Teaching

CH235: Computer Oriented Numerical Analysis

Introduction

Programming for numerical solutions with high-level computer languages (Fortran, C) and mathematical packages (Mathematicaâ , Matlabâ ). Computer arithmetic and errors. Types of errors, error estimates and its propagation.

Matrix algebra

Definitions. Basic properties and operations. Numerical evaluation of the norm, condition number, rank and determinant of a matrix. Methods to solve banded and sparse matrices.

Linear algebraic equations

Solutions of systems of algebraic equations, existence and uniqueness of solutions. Numerical evaluation using Cramer’s rule, Gauss elimination with and without pivoting, LU decomposition, Cholesky factorization and Gauss-Jordan technique. Iterative techniques using the methods of Jacobi, Gauss-Seidel and overrelaxation. Convergence criteria and error estimation.

Eigenvalues and eigenvectors

Definition and properties. Numerical evaluation using Faddeev-Leverrier technique, power, inverse power and modified power methods. Application of Householder, Rutihauser LU and QR algorithms.

Non-linear polynomial equations

Numerical solutions using fixed point iteration method, Aitken acceleration, Newton-Raphson, regula falsi and Birge-Vieta. Methods for initial approximation and determination of complex roots with the methods of Lin and Baristow.

Function approximation

Linear regression. Interpolation using Newton’s forward, backward, divided differences. Properties, uses and types of interpolating polynomials like Bessel, Stirling and Lagrangian. Interpolation with periodic and non-periodic cubic splines and polynomial approximation of surfaces. Chebyshev polynomials and Pade’s approximation with rational functions.

Numerical integration and differentiation

Application of trapezoidal, Simpson, midpoint, Romberg and Monte-Carlo techniques. Adaptive integration and multiple integrals. Gaussian Quadrature. Numerical differentiation and derivatives of interpolating polynomials.

Ordinary differential equations

Initial value problems. Numerical solutions using Adams-Bashforth, Adams-Moulton, Euler and modified Euler methods. Application of Runge-Kutta methods and predictor-corrector techniques. Stability and convergence criteria, step-size control and error estimation. Higher order equations and systems of equations. Solutions of equations coupled with algebraic equations. Stiffness and Gear’s technique for stiff equations.

Boundary value problems. Shooting method. Solving characteristic value problems and problems with derivative boundary conditions. Formulation and application of finite differences. Application of orthogonal collocation and orthogonal collocation on finite elements for sharp gradients. Solutions with the Rayleigh-Ritz method.

Partial differential equations

Solutions of parabolic, hyperbolic and elliptic equations. Representation as a difference equation. Solution using the explicit, ADI and Crank-Nicholson techniques. Numerical stability and convergence criteria. Solving complex grids and irregular boundaries. Application of OC and OCFE techniques. Application of the Galerkin finite element method.

References

• Chapra, S.C. and Canale, R.P., Numerical Methods for Engineers, McGraw Hill, NY, 6th edition (2010).

• Gupta, S.K., Numerical methods for Engineers, New Age Publishers, India (2009).

• K.J. Beers, Numerical Methods for Chemical Engineering, Cambridge Univ. Press, Cambridge, UK (2010).

Course Policies

Grading

Two exams - 40%

Assignments - 10%

Final exam - 50%

All exams will be open notes. The final grades will be based on the total marks obtained relative to the class average.

Assignments

Assignments are an essential part of the learning process, especially in computational courses. All assignments will involve working with a computer using Fortran/C and Mathematica/Matlab. You will be required to submit assignments on time at regular intervals.

CH 236: Separation Processes

CH 237: Polymer Engineering and Science

Types of separation processes.

Types of polymerization processes.

Thermodynamics of separation processes: Nonideal property models and activity coefficient models.

Definitions; polymer, plastic, rubber, thermoplastic, thermoset, composite, glass transition; Size of polymers in solution and the molten state; number and weight average molecular masses, distribution of mass, polydispersity index; concepts of amorphous and crystalline polymers.

Single equilibrium stages and flash calculations: Multicomponent bubble and dew point calculations. Multicomponent Liquid - liquid, Solid - liquid, Gas - liquid, Gas - solid and multiphase systems.

Addition polymerisation; examples of addition polymers. kinetics of chain growth polymerisation; radical polymerisation, general concepts; initiation of radical polymerisation, types of initiation, chemistry of initiation, kinetics of initiation; initiator half lives; propagation of radical polymerisation.

Cascades: Configurations. Solid-liquid, liquid-liquid and vapor-liquid cascades.

