Aquacultural Engineering 50 (2012) 46–54
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Aquacultural Engineering
journal homepage: www.elsevier.com/locate/aqua-online
A note on oxygen supply in RAS: The effect of water temperature
Ido Seginer a,∗ , Noam Mozes b
a
b
Civil and Environmental Engineering, Technion, Haifa 32000, Israel
Fisheries and Aquaculture Department, Ministry of Agriculture & Rural Development, Beit Dagan 50250, Israel
a r t i c l e
i n f o
Article history:
Received 6 October 2011
Accepted 26 March 2012
Keywords:
RAS
Seabream
Steady-state population
Airlifts
Fish oxygen requirement
CO2 stripping
Response to temperature
a b s t r a c t
Two methods of supplying oxygen to recirculating aquaculture systems (RAS) are considered. One is
aeration, here by means of airlifts, and the other is pure oxygen, here by liquid oxygen (LOX). Simplified
steady-state models are used to compare the performance of these two methods over a range of water
temperatures. Biological information for Mediterranean seabreams, as well as engineering and economic
information, was obtained from the literature and from practice in Israel. The results, to a first approximation, are: (1) the feed and oxygen consumed by a fish to grow to a certain size are independent of
temperature. (2) Supply of oxygen by aeration is controlled by its (minimal) required concentration in
the water. As the temperature increases, this concentration approaches the saturation value, thus reducing the driving gradient. (3) Data of required oxygen concentration as a function of temperature are not
consistent. Here we assume that for seabreams it is a constant absolute concentration, independent of
temperature. (4) The optimal air discharge of an airlift does not depend on the gas to be transferred
(oxygen or carbon dioxide), nor on temperature. (5) In operation mode, all available oxygen supplying
airlifts should be operated simultaneously at the same air discharge, which together satisfy the oxygen
demand. (6) At high temperatures, oxygenation with pure oxygen has a relative advantage over airlifts
(aerators), and vice versa. The advantage of airlifts is larger for lower (safer) permissible carbon dioxide
levels in the water.
© 2012 Elsevier B.V. All rights reserved.
1. Introduction
Intensive aquaculture requires oxygen supplementation.
Aerators may be installed to deliver atmospheric oxygen, or else,
pure oxygen may be used for that purpose (Timmons et al., 2002,
Section 8.3). Here we focus on the effect of temperature on the
supply of oxygen by these two means. The former is common
in low head (LH) systems, such as driven by airlifts, while the
latter is common in high head (HH) systems, generally driven by
centrifugal pumps. Simplified models of the two oxygen supply
systems are developed, and qualitative conclusions are drawn.
Interaction with CO2 stripping is considered. The main hardware
element to be modeled is an airlift developed at the National
Abbreviations: BM, live body mass; FCR, feed conversion ratio; HH, high head;
LH, low head; LOX, liquid oxygen; NCM, National Center for Mariculture, Israel; $,
US dollar.
∗ Corresponding author. Tel.: +972 4 829 2874; fax: +972 4 829 5696.
E-mail addresses: [email protected] (I. Seginer), [email protected]
(N. Mozes).
1
Main symbols: Unit in text may differ from those in list (e.g., g instead of kg).
∗
Indicates that the units of the ˛’s could be simplified by normalizing (scaling) M
(e.g., M/Mf ). We chose to stay with the conventional form to preserve the familiar
values of the ˛’s and for lack of a universal normalizing constant.
0144-8609/$ – see front matter © 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.aquaeng.2012.03.005
Center for Mariculture (NCM) in Eilat, Israel. Additional information is obtained from other local sources and from the literature.
Characteristic behavior of Mediterranean seabreams is used to
describe the fish.
The formulation of the model, intended mainly for the design
phase of a project, assumes idealized steady-state conditions,
where temperature is kept constant throughout the residence time
of the fish, and feeding is to satiation. A virtual RAS module is analyzed, where each day one fingerling is introduced into the module
and one marketable fish is removed (harvested). Fish mortality is
ignored, but can be accounted for if so desired (Seginer and BenAsher, 2010, Section 3.4). The results are given in terms of amounts
(such as feed) required to produce one fish, and as it turns out,
several of these are, to a first approximation, independent of temperature.
2. Model
2.1. Fish growth
On the assumption that oxygen requirement is a function of feed
consumption, the required feed to grow one fish to its marketable
size is calculated first. To do that, a growth function and a feed
function are required.
