### Master’s Degree

Currently, 22 credits are required to obtain a Master's Degree in Chemical Engineering (M. Eng.) At UFPA's PPGEQ, as detailed below:

a) 08 credits in compulsory subjects;

b) 10 credits in optional subjects of the PPGEQ or credits of other Graduate Programs of related areas.

Note: The number of credits transferred from courses of other postgraduate programs may not exceed 1/3 (one third) of the total number of credits required to obtain the degree. Only credits obtained up to 5 (five) years prior to the request will be accepted for revalidation.

c) 04 credits in complementary subjects of the PPGEQ:

- Directed Study - which consists of preparing and submitting a scientific article in a periodical of recognized quality in the area or related;

- Seminar of Chemical Engineering.

Also required are other curricular activities that do not add credits for the course payment, but are compulsory:

- Pass the English language proficiency test,

- Qualification examination and

- Defense of the dissertation.

Required Subjects (C.H. = 30 and C.U. = 02):

**PPGEQ0029 - Chemical Reaction Engineering I**

Kinetics of homogeneous reactions. Interpretation of kinetic data in discontinuous reactors. design of ideal reactors operating in isothermal conditions, in a homogeneous phase. Deviation of behavior in real reactors. Liquid phase reactions. Chain reactions. Solid catalysed reactions. Kinetics of fluid-solid catalytic reactions.

**PPGEQ0030 - Mathematical Methods in Chemical Engineering I**

Ordinary Differential Equations. Fourier series. Taylor Series. Series Solutions of Ordinary Differential Equations. Equations of Bessel. Equations of Legendre. Equations of Chebishev. Solutions of Laplace Transform ODEs. Partial Differential Equations: Separation of variables. Approximate integral methods for EDP solutions.

**PPGEQ0031 - Chemical Thermodynamics I**

Fundamental Concepts. Thermodynamics of Equilibrium. Thermodynamic Properties of Pure Substances. P-V-T relationships. Thermodynamic Treatment of Solutions. Theory of Solutions. Chemical Potential. Fugacity and Coefficient of Fugacity. Equations of State. Chemical balance. Balance in Homogeneous Systems. Balance in Heterogeneous Systems.

**PPGEQ0032 - Quantity Transfer of Motion**

Introduction to Transport of Quantity of Movement. Continuity equation. Equations of Motion. Tensor Voltage and Constitutive Equations. Newtonian and Non-Newtonian Fluids. Single and Two-Dimensional Flows. Introduction to Turbulent Flow. Limit Layer Theory. Functions Materials for Non-Newtonian Fluids. Equations Constitutive. Particular solutions of the Equations of motion in the Laminar Flow of Non-Newtonian Fluids.

Elective Subjects (C.H. = 45 and C.U. = 03):

Transport of Heat in Solids and Fluids. Equation of Energy. Differential and integral formulation. Thermal Limit Layer. Forced convection in the interior of ducts. Natural convection in laminar regime. Applications: Heat Exchangers.

**PPGEQ0019 - Liquid Waste Control**

Characterization of the liquid waste according to its origin. Main processes used in the treatment. Identification of process parameters. Environmental impacts caused by liquid waste.

**PPGEQ0011 - Kinetics and Calculation of Chemical Reactors**

Stoichiometric Calculations. Thermodynamics of Chemical Reactions. Chemical Kinetics of Homogeneous Reactions. Design Calculations for Isothermal Reactors. Design Calculations for Non-Isothermal Reactors. Design Calculations for Non-ideal Reactors.

**PPGEQ0038 - Enzymatic Kinetics and Bioreactors**

Enzymatic kinetics in homogeneous phase. Catalytic properties of the free enzyme. Biocatalysts immobilized. Applications of enzymatic catalysis in aqueous and organic media. Design and analysis of bioreactors.

**PPGEQ0033 - Quality Control of Biofuels**

Quality of vegetable oils used in the production of biodiesel. Analytical techniques and methodologies of vegetable oils (AOAC, AOCS, scientific literature). Quality control of biodiesel. Biofuel analytical techniques and methodologies (ASTM, ABNT and scientific literature). Factors Affecting the Quality of Vegetable Oil and Biodiesel

**PPGEQ0007 - Solid Waste Control**

Characterization of solid waste. Segregation and pretreatment. Projects of treatment and / or final disposal systems. Constructive, operational and maintenance aspects.

