Multiphase systems
Multiphase systems
Phase diagrams
Phase diagram for water
P
Supercritical
Fluid
218.3 atm
1 atm
Critical
Point
Liquid
d
Gas
So
li
A plot of one system variable against another showing conditions
at which a substance exists as a solid, l
Distillation
Distillation
Distillation
Flash vessel
V, y
The most common or prevalent method of separating mixtures for
purification is distillation:
Flash Distillation versus Rectification Distillation :
I
I
both based on boiling of liquid mixtures but l
Introduction to Chemical Reactors
Part of CENG1004 Course, Introduction to Chemical
Engineering
A. Gavriilidis
1
Some recommendations
Aide memoir
Take notes
Useful Books
Coulson and Richardsons, Chemical Engineering, Volume 3, Chapter 1, 3rd
Edition, 1994
Energy Balances
Energy Balances
Energy Balances
Example 7.2-1
Forms of energy:
kinetic due to motion relative to some frame of reference:
Ek = 12 mv 2 where v is the velocity (and E k = 12 mv
2 ).
potential due to position within a potential field, such
Sensible & Latent heats
Sensible & Latent heats
Types of heat
Sensible heat
In working with materials, we can classify heat in two ways depending
on what effect it has on material:
sensible heat which signifies heat that must be transferred to
raise or lo
Introduction
Recommended textbooks
Process Analysis
Mass and energy balances
1
Professor Eric S Fraga
2
Room 2.05, Engineering Front Building
Department of Chemical Engineering
phone: 020 7679 3817 / x33817
email: e.fraga@ucl.ac.uk
web: www.homepages.ucl.
Heats of reaction
Heats of reaction
Observations
Heat of reaction
r (T , P) is the enthalpy change for a process in which
H
stoichiometric quantities of reactants at temperature T and pressure
P react completely in a single reaction to form products at t
Material balances for reactions
Material balances for reactions
Chemical Reactions
Stoichiometry
Mass balance analysis for processes involving reactions must include
the consumption and generation terms from the general mass balance
equation:
input + gene
Single phase systems
Single phase systems
Estimates of density
Ideal Gases
Liquids and solids are essentially incompressible. We can estimate the
average density of a mixture, by
1 X xi
=
i i
The ideal gas equation of state
if we assume volume additivity
Engineering Mathematics 2
Assignment 9
1. State the Divergence Theorem. Evaluate both sides of the Divergence Theorem for the vector
field =
over a volume V which is the interior of the unit cube, i.e. the cube whose
vertices are (0,0,0, (1,0,0), (0,1,0),
Engineering Mathematics 2
Assignment 12
1. A 2 - periodic function ( ) can be represented in Fourier-series form
( )=
(
+
cos
+
sin
)
Show that the coefficients are given by Eulers formulae
=
=
=
1
1
1
2
( )d
( ) cos
d
( ) sin
d
n =1, 2,3,
2. Consider
Engineering Mathematics 2
Assignment 11
1. Evaluate
.d
where, is the circle
+
= 4, = 3 orientated counterclockwise as seen by a person
standing at the origin, and with respect to right-handed Cartesian coordinates.
Here,
=
+
Use Stokes Theorem to evaluate
Engineering Mathematics 2
Assignment 8
1. Calculate
.d
where
=4
(a) C:
=
(b) C:
=
2. If
=
3 +2
+ +
0 1
+ +
+
over each of the following curves from (0, 0, 0) to (1, 1, 1)
0 1
, evaluate
. d
where S is the rectangular box formed by the six planes
= 0, =
Engineering Mathematics 2
Assignment 10
1. Verify the conclusion of Greens Theorem (Curl integral) by evaluation of both sides of
Greens Theorem for the field = + . Take the domains of integration in each case to be
the disk R: +
and its bounding circle
Nazarbayev University, School of Engineering, Eng Maths 2
Engineering Mathematics 2
Assignment 4
Learning Outcomes: This assignment will give you practice in
Div, Grad and Curl
Taylor Series for more than one variable
1. (a) Find the gradient of the scala
Nazarbayev University, School of Engineering, Eng Maths 2
Engineering Mathematics 2
Assignment 2
Learning Outcomes: This assignment will give you practice in
investigating the equations of cross-sections for a function of 3 variables
parameterizing a spac
Nazarbayev University, School of Engineering, Eng Maths 2
Engineering Mathematics 2
Assignment 1
Learning Outcomes: This assignment will give you practice in
double and triple integrals
curves and surfaces
vectors including scalar and vector products
grad
CENG1001 Transport Processes I Deadlines: Qu 1 & 2 : Qu 3 & 4: Friday 18th December 2009 Friday 15th January 2010
Coursework
1.
2009, Q6 Heat is conducted through a large flat wall of uniform thickness, which is made of material whose thermal conductivity