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
Nomenclature
{}
A
C
D
F
f
h
K
M
O
p
S
T
t
uE
uL
uO
˛F
˛M
ˇ
ε
˚
ω
curled brackets are used exclusively to enclose the
arguments of functions
air discharge of one airlift, m3 [air]/(airlift d)
gas concentration in water, g[gas]/m3 [water]
carbon dioxide produced by a single fish, g[CO2 ]/fish
feed consumed by a single fish, g[feed]/fish
number (fraction) of airlifts to support the fish population ˚, airlift/(fish/d)
gas transfer coefficient, airlift of one airlift,
m3 [water]/(airlift d)
cost term, $/fish
live mass of a single fish, g[BM]/fish
oxygen consumed by a single fish, g[O2 ]/fish
power requirement of a single airlift, J/(airlift d)
discharge of oxygen per one airlift, g[O2 ]/(airlift d)
water and fish temperature, K or ◦ C
time, d
unit cost of electricity, $/J
capital cost of one airlift, $/(airlift d)
unit cost of liquid oxygen, $/g[O2 ]
∗ feed rate-coefficient, g[feed]/(gˇF [BM] fish1−ˇF d)
*growth rate-coefficient, g1−ˇM [BM]/(fish1−ˇM d)
size-exponent
temperature-coefficient, 1/K
gas transfer cost-ratio: O2 to CO2
feed conversion ratio (FCR), g[feed]/g[BM]
equivalence
coefficient,
oxygen
to
feed,
g[O2 ]/g[feed]
ratio of carbon dioxide production to oxygen consumption, g[CO2 ]/g[O2 ]
discharge exponent in airlift power expression
discharge exponent in airlift transfer ability
coefficient
in
airlift
transfer
ability,
m3 [water]/(m3 [air]airlift1− d1− )
standing stock of fish to produce one marketable fish
per day, g[BM]/(fish/d)
coefficient
in
airlift
power
expression,
J/(m3 [air]airlift1− d1− )
ratio of airlift transfer coefficients: CO2 to O2
Subscripts
D
carbon dioxide
feed
F
f
at final (marketing) time
i
at initial (stocking) time
M
body mass
oxygen
O
r
reference
stock of one module required to produce one mar˚
ketable fish per day
Superscripts
ˆ
at saturation
lift
airlift
pur
pure oxygen
47
Here M is live body biomass (BM = ‘weight’) of a single fish (in
g[BM]/fish), t is time (in days), T is water (and fish) temperature
(in ◦ C), and ˛M , ˇM and M are positive coefficients (Table 1). Other
growth functions for gilthead seabream are also available (Petridis
and Rogdakis, 1996; Hernández et al., 2003; Seginer and Ben-Asher,
2010), but these have been found not to satisfy the needs of the current study. Eq. (1) is obviously only an approximation within the
practical range, because (1) for sufficiently large fish, M as a function of time must have an inflection point (sigmoid function), and
(2) at a sufficiently high temperature, growth rate must decrease
with increasing temperature (Hernández et al., 2003, Fig. 3; Pörtner
and Knust, 2007, Fig. 1B).
Integration of Eq. (1) with respect to time, assuming constant
temperature, produces the mass of a single fish at time t:
M = [Mi1−ˇM + (1 − ˇM )˛M exp{M T }t]
1/(1−ˇM )
,
(2)
where Mi is initial mass (stocking mass) of a single fish. Time to
grow from Mi to the final (marketable) size Mf is the residence time,
which for constant temperature is
1−ˇM
tf =
Mf
1−ˇM
− Mi
(1 − ˇM )˛M exp{M T }
(3)
,
and the standing-stock biomass required to produce, at steadystate, one marketable fish per unit time (one module), is
˚=
tf
Mdt =
o
o
2−ˇM
=
tf
Mf
([Mi1−ˇM + (1 − ˇM )˛M exp{M T }t]
1/(1−ˇM )
)dt
2−ˇM
− Mi
(2 − ˇM )˛M exp{M T }
,
(4)
where ˚ is in g[BM]/(fish/d).
The size distribution of the fish population in each module whose
total biomass is ˚, is independent of temperature. However, while
the smallest fish is always of size Mi and the largest is of size Mf ,
the number of fish (equal to the number of days in residence), and
(as Eq. (4) shows) also the total biomass, are smaller at higher temperatures. This means that for any given biomass density (carrying
capacity; in kg[BM]/m3 [water]), less rearing space is required as
the temperature increases.
2.2. Feed consumption
Feed intake (consumption) to satiation of a single (gilthead
seabream) fish is also given by Lupatsch and Kissil (1998) as a
function of fish size and temperature. Specifically,
dF
= ˛F M ˇF exp{F T },
dt
(5)
where dF/dt is feed intake rate (in g[feed]/(fish d)), and ˛F , ˇF and F
are positive coefficients (Table 1). Eq. (5) is also an approximation,
because at a sufficiently high temperature, feed consumption must
decrease with increasing temperature.
Substituting from Eq. (2) into Eq. (5), yields
dF
ˇ /(1−ˇM )
= ˛F exp{F T } [Mi1−ˇM + (1 − ˇM )˛M exp{M T }t] F
, (6)
dt
Lupatsch and Kissil (1998) proposed the following equation for
the biomass gain of gilthead seabream (Sparus aurata) fed to satiation, as a function of size and temperature:
which, by integration with respect to time, and substituting for tf
from Eq. (3), gives the feed consumed by a single fish throughout
its residence in the system:
dM
= ˛M M ˇM exp{M T }.
dt
Ff =
(1)
1
˛F exp{F T }
·
· [Mf1+ˇF −ˇM − Mi1+ˇF −ˇM ].
1 + ˇF − ˇM ˛M exp{M T }
(7)
48
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
Table 1
Growth, feed intake, and respiration coefficients for gilthead seabream (Lupatsch et al., 2003, p. 245; personal communication). The values are valid for water temperature
ranging from 19 to 27 ◦ C and for fish sizes from 1 to 450 g[BM]/fish. The coefficients are to be used in Eqs. (1) and (5), in conjunction with M in g[BM]/fish, F in g[feed]/fish, T
in ◦ C and t in days.
Coefficient
Growth
M
Feed intakea
F
Growth
respiration
Maintenance
respiration
˛
ˇ
0.024
0.51
0.060
0.029
0.60
0.057
0.0072
0.60
0.060
0.0018
0.82
0.074
a
In the calculations: ˛F = 0.027, F = 0.06.
This is also the daily amount of feed consumed by the steady-state
fish population, ˚, required to produce one marketable fish per day
(one module). Thus
F˚ = Ff .
(8)
Note that if
F = M ,
(9)
as it approximately is (Table 1), the feed consumed to grow a fish
to its final size (Eq. (7)) is independent of temperature.
