Efficient and economical way of operating a recirculation aquaculture system in an aquaponics farm

19 Pages·2016·1.45 MB·English

by  Divas Karimanzira

Aquaculture Economics & Management
ISSN: 1365-7305 (Print) 1551-8663 (Online) Journal homepage: http://www.tandfonline.com/loi/uaqm20
Efficient and economical way of operating a
recirculation aquaculture system in an aquaponics
farm
Divas Karimanzira, Karel Keesman, Werner Kloas, Daniela Baganz & Thomas
Rauschenbach
To cite this article: Divas Karimanzira, Karel Keesman, Werner Kloas, Daniela Baganz &
Thomas Rauschenbach (2016): Efficient and economical way of operating a recirculation
aquaculture system in an aquaponics farm, Aquaculture Economics & Management, DOI:
10.1080/13657305.2016.1259368
To link to this article: http://dx.doi.org/10.1080/13657305.2016.1259368
Published online: 14 Dec 2016.
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AQUACULTURE ECONOMICS & MANAGEMENT
http://dx.doi.org/10.1080/13657305.2016.1259368
Efficient and economical way of operating a recirculation
aquaculture system in an aquaponics farm
Divas Karimanziraa, Karel Keesmanb, Werner Kloasc, Daniela Baganzd, and
Thomas Rauschenbacha
aDepartment of Surface Water and Maritime Systems, Fraunhofer I0SB-AST, Ilmenau, Germany;
bDepartment of Biobased Chemistry & Technology, Wageningen University, Wageningen, The
Netherlands; cDepartment of Endocrinology, Institute of Biology, Humboldt University Berlin,
Berlin, Germany; dDepartment of Biology and Ecology of Fishes, Leibniz–Institute of Freshwater Ecology
and Inland Fisheries, Berlin, Germany
ABSTRACT KEYWORDS
In this article, optimal control methods based on a metabolite- Aquaponics; dynamic
constrained fish growth model are applied to the operation of modeling; economics;
fish production in an aquaponic system. The system is optimization
formulated for the twin objective of fish growth and plant
fertilization to maximize the benefits by optimal and efficient
use of resources from aquaculture. The state equations, basically
mass balances, required by the optimization algorithms are
given in the form of differential equations for the number of
fish in the stock, their average weight as mediated through
metabolism and appetite, the water recirculation and waste
treatment, hydroponic nutrient requirements and their loss
functions. Six parameters, that is, water temperature, flow rate,
stock density, feed ration size per fish, energy consumption rate
and the quality of food (percentage of digestible proteins)
are used to control the system under dynamic conditions. The
time to harvest is treated as a static decision variable that is
repeatedly adjusted to find the profit-maximizing solution. By
modeling the complex interactions between the economic and
biological systems, it is possible to obtain the most efficient
decisions with respect to diet composition, feeding rates,
harvesting time and nutrient releases. Some sample numerical
results using data from a tilapia-tomato farm are presented and
discussed.
Introduction
Aquaponics is gaining increased attention as a bio-integrated food production
system and belongs to the class of large-scale systems, which can be viewed as
a network of interconnected subsystems. A common feature of these systems
is that subsystems must make control decisions with limited information.
The hope is that despite the decentralized nature of the system, global
performance criteria can be optimized. There are mainly two objectives in
CONTACT Divas Karimanzira [email protected] Department of Surface Water and
Maritime Systems, Fraunhofer I0SB-AST, Ilmenau, Germany.
Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/uaqm.
© 2016 Taylor & Francis
2 D. KARIMANZIRA ET AL.
aquaponics. The first and most important objective is the biophysical
objective, which is raising the fish to maturity with low mortality while
producing enough waste for the crops. The second objective is a commercial
one, which forces the fish and the plants to be raised in an economic way.
Unfortunately, the nature of recirculating system operation dictates that
producers stock their systems at high densities to overcome the higher
fixed and variable costs normally associated with closed system operation
(Kazmierczak, 1996).
However, as the use of resources in aquaponic systems gets intensified,
the role of management ability becomes critical to their economic success.
This fact is confirmed in Tokunaga, Tamaru, Ako, and Leung (2015), who
collected economic and production information from three aquaponic
farms to investigate the economic feasibility of the aquaponics industry in
Hawaii. They conducted sensitivity and decision reversal analysis to inves-
tigate how output prices and operational cost parameters affect the overall
economic outcome. At this point, it can be noted that the combination of
aquaponic dynamics and the economics of producer decision making is
scarce in the literature.
In Cacho, Kinnucan, and Hatch (1991) a bioeconometric model of pond
catfish production was developed and used for the determination of cost-
effective feeding regimes. Some researchers have also used bioeconometric
models of varying degrees of sophistication to examine open system rearing
of fish (Karmierczak, 1996; Liu & Chang, 1992; Love, Uhl, & Genello, 2015).
