NITROGEN-CYCLE
DYNAMICS
OF
A WASTE
RECYCLING
OYSTER
CULTURE
SYSTEM
by
DIANE HOLBERT
Submitted
of
the
in
RIKER
Partial
Fulfillment
Requirements
Degree of Bachelor
at
MASSACHUSETTS
for
of
the
Science
the
INSTITUTE OF
JANUARY,
TECHNOLOGY
1978
Signature redacted
Signature of Author...u ...... , .
. .................
Department of Mechanical Engineering, Jaiuary 19, 1978
Signature redacted
Signature redacted
Certified by...
Thesis
Accepted by..
C airman,
Dep
ARCHIV&3
APR
7 1978
ental
..................
Committee
Supervisor
on
Theses
Page
2
NITROGEN-CYCLE DYNAMICS
OF
A
WASTE
RECYCLING OYSTER CULTURE
SYSTEM
by
DIANE
HOLBERT
RIKER
Submitted to the Department of Mechanical Engineering
on January 19, 1978 in partial fulfillment of the requirements for the Degree of Bachelor of Science.
ABSTRACT
A nitrogen-cycle model of a waste recycling oyster
culture system was developed, simplified, and simulated to
examine the influence of various parameters on maximization
of oyster-protein yield in comparison to a pilot plant constructed at the Environmental Systems Laboratory at Woods
Hole Oceanographic Institution. Simulation results indicate
increases in oyster-protein with increases in algae ingestion
rate, fluid flow rate, and initial algae content in the inflow
water. Decreases in oyster nitrogen content coincide with increases in ammonia excretion rate and ingestion half-saturation
coefficient. These results are consistent with the values reported by ESL. Further work on this model should include
light intensity analysis and study of an appropriate set of
consistent units easily measured by both biological and engineering teams.
Thesis
Supervisor:
Title:
Alician
Assistant
V.
Quinlan
Professor
of
Mechanical
Engineering
Page
3
ACKNOWLEDGMENTS
Roger Mann and
John Ryther of
Rosalie
ESL
Bright
Douglas White,
Astrid Howard,
Anna Piccolo
-the
original
supportive
-the solution
problem
and
-suggestions
-humor and
James
-typing,
A.V.
Quinlan
to
and
H.M. -Paynter
Hutchison
idea
and
documentation
DYSYS
editing
the
respiration
inspiration
instruction
and
dinner
-solution to biological and
psychological
dilemmas and
paper shortage
Page
CONTENTS
Abstract
2
Acknowledgments
3
List
of
5
Figures
6
Introduction
Model
and Simplifications
10
Model
Behavior:
20
Discussion
The Simulation
and Conclusions
25
Recommendations
28
References
29
Personal
Communications
30
Appendix 1
31
Appendix 2
34
Appendix
3
36
Appendix 4
40
4
Page
FIGURES
10
1.
Rudimentary N-Cycle
2.
Complete Nitrogen Cycle
3.
Walne,
Food Consumption Rate
versus Food Concentration
16
4.
Method
for Defining
17
5.
Nitrogen
6.
Quinlan
7.
Nitrogen
8.
Parameter Sensitivity
Steady-State Solutions
23
9.
Nitrogen Data
26
Cycle
/
Paynter
Model
I
Model
18
Results
Concentration
from Mann
11
21
versus Time
22
5
Page
6
INTRODUCTION
Hole
saves treatment
proposed
system
logical,
rather than physical or
cation method which
protein
ically
foodstuff.
attractive:
such
chemical,
a standard
earn
profit per
(Hugenin and
Smith,
test
Mann of
the
ESL has
effluent
is
feasibility
created
fed to
nutrient nitrogen
into
tanks
of
The protein
nitrogen
and by
the
intake
edulis,
as
the
light
gigas
European
a commercial
a town's
$10,000
1975).
Roger
Secondary
algae.
strip
the
The
algae
and then
oysters
are
excess
pumped
feed on
the
oyster.
By
source.
is
is
Four
is
tanks
and
optimal
water
en-
maximized.
being evaluated:,
a Japanese oyster;
gigas
excretion,
salinity,
creating an
species
C.
determined by
their nitrogen
protein production
(Thunberg),
food
oysters is
intensity,
environment.
performance of two
a
econom-
plant operation.
relative to
the oyster's
Crassostrea
approximately
effluent,
content of
flow-rate of their
The
nutritional
algae.
temperature,
vironment,
of
oyster beds where
nitrogen-enriched
their
a culture
from the
purifi-
sewage
of the proposed method,
a pilot
The
a bio-
system would pay for
operation and
To
of
the proposed method is
secondary plant
year
a method for
by use
costs
a marketable,
produces
As
devising
at Woods
to high-quality protein.
sewage
secondary
converting
is
Institution
Oceanographic
(ESL)
Systems Laboratory
Environmental
The
the
oyster
were
set
and Ostrea
harvested
up
for
Page
each of
in
four temperatures.
each tank
The
on plastic
Two hundred oysters
trays,
twenty
costatum,
algae,
Skeletonema
outdoor ponds
fed by
secondary-treated
seawater.
algae
The
oyster tanks
at
and seawater were
rate of
a constant
were placed
individuals
food
were
sewage
then
7
per tray.
in
grown
effluent
pumped
in
into the
Pl/min. and 8 L/min.,
800
respectively.