The feed conversion ratio (FCR), (in g[feed]/g[BM]), is obtained
by dividing Eq. (5) with Eq. (1), to result in
=
dF
˛F ˇF −ˇM
M
exp{(F − M )T },
=
˛M
dM
(10)
which for F = M is also independent of temperature. It increases
significantly, however, with the size of fish, because ˇF is significantly larger than ˇM (Table 1). For the steady-state fish population
as a whole, the FCR is
˚ =
F˚
∼ F˚ .
=
Mf − Mi
Mf
(11)
2.3. Oxygen consumption and carbon dioxide excretion
The respiration rate of fish, usually measured in terms of oxygen consumption, may be divided into maintenance respiration
and growth respiration (Lupatsch and Kissil, 2005). For feeding to
satiation, both depend on body size and temperature, similarly to
growth and feed consumption (Eqs. (1) and (5)). If the body size
and temperature coefficients of maintenance and growth respiration are similar to those of feed intake, as they roughly seem to be
(Table 1), the ratio of oxygen-consumption to feed-consumption
is approximately constant, independent of size and temperature.
Making this assumption, oxygen demand to produce one marketable
fish (or to support the population ˚), may be written as
O˚ = Of = F˚ ,
the largest driving gradient from air to water. The limiting value
is obtained experimentally by gradually reducing the oxygen level
until a reduction in the relevant fish performance (growth in our
case) is observed. For most fish (the ‘regulators’) normal performance is maintained down to a critical oxygen concentration and
then drops rapidly off, exhibiting a break-point (Brett, 1979, Fig. 15;
Pedersen, 1987, Table 2; Jobling, 1994, Fig. 10.7; Zakhartsev et al.,
2003, Fig. 2A; Cerezo-Valverde et al., 2006, Fig. 4).
While growth is the relevant process for aquaculture (Jobling,
1994, Chapters 9–11, Brett, 1979), most available data are related
to processes which are measurable over shorter periods of time.
The critical point for each of these processes may be different,
as is clearly shown in Fig. 1 by results of Cerezo and Garcia
(2004) and Cerezo-Valverde et al. (2006), for two Mediterranean
seabreams (Diplodus puntazzo and Dentex dentex). Three separate
critical points are shown: one, where ventilation frequency starts to
increase (‘Ventilation’ in figure); second, where oxygen consumption starts to fall off (‘Oxygen’); and third, where half the fish die
(‘Lethal’). The ‘oxygen’ critical point which is measured most often
and is usually called just ‘the critical point’, is considered by the
authors not to ensure stress-free conditions. They suggest, instead,
that the ventilation critical point be used as the operating level for
aquaculture. Fig. 1 shows (1) that the two fish behave in a similar manner (probably also similarly to the gilthead seabream), (2)
that all three critical concentrations are independent of temperature, and (3) that the constant oxygen level based on practice
(12)
where Of (in g[O2 ]/fish) is the amount of oxygen required to grow
one fish to harvest size. In practice, should be corrected for the
oxygen consumption of micro-organisms in the system.
To a first approximation, the excretion of carbon dioxide by
the fish is also proportional to metabolism, and hence to oxygen
consumption and to feed. Thus,
D˚ = O˚ = F˚ ,
(13)
where D˚ (in g[CO2 ]/fish), is carbon dioxide produced by a single
fish throughout its residence in the system, and (in g[CO2 ]/g[O2 ])
is the ratio of carbon dioxide production to oxygen consumption.
2.4. Required oxygen concentration in water
When oxygen is supplied by means of aerators, the economically optimal level of dissolved oxygen in the water, CO (in
g[O2 ]/m3 [water]), is the lowest permissible, because this produces
Fig. 1. Oxygen critical points for seabream, as a function of water temperature. The top curve is oxygen saturation of fresh water, the second is for sea
water (Eilat, ∼40 kg[salt]/m3 [water]), and the third is 80% of sea water saturation,
the relationship used in practice for aquaculture at Eilat. The horizontal line at
5.5 g[DO]/m3 [water] is drawn through the 80% saturation point for the mean temperature (22 ◦ C) at Eilat. The open squares are for Diplodus puntazzo (Cerezo and
Garcia, 2004, Table 1) and the filled triangles are for Dentex dentex (Cerezo-Valverde
et al., 2006, Table 1). The three horizontal segments (‘Ventilation’, ‘Oxygen’ and
‘Lethal’) are means for both fish.
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
Fig. 2. Critical oxygen concentration (‘Oxygen’ of Fig. 1) as a function of temperature
from various sources. The upper three sloping curves and the horizontal line ‘Const’
are as in Fig. 1. (1) Atlantic cod, Sollid et al. (2005, Fig. 2); (2) dogfish, Butler and
Taylor (1975, Fig. 4); (3) Atlantic cod, Schurmann and Steffensen (1997, Fig. 4); (4)
goldfish, Sollid et al. (2005, Fig. 2); (5) crucian carp, Sollid et al. (2005, Fig. 2); (6)
eelpout, Zakhartsev et al. (2003, Fig. 8); (7) ‘Oxygen’ average, from Fig. 1.
(line labeled ‘Const’) is above (safer than) the measured ventilation
critical level.
The simple picture of Fig. 1 becomes less orderly when data from
other sources are considered: Fig. 2 is a collection of oxygen critical
point values (at least 3 per data set) for cold and warm water fish
(left and right of figure, respectively). It shows the following: (1)
There is a wide range of results, probably due to differences among
species and experimental techniques (note the difference between
sets 1 and 3, both for Atlantic cod). (2) Unlike the data of Fig. 1, the
critical oxygen level increases with temperature in most cases, possibly due to the need for a larger gradient from water to fish when
the metabolic rates are higher. (3) Even at the highest temperature
for a species, the critical level is still considerably below the relevant saturation level (carp and goldfish, data sets 4 and 5, are fresh
water fishes).