However, no study has examined the optimization of recirculating aquaponics
systems incorporating not only realistic metabolite-constrained fish growth
over time, but also the economic and nutrient requirement constraints for
crop growth. Metabolite-constrained fish growth model describes a model that
considers the effects of water quality on fish growth and mortality.
In this article, a model for determining cost-effective feeding regimes and
dietary protein composition for fish reared in aquaponic recirculation
aquaculture (RAS) and maximizing the fertirrigation releases is developed,
and the interplay among ration size, feed quality (protein percent), water
quality and harvest date are quantified.
System description
The features of the “Innovative Aquaponics for Professional Application”
(INAPRO) aquaponics system can be seen in Figure 1. It is based on
the ASTAF-PRO technology as described in Kloas et al. (2015). In contrast
to conventional aquaponics, the INAPRO system is a double recirculation
system whose two subsystems, a recirculating aquaculture system (RAS)
and a recirculating hydroponics unit within a greenhouse, are mutually
unidirectional connected to (a) deliver fish water containing nutrients into
AQUACULTURE ECONOMICS & MANAGEMENT 3
Figure 1. Structure of an aquaponics management system as a two-player system.
the hydroponic reservoir as fertilizer and (b) return the condensed plant
evapo-transpirated water into the aquaculture part to minimize the overall
water consumption of the system and to ensure that optimum conditions
can be set up in each subsystem independently from the other.
Practical experience on the INAPRO system and discussions with several
aquaponics stakeholders have shown that, for optimal operational manage-
ment of aquaponics, trying to find a holistic criterion for optimizing both
parts at the same time is not necessary if the nutrient buffer tank between
the fish and the crops is well dimensioned in the design phase. Therefore,
this article deals with the optimization of the RAS using information about
nutrient uptake from an optimized hydroponic system to achieve the holistic
objective of the aquaponic system.
Methods
Here we describe the optimization framework and present the general
management problem faced by system managers. In aquaponics, management
primarily affects the variable costs associated with short-term decision making
over a fish growth-cycle, which is assumed to be significant for the crop
growth cycle as well. Along with the direct financial costs related to stocking,
feeding, and electrical power use, indirect costs can arise when the waste
filtering devices do not completely remove metabolic waste material (Rackocy,
Masser, & Losordo, 2006). These indirect costs appear in the form of retarded
fish and crop growth and increased fish mortality. Considering that RAS
managers seek to maximize returns above variable costs and objectives are
conflicting, a multi-objective approach is put forward, which reduces to the
maximization of discounted profits. The cost function to be maximized is
the profit J(t), which is the difference between the wholesale purchase price
f
4 D. KARIMANZIRA ET AL.
per unit weight C times the average weight W times the number of fish
w
N and the cost spent throughout the growout cycle t ∈ [t , t] of the fish L
0 f
(t), i.e.,.
f
(cid:0) � (cid:0) � (cid:0) � (cid:0) �
J t ¼ C W t N t (cid:0) L t ð1Þ
f w f f f
This problem falls in the category of optimal control problems with general
path and boundary constraints, free final time t and with some unknown
f
parameters.
(cid:0) �
max J xðtÞ;uðtÞ;dðtÞ;t;p;t
f
uðtÞ;tf;p;x0
subject to x_ðtÞ ¼ f½t;xðtÞ;uðtÞ;dðtÞ;p�;xð0Þ ¼ x0 ð2Þ
h½t;xðtÞ;uðtÞ;dðtÞ;p� ¼ 0 ð3Þ
g½t;xðtÞ;uðtÞ;dðtÞ� � 0 ð4Þ
xðtÞLB� xðtÞ � xðtÞUB;uðtÞLB� uðtÞ � uðtÞUB;and pLB � p � pUB
where f is a vector of differential equations describing the system state dynamics,
h is a vector of equality constraints, g is a vector of inequality constraints, the
state vector xðtÞ ¼ ½WðtÞ NðtÞ LðtÞ�T, x0 comprises the process initial con-
� �
T
ditions, the control vector uðtÞ ¼ TðtÞ RðtÞ R ðtÞ SðtÞDCðtÞ t , the
e f
superscripts LB, UB indicate the lower and upper bounds for the parameters
p, states and the controls, and d(t) are disturbances. The state variables are the
average weight of the fish stock W, the average number of fish in the stock N,
and the average cost of the fish stock L (the costs incurred by aeration, heating,
electricity, extra fertilizers for the crops, etc.).