Chemistry of propagation in radical polymerisation; termination in radical polymerisation, chemistry and kinetics, rate of radical polymerisation; chain transfer in radical polymerisation; kinetic chain length; molecular mass of radical polymerisation; chain transfer coefficients. Step growth/condensation polymerisation; examples of condensation polymers, general considerations for step growth polymerisation.

Distillation of Binary systems. LLE of ternary systems.

Methods for Multicomponent, multistage absorption, stripping, distillation and extraction : FUG, Equation-tearing, Inside-Out, Mesh methods.

Brief introduction to ionic polymerisation; process considerations in anionic polymerisation; concept of living polymerisation; PDI in anionic polymerisation.

Molecular masses of condensation polymers; effects of non stoichiometry; extent of reaction, Carothers equation; calculating Mn and Mw from extent of reaction; Flory-Schulz distributions; kinetics of step growth

Further examples of condensation polymers; consideration of the effects of side reactions in synthesis; biodegradable polymers

Copolymerization; types of copolymers; copolymer equation; reactivity ratios; determination of reactivity ratios; Kelen-Tudos; Mayo-Lewis.

Isomerism; sequence isomerism; stereoisomerism; bond structure; conformation; random walks.

Crystallization of polymers: Theory, population balance models and crystal size distributions. XRD; Flory model

Characterisation of polymers; solution viscometry; Lattice model; regular solution theory; Mark Houwink equation and constants; viscosity equations; Flory-Fox equation; hydrodynamic volumes, Factors affecting Tg; Phase behavior;

Determination of molecular weight; Viscosity based methods; Light scattering techniques; Gel permeation chromatography/ Size exclusion chromatography;: Theory and applications.

Mechanical properties; Maxwell mode; Voigt model; Elasticity theories; Rubber elasticity.

Chemistry and applications of commercial plastics; polymer processing extrusion, calendering, injection and compression moulding - engineering basis and applications

Course Policies

The course assumes the student has a good knowledge of chemistry and mathematics at the pre-university level.

Grading

Two exams - 50%

Final exam - 50%

The two exams are open notes and will be held from 9-11 am on the second or third Saturday of September and October. The final exam will be a combination of closed notes and open notes. The final grades will be based on the total marks obtained relative to the class average.

In addition, each student will be required to submit a term paper near the end of the semester. A list of possible topics for the paper are in the syllabus; other topics are highly encouraged. The paper should be about 10 pages of double spaced text, but fewer pages will be happily accepted as long as the paper has sufficient content. The paper will be graded as to 1) understanding of the topic (25%), 2) depth of search (25%, go narrow and deep, not wide and broad, for wide is the gate and broad is the way that leadeth to low scores), 3) critical analysis or engineering analysis (25%), and 4) report presentation (25%, grammar, length, neatness, etc.).

Enhanced distillation: Extractive, Salt, Reactive, Pressure - swing.

Supercritical extraction: Theory and applications.

Adsorption: Sorbents, equilibrium, kinetics and transport considerations. Modeling adsorption breakthroughs and desorption profiles. Types of adsorption including pressure-swing, thermal swing and slurry.

Chromatography: Theory and applications.

Crystallization: Theory, population balance models and crystal size distributions.

Course Policies

The course assumes the student has a good knowledge of thermodynamics, mass transfer and numerical methods.

Grading

Two exams - 30%

Projects - 20%

Final exam - 50%

The two exams are open notes and will be held from 9-11 am on the third or fourth Saturday of February and March. The final exam will be a combination of closed notes (10%) and open notes (40%). The final grades will be based on the total marks obtained relative to the class average. The projects will be entirely based on the usage of ASPEN PLUS* to solve various problems.

<>*ASPEN is a process-simulation software package that is widely used in industry. Given a conceptual process design, ASPEN uses mathematical models of process equipment and physical/thermodynamic properties to predict the performance of the process. This information can then be used in an iterative fashion to optimize the design. ASPEN can handle very complex processes, including multiple-column separation systems, chemical reactors, distillation of a chemically reactive compounds, and even electro­lyte solutions like mineral acids and sodium hydroxide solutions. It should be emphasized that ASPEN does not design the process. It takes a design that the user supplies and simulates the performance of the process specified in that design. A solid understanding of the underlying chemical engineering principles is needed to supply reasonable values of the input parameters and to evaluate the suitability of the predicted results. For instance, a user should have some idea of process equipment behavior before attempting to use ASPEN. Our goal in using ASPEN is to become familiar with its basic operation and to perform several material and energy balance calculations. Subsequently, you will use the full capability of ASPEN in simulating processes.