For design purposes a particular critical curve must be selected.
Here three qualitatively different approaches are considered, all
schematically shown as a function of temperature in Fig. 3: (1)
Constant saturation fraction, (2) constant absolute concentration,
and (3) absolute concentration increasing with temperature. The
first approach, often expressed in terms of constant partial gas
pressure (or ‘tension’), appears to be dominant in the aquaculture
literature. Quoting Timmons et al. (2002, p. 99): “partial oxygen
pressure appears to be a more valid way to determine the lower limits”. This approach is in accord with the observation that cold water
fish tend to require higher (absolute) oxygen levels than warm
water fish. The second approach is strongly supported by the results
of Cerezo and Garcia (2004) and Cerezo-Valverde et al. (2006), and
our Fig. 1. The third approach, which is supported empirically by
Fig. 2, can be further justified by the following argument: Fish
metabolic rate, directly affecting feed consumption and growth,
increases with temperature. There is evidence that increased feed
rations result in higher oxygen consumption (Eq. (12), Timmons
et al., 2002, bottom of p. 275) and require higher oxygen concentrations (Brett, 1979, Fig. 17). Jobling (1994) shows a similar
relationship for feed consumption (his Fig. 10.7), and summarizes
the effect of temperature as follows (p. 256): “. . .an increase in temperature will often. . . give rise to an increase in the rate of oxygen
consumption. . . and to. . . a higher PC [critical oxygen tension]”.
As, however, Jobling expresses the critical oxygen level in terms
49
of tension (saturation fraction), it is not clear from this statement
whether the required absolute concentration increases or decreases
with temperature. However, data presented in his Table 15.3, when
converted to absolute concentration, show a slight increase with
temperature.
While the current practice is to design for a constant nominal saturation level (about 80%, or 130 mm Hg), the evidence of
Figs. 1 and 2 seems to represent a different reality, and may lead
to different choices of oxygen supply technology. Following current practice produces the down-sloping curve 1 of Fig. 3, where
the oxygen gradient (air to water, arrow 1) decreases very slowly
with increasing temperature and never vanishes. If any of the other
two options is chosen, then, as the temperature increases, the relevant critical curve (2 or 3) eventually reaches the saturation curve
(empty circles in Fig. 3, where the oxygen gradient from air to water
vanishes), which indicates the onset of anaerobic metabolism and
eventual death (Pörtner and Knust, 2007, Fig. 1E). As this point is
approached, an ever increasing aerators capacity is required to supply the necessary oxygen, increasing thereby the relative advantage
of pure oxygen, which cost is independent of temperature (as will
be shown below).
For lack of accepted criterion and in view of the recent detailed
results of Cerezo and Garcia (2004) and Cerezo-Valverde et al.
(2006), and our Fig. 1 for Mediterranean seabreams, we choose in
this paper to calculate for line 2 of Fig. 3 (constant absolute critical concentration at 5.5 g[O2 ]/m3 [water]). This is somewhat safer
(higher) than the ‘Ventilation’ line of Fig. 1. This choice predicts, by
extrapolation, a maximum feasible temperature of 36 ◦ C, not very
different from the lethal temperature of Hernández et al. (2003)
for seabream, where, incidentally, the actual cause of death may be
other than lack of oxygen. Furthermore, at such a high temperature,
Eqs. (1) and (5) may no longer approximate the actual processes
sufficiently well.
2.5. Oxygen supply by airlifts
In an airlift (or any other aerator), the flux of oxygen from (atmospheric) air to water is proportional to the oxygen concentration
difference between the equilibrium-with-air level (‘saturation’),
ĈO {T }, and the bulk concentration in the water, CO (required, critical
level), defined by the needs of the fish. Thus
S = h(ĈO {T } − CO ),
(14)
Fig. 3. Three different schematic formulations of the minimum oxygen concentration for aquaculture (in sea water): (1) constant saturation fraction; (2) constant
absolute concentration; (3) absolute concentration increasing with temperature.
The solid arrows indicate the direction of oxygen transfer, from air to water. The
crossings of the minimum permissible oxygen curves with the saturation curve are
indicated by empty circles. In the background, in dashed lines, the transfer of CO2
from water to air is indicated. A range of permissible CO2 concentrations is indicated
at the top of the frame.
50
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
where S is the discharge of oxygen delivered by a single airlift (in
g[O2 ]/(airlift d)), and h is the oxygen transfer coefficient of the airlift
(in m3 [water]/(airlift d)). The transfer coefficient increases with air
d)), and to some
discharge through the airlift, A (inm3 [air]/(airlift
extent with temperature. Thus, h A, T .
Indicating by f (in airlift/(fish/d)) the number (or fraction) of
airlifts required to support the fish population ˚, the oxygen
requirement of the fish, O˚ (in g[O2 ]/fish), becomes
O˚ = fS.
(15)
There is a trade-off between f and A, namely between investment
(capital) and operating costs. The best combination of f and A is
selected as follows: Given the cost of capital for one airlift,
uL (in
$/(airlift d)), the power required to operate the airlift, p A (in
J/(airlift d)), and the cost of electricity, uE (in $/J), the cost of providing the necessary oxygen for the population ˚ by means of the
lift
airlifts (KO , in $/fish), is
lift
KO = f (uL + uE p{A}),
(16)
which, utilizing Eqs. (15) and (14), becomes
lift
KO =
O˚
uL + uE p{A}
·
.
h{A, T }
ĈO {T } − CO
(17)
The oxygen transfer coefficient h A, T
uct
(18)
where the exponential function is a temperature correction
(Tchobanoglous et al., 2003, p. 427) relative to a reference temperature, Tr . It is convenient to incorporate the temperature correction
into f, which may be expressed as
fr
,
exp{O (T − Tr )}
(19)
where fr is the required number of airlifts at the reference temperature (at which the calibrating data are collected). Hence, Eq. (17)
may be written as
lift
KO {T } =
1 + (uE /uL )p{A}
·
h{A}
uL O˚
1
·
exp{O (T − Tr )} ĈO {T } − CO
.