Over a
cretion
At
period of nineteen weeks,
rates
biweekly
oysters per
tank
to
specimens were
monitored
beginning with week
sacrificed
results
to
for C.
1,
gigas
are
ex-
(Tables 1 &
one tray
determine
results
occurs
the
at
or
oyster's
indicate
below
that
their
shown
in
180
C.
reproductive
maximum protein
3).
of
chemical
tables
aid in
Mann
optimal
organs,
diverting
carbohydrate
stim-
some
of
consumption
spawning ability.
(1977)
culture
minimum time,
product,
pro-
Higher temperatures
protein-producing metabolism to
states
include
that the
"a
culturing
of
reserves
major
marketable
a maximum conversion
maximum nitrogen
or
unforseen
growth and
3.
duction
the
was
The
Mann's
ulate
the
intervals
composition.
1 and
of
the
an
with
an
environmental
accompanying
stress."
size
protein)
a large
ability
for the
product
efficiency
(and hence
organism that has
criteria
of
in
a
food to end
production,
metabolic store
to
withstand
any
p
0
V
11
VP
All data are expressed
1. Growth and biochemical composition of. mltss t temperatures of 12, 15, 18 and 21'C over a 19-weck period.
N mg, nitrogen
tissues;
of
soft
content
carbon
on a per indivi~1us1 basis W t, live weight; M mg, dry weight; S , dry shell weight; C mg,
of
content
soft
ash
me,
tissues.
ASH
tissues;
(After:
soft
of
content
Mann,
carbohydrate
mg,
Clo
1977)
content of soft t1-sues;
.
Table
Weeks
Parameter
0
W5
N
ig
Sg
12
5.2
6.2
88.7
256.6
3.13
2.48
5
7.2
400.0
3.56
8.0
9.4
524.0
646.0
3.86
5.38
11
15
13
12.8
14.3
16.5
972.0
1141.0
1414.0
391.0
6.76
415.6
477.0
621.0
96.9
302.3
113.0
106.8
114.2
7.06
10.8.
101.8
18.9
158.9
30.2
216.9
40.6
70.5
0.9
43.3
62.4
138.8
178.8
52.1
281.5
61.6
CHO 0 g
AS1.1 rg
331.0
46.7
86.2
87.8
383.6
86.4.
10.8
12.5
844.0
18.8
21.3
1266.3
1614.0
38.4
72.0
6.2
8.1
11.2
718.0
%2
ms
S a
5.6
131.5
2.67
228.7
3.21
462.0
C ag
43.2
88.1
310.4
17.5
196.1
36.9
3.7
5.71
101.0
443.0
163.7
331.0
199.0
64.7
58.6
140.6
198.2
275.9
109.5
12.2
15.6
641.7
851.0
17.9
751.0
110.6
35.8
43.1
65.1
Wa
M me
5.7
6.7
94.0
5.91
202.4
273.6
19.2
34.8
47.0
39.9
60.3
166.3
ASH crg
24.1
33.1
52.7
57.1
7.5
10.6
M Mg
5.6
134.0
12.4
742.0
S C
C rg
N mg
C010
-g
ASH rig
2.67
44.5
374.0
3.77
570.6
5.04
157.2
238.5
45.6
5.8
30.4
78.5
36.1
60.6
10.4
14.29
78.9
37.9
7.9
4.9
530.5
363.3
37.7
N g
969.3
9.78
53.8
ASH rgZ
110.0
665.0
241.5
178.2
32.6
1253.0
183.8
4.9
270.0
3.02
28.2
2211.0
14.85
55.1
10.1
2.56
8.8
525.6
31.2
390.2
366.6
N mi
8.7
0.74
8.15
23.5
1736.0
11.37
.750.5
259.3
44.1
CHO mg
491.0
4.23
696.0
5.74
19
10.4
41.5
27.1
17
918.0
5.76
Cr3
N rg
S g
21
3
9
272.6
47.9
W g
15
1
7
6.33
8.11
341.2
48.9
200.7
84.6
18.3
1145.0
9.35
8.57
19.2
888.0
9.93
93.7
23.6
29.6
34.6
1122.0
1425.0
14.6
1322.0
16.3
87.1
593.2
110.7
525.9
114.5
178.4
186.7
133.1
189.6
157.3
176.9
12.07
305.1
352.9
442.6
53.9
144.7
84.0
60.6
167.4
127.9
22.5
1054.7
9.65
19.6
25.2
29.8
38.7
to
703.6
10.12
1136.0
12.72
1286.0
15.25"
1219.0
0,
18.97
319.7
456.5
399.6
253.1
450.8
510.?