The variables applied in this article as control variables are mainly the tem-
perature T, the water recirculation and waste treatment R accounting for how
e
much water is allowed to be recirculated without violating the metabolite
critical values, the stocking density S or the amount of space per fish S ,
p
the ration size R, and the dietary protein composition DC. The three variables
R, R , and S are dimensionless with a value domain between zero and one.
e p
For example, the ration size R is defined in relation to the maximum ration
which would lead to satiation. R is equal to 0 when there is no feeding and
approaches 1 at satiation level. The rate of aeration (A) is automatically
t
adjusted in response to the fish oxygen demand to keep the dissolved oxygen
level at 5 ppm. The initial stocking density is fixed for any given set of
simulation optimizations over, but allowed to vary between optimizations.
The results of optimizations of different stocking densities are compared
and analyzed for the impact of S on the potential returns. Because initial
stocking density S and t are fixed, i.e., a given number of fish/l are given
0 o
at the beginning of the cyclogram, the control problem is reduced to finding
the optimal combination of R, DC, R and t. Furthermore, an external
e f
AQUACULTURE ECONOMICS & MANAGEMENT 5
variable, considered as a disturbance to take care of the crop nutrient
requirements ; is also included.
Additionally, the technical and biological relationships embedded in
Equation 2 can be defined by the following equations:
� �
W ¼ w Wðt(cid:0) 1Þ; F ðtÞ; B ðtÞ; RðtÞ; DCðtÞ;T;BE ; ð5Þ
t t t;i
N ¼ nfS ;M g; ð6Þ
� t 0 t �
L ¼ l N ;W ;T ;S ;QðtÞ;G;; ðtÞ;K ð7Þ
t t t t p t L
A ¼ afWðtÞ;TðtÞ;RðtÞ;DCðtÞ;SðtÞ;QðtÞg; ð8Þ
t
B ¼ bfWðtÞ;SðtÞ;F ðtÞ;RðtÞ;R ðtÞ;DCðtÞ;TðtÞ;BE;MEg;i ¼ 1...N; ð9Þ
t;i t e
E ¼ efA ;WðtÞ;TðtÞ;RðtÞ;DCðtÞ;SðtÞ;QðtÞg; ð10Þ
t t
F ¼ rfWðtÞ;TðtÞg; ð11Þ
�t �
M ¼ m SðtÞ;WðtÞ;DCðtÞ;B ðtÞ ð12Þ
t t;i
where B is the production rate of metabolite i at time t, BE is the biological filter
t, i
efficiency, ME is the mechanical filter efficiency, G is uneaten feed, Q is the water
flow, E is the rate of energy use, M is the rate of mortality, ; ¼ω{P , N } is the
t t t d d
crop nutrient requirements for phoshorus P and nitrate N and K are diverse
L
costs contributing to the discount function. Furthermore, P and N releases from
the RAS (;) should be sufficient to meet ; at least by a fraction e van Straten,
s d
van Willigenburg, van Henten, and van Ooteghem (2010), i.e.,
; � E�; ð13Þ
s d
Equations (1)–(13) describing the optimization model require that the
technical and biological relations embedded in the model be fully described
and must be empirical. The bioenergetic fish growth model simulates protein
and fat dynamics as affected by temperature, body weight, ration size, and diet
quality. Besides these factors, fish growth is also a function of other environ-
mental factors, such as dissolved oxygen demand (DO), unionized ammonia
(UAN), space or stocking density (S), and biochemical oxygen demand (BOD)
FAO (2014). The differential equation describing the fish growth including
all important limiting environmental factors and assuming a multiplicative
influence may be expressed as follows:
dW YN
¼ S�W � B ð14Þ
D i
dt
i¼1
where N is the number of metabolites and B is the metabolite and W is the
i D
theoretical growth rate. Detailed description of the effects of metabolites on
fish feed consumption, mortality and reduced growth and how they are
implemented can be obtained upon request. The effects of space, S , UAN
p
and DO on growth and mortality of the fish are shown in the following as
examples. An inverse relationship between survival rate and stocking density
6 D. KARIMANZIRA ET AL.
has been found in several studies (Winberg, 1971; Abdel-Fattah, 2002;
Osofero, Otubusin, & Daramola, 2009, etc.). The function of the limiting
relation assumed here is similar to limiting-growth models for other species
under other conditions (Winberg, 1971)
dW=dt ¼ W S ; ð15Þ
D p
where S ¼1 − (W/W )μ, W is the limiting weight which is a function of
p max max
space, and μ is an empirically determined constant. The relationship between
S , and the mortality rate was determined using the anti-logistic model
p
(Chachuat, Srinivasan, & Bonvin, 2009) expressed as
S ¼ 1(cid:0) M ; and M ¼ M =ð1þ½ðM (cid:0) M Þ=M �e(cid:0) ztÞ ð16Þ
t t 1 1 0 0
where M, is the cumulative mortality rate (%) at the experimental period
t
t, M is the theoretical asymptotic cumulative mortality rate, M is the
∞ 0
hypothetical cumulative mortality rate at the beginning and z is the mortality
coefficient.