(20)
lift
The cost KO can be minimized with respect to the air discharge
A, irrespective of the temperature and of the oxygen demand,
which are restricted to the square bracketed factor. For a given
airlift design and operating head, therefore, the optimal discharge
depends only on the price ratio uE /uL .
The number of oxygen-supplying airlifts to produce one fish per
day (from Eqs. (16)–(18)),
fO =
O˚
h{A}exp{O (T − Tr )}(ĈO {T } − CO )
,
(21)
depends very much on the difference (gradient) ĈO {T } − CO . For the
chosen Scheme 2 (constant absolute CO ; Fig. 3), the concentration
gradient approaches zero as the temperature increases, and therefore fO increases indefinitely with temperature. With this scheme,
proper oxygen supply by means of airlifts (and aerators in general)
may become economically unviable at sufficiently high temperatures.
The airlift power requirement, p {A}, and the transfer coefficient,
h {A}, may be conveniently approximated by power expressions:
p{A} = A ,
(22)
and
h{A} = A ,
lift
KO {T } =
1 + (uE /uL )
A
·
A
(23)
1
uL O˚
·
exp{O (T − Tr )} ĈO {T } − CO
.
(24)
2.6. Operational considerations
Once a system is constructed, its operation must be considered.
The appropriate scaling in the design phase (as in the preceding
analysis), is with respect to production rate (e.g., f in airlifts per
fish/d). System operation, on the other hand, is more naturally
scaled with respect to the (already) installed capacity of the system (e.g., S in g[O2 ] per airlift · day). Suppose that, for one reason or
another, the oxygen demand per airlift, designed to be S = O˚ /f (Eq.
(15)), changes. If it increases, the only solution is to increase, at an
additional cost per unit oxygen, the air discharge of the airlifts. If
the oxygen demand falls below the design value, however, there is a
choice between operating all the airlifts at a reduced air discharge,
or a smaller number of airlifts at the previously obtained optimal
discharge. As the capital cost, uL , is no longer relevant, setting it to
zero in Eq. (24) yields the operating cost
lift
KO {T } = uE
(−)
·
A
may be written as a prod-
h{A, T } = h{A} exp{O (T − Tr )},
f =
which, when introduced into Eq. (20) yields
1
O˚
·
exp{O (T − Tr )} ĈO {T } − CO
.
(25)
As will be shown below, − > 0. Hence the operating cost is minimal at the lowest air discharge A which supplies the required
oxygen. In other words, all available airlifts should be operated all
the time, varying the air discharge to exactly match the demand for
oxygen. Note that if in practice the load of the various fish tanks is
not the same, all the airlifts supplying a given tank should operate
at the same discharge, suitable for the particular load of that tank.
2.7. Oxygen supply by pure oxygen
Just as with aerators, there is also a range of designs for oxygenation with pure oxygen, whether in the liquid phase (LOX) or as
pressurized gas (Timmons et al., 2002, p. 275). For our purpose two
main properties, common to all variants, are important, namely (1)
that a bulk saturation level (in water) of 100% (the maximum permissible) is achievable, which is impossible with airlifts, and (2)
that the cost of supplying the oxygen is, to a first approximation,
independent of temperature, due to the high concentration at the
source.
As a result, the cost of supplying pure oxygen may be formulated
simply as
pur
KO
= uO O˚ = uO F˚ ,
(26)
where uO (in $/g[O2 ]) is the unit price of oxygen actually consumed
by the fish (including costs of generation and pressurization and
considering dissolving efficiency). The cost is proportional to the
feed consumed (by Eq. (12)) and hence, from this point of view as
well, practically independent of temperature.
2.8. Carbon dioxide stripping by airlifts
Carbon dioxide stripping is usually effected by (atmospheric)
aeration, whether with airlifts, trickling nitrification biofilters or
stripping columns (Timmons et al., 2002, Section 8.4). The mechanism for stripping excess CO2 is analogous to that of supplying
oxygen, except in the opposite direction. To a first approximation,
the production of carbon dioxide is proportional to the consumption of oxygen (Eq. (13)) and the transfer coefficients of the two
gasses are proportional to each other over the relevant range of
air-discharge and temperature. Hence, the cost of CO2 stripping
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
with airlifts is calculated with an equation analogous to Eq. (24),
namely
lift
KD {T }
1 + (uE /uL )
A
=
·
ωA
1
uL O˚
,
·
exp{O (T − Tr )} CD − ĈD {T }
lift
KO {T }
lift
KD {T }
=
ω CD − ĈD {T }
.