473. Z
75.7
117.5
67.8
137.1
190.2
89.2
150.6
60.9
99.3
100.2
92.0
102.0
184.3
102.3
129.2
56.8
65.8
119.0
136.3
156.4
89.8
117.7
160.2
-
Temp.*C
0
W
'
Table 3.
1
V
W
0
0
21 0 C
1977).
Weeks
0
180 C
0
of 12, 15, 18 and 21C
Each value gives the mean and standard error of 4-6 individual assays. (After: Mann,
Temp. oC
15 0C
V1U
W
Ammonia excretion rate (ug NH 3 -N/gm dry meat/hr) of Crasooetrea gigao at temperatures
over a 19 week period.
120 C
UV
'
W
Mean
13.63
S.E.
2.05
Mean
1
3
30.3
37.03
5
20.27
7
19.5
9
11
13
15
17
19
8.98
12.24
14.46
11.23
7.94
4.99
6.38
2.01
1.83
1.59
1.81
2.23
0.96
1.17
0.68
27.91
28.33
19.57
9.17
11.42
18.69
10.17
0.89
1.78
1.21
10.46
1.13
9.71
0.83
S.E.
5.21
3.39
2.81
1.87
1.09
Mean
28.05
33.38
26.80
23.63
0.05
17.73
12.76
21.22
21.53
31.87
0.91
2.86
0.87
2.97
2.07
1.31
S.E.
3.80
3.61
4.63
2.85
Mean
11.45
29.91
23.58
16.01
8.22
'11.89
17.24
13.52..
23.66
39.28
S.E.
4.8
3.52
1.67
1.44
1.92
3.34
1.06
5.09
1.27
3.33
9,
Page
MODEL AND
A
SIMPLIFICATIONS
dynamic-systems model
influences
Mann's
of parameters
pilot
The
plant
cycle
appropriate
on
at
original
triangular
can be
to
maximization
examine
of yield
the
in
Roger
ESL.
model
devised
of nitrogen
inflows
used
at M.I.T.
in
the
and outflows,
tank
as
represented a
environment with
shown
in
Figure
1 below.
OYS TE _V- ct
4 G4Z-t
/O
RUDIMENVTARY
\
A/-C YCL E
O
AMMONI A-IAN
1
F IGURE
Each
node
represents
ticular state.
and
outflows
parameters
oyster
ation)
the
Each
including
and
that
original
state.
The
certain
level
already
model
accumulation
of nitrogen
of
present
appears
in
upon
flows are
feedback
which depends
on the
is
an
accumulation depends
to that
ingestion,
available
10
on
the
an
Appendix
saturation
oyster.
1.
A
by
example
the quantity of
the
inflows
regulated
terms:
ingestion
in
in a par-
rate
is
food
(sati-
summary
of
1W
w~ w
W
*
0
InfI
-Outf
W
Ww
(41
DON
N
low
/ZOyster-N
Algal-N
IngestionA
f
Rudimentary--s
Nitrogen
6 Cycle
SW
PON
N5
.001Outf
Ammonia-N
N3
0
Z-
Figure
w
0
2.
Complete
/
W
Nitrogen
Cycle
Model
low
Page
VARIABLES
The
in
the
tank
out
tem is
N1
is
of
is
N1
N2
the
ingested by
the
the oyster
processes
(excretion,
production)
occur.
N2
is
creases
in
growth
The
all
flow.
the
tial
the
the
.
the
A water
excreted
consumption
flow
ammonia
The
concentration of
and
uptake
N3'
re-
egestion
respiration,
and
ammonia
the nitrogen
ingestion
rate
is not
of this
structure
algal-nitrogen outflow
of
system.
and
reflected by an
Accumulated nitrogen
algal
the
it determines
content
equation.
increase
concentration of ammonia-nitrogen
by N
itself.
in
In-
total
tissue.
content of
represented
that
tank
the sys-
ingestion
specifically
the growth term of
If
of nitrogen which
after the
to
are
the
of
concentration
related
nitrogen
in
elimination,
term N
oysters or may
the
variable because
tissues
the
consumed.
regulatory mechanisms
represents
in
by
accumulate
may
considered a state
of
represented
system without being
the
stagnant,
effects
mains
any point
N 1 may either be
Incoming
pass
at
actually present
of algal-nitrogen
concentration
.
STATE
12
ammonia
can
the
form may
system is
established
eliminated by
creating
content
be
in
such
the out-
feed back
into
a higher poten-
to the
oyster
limits both potential
culture.
outflow
Page
CONTROL
VARIABLES
The
oyster
is
concentration
tanks
is
density
of
the system.
algal
yields the
The
activity which
duction.
protein
This
to
is
of
determined
the nitrogen
tank,
T,
correct environment
of
in
in
the
reproductive
the conversion
of
of
egestion
the
oysters.
Temperature
concentration
a control
algal
content
these
cell
from a
two terms
concentration,
N0
algal cells
ml inflow
determines
Certain
the
level
values of
for maximum protein
this
addition,
This
.
from the
algal-N
algal cells
the
into the
considered
the oyster exhibits.
production;
results
is
range
result
in
systems
of the
pro-
reduced
higher temperatures
result
oysters.
metabolism from protein
lipid production with a subsequent
rate
also
decrease
aids
in
in
the growth
regulation
of
rates.
