3.51 A hollow-fiber membrane device like the one described in Problem 3.17: operated to achieve the fermentation of glucose to ethanol using yeast cells Yeast cells are immobilized on the outside walls of the hollow fibers (i.e. the yeast cells are in the outer, annular space). To seed the unit, 1.0 × 10 celle are added to the reactor. The cells attach to the fibers. Initially after seeding the cell generation rate increases. However, as the cells begin to cover the fibers, the generation rate slows. The change in cell reproduction rate occurs as shown in Figure 3.45. The generation rate, Veens is modeled as follows: (kdeg, kes Vss Rrec cells V gen = 1.0 X 106. day sin 12 days. where t is the time in units of days. Cells die at a constant rate of 1.0 X 104 cells/day. Determine the number of cells in the reactor at 12 days. 1.0E + 06 9.0E + 05 8.0E + 05 7.0E + 05 H (aoobrs) 6.0E + 05 H 5.0E + 05 H0S bruod 4.0E + 05 H 3.0E + 05 H h Innstib hue od 2.0E + 05 1.0E + 05 0.0E + 00 0. nODEL 4 12 to 6. 8 10 Cell generation rate (cells/day)
3.51 A hollow-fiber membrane device like the one described in Problem 3.17: operated to achieve the fermentation of glucose to ethanol using yeast cells Yeast cells are immobilized on the outside walls of the hollow fibers (i.e. the yeast cells are in the outer, annular space). To seed the unit, 1.0 × 10 celle are added to the reactor. The cells attach to the fibers. Initially after seeding the cell generation rate increases. However, as the cells begin to cover the fibers, the generation rate slows. The change in cell reproduction rate occurs as shown in Figure 3.45. The generation rate, Veens is modeled as follows: (kdeg, kes Vss Rrec cells V gen = 1.0 X 106. day sin 12 days. where t is the time in units of days. Cells die at a constant rate of 1.0 X 104 cells/day. Determine the number of cells in the reactor at 12 days. 1.0E + 06 9.0E + 05 8.0E + 05 7.0E + 05 H (aoobrs) 6.0E + 05 H 5.0E + 05 H0S bruod 4.0E + 05 H 3.0E + 05 H h Innstib hue od 2.0E + 05 1.0E + 05 0.0E + 00 0. nODEL 4 12 to 6. 8 10 Cell generation rate (cells/day)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
Q: Determine the number of cells in the reactor at day 12.
![1 107
(kdeg, kes Vss Rrec
3.51 A hollow-fiber membrane device like the one described in Problem 3.17 :.
operated to achieve the fermentation of glucose to ethanol using yeast cell.
Yeast cells are immobilized on the outside walls of the hollow fibers (i.e. the
yeast cells are in the outer, annular space). To seed the unit, 1.0 × 105 cell.
are added to the reactor. The cells attach to the fibers. Initially after seeding
the cell generation rate increases. However, as the cells begin to cover the
fibers, the generation rate slows. The change in cell reproduction rate occurs
as shown in Figure 3.45. The generation rate, cen, is modeled as follows:
cells
gen = 1.0 X 106
day
sin
12 days]
mo
where t is the time in units of days. Cells die at a constant rate of
1.0 X 104 cells/day. Determine the number of cells in the reactor at 12 days.
cccbrot 2kur
1.0E + 06
9.0E + 05
no
8.0E + 05
7.0E + 05 E
(eiaobes) aoesilamsm
6.0E + 05
rimn
5.0E + 05
ngizab viebnud mnt
i aseve e weid (e)
4.0E + 05 H
HO 2101
3.0E + 05
2.0E + 05
1.0E + 05
0.0E + 00
0.
4
6.
8
10oE12 maa
to
Cell generation rate (cells/day)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff56da61c-cf9d-4d3e-85c9-7bfd1af82491%2F68ea74d0-512d-4ba1-aedc-65bad44a7b39%2F6qot8cp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1 107
(kdeg, kes Vss Rrec
3.51 A hollow-fiber membrane device like the one described in Problem 3.17 :.
operated to achieve the fermentation of glucose to ethanol using yeast cell.
Yeast cells are immobilized on the outside walls of the hollow fibers (i.e. the
yeast cells are in the outer, annular space). To seed the unit, 1.0 × 105 cell.
are added to the reactor. The cells attach to the fibers. Initially after seeding
the cell generation rate increases. However, as the cells begin to cover the
fibers, the generation rate slows. The change in cell reproduction rate occurs
as shown in Figure 3.45. The generation rate, cen, is modeled as follows:
cells
gen = 1.0 X 106
day
sin
12 days]
mo
where t is the time in units of days. Cells die at a constant rate of
1.0 X 104 cells/day. Determine the number of cells in the reactor at 12 days.
cccbrot 2kur
1.0E + 06
9.0E + 05
no
8.0E + 05
7.0E + 05 E
(eiaobes) aoesilamsm
6.0E + 05
rimn
5.0E + 05
ngizab viebnud mnt
i aseve e weid (e)
4.0E + 05 H
HO 2101
3.0E + 05
2.0E + 05
1.0E + 05
0.0E + 00
0.
4
6.
8
10oE12 maa
to
Cell generation rate (cells/day)
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