·
ĈO {T } − CO
3.1. Fish characteristics
(28)
While the cost of oxygen supply increases with temperature, due to
the decrease of ĈO {T } − CO (Fig. 3, Curve 2), the cost of carbon dioxide stripping decreases slightly with temperature (dashed curves in
Fig. 3). Hence, if the cost of supplying oxygen is higher than the cost
of carbon dioxide stripping (ε > 1) at the lower end of the temperature range, it will be even higher at higher temperatures. By Eq. (28),
ε is rather sensitive to the gradients ratio (CD − ĈD {T })/(ĈO {T } − CO ),
namely to the concentrations CO and CD required by the fish. Note
that the cost ratio ε is also the ratio between the number of airlifts
required to supply oxygen, and the number required to remove
carbon dioxide, namely
ε=
fO
.
fD
(29)
Assuming, as already mentioned, that the temperature coefficients, , of growth and feed consumption are the same, the
coefficients of the feed column of Table 1 have been slightly modified by refitting (these values apply to the particular feed used in
the original experiments). The final coefficient values are
˛F = 0.027
˛M = 0.024
g[feed]
gˇF [BM]fish1−ˇF
g1−ˇM [BM]
fish1−ˇM d
;
;
d
ˇF = 0.60;
ˇM = 0.51;
F = 0.06 1/K
M = 0.06 1/K
From practice
Mi = 2 g[BM]/fish;
Mf = 400 g[BM]/fish.
With these values, one obtains
F˚ = 706 g[feed]/fish (= Ff ;
Eq. (7))
and the FCR (Eq. (11)) becomes
˚ ∼
= 1.8.
2.9. An alternative oxygen supply configuration
It has been mentioned above (Section 2.5) that proper oxygen
supply by means of airlifts may become prohibitively expensive at
sufficiently high temperatures. One alternative is to use pure oxygen for oxygenation. Experience, as well as an estimation of ε to be
presented below, show that oxygen supply by airlifts is more limiting than the stripping of carbon dioxide. Hence, if a LH system based
on airlifts is using pure oxygen for oxygenation, the airlifts may be
designed for just CO2 stripping (and water circulation). Depending on the allowable CO2 concentration, CD , stripping may require
a considerably smaller airlift capacity than does oxygen supply. In
terms of costs (Eqs. (24) and (27)), this may be written as
lift
example only, as there is a wide variety of RAS facilities, and estimates are obtained in different ways and to a different accuracy by
the various sources.
(27)
where ω is the ratio between the transfer coefficients for carbon
dioxide and oxygen. In view of Eq. (27) the optimal air-discharge
for carbon dioxide stripping is the same as for oxygen supply (independent of ω).
The cost ratio (oxygen to carbon dioxide), obtained by dividing
Eq. (20) with Eq. (27), is
ε≡
51
lift
KD < KO .
(30)
Hence, two design options may be considered: Configuration 1,
where supplying oxygen and stripping of CO2 are effected by the
same airlifts, and Configuration 2, where CO2 stripping is effected
by airlifts, while oxygenation is using pure oxygen. In view of Eq.
lift
(30), the operating cost of the first configuration is KO (Eq. (25)),
lift
pur
while employing the second configuration costs KD + KO
(27) + (26)).
(Eqs.
3. Parameter values
The parameter values for the sample calculations are based on
physical and biological information from the literature, and on typical conditions in Israel. In particular, fish characteristics were taken
from the already mentioned seabream nutritional model, developed over the years by Lupatsch and Kissil (1998, 2005), Lupatsch
et al. (2003) and Lupatsch (personal communication). Airlift characteristics and costs were taken from internal reports of the National
Center for Mariculture (NCM) for a pilot plant in Eilat, Israel, and
data for a LOX system were obtained from a seabream RAS at Ein
Hamifrats, Israel. One should view these data as an illustrative
There is a wide range of experimental results for in the literature, depending on species, fish size, feed composition and ration.
Timmons et al. (2002, pp. 99–100) quote a representative value of
= 0.25. A more recent study (Merino et al., 2009, Table 4) suggests, for halibut of similar size and feeding ration as our seabream,
a mean value of = 0.5 kg[O2 ]/kg[feed]. Measured values of are
rare. Timmons et al. (2002, p. 287) suggest a theoretical value of
1.38 kg[CO2 ]/kg[O2 ].
Here we choose to use values obtained from the detailed
empirical model of Lupatsch for seabream (Lupatsch, personal
communication). On average, for the range of temperatures
20 ◦ C < T < 30 ◦ C, the following equivalents are obtained
= 0.63 kg[O2 ]/kg[feed],
= 1.14 kg[CO2 ]/kg[O2 ].
In practice, the supply of oxygen is augmented to offset inefficiencies and to provide for oxygen-consuming micro-organisms in the
system. Hence, the value of for the subsequent calculations (for
both configurations) is increased to
= 0.75 kg[O2 ]/kg[feed].
This value is supported by bulk data obtained recently at Ein Hamifrats: Over a period of one year a total of 203 (metric) tons of feed
and 157 tons of liquid oxygen have been purchased, resulting in a
very similar ratio: = 0.77 kg[O2 ]/kg[feed].
3.2. Capital cost of airlifts
The pilot plant at Eilat has 208 oxygen-supplying airlifts, which
cost $ 196,000, including blowers, to construct and install. At a
return rate of 0.15/y, the capital cost of an airlift is determined
as
uL = 0.39 $/(airlift · d)
52
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
3.3. Optimal air discharge through the airlifts
The optimal air discharge through an airlift is obtained by minimizing Eq. (24), namely by minimizing [1 + (uE /uL )
A ]/(A ) with
respect to A. For the installation under consideration (NCM data)
uE = 0.10 $/kWh (0.028 $/MJ)
limiting than the stripping of carbon dioxide, and that the cost of
lift
lift
operation needs to be calculated by means of KO (Eq. (24)), not KD
lift
(Eq.(27)). To determine KO {T } via Eq. (24), O˚ and O are required.
O˚ is evaluated with Eq. (12) as
O˚ = 530 g[O2 ]/fish.
and O is set, following Tchobanoglous et al. (2003, p. 427) to
= 0.00543 and
= 1.134 for A in m3 [air]/h and p in kW
(Eq. (22))
O = 0.024 1/K
at Tr = 23 ◦ C
lift
= 7.8 and
= 0.675 for A in m3 [air]/h and h in m3 [water]/h
With these values, KO {T } varies between 20 and 30 ◦ C from 0.18 to
0.43 $/fish, indicating a considerable increase with temperature, as
expected.