Light
model;
intensity was not
however,
it
thetic processes
the
thus
Temperatures outside
activation
term N
Multiplication of
algal-N
ml inflow
=
the
N
the
input algal-nitrogen
temperature
T provide
and
tank and
cells.
total
0
by
represented
entering the
sample of
in
of algal-nitrogen pumped
controlled externally,
variable
of
13
amount
of
conversions.
of
solar
Light
does
the
play
incorporated in
an important
phytoplankton
radiation
intensity
available
also
role.
(algae)
to
the
aid
influences
simplified
The photosyn-
are
controlled by
in metabolic
the
activity
Page
of
the
oyster
Mann
population.
actually
increase their
that
oysters
the
which may
vibrations
The
of
the
daytime
induced by
system
is
Another
indicating
factor
sensitivity
to
daytime noise.
and algae
seawater
"q" is
q.
labelled
constant throughout
mains
is
may
oysters
at night,
feeders.
rates
feeding
flow of
volumetric
the
feeding activity
be nocturnal
may
reduce
(1977) notes
14
set
and
re-
and
externally
out
experiments performed
set of
the
into
at ESL.
The
volume
scale
ative
the
of
tank,
culture
of the
model.
It
used to
be
can
represents
V,
for
maximum potential oyster concentration
the
determine
relthe
any particular
size.
tank
RATE VARIABLES
The
inflow
rate
of
is
algal-N
(I)N
V
states that
which
the
rate
inflow rate
divided by
centration,
in terms
of
the
is
a
given
by the
expression
0
function
volume of
concentration
the
of
the volumetric
tank
flowing
times
the
con-
in per unit
time.
The
expression
(q)N
V
1
outflow rate of
is
the
of
algal-N
the
in
the
same method
as
tank
algal-N
per
unit
inflow rate.
in
terms
time.
It
of
is
the
concentration
calculated by
Page
Similarly,
the
15
expression
(a)N3
V
3
is
The
by
the
on
ingestion
rate
the
rate
ingestion
amount of
algae
oyster,
outflow rate
algae by
of
i,
and on
of
ammonia-N.
is
oysters
the
by the
available,
reflected by
rates
coefficient,
the
physical limitations
the value
the present
determined
of
the
ingestion
state of
satiation
I.
N
(ingestion rate
This
the
relation
ingestion
The
states
rate
ammonia
ingestion
that
at high
saturates
uptake
rate
for
i-
S
of algal-N)
food
concentrations
egestion
are
shows
the
behavior
same
ammonification,
of
functions
linear
as
the
3
-
E u-
of ammonia-N)
U +N 3
excretion,
and eliminwith
oyster-nitrogen,
(a,
coefficients
temperature-dependent
d,
and p).
PARAMETERS
The
ingestion
verting the
per
rates:
all
respective
RATE
(N1
food.
N
ation
2
rate:
(uptake rate
The
N
1
I +N
oyster
This
value
rate
coefficient,
published values
to algal-nitrogen
is
then
nitrogen
fraction
solution
for the
of
algal
i,
is
cells
determined by
eaten
per
con-
hour
consumed per hour per oyster.
multiplied by the reciprocal of the algalN
(
)
to
give the final algebraic
I +n
ingestion rate
coefficient as
follows:
Page
ingestion
oyster
cells/hr X
oyster
nitrogen
rate
algal-N
cell
ingestion
_
cells/hr
oyster
_
algal-N/hr
oyster
rate
oyster
.
nitrogen
A value
1972,
imum
as
algae
shown
I
rate
rate
1
+N1
+N
1
ingestion rate/oyster was
in Figure
ingestion
.
=seI
oyster
N2
ingestion
N2
rate
o yster
3 below.
It
from Walne,
taken
corresponds
of Phaeodactylum algal
cell
to
the max-
consumption
oysters.
-rIax iIehon- rale
Figure
/00
3.
Ctls
80
Walne, 1972. Fig. 2f,
page 350. FOOD CONSUMPTION RATE VERSUS
FOOD CONCENTRATION.
rate
Maximum ingestion
is superimposed.
ea'cen
per
t.0
- ,
by
of
X
ingestion
nitrogen
)
algae
16
X
40
zo
50
0
/00
200
150
Ces er,147
Similar data was unavailable
in
the pilot
Figure
plant studies.
3 is assumed
for S.
costatum, which was
The parameter
value
from
appropriate because Phaeodactylum are
similar to S.
costatum in size and nitrogen
justification
for this assumption
S.
derived
used
content.
Further
comes from the use of
costatum in the final ESL system;
Phaeodactylum was used
originally.