**PPGEQ0020 - Phase Equilibration at High Pressure**

Equations of state. Phase diagrams. Treatment of the phase equilibrium with state equations. Solubility of solids and liquids in supercritical gases. Correlation of phase equilibrium data with cubic state equations. Modeling and simulation of the liquid-vapor equilibrium with cubic state equations of multicomponent systems

**PPGEQ0048 - Fundamentals and Applications of Electrochemistry**

electrochemical Thermodynamics. The double electric layer. Kinetics of electrode reactions. Mass transfer by migration and diffusion. Main DC and AC techniques of electrochemistry. Rotary disc electrode theory.

**PPGEQ0041 - Modeling and Simulation of Separation Processes**

The thermodynamics of multicomponent mixtures. Modeling the phase equilibrium of multicomponent systems at low and high pressures. Mathematical methods and computational techniques applied to the modeling and simulation of separation processes. Thermodynamic analysis of the separation of complex systems. Simulation of separation processes employing process simulator.

**PPGEQ0081 - Thermodynamic Modeling of Complex Systems**

Supercritical fluid-fluid equilibrium and supercritical fluid-solid equilibrium. Methods for the correlation of equilibrium data at high pressures using the flash, bubble and dew algorithms. Mathematical methods for the determination of binary interaction parameters of state equations. Functions Objective. Correlation of supercritical fluid-fluid equilibrium data and supercritical solid-fluid equilibrium of natural products in supercritical carbon dioxide. Optimization of equilibrium data regression.

**PPGEQ0034 - Mathematical Methods in Chemical Engineering II**

Partial Differential Equations. Variable Separation Method. Green Functions. Duhamel's theorem. Problems of Sturm-Liouville. Technique of the Classical Integral Transformation. Generalized Integral Transformation Technique. Laplace transform. Nonlinear Problems: Kirchhoff's Transform.

**PPGEQ0035 - Numerical Methods in Chemical Engineering**

Interpolation; Numerical integration; Numerical differentiation; Solution of systems of linear equations; Solution of equations of non-linear systems (Polynomial and transcendental); Numerical solution of ODEs; Numerical solution of EDPs.

**PPGEQ0017 - Experiment Planning**

Fundamentals of descriptive and inferential statistics: measures of central tendency and variability, confidence intervals and hypothesis tests. Correlation and regression analysis. Analysis of variance. Planning and analysis of experiments: complete and fractional factorial planning. Surface response methodology. Statistical optimization of processes. Case studies in Chemical Engineering.

**PPGEQ0042 - Processes of Transformation of Vegetable Oil**

Pretreatment: Particle size, heat effect, moisture, etc .; Methods of Vegetable Oil Extraction: Press extraction, solvent extraction and pressurized solvent extraction; Characterization techniques: Iodine index, acid number, saponification index, peroxide, gas chromatography, high performance liquid chromatography, density, viscosity, flash point, UV / VIS spectrophotometry. Composition and properties of vegetable oils. Techniques of production and treatment of vegetable oils. Chemical transformation of vegetable oils. Transesterification. Thermal cracking. Production of biodiesel: reaction and purification.

**PPGEQ0013 - Drying: Fundamentals and Practice**

Introduction. Fundamentals of solid drying. Mechanisms and drying kinetics. Experimental techniques in drying. Basic calculation processes in drying. Classification and selection of dryers. Industrial Drying: drying of agricultural products, drying of granular material, drying of fibrous material, drying of pastes.

**PPGEQ0077 - Process Simulators and Thermodynamic Models**

Thermodynamics of multicomponent mixtures. Prediction of properties of pure substances and mixtures. Thermodynamic packages available on Aspen Hysys, Aspen Properties and Aspen Plus simulators. Prediction of phase equilibrium using the UNIFAC method for the liquid phase. Determination of model interaction parameters for the liquid phase. Determination of interaction parameters for cubic state equations. Case studies in process simulators with different thermodynamic models involving: reaction, absorption, liquid-liquid extraction, distillation and supercritical extraction

**PPGEQ0008 - Phase Equilibrium Thermodynamics**

Phase Balance. The liquid and vapor phases. Liquid-vapor balance. Liquid-liquid balance. Solid-liquid balance. Treatment of the phase equilibrium at low pressures. Experimental determination of phase equilibrium data. Correlation and prediction of liquid-vapor and liquid-liquid balance data.