3.5. Oxygenation by means of liquid oxygen
(Eq. (23))
Hence, the optimal air discharge is
pur
A = 29.2 m [air]/(airlift · h),
The cost of KO depends on the system used to deliver the oxygen. Here we use the cost of liquid oxygen determined from the
actual expenses at Ein Hamifrats, namely
which is about a third of the maximum air discharge for which the
airlifts have been tested.
O = 0.43 $/kg[O2 ],
3
3.4. Oxygen supply and CO2 stripping by means of airlifts
Whether supply of oxygen or carbon dioxide stripping is the
limiting factor of the airlift operation, can be decided by evaluating
Eq. (28). For our conditions (seabream in red sea water) the design
(limiting) concentration of oxygen is considered to be around
CO = 5.5 g[O2 ]/m3 [water]
which is represented by the ‘Const’ lines of Figs. 1 and 2, and by line
2 of Fig. 3.
There is considerable uncertainty regarding the limiting carbon
dioxide concentration, so here we consider the range
10 ≤ CD ≤ 20 g[CO2 ]/m3 [water].
The limiting oxygen and carbon dioxide concentrations are shown
by horizontal lines in Fig. 3.
At the low end of the seabream temperature range, 20 ◦ C, and
for salinity of 40 g[salts]/kg[water], the gas concentration equilibria
with a standard atmosphere (based on Weiss, 1970, 1974), are
ĈO {20 ◦ C} = 7.2 g[O2 ]/m3 [water] and ĈD {20 ◦ C}
= 0.50 g[CO2 ]/m3 [water].
These points lie on the corresponding saturation curves of Fig. 3.
It should be clear from the figure that while the oxygen gradient
of line 2 decreases rapidly with increasing temperature (vanishing at 36.3 ◦ C), the carbon dioxide gradient is large and essentially
constant with temperature.
There are only a few carbon dioxide transfer data. It seems
that the value of ω (Eq. (27)) depends on the aerating equipment
and may differ significantly from the theoretical value of ω ≈ 0.9
(Summerfelt et al., 2000; Eshchar et al., 2003; Aitchison et al., 2007).
Unpublished NCM data for the airlifts in question indicate a value
as low as
ω ≈ 0.3.
Even for this low value and the lowest maximum permissible CO2
concentration (CD = 10 g[CO2 ]/m3 [water]), the cost ratio, ε, is considerably larger than 1:
ε{20 ◦ C} =
fO
= 1.50 > 1.
fD
This implies that for the ranges of temperature and carbon dioxide
concentrations considered here, oxygen supply by airlifts is more
of which about 10% is attributed to the cost of the required equipment, 5% to imperfect dissolving efficiency and about 0.15 $/kg[O2 ]
to the cost of electricity for the water pressurizing pumps. Incidentally, the cost of generating oxygen on location is lower in terms of
energy for generation, higher in capital cost and about the same in
terms of dissolving efficiency and pressurization costs. Altogether,
possibly somewhat less expensive.
Multiplying O by and F˚ , the cost of oxygenation with pure
oxygen is calculated via Eq. (26) to be
pur
KO
= 0.23 $/fish,
independent of temperature.
lift
The cost KD {T } is calculated, with the already specified parameters, via Eq. (27). It decreases between 20 and 30 ◦ C from 0.123
to 0.095 $/fish for the lower permissible CO2 concentration of
10 g[CO2 ]/m3 [water], and from 0.060 to 0.047 $/fish for the upper
permissible CO2 concentration of 20 g[CO2 ]/m3 [water].
If oxygen is supplied by pure oxygen, the airlifts duty is mainly
CO2 stripping, which requires a considerably lower airlift capacity (number of airlifts). On the assumption that the bulk oxygen
concentration in the water for this configuration is 100% saturation, the total cost of oxygen supply and carbon dioxide stripping
lift
pur
is KD + KO (sum of Eqs. (27) and (26)).
4. Results, discussion and conclusions
4.1. Constant temperatures
Costs of supplying oxygen and stripping of carbon dioxide for
the set of parameters of Section 3, are compared in Fig. 4. The cost
of effecting these two processes simultaneously by means of the
same airlifts, is represented by the increasing curve (empty circles,
lift
Eq. (24)). It is tagged with KO , and approaches infinity (impos◦
sibility) at about 36.3 C. The cost of supplying oxygen by means
of pure oxygen (here LOX), is independent of temperature and
is represented by the horizontal line (diamonds, Eq. (26)) tagged
pur
with KO . Utilizing pure oxygen reduces the required capacity of
the airlifts, which now are needed for just CO2 stripping. When
lift
the cost of stripping, KD , is added to the cost of oxygenation, the
lift
pur
result is a curve, tagged with KD + KO , which decreases slowly
with temperature and which level depends on the permissible CO2
concentration (here between 10 and 20 g[CO2 ]/m3 [water]).
In summary: Fig. 4 shows (1) that the cost of supplying oxygen by means of airlifts increases ‘exponentially’ with temperature;
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
53
4.2. Variable temperatures
Fig. 4. Cost of supplying oxygen and stripping carbon dioxide to produce one fish
lift
of 400 g[BM] (left scale) or one kilogram of BM (right scale). KO is the cost of suppur
plying oxygen and carbon dioxide stripping by means of the same airlifts. KO is the
lift
cost of oxygenation with pure oxygen. KD is the cost of carbon dioxide stripping by
airlifts, the subscript 10 or 20 indicating the maximum permissible CO2 concentration. The filled circles are the optimal choices for maximum CO2 concentration of
10 g[CO2 ]/m3 [water].
