ChE 154 lecture 2a.pdf
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Transcript of ChE 154 lecture 2a.pdf
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Asst. Prof. Jewel A. CapunitanDepartment of Chemical EngineeringCollege of Engineering and Agro-Industrial TechnologyUniversity of the Philippines Los Baños
ChE 154 - Transfer Operations II1st sem. 2015-2016
PROPERTIES OF SOLIDS
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MIXTURE OF PARTICLES
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HOMOGENEOUS MIXTURE
mixture consisting of uniform particles.
the uniformity of the particles in the mixture must be
described by the following properties:
1. DENSITY (ρp
: same all throughout)
2. SHAPE (Φs : same all throughout)
3. PARTICLE SIZE
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HOMOGENEOUS MIXTURE
4. NUMBER OF PARTICLES (N)
N =
where : mt= total mass of sample
mρ
= mass of 1 particle
ρp
= density of 1 particle
Vp
= volume of 1 particle
m t
mρ
=mt
ρp v p
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HOMOGENEOUS MIXTURE
5. TOTAL SURFACE AREA (A)
A = NSp
=
where Sp
=surface area of 1 particle
6m t
φs ρ p D p
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HETEROGENEOUS MIXTURE
mixture of particles having various sizes and densities
sorting is done in order to separate the particles (i.e.
screening)
properties are not described by a single value but a
range or distribution of values due to the non-
uniformity of the particles present in the mixture.
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HETEROGENEOUS MIXTURE
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HETEROGENEOUS MIXTURE
1. PARTICLE SIZE DISTRIBUTION
shows the proportionate fraction of each size of
individual particles in the mixture
assumes that size is constant per fraction
Two methods of analysis:
a. Differential / Fractional Analysis
b. Cumulative Analysis
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HETEROGENEOUS MIXTURE
Example of PSD
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HETEROGENEOUS MIXTURE
Differential/Fractional Analysis
plot of mass fraction vs. average particle size
consists of a histogram along with a continuous curve
showing the distribution of the particles
The plot shows the intermediate fraction that has the
highest composition in the feed.
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HETEROGENEOUS MIXTURE
Example of Differential/Fractional Plot
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HETEROGENEOUS MIXTURE
Cumulative Analysis
plot of the cumulative sums of mass fractions versus thecorresponding particle size
consists only of a continuous curve
does not require the computation of the average screendiameter but the addition of fractions passing through thescreens
can be done in two ways:
a. Cumulative mass fraction larger than Dpi vs Dpi
b. Cumulative mass fraction smaller than Dpi vs Dpi
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HETEROGENEOUS MIXTURE
Example of Cumulative Plot
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HETEROGENEOUS MIXTURE
2. TOTAL SURFACE AREA
sum of the surface area of each fraction
where: Ai = area of each fraction
n = number of fractions
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HETEROGENEOUS MIXTURE
2. TOTAL SURFACE AREA
For each fraction:
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HETEROGENEOUS MIXTURE
3. NUMBER OF PARTICLES
sum of the number of particles in each fraction
particle
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HETEROGENEOUS MIXTURE
4. SPECIFIC SURFACE, AW
sum of the surface area of the particles in a fraction
equivalent to the total surface of the particles in a
fraction divided by the total mass of the fraction
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HETEROGENEOUS MIXTURE
5. AVERAGE PARTICLE SIZE
a. Volume-Surface Mean Diameter,
aka Sauter Mean Diameter
parameter mostly applied in chemical engineering
when surface area per unit volume is important such
as packing materials in gas absorption and
adsorption.
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HETEROGENEOUS MIXTURE
5. AVERAGE PARTICLE SIZE
a. Volume-Surface Mean Diameter,
obtained by measuring the volume and area of
entire sample and getting their ratio
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HETEROGENEOUS MIXTURE
5. AVERAGE PARTICLE SIZE
b. Arithmetic Mean Diameter or
Mean Length Diameter,
summation of all particle dimensions divided by the
total number of measurements.
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HETEROGENEOUS MIXTURE
5. AVERAGE PARTICLE SIZE
c. Mass Mean Diameter,
can be determined by taking the sum of all the
weighted mass of the particles and dividing it by the
total mass of particles
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HETEROGENEOUS MIXTURE
5. AVERAGE PARTICLE SIZE
d. Volume Mean Diameter,
gives the average volumes of the particles in the
mixture
can be obtained by getting the total volume of the
particles and dividing it by the total number of
particles
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HETEROGENEOUS MIXTURE
6. SPECIFIC NUMBER OF PARTICLES IN THE MIXTURE, NW
summation of the number of particles in a fraction
per total mass of particles
assumes that each particle has the same shape and
density
where a = is the volume shape factor:
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HETEROGENEOUS MIXTURE
Example 3 (McCabe et al., 1993)
The screen analysis shown in Table 3 is applicable to a
sample of crushed quartz. The density of the particles is
2650 kg/m3 and the shape factors are a=2 and Φs=0.571.
(a) Based on Table 3, construct differential and cumulative
plots.
(b) For the material between 4 mesh and 200 mesh in
particle, calculate the specific surface in mm2/g, the
specific number of particles in particles per gram, volume
mean diameter, Sauter mean diameter, and number of
particles for the fraction at mesh 150/200.
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HETEROGENEOUS MIXTURE
Given PSD for Example 3
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Solution
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Solution
(a) Differential & Cumulative Plots
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Solution
(a) Differential & Cumulative Plots
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Solution
(b) Specific surface, AW
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Solution
(b) Specific number of particles, NW
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Solution
(b) Volume mean diameter
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Solution
(b) Sauter mean diameter
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Solution
(b) Number of particles for the fraction at mesh 150/200
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METHODS OF DETERMINING PARTICLE SIZE
method to be used depends on (a) size range, (b) physicalproperties of the particles and (c) moisture content of theparticles.
1. Microscopic Method
Particles are enlarged under the microscope and are directlymeasured (ex. Putting scale on top of the particles image)
Usually used in determining effectiveness of air bag filters andmeasuring dust particles in the air
Disadvantages:
a. Collection of sufficient data to ensure adequate precision
b. Operator fatigue
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METHODS OF DETERMINING PARTICLE SIZE
2. Sedimentation Method
Done by mixing a sample of solid in water and then shaking
The size can be determined by making use of the settling
velocity equations, which is a function of Dp
3. Screening Method (use of standard sieves)
Can be done by either mounting the screens on a vibrator
(horizontal and/or vertical shaking) or may be hand shaken
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END OF LECTURE
REMINDERS!
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