Diffusivity and mass transfer mechanisms. Mass balances. Continuous diffusion without chemical reaction. Diffusion with chemical reaction. Transient diffusion. Mass transfer by convection. Mass transfer between phases. Mass transfer porous media.

**PPGEQ0052 - Special Topics in Environmental Control: Adsorption and Environmental Applications**

Principles of Adsorption. Properties and selection of adsorbents; Adsorption equilibrium (theoretical and experimental). Adsorption kinetics (transport mechanisms). Continuous adsorption in fixed bed column: mass transfer zone and rupture curve, design parameters. Fixed-bed adsorber design: scale-up method and kinetic method Environmental processes and applications: removal of gaseous and liquid current pollutants. Seminar: study case.

Access to genetic heritage with associated traditional knowledge. Collection, transport and storage of natural products. Treatment of the raw material. Extraction processes. Methods of isolation. Spectroscopic methods of analysis

**PPGEQ004303 - Special Topics in Chemical Engineering: Thermal-Catalytic Cracking of Vegetable Oils**

(IR, GC-MS, etc.), Influence of Process Parameters (Temperature and Catalyst Content) on the Quality and Efficiency of the Liquid Product, Methods of Purification (Distillation, Liquid-Liquid Extraction, Adsorption)

**PPGEQ004305 - Special Topics in Chemical Engineering: Crystallization in the Bayer Process**

Industrial Crystallization: Nucleation, Crystalline Kinetics, Particle Characterization, Crystal Growth, Precipitation, Introduction to Population Balance, Precipitation Control

**PPGEQ0043010 - Special Topics in Chemical Engineering: Computational Fluid Dynamics**

Review and classification of flows. Conservation equations: mass, momentum and energy. Fundamentals of numerical simulation of flows. Concepts of finite differences and volumes. Discretization of equations. Numerical formulations for the approximation of the convective term. False diffusion. Permanent and transient regime (explicit and implicit methods). Coupling Speed-Pressure: SIMPLE, SIMPLEC, FLOOR and Coupling. Incompressible iterative algorithms for flow. Segregated and coupled methods. Stability and precision of the numerical solution. Structured and unstructured meshes. Generation of mesh. Application of commercial software for the solution of real problems of mechanics of the fluids and transfer of heat.

**PPGEQ0043011 - Special Topics in Chemical Engineering: Biotechnological Process Engineering**

Introduction to Bioprocess Engineering. Ideal Biochemical Reactors: Material balance equations. Aeration and agitation of bioreactors. Instrumentation and control of bioreactors and non-conventional bioreactors. Transport Phenomena in Bioprocess Engineering. Kinetics Enzyme: General principles, advantages and disadvantages in biocatalysis; Enzymatic properties; Aspects of the mechanisms of enzymatic reactions; Ranking; Nomenclature; Coenzymes; Source of enzymes; Main types of enzymatic reactions: hydrolysis, reduction, oxidation, formation of carbon-carbon bonds. Magnification of scale. Case Study.

**PPGEQ004302 - Special Topics in Chemical Engineering: Heterogeneous Fluidization**

Characterization: Particle Size and Shape, Flow in Porous Media: Mixture Theory and Constitutive Equations. Foundations and industrial applications of fluidized beds. Classification of Systems. Conventional Fluidized Bed: Bubble Flow and Formation Model, Heat and Mass Transfer, Dimensioning and Optimization of Equipment. Jet bed: Jet dynamics. Non-Conventional beds: Jet-Fluidized, Vibro-Fluidized, Fluidized mechanically stirred, pulse-fluidized.

Theoretical fundamentals of supercritical fluid technology. Differential mass balance in packaged beds. Types of kinetic curves of supercritical extraction. Determination of the dynamic solubility and other kinetic parameters of solutes in supercritical solvents from data of global curves of extraction of solid matrices. Mathematical models of mass transfer.

**PPGEQ004307 - Special Topics in Chemical Engineering: Molecular Modeling of Biofuels.**

Application of the Theoretical Methods of Molecular Dynamics, Monte Carlo Method and Functional Density Theory in the Prediction of Physical and Thermophysical Properties of Biodiesel Chemicals and Biofuels Fractions (Green Gas, Green Kerosene, Light Diesel and Green Diesel) obtained by Distillation of PLO (Organic Liquid Product). This discipline aims to apply computational methods (theoretical methods of Molecular Dynamics, Monte Carlo Method and Functional Density Theory) to understand the physical behavior of the constituent molecules of Biofuels, as well as to analyze the limitations and prediction potential of theoretical methods.

