TASK 1: A suspension is divided in two different aliquots containing 24 mL of solvent phase. Each aliquot is filtered under constant pressure conditions using different filtration conditions: slurry A is filtered using a pressure drop of 200 mbar, while slurry B is filtered using a pressure drop of 700 mbar. The diameter of the Nutsche filter is 27 mm. The slurry comprises ethanol (solvent density 0.789 g/cm³ and dynamic viscosity 1.095 CP) and spherical particles. Volume of cake formed by the passage of unit volume of filtrate is equal to 3. Filtration flow rate and time/volume of filtrate versus volume of filtrate removed during filtration for the two slurries are reported in the tables below. Slurry A Filtrate Volume A (mL) Filtrate Volume A (m³) Time A (s) Time/Volume A (s/m³) 0 0 15 1.5 x 10 22 2.2 x 10 24 2.4 x 10-5 Slurry B Filtrate Volume B (mL) 0 12 20 24 Time/Filtrate volume (s/m³) 2.5E+06 2.0E+06 1.5E+06 1.0E+06 5.0E+05 0.0E+00 Filtrate Volume B (m³) 0 1.2 x 10-5 2 x 10-5 From the filtration of slurries A and B, the graph of time/filtration volume is shown below. For each filtration a linear fit is shown. 2.4 0.E+00 x 10-5 -Filtration A -Filtration B 0 10 15 18 Time B (s) 0 15 34 47 N/A 6.67 x 105 6.82 x 105 7.5 x 105 Time/Volume B (s/m³) N/A 1.25 x 108 1.7 x 108 1.96 x 108 CP414 Particle Technology Workshop 7 y = 8.12E+10x +9.03E+04 1.E-05 2.E-05 Filtrate volume (m³) y = 3.10E+10x + 5.18E+04 3.E-05 (a) Calculate the compressibility index, n (-). (b) Identify if the cake is incompressible, compressible or highly compressible, to understand if Darcy's law is valid for this suspension.
TASK 1: A suspension is divided in two different aliquots containing 24 mL of solvent phase. Each aliquot is filtered under constant pressure conditions using different filtration conditions: slurry A is filtered using a pressure drop of 200 mbar, while slurry B is filtered using a pressure drop of 700 mbar. The diameter of the Nutsche filter is 27 mm. The slurry comprises ethanol (solvent density 0.789 g/cm³ and dynamic viscosity 1.095 CP) and spherical particles. Volume of cake formed by the passage of unit volume of filtrate is equal to 3. Filtration flow rate and time/volume of filtrate versus volume of filtrate removed during filtration for the two slurries are reported in the tables below. Slurry A Filtrate Volume A (mL) Filtrate Volume A (m³) Time A (s) Time/Volume A (s/m³) 0 0 15 1.5 x 10 22 2.2 x 10 24 2.4 x 10-5 Slurry B Filtrate Volume B (mL) 0 12 20 24 Time/Filtrate volume (s/m³) 2.5E+06 2.0E+06 1.5E+06 1.0E+06 5.0E+05 0.0E+00 Filtrate Volume B (m³) 0 1.2 x 10-5 2 x 10-5 From the filtration of slurries A and B, the graph of time/filtration volume is shown below. For each filtration a linear fit is shown. 2.4 0.E+00 x 10-5 -Filtration A -Filtration B 0 10 15 18 Time B (s) 0 15 34 47 N/A 6.67 x 105 6.82 x 105 7.5 x 105 Time/Volume B (s/m³) N/A 1.25 x 108 1.7 x 108 1.96 x 108 CP414 Particle Technology Workshop 7 y = 8.12E+10x +9.03E+04 1.E-05 2.E-05 Filtrate volume (m³) y = 3.10E+10x + 5.18E+04 3.E-05 (a) Calculate the compressibility index, n (-). (b) Identify if the cake is incompressible, compressible or highly compressible, to understand if Darcy's law is valid for this suspension.