The
value
of
ingestion half-saturation
coefficient,
I,
is the
the concentration of algal-nitrogen, N1 , which
Page
corresponds
ingestion
After
to
an
rate
ingestion
coefficient
appropriate unit
is
3 by
ingestion
curve
which
on the
corresponds
Figure
to
uptake
saturation
to
that
The
are
for
the
ammonification
excretion
gen)
elimination
the
a,
sum
of
for
e
a value
for
I can
be
a maximum value
(i/2)-N2
U,
rate,
rate,
d;
rate,
value
(see
for
of
Figure
N1
4).
can
estimated by
rate
half-
a method
similar
coefficients.
functions of
egestion
(dissolved organic nitro-
and
PON
(particulate organic nitro-
Since
rate
Roger
such
(a
derived
Mann
only gives
coefficient will
egestion
=
0
uptake
the
DON
this
and p)
be
and
a;
p.
aggregate
d,
are
u,
describing the
e-N
Values
of
ingestion
"excretion rate",
the
potential value.
determining the
Nj=
N,
coefficient,
coefficients
instead of
and
The
.
I.
rate
gen)
for
its
establishing
the value
coefficient,
used
half
(i/2) -N
to
4.
METHOD FOR DEFINING
The
equal
conversions,
estimated from Figure
rate
rate
17
coefficient
+ d + p)-N2
Table
3,
page
be used
(equalling
that:
from
values
9.
Page
ACCUMULATION
There
RATES
are three
Their units
They are
rates, n,
n 2'
and N3*
governed by the
same rules as are
followed by
models.
(N
rates of accumulation
,
N 2 , and &
) depend on
sum of the inflows and outflows to each node with the
appropriate
sign conventions.
"word model"
describing the accumulation terms
Nitrogen Cycle Model.
model which
their
Figure 5 below shows the
Following this
for this
is a mathematical
substitutes the quantitative
relations
for
word equivalents.
Figure
5:
NITROGEN
Word Model Algal
CYCLE MODEL
Rate
Conservation
Accumulation
=
(inflow -
Oyster Accumulation =
Ammonia
Production =
Mathematical
outflow)+ uptake
-=
-(N
ammonification
-
uptake -
Model
V
0
-
N
1
) + u
U +N3
N
-
i-
N1
N
2
i-
I +N
N
2
-
[a +
d + p]*N
N3
N
3
a-N
2
-u-
U +N
N
3
ingestion
ingestion -(ammonification
excretion + elimination)
N 3N1
N
-
+
the
accumulation
are in terms of concentration per unit time.
node-branch
The
18
1
-
q-N
V
3
2
I +N
N
2
outflow
Page
Simplification
of this model
damped system with
limited
(N 3)
system was
branch
observed
the
of the
no
system
accumulation
not
and
for
with were
the
method
The
of
light
in
i,
I,
and
in
accumulation
sum
the
ingestion
of
due to
rate
using
of
The
Roger Mann
rate of
1977).
and elimination,
previous
of N 1 ,
ammonia-N
high flow
res-
therefore they were
The
values
rate parameters
calculated
by
section.
Nl,
inflowing algal-nitrogen
rate
the
unavailable;
the
second-order
Roger Mann,
intensity
e,
a
growth.
the numerical model.
described
the
to
eliminated because
of N3
uptake were
accounted
dealt
exponential
(Personal Communication,
Measurements
piration,
leads
19
is
assumed to equal
minus
the
outflow minus
algal-nitrogen.
N
N
The
is
1
V
expression
simplified by
and p.
=
(N
0
for
-
N
1
the
)
)N
+N
I
accumulation
elimination
The parameter e
i-(
-
of
the
has been
2
of N
rate
sum of
N
2 2'
parameters a,
d,
substituted.
N1
2
The
accumulation
excretion
and the
this
rate,
i-(
rate
the uptake
outflow rate of
model
because
accumulation
A
=
rates
summary
high
I +N
)-N
of N 3 ,
rate
2
-
N3 ,
of N3
ammonia-N.
N3
outflow rates
e-N
2
depends
by
the
is not
upon
algal
the
oyster
culture,
considered in
dominate any potential
(Mann, 1977).
of the
simplified model
appears
in
Appendix 2.
Page
MODEL
BEHAVIOR
THE
SIMULATION
The
original
Facility
(JCF)
model
using
was run
on
the
CE/ME
Joint
Computer
DYSYS,
Dynamic
System Simulation,
predesignated values
of
Quinlan
/
Results
Figure
are
The
shown in
Roger Mann's
were
unavailable
were
used to
The
with
i,
the
10%
I,
curves
of N2
q',
in
B
the
in
oyster-N.
a
Any values that
final
where
q'is
The
shows
same
of q'and N
of
rate
causes
values
that
of N
and N2
the
model
V
solution
are
seen
As
a decrease
the values
indis-
for sensitivity
in
can be
for
virtually
as
e.
to
q
to the
in
results
the
the total
Curve
from
anal-
curves
Curve
expected,
protein.
algal-nitrogen which
Figure 7,
decrease
result applies
converted to
in
exponential
as
solutions
increased
other work
following quantities:
defined
curve
I.