Methods of Finite Differences: Discretization of the heat and mass diffusion equations with chemical reaction in permanent and transient regime; Discretization of heat and mass transport equations by convection with chemical reaction in permanent and transient regime. Programming in Fortran language: Informal concept of algorithms. Introduction to programming logic. Structured programming. FORTRAN: Elements of language and applications. Symbolic Programming in Mathematica: Basic commands and instructions. Programming in Mathematica. Development of automata in Mathematica.

**PPGEQ004308 - Special Topics in Chemical Engineering: Computational Methods**

Fundamental concepts: Physical and mathematical models. Differential equations: elliptic, parabolic and hyperbolic problems. Energy conservation equations, Convection heat transfer. Methods for solving systems of algebraic equations. Iterative method for approximation of nonlinear equations. Methods of Finite Differences: Concept, derivation of finite difference schemes, Implicit and explicit schemes. Consistency, stability and convergence. Discretization of the thermal diffusion equations in steady state, convection and the wave equation. Analysis of the stability and order of time advance schemes: Crank-Nicolson, implicit, explicit, Lax, Lax-Wendroff, MacCormack and Upwind. Treatment of boundary conditions. Two-dimensional and three-dimensional problems. Application in solving diffusion problems. Numerical Mesh Generation: Definition. Application. Arbitrary domain mappings for regular domains, coordinate transformation equations, using the Poisson and Laplace equations. Transformation of the differential equation

(Acidity Index, Saponification Index, Iodine Index, Peroxide Index, Density, Viscosity, Refractive Index, Water Content, Ash Content, etc.) Chemical Processes (IR, GC, etc.), Process Parameters Influence (Temperature, Catalyst Content, Molar Oil / Alcohol Ratio) on Biodiesel Quality and Efficiency, Methods (Distillation, Centrifugation, Decanting, Liquid-Liquid Extraction, Adsorption), Biodiesel Quality Control according to ANP.

**PPGEQ004309 - Special Topics in Chemical Engineering: Membrane Separation Processes**

Classification of membrane processes and their applications. Preparation techniques of the different types of polymer membranes. Mechanisms of transport and models. Types of modules and their main characteristics. Reverse osmosis and ultrafiltration: theoretical underpinnings, phase inversion membrane synthesis; influence of the synthesis variables on the transport characteristics of the membranes. Polarization of concentration. Influence of operational variables; applications. Design for a specific application. Pervaporation and separation of gases: theoretical foundations; synthesis of dense and composite membranes. Influence of operating variables. Design for a specific application.

**PPGEQ0047 - Special Topics in Chemical Engineering: Separation Processes**

Treatment of particulate solids. Processes of mechanical separation: filtration, sedimentation, etc. Electrical and magnetic separations. Flotation. Crystallization

**PPGEQ0057 - Special Topics in Chemical Engineering: Industrial Processes**

Introduction. General considerations. Review of Concepts. Direct Heating. Steam Heating. Evaporation: Types of evaporators. Operation of the Evaporator. Heat Transfer Coefficients. Boiling point rise. Methods of Calculation of Simple and Multiple Effects Evaporators. Mass and Energy Balances. Application Exercises. Industrial Process of Zeolites. Industrial Processes of Mineral-Metallurgical Industry Waste: Case studies.

Foundations and importance of the production of biofuels. Technological routes for the production of biofuels. Application of separation processes in the treatment of biofuels. Importance and application of catalysts. Production of catalysts. Deactivation of catalysts. Elaboration of process parameters of biofuel production from the technological cracking route.

**PPGEQ0074 - Special Topics in Chemical Engineering: Supercritical Extraction Process Design**

Fundamental aspects for the design of the supercritical extraction process. Analysis of the global curves of supercritical fluid extraction of solid matrices. Mathematical modeling of global extraction curves. Correlations for scale expansion of the supercritical fluid extraction process in packaged beds. Preparation of a database of the parameters required for the process design. Expansion of scale employing process simulators.

