, mediante o Método das Diferenças Finitas e o modelo do processo é resolvido com a técnica de Colocação Ortogonal. A integração dos sistemas de equações diferenciais ordinárias resultantes é realizada mediante o método de Runge- Kutta. O Controlador Preditivo foi comparado com um Controlador Proporcional-Integral (PI). Os estudos mostraram que o CPNL possui melhor desempenho, apresentando uma resposta mais rápida e valores da Integral do Erro Absoluto (IAE) e a Integral do Erro Quadrático (ISE) menores que os calculados para o controlador PI.