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
ANSWERS ARE
W7/T1 (a) 2.58 for suspension A and 2.49 for suspension B
SHOW WORKING ON HOW TO REACH THESE PLEASE DONT COPY AND PASTE FROM OTHER ANSWERED QUESTIONS AS THESE ARE WRONG
Transcribed Image Text:TASK 1:
A suspension is divided in two different aliquots containing 24 mL of solvent phase. Each
aliquot is filtered under constant pressure conditions using different filtration conditions: slurry
A is filtered using a pressure drop of 200 mbar, while slurry B is filtered using a pressure drop
of 700 mbar. The diameter of the Nutsche filter is 27 mm.
The slurry comprises ethanol (solvent density 0.789 g/cm³ and dynamic viscosity 1.095 CP)
and spherical particles. Volume of cake formed by the passage of unit volume of filtrate is
equal to 3. Filtration flow rate and time/volume of filtrate versus volume of filtrate removed
during filtration for the two slurries are reported in the tables below.
Slurry A
Filtrate Volume A (mL)
0
15
22
24
Slurry B
Filtrate Volume B (mL)
0
12
20
24
Time/Filtrate volume (s/m³)
2.5E+06
2.0E+06
1.5E+06
1.0E+06
5.0E+05
From the filtration of slurries A and B, the graph of time/filtration volume is shown below. For
each filtration a linear fit is shown.
0.0E+00
Filtrate Volume A (m³) Time A (s)
0
0
1.5 x 10
10
2.2 x 10-5
15
2.4 x 10-5
18
Filtrate Volume B (m³)
0
1.2 x 10-5
0.E+00
2 x 10-6
2.4 x 10-5
-Filtration A
-Filtration B
Time B (s)
0
15
34
47
Time/Volume A (s/m³)
N/A
6.67 x 105
6.82 x 105
7.5 x 105
ON TENDEN
Time/Volume B (s/m³)
N/A
1.25 x 108
1.7 x 106
1.96 x 108
CP414 Particle Technology Workshop 7
y = 8.12E+10x + 9.03E+04
1.E-05
2.E-05
Filtrate volume (m³)
y = 3.10E+10x + 5.18E+04
3.E-05
(a) Calculate the compressibility index, n (-).
(b) Identify if the cake is incompressible, compressible or highly compressible, to understand
if Darcy's law is valid for this suspension.
![Example: leaf filtration
Leaf area=0.5m²
Constant pressure drop-500kPa
Incompressible cake produced
Volume of filtrate 0.1
collected (m³)
Time [s]
Solution point 1
140
Constant pressure filtration:
EL
Ees
et
EL
Calculate:
1. Time required to collect 0.8m² of filtrate at constant pressure drop of 700kPa
2. Time required to wash the resulting cake with 0.3m³ of water at pressure drop of 400kPa.
0
This worked example is reported in the suggested book "Introduction to particle technology" by Martin Rhodes.
This book is available through myPlace through the library (digital version available).
200
Solution point 2
0.2
360
NO
bationi
cuppe
24²(-6P) = 4000
Ergun equation:
-AP
0.3
1000
1dV
Adt
660
t
cropμ
R40μ
V 24²(-AP) A²-AP). In this case you don't need the value of Rm
GRADIENT
because you are just considering the
gradient and the intercept
A=0.5m² and (-AP) = 500 10³ Pa, app = 1 × 10° Pas/m² and V-0.125 m³
So substituting values in
510(4V+1) gives t-2400s (40mins)
(-AP)
INTERCEPT
Filtration cake resistance: a =
www
ZADO
= 150 HU(1-8)²
x²3
ΔΡ
Euler number: Eu =
Pp0²/2
M
500
Ru
4²(-AP) V-1000
During filtration:
• cake thickness continuously increases
• The volume of flow rate of filtrate continuously decrease (constant pressure case)
0
(-AP)A
au(V+Veg)
t
Constant pressure drop filtration: ==
0.4
1040
150(1-ɛ)²
£3
flow rate of wash (at 400kPa) = 1.89 +10 200-101.0810 m³/s
Hence the time needed to pass 0.3m³ of wash solvent at this flow rate is 2778s (46.3min).