limited
corresponding
the
from
the
model appear
steady state
of
in
analyses were performed
simplified
oyster-nitrogen
data.
quantities.
expected
original
results
excretion
crease
the
in Figure 7
i and
the
known
simplified
in each
and No,
sensitivities
shows
in
1976.
constructed with values
experimental
Sensitivity
changes
tinguishable
yses of
the
show
increases
e,
then
oyster-nitrogen with
Curve
in
of
with
6.
supplement the
algal-nitrogen.
examine
Paynter run,
from Mann but well-documented
results
page .22. All
growth of
the
simplified model was
derived from
in
20
A.
for
Curve
increase
amount of
D shows
increase
the
in
de-
C
0.45
L3
SePi
0
Lee
so
IL50
m0
250
TE
Figure
6:
Quinlan
/
Paynter
Results
30
Page
22
600-
bo
WO
i
<
47
-00
-
-O
S200-
A
N =0-0
U
20
5
25
30
40
35
45'
50
HOURS
Figure
NITROGEN
7
Curve
Curve
A:
B:
CONCENTRATION VERSUS TIME
N2
sensitivity
in
q
results
for 10%
increases
and N0'
Original
simplified model
sensitivity
results
Curve
C:
N2
sensitivity
Curve
D:
N1
results
for
for 10%
results
all
for
models.
N2, and N2
increases in
for
10%
increase
i and I.
in
e.
Page 23
Inspection of
ima
and
minima
and
N 2)
shows
not
resolvable
thus
are not
predicted
analyses
model
the
slight
by
the
visible
actual
percent
solution.
CRT screen
in
calculations
of
steady
values
increases
Figure
results of
and
of
7.
difference
total nitrogen.
In
analyses
of q
state
decreases
the
JCF
Figure
the
from
the
values
for N 1
that
are
machinery
and
below,
gives
the
simplified
original
represents
of
an
represents
results
for
increase
a
N1
Parameter
+10%-_
Results-
STEADY-STATE
_
_
_
_
____
Predicted Actual Predicted Actual
i
-9.8
-10
+.08
08
+10
+10
-.
e
+10.8
+11
-9.2
-9
-.
1
qA
-
-
+10
+10
N0
-
-
+10.1
+10
The predictions are
shown
in
8.
computed
Appendix
according
3.
*
method
Results
Results
of
of
_
+.j
I
Figure
Predicted:
Actual:
SOLUTIONS
Results-N 2
N
Steady-State
Computer
Analysis
Simulation
to
decrease.
did not
from their original values.
PARAMETER SENSITIVITY
the
sensitivity
A negative percentage
and N
8,
final max-
steady-state
A positive percentage
in
differ
computer
(corresponding to
and
in
the
the
Page
Derivation
and
can
the
then
be
found
in
sensitivity is
for N1
changes
in parameter values.
in
and
does
not oscillate.
the
quadratic
solution
negative.
The
positive
(o2-4g)
so
Appendix
4 derives
the
borhood
of
and N
and 2
for
the
the
respect
the
the
gives
used in
the
of
and
a
the
for
the
the
gives
to
region
is
always
real
stable
portion of
is
is
always
always
oscillate.
linearized perturbed
in
solution
comparative
analysis.
of
changes
the
stability
values
each
governing
solution
sample
changed
sensitivity
solutions
to
linearized system
conditions
various
system
system does not
model,
for
of
because
equations of
steady-state,
simplified
respect
and N2 with
is
anal-
the partial
show the
shows that the
This
N2
n 1 and nI2 are solved;
equations
imaginary portion
describes
(,S,
N1
and
sensitivity
steady-state
Stability analyses
steady-state
system,
The
and N2 with
These
bounding
original
3.
for N1
determined by establishing
solutions
for
equations
parameter
equations of
parameters tested.
relations
for the
Appendix
differential
derivative
the
steady-state
governing equations
yses
for
of the
24
of
i,
the neighfor the
values
I,
e,
of
q,
Page
DISCUSSION AND
The
given
CONCLUSIONS
simplified model
by
results
at
shows
5 time
factors
scale
the model
in
terms of
50
hours.
to
The ESL
show the
the
how
10%
This
of
the
increased or
The
model
control
to
i
and
In
or
N
growth;
All
system is
and
over
original
growth with
the
effects
however,
rates
in
a
form
were
of
the
time
calculated
saturation
after
longer time
scale.
simulation were performed
of changes
in
the
system parameters
changes have
on
the
final
nitrogen
in
the
is
useful
and
in
Figure
i,
I,
the
variables
are
pilot plant
can be
that
Results
i and
also
and NO0
q,
can
analyses
for at
be
show
most effectively
I would
suggest
to uncertainty
23,
influenced
operation
sensitivity
decreased to maximize oyster
insensitive
page
parameter uncertainty
second,
suggests
8,
e,
and
values of
contents
parameters
first,
control
parameters.
relatively
The
incorrect.
the model
reasons:
accounted for;
which
is
steady-state
increases
two
9).
and algal-nitrogen.
information
least
Figure
(see
exponential
effects
the
growth
system responds
results these
shows
the
unlimited exponential
analyses
oyster-nitrogen
by
on
hours:
Sensitivity
sxhibit
units corresponding to
limiting
of
does
from ESL
simplified model
a break
in
meat
not
content.
make good
that the model
values
is
assigned
I.
contrast
will
25
to
changing
produce nearly
i or
I,
a
10%
change
an equal percentage
in
e,
change in
q,
Page
150
140
li
WI
:jL
T1
A.