(2) that the cost of CO2 stripping decreases slightly with temperature; and (3) that the cost of CO2 stripping decreases when the
permissible (‘design’) CO2 concentration increases. As a result, the
temperature where the optimal design switches from one configuration to the other increases (1) with decreasing permissible
CO2 concentration, and (2) with increasing relative cost of pure
oxygen.
With the parameter values of this study, and selecting the low
(safer) bound of CO2 concentration, namely 10 g[CO2 ]/m3 [water],
the broken curve with filled circles in Fig. 4 indicates that Configuration 1 (airlifts) has the advantage at temperatures lower than
27.7 ◦ C, while Configuration 2 (mixed) is more economic for higher
temperatures. If the CO2 concentration is allowed to increase to
20 g[CO2 ]/m3 [water], the switching temperature goes down to just
26 ◦ C, and pure oxygen becomes the better choice over a wider temperature range. The difference in cost between systems is of the
order of 0.05 $/fish (0.12 $/kg[BM]).
There is considerable uncertainty regarding several of the
assumptions and parameter values, even for the selected species
(seabream). As an example, if the value of ω (Section 3.4) is closer
to its theoretical value (higher than assumed), CO2 stripping is more
efficient (less expensive), and the switching temperature is diminished. The same effect is obtained by reducing the cost of pure
oxygen. It should also be clear that the relative advantage of pure
oxygen increases as the slope of the oxygen curves of Fig. 3 increases
(Curve 1 to 2 to 3). Our choice of Curve 2 (zero slope), based on Fig. 1,
is, in this respect, an intermediate choice.
Future changes in energy prices may also affect the relative
advantage of the alternatives. For example, the current trend in
European aquaculture seems to be that “pumps become more
efficient or replaced by airlifts” (Martins et al., 2010, Section
3.1.3). If this trend (to reduce energy costs) persists, ‘mixed’
systems with airlifts for stripping (and for submerged nitrification biofilters), and liquid oxygen for oxygenation, may become
more popular, especially for warm water RAS. When the approach
suggested here is to be applied to another species, installation
and/or economic environment, a new set of parameters must be
obtained.
The approach described so far and illustrated in Fig. 4, is suitable for making choices regarding constant-temperature systems.
If, however, the temperature varies significantly over the annual
cycle (e.g., 20–28 ◦ C as at Eilat), the steady-state analysis of Section
2 is no longer strictly valid (Seginer and Halachmi, 2008; Seginer,
2009). Furthermore, the cost curves of Fig. 4 also do not strictly
apply, because each point on these curves represents a (physically)
different system (e.g., more airlifts at higher temperatures). When
the temperature fluctuates, proper integration of the seasonal costs
requires that a particular rearing system, as well as a particular
stocking and harvesting policy, are specified. In addition, capital
and operating costs should be treated separately: while the former
stays constant with time, the latter varies in response to the changing temperature. All this can be done by simulation, but may not be
justified as long as the accuracy of key parameters is questionable.
At the present time it would seem that as a rule of thumb, if the mean
seasonal water temperature is below the switching temperature,
Configuration 1 (airlifts) should be preferred over Configuration 2
(mixed), and vice versa.
If the temperature distribution is wide and nearly uniform (e.g.,
as resulting from a sinusoidal variation with time; Seginer et al.,
2008, Fig. 4), a ‘hybrid’ system may be contemplated. Such a system utilizes the airlifts for oxygen supply at low temperatures and
switches to pure oxygen at a temperature selected to minimize the
operational costs (pure oxygen as a backup system). Such a combination would reduce the capital cost of the airlifts (fewer than
required to cover the needs at higher temperatures), but, on the
other hand, would add the expense of installing the pure oxygen
equipment. A more detailed analysis of such a hybrid system is
possible, but is beyond the scope of the present paper.
4.3. Conclusions
The first-order analysis presented in the preceding sections may
be summarized as follows:
1 For seabream fed to satiation, and probably for some other fish as
well, growth rate, feed consumption, and oxygen consumption,
all increase with temperature at the same rate (about 6%/K in the
low temperature range). As a result, the quantities of feed and
oxygen consumed by a fish to grow to a certain size (Ff and Of ),
are, to a first approximation, independent of temperature (Eqs.
(7) and (12)).
2 The factor which limits the transfer of oxygen into the water by
means of aeration, is the (absolute) bulk concentration of oxygen
below which a reduction in fish growth occurs. As temperature
increases, this limiting concentration approaches the oxygen saturation curve (Fig. 3), resulting eventually in hypoxia.
3 For seabream in the practical range, the limiting (absolute) oxygen concentration is most likely independent of temperature
(Fig. 1).
4 Any given airlift (operating at a given head) has an optimal air
discharge which depends only on the cost ratio of electricity to
capital, uE /uL , not on the gas to be transferred, nor on temperature
(Eq. (27)).
5 In operation mode, all oxygen-supplying airlifts available to a
certain fish tank, should be operated simultaneously at the same
air discharge which together satisfies the oxygen demand (Eq.
(25)).
6 The cost of oxygenation with liquid oxygen is, to a first approximation, independent of temperature (Eq. (26)), and hence, this
method may have a relative advantage over airlifts (aerators) at
high temperatures (Fig. 4).
54
I. Seginer, N. Mozes / Aquacultural Engineering 50 (2012) 46–54
Acknowledgement
We are grateful to Raz Ben-Asher, who provided data representative of Ein Hamifrats Fisheries.
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