Cake compressibility index: In a = n In AP
Substituting the filtrate passed at the end of filtration (0.8m3), using apu = 1+ 10⁹ Pas/m², V-0.125 m³ and (-AP) = 700.
10³ Pal
• Gradient part of the question is related to
cake resistance
1.89 104 m³/s
Assuming the wash solvent (water) has the same properties as the filtrate (density and viscosity), wash rate is equal to 1.89
10 m³/s at (-AP) = 700 + 10³ Pa.
However, during the washing the applied pressure difference is 400 10³ Pa:
αφμ
V 24²(-AP)
• Intercept part of the equation is related to
media resistance
-4000-1000
Gas cyclone characteristic gas velocity: v =
Va of
+1.75 PfU²(1-8)
XE³
0.5
1500
Correct solution:
три
• Divide axu by 2²(4)
• Divide (4V + 1) by 2-
(2V+0.5)
ES
-V+
2AP
Eu pf
RmDu
A²(-AP)
DE
Vea](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fde55ad6b-27eb-44c5-bca1-afdb32f2dfc7%2F31838e99-bc2a-4b4f-bf76-a105f49142df%2Fzdpggj_processed.png&w=3840&q=75)
Transcribed Image Text:Example: leaf filtration
Leaf area=0.5m²
Constant pressure drop-500kPa
Incompressible cake produced
Volume of filtrate 0.1
collected (m³)
Time [s]
Solution point 1
140
Constant pressure filtration:
EL
Ees
et
EL
Calculate:
1. Time required to collect 0.8m² of filtrate at constant pressure drop of 700kPa
2. Time required to wash the resulting cake with 0.3m³ of water at pressure drop of 400kPa.
0
This worked example is reported in the suggested book "Introduction to particle technology" by Martin Rhodes.
This book is available through myPlace through the library (digital version available).
200
Solution point 2
0.2
360
NO
bationi
cuppe
24²(-6P) = 4000
Ergun equation:
-AP
0.3
1000
1dV
Adt
660
t
cropμ
R40μ
V 24²(-AP) A²-AP). In this case you don't need the value of Rm
GRADIENT
because you are just considering the
gradient and the intercept
A=0.5m² and (-AP) = 500 10³ Pa, app = 1 × 10° Pas/m² and V-0.125 m³
So substituting values in
510(4V+1) gives t-2400s (40mins)
(-AP)
INTERCEPT
Filtration cake resistance: a =
www
ZADO
= 150 HU(1-8)²
x²3
ΔΡ
Euler number: Eu =
Pp0²/2
M
500
Ru
4²(-AP) V-1000
During filtration:
• cake thickness continuously increases
• The volume of flow rate of filtrate continuously decrease (constant pressure case)
0
(-AP)A
au(V+Veg)
t
Constant pressure drop filtration: ==
0.4
1040
150(1-ɛ)²
£3
flow rate of wash (at 400kPa) = 1.89 +10 200-101.0810 m³/s
Hence the time needed to pass 0.3m³ of wash solvent at this flow rate is 2778s (46.3min).
Cake compressibility index: In a = n In AP
Substituting the filtrate passed at the end of filtration (0.8m3), using apu = 1+ 10⁹ Pas/m², V-0.125 m³ and (-AP) = 700.
10³ Pal
• Gradient part of the question is related to
cake resistance
1.89 104 m³/s
Assuming the wash solvent (water) has the same properties as the filtrate (density and viscosity), wash rate is equal to 1.89
10 m³/s at (-AP) = 700 + 10³ Pa.
However, during the washing the applied pressure difference is 400 10³ Pa:
αφμ
V 24²(-AP)
• Intercept part of the equation is related to
media resistance
-4000-1000
Gas cyclone characteristic gas velocity: v =
Va of
+1.75 PfU²(1-8)
XE³
0.5
1500
Correct solution:
три
• Divide axu by 2²(4)
• Divide (4V + 1) by 2-
(2V+0.5)
ES
-V+
2AP
Eu pf
RmDu
A²(-AP)
DE
Vea
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