120
110
0100
Li
g2o
0
z?0
0f
1
91315/
~~WEEKS
Figue
Reult 9frm MnnTabe2 1
N TOE
20
10
0
AAA
2C
26
Page
oyster-nitrogen
these
three
tainty
in
The
of
its
rate
the
feed
the
of
system can
seawater
q or N
steady-state.
steady-state
of
Increases
and
the
in
oyster-protein content
system temperature,
equivalent
flow
uncer-
values.
limited expontential
in
the
increases
inflow,
oyster-nitrogen growth.
should result
concentration.
an
Uncertainty in
oyster-nitrogen
and algae,
concentration
in
produce
expect
oyster population.
increases
able
at
parameters will
ESL
nitrogen
in
content
will
In
be
rate,
in
the
in
N
.
flow
algal-
cause the
increased
tank
growth
volumetric
general,
10% increases
can
27
greatest
10%
increases
The
market-
by monitoring
level,
and
algal
Page
RE COMMEN DATI ONS
1)
Incorporate
2)
Attempt
light
to establish some
measurement
3)
duplicate
work.
tends
This
Identify
5)
Run
of
values
the model
back
the
of
all
Compare
the original model
the
chemical
outflows
flow
algal
be
results
assays.
rate
to allow
culture
taken
quantitative
of
experimentally.
proposed in
in parameter
hinders
used in other
and contrast
care must
uncertainty
uncertainty
consistent
in verification
a slower
ammonia-N to
effects.
report
for
species
to help
for
at
In particular,
this
the
comparison of various
4)
system
units.
Attempt to
and
6)
intensity.
and monitor
results
this
feed-
to
those
paper.
to reduce
or
values because
analysis.
28
Page
29
REFERENCES
Ali,
R.M., "The Influence of Suspension Density
erature on the Filtration Rate of Hiatella
Marine Biology 6, 291-302, 1970, pg. 297.
Fogg,
G.F.,
Algal
Madison: The
pp. 39-40.
Cultures
University
and Temparctica,"
and Phytoplankton Ecology,
of Wisconsin Press,
1966,
Goldman, J.C., "Temperature effects on phytoplankton growth
in laboratory
cultures,
Note to
Limnology and Oceanography,"
WHOI Annual Report, 1976, Figure 2,
Skeletonema costatum,
1.2-1.7
g/ million
cells.
Hugenin, John E. and Smith,
Wastewater-Aquaculture
pp. 285-293.
Mann,
Leah J., "The Economics of
Systems," IEEE Ocean '75,
Roger, "Some Biochemical and Physiological Aspects
of Growth and Gametogenesis in Crassostrea gigas
(Thunberg) and Ostrea edulis L. Grown at Sustained
Elevated Temperatures," First Draft for publication
in J. Mar. Biol. Ass. U.K., Contribution No. 4040
from WHOI, Woods Hole, Mass.
Quinlan, Alician V., "Linearization of Nonlinear Systems
About Singular Points," (unpublished).
Quinlan,
A.V., Mann, Roger, and Ryther,
John, "NitrogenCycle Dynamics of a Waste Recycling Oyster Culture
System," Proposal for Joint Research Seed Funds;
Submitted to M.I.T.-WHOI Joint Program in Oceanography,
January,
1977.
Quinlan, A.V. and Paynter, H.M., "Some Simple Nonlinear
Dynamic Models of Interacting
Element Cycles in
Aquatic
Ecosystems," J. Dynamic Systems, Measurement
and Control, A.S.M.E. Transactions, Series G, 98: 9-16,
1976.
Ryther, John H., "Bivalve mollusc culture in a waste
cycling aquaculture system," Sea Grant Proposal
R/A 1, February 1, 1972.
Walne, P.R., Culture of Bivalve
Fishing News (Books) Ltd.,
Walne,
P.R.,
"Growth
rates
and
Molluscs,
1974.
nitrogen
contents of juvenile clams,
three species of algae," J.
30: 1825-1830.
and
Surrey,
re-
England:
carbohydrate
Saxidomus giganteus, fed
Fish. Res. Board Can.,
Page 30
REFERENCES
Walne, P.R., "The influence of current speed, body size
and water temperature on the filtration rate of five
species of bivalves," J. Mar. Biol., U.K., 1972,
52: 345-374.
Walne, P.R., "Observation on the influence of food supply
and temperature
on the feeding
and growth of the
larvae
of Ostrea edulis L.," Fisheries Investigations, Series
Volume XXIV, Number 1, 1965.