**PPGEQ004304 - Special Topics dm Chemical Engineering: Solvatation**

Thermodynamic formulation for solvation, free energy of solvation, cavitation, cavitation energy, van der Waals energy, molecular geometry in solutes, dispersion energy, solvation models, solvation dynamics

Fundamental aspects of supercritical technology. Separation processes in countercurrent of liquids. Supercritical separation process in countercurrent in multistage. Applications of the supercritical technology to the fractionation of liquid mixtures: citrus oils deterpenation; deacidification of vegetable oils, fractionation of distillates from deodorization of vegetable oils, extraction and concentration of nutraceuticals, separation of organic from aqueous solutions; separation of reagents and reaction products in supercritical medium.

**PPGEQ0043013 - Special Topics in Chemical Engineering: Materials Characterization Techniques**

1) Chemical bonds. 2) Solid state physics Crystallography Chemical bonding Crystalline structure of solids X-ray diffractometry - Brag's law Spectrometric analytical methods Emission spectrum spectrometry Atomic absorption spectrometry Ionic plasma spectrometry (ICP) 3) Characterization of metallic materials - Metallography of Materials ferrous alloys (Fe-C alloy), (carbon steels and cast iron) - Metallography of Stainless steels. Non-destructive tests: - Ultrasonography - Magnetic dust - Penetrant liquid - Thermal treatment and its phase change 4) Characterization of Ceramic Materials Thermal Analysis - ATD (Differential Thermal Analysis) - ATG (Gravimetric Thermal Analysis) Granulometric Analysis - Analysis granulometry by laser 5) Microscopy - Conventional Optical Microscopy - Scanning Electron Microscopy.

**PPGEQ0051 - Special Topics in Materials: Post-Ceramic Technology**

Introduction to Ceramics: Introduction; Basic Principles and Definitions of Refractory Oxides; Flux Oxides; Oxides of Glass; Sintering. Classification: Types of Ceramics - Classification: Traditional Ceramics; Red Ceramics; White Ceramics; Fine Ceramics (Porcelain); Refractory; Thermal insulation; Glass. Raw Materials: Kaulins; Plastic clays; Baby powder; Pyrophyllite; Wollastonite; Feldspars; Quartz; Auxiliary materials; Deflocculants; Flocculants; Binders; Wetting Lubricants. Methods of Analysis and Control in Ceramics: Chemical Analysis; X-ray diffraction (XRD); Differential Thermal Analysis (ATG); Thermogravimetric Analysis (ATG); Sieve analysis; Scanning Electron Microscopy (SEM); Apparent Specific Mass Measurement (MEA); Porosity; Flexural rupture stress (TRF) in Ceramic Materials. Manufacturing Processes: Crushing; Milling; Homogenization; Drying and Types of Dryers; Manual Conformation; Dry Pressing; Conformation by Plastic Press; Extrusion Conformation; Conforming by Bonding; Injection Conformation; Burning or sintering; Types of Ovens; High Temperature Chemical Reactions. Use of Phase Diagrams in Ceramics: Binary Diagrams; Ternary Diagrams; Formulation of Pasta and Barbin from Phase Diagram. Materials Balance in Ceramic Processing. Energy Balances in Ceramic Processing. Advanced Ceramics: Raw Materials; Ceramics of Aluminas; Zirconium; PZT. Advanced Ceramics Manufacturing Processes - Ceramic Post Synthesis.

**PPGEQ0025 - Special Topics in Modeling and Simulation of Processes: Hybrid Methods**

Classification of EDPs. Classical problems, mathematical representations. The classical integral transform method. The generalized integral transform method. Laplace transform with numerical inversion. applications

**PPGEQ0026 - Special Topics in Separation Processes**

Distillation, Absorption, Liquid-Liquid Extraction, Adsorption, Solid-Liquid Extraction.

**PPGEQ0043 - Special Topics in Chemical Engineering: Introduction to Nanotechnology**

Introduction to nanotechnology (quantum confinement effect, property due to size, surface effects); - Techniques for the preparation of botom up and top-up nanomaterials (sol-gel, colloidal methods, CVD, template etc .; - Main techniques of characterization of nanomaterials and their applications (TEM, MEV, IR spectroscopies, Raman, UV-Vis); - Nomenclature (basic concepts and examples) - Polymeric nonocomposites: Classification, production, application and examples - (Basic concepts, production methods and examples) - nono-structured films (basic concepts, production methods and examples) - metallic, ceramic and polymer nanoparticles: methods of preparation, classification, characterization and applications.

**PPGEQ0043 - Special Topics in Chemical Engineering: Rheology - Principles and Applications**

Tension and deformation. Conservation equations. Non-Newtonian fluids and viscoelasticity. Rheometria. applications