Walne, P.R., "Studies on the food value of nineteen genera
of algae to juvenile bivalves of the genera Ostrea,
Crassostrea, Mercenaria, and Mytilus," Fisheries
Investigations, Series II, Volume XXVI, Number 5,
1970.
PERSONAL COMMUNICATIONS
Mann,
Roger,
1977,
ESL,
Paynter, H.M., 1977,
M.I.T.: DYSYS.
WHOI,
Woods Hole,
Department of
Mass.
Mechanical Engineering,
Quinlan, A.V., 1977, Department of Mechanical Engineering,
M.I.T.: Steady-State Solutions, Parameter Sensitivity
Analysis, System Linearization, and Stability Analysis.
II,
Page
APPENDIX
A.
ECODYNAMIC DESCRIPTION
N\o
1
OF SYSTEM
.4.OLYSTER-IVgg
WOGEST ION
PON
ANMON1.A - At
State
Variables
N
=
N2
=
N3
=
Control
concentration
ncentration
concentration
of
algal-nitrogen
of
oyster-nitrogen
of
ammonia-nitrogen
in
culture
culture
in
in
culture
Variables
q =
No =
volume rate
of inflow
and
outflow
concentration of algal-nitrogen in
T =
temperature
L =
light
V =
volume
of
intensity
of
culture
tank
in culture
culture
tank
tank
tank
inflow
tank
tank
31
Page
Rate
32
Variables
inflow
of
algal-N
=
[q/V]-N 0
outflow
of
algal-N
=
[q/V-N 1
outflow
of
ammonia-N
=
[q/V]-N 3
ingestion
of
algal-N
ammonification of
excretion
= oyster-N
=
a-N 2
=
p-N2
of oyster-N
= uof
*- N
+N
2
of oyster-N
elimination
uptake
*N
I
ammonia-N
N3
-N
U +N
*1 1
Rate Parameters
=
i(T,L) =
ingestion rate coefficient;
temperature and light
I
=
I (T,L) =
ingestion
may depend
half-saturation coefficient
u =
u (T, L)
=
uptake
rate
U=
U (T, L)
=
uptake
half-saturation
coefficient
coefficient
a
=
a (T)
=
ammonification
d
=
d (T)
=
dissolved organic nitrogen (DON)
excretion rate coefficient
p =
p(T)
=
particulate organic nitrogen (PON)
elimination rate coefficient
NITROGEN-CYCLE
on
rate
coefficient
MODEL
Word Model
Algal
Accumulation =(inflow -
Oyster Accumulation
Ammonia Production
=
=
outflow)+ uptake
ingestion
-
ingestion
-(ammonification
excretion + elimination)
ammonification -
+
B.
i
uptake
-
outflow
Page
Mathematical
N
1
Model
=-(N
V
0
q
-N)
N
+ u
U +N
N
N
3
-i-
1
I
N
N
N
i
2
3
=a-N
N
1I+N
2
u-
2
-
N3
U +N
[a
+ d + p]-*N
N
3
1
q
-N
V
3
2
+N
N
2
33
Page
34
APPENDIX 2
SIMPLIFIED
MODEL
PO
V
ALCAL-N
INPLOW
OYSTER-1V
ct
A
iV/
N ES 7' O/V
/V2
P_
ELIMINATION
Ct
F Ip
AL
M\o
Alo
ALG4L-Al
/NFLOW
OYSTE-
A/1
A3
N2
VrrESTIOAI
CRCer1og
Variables
State
N,
=
2 =
N3
Control
=
concentration of
ncentration
of
concentration of
algal-nitrogen
in
oyster-nitrogen
culture
in
ammonia-nitrogen
culture
in
culture
Variables
q
=
volume rate
No
=
concentration
T
=
temperature
V
=
volume of culture tank
of
inflow and
of
of
outflow
algal-nitrogen
culture
tank
in
tank
inflow
tank
tank
Page
Rate Variables
inflow
Rate
=
[q/V]-N0
outflow algal-N
=
[q/V]-N1
outflow ammonia-N
=
[q/V]-N 3
N
i)-N
2
I +N
algal-N
ingestion
of
excretion
of oyster-N
-
algal-N
e-N 2
=
Parameters
=
i(T,L)
=
ingestion rate
temperature
I =
I(T,L)
=
ingestion
half-saturation
e(T)
=
excretion
rate
i
=
e
NITROGEN-CYCLE
MODEL
coefficient;
and light
may depend on
coefficient
coefficient
(SIMPLIFIED)
Word Model
algal-N
accumulation
rate
oyster-N accumulation rate
-
(inflow
=
=
ingestion
outflow)-
ingestion
excretion
Mathematical Model
N
N
1
=
S(N
V
0
=
i
1
I +N
-N)-i
1
N
2
N1
N
2
I +N
-N
e-N
2
2
OBJECTIVE
identify
which maximize
values
of
control
accumulation
variables
rate
of
(q,
oyster-N,
No,
N2'
T,
and V)
35
PAGe
APPEND i.
3
(QUINLAN,1978)
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