Each food composition j is assumed to have a separate growth rate constant
and a separate mortality M (%) with mortality rate constant P. The
Q j
optimization problem involves deciding when to switch from one food to
another. Consequently, we can derive the number of surviving fish N from
the mortality rate constant P given the initial number of fish in stock to
j
M ¼ (cid:0) PS ð17Þ
Q j
Furthermore, mortality is also induced by the water quality. While no
complete information exists on tilapia mortality for various levels of UAN
over time, the acute toxic UAN levels for channel catfish (Ictaluras punctatus)
closely resemble those for tilapia. Using catfish data from Tomasso, Simco, &
Davis (1979), an expression for daily percent UAN-induced mortality (M
UAN
(%)) could be derived:
� �
1
MUAN ¼ (cid:0) 100� 0:5aþbe(cid:0)cUANðtÞ (cid:0) 1:0 ð18Þ
where a, b and γ are parameters with corresponding values of 0.16, 1420.5,
and −1.97, respectively. Given (Equation 18), mean daily mortality increases
gradually as UAN concentrations rise to 3 mg/liter and then increases rapidly
for UAN concentrations between 3 and 5 mg/liter.
There is data for DO-induced mortality in tilapia (Drummond, Murgas, &
Vincetini, 2009). With this information, mean daily mortality relative to DO
level M (%) was calibrated as
DO
� �
MDO ¼ 100� 0:5e(cid:0)cðDOð1tÞ(cid:0)DOsat (cid:0) 1:0 ð19Þ
where γ is a parameter equals to 19 L/mg. DO equation (19) provides for
subtle mortality effects just below the maximum lethal DO concentration of
AQUACULTURE ECONOMICS & MANAGEMENT 7
1.5 mg/liter. These mortality effects increase gradually down to DO
concentrations of 0.8 mg/liter and then increase rapidly as DO concentration
falls below 0.7 mg/liter.
To be able to calculate these effects of the environmental parameters,
their production rates are required. The general metabolite production
Equation (9) is a function of the fish weight W, the stocking density (S),
the individual fish appetite at time t (F), the number of fish/liter (D), the feed
t
ration size (R) and the water treatment efficiency (E). For example the
production of UAN at time t is calculated as a fraction of the TAN in the
system (Emerson, Russo, Lund, & Thurston, 1975), i.e.,
� �
logð9:375Þ W
UAN ¼ 0:008�exp �T �S�DC� �D�F �R; ð20Þ
t t
30 1000
|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
Conversion TANProduction
and finally, due to recirculation through the biological filter and the residual
UAN from the previous time step,
UAN ¼ ð1(cid:0) BEÞðUAN þUANðt(cid:0) 1ÞÞ ð21Þ
t t
Exchange of water (WT ¼1 − R (t)) was allowed, so that more fresh water
e
is added to the system at higher limiting metabolite concentrations.
The consumption of oxygen (BOD), arises from three sources; fish
respiration (BOD ¼K * S * Wσ), oxidation of ammonia compounds
fish M1
by autotrophic bacteria (BOD ¼K * D * S * F * R), and the decompo-
ox M2 t
sition of organic solids by heterotrophic bacteria ðBODoxÞ (Wheaton, Hochhei-
ME
mer, & Kaiser, 1991), where ME is the mechanical filter efficiency, K and σ
M
are constants associated with each oxygen demand.
Sub-models for energy use in the aquaponic system are also required. The
amount of pumped water Q is proportional to the energy E [kWh] used for
p
this purpose, i.e., Q ¼ E � gps where ρ is the water density [kgm−3], g is
p q�g�h
the gravity constant acceleration [ms−2]; η is the pumping system efficiency
ps
and is the height of pumping. Energy used for aeration is estimated by
A ¼ DOd, with OT ¼ OT bDOs(cid:0) DOp 1.024T − 20a and DO is oxygen demand
t OTp p s 9:07 d
(kg/l/day) and OT represents oxygen transfer rate into the rearing basin
p
(kg/kWh) and is defined as in (Boyd et al., 1986), where OT is standard
s
oxygen transfer rate (kg/kWh) (provided by the aerator manufacturer); DO
s
is oxygen saturation level at temperature T; DO is the dissolved oxygen level
p
in the rearing basin; a ¼0.77 and ß ¼0.94 L/mg are correction factors.
The last functional constraint is related to the greenhouse crop nutrient
requirements ;. Real data for a good year from a tilapia-tomato farm
t
was used as in Mischan, Passos, Pinho, and Carvalho (2015) to fit a logistic
function to determine the model for N&P uptake (;) by the plants during
t
the growth cycle.
8 D. KARIMANZIRA ET AL.
The models of the discount function L are described in the following. The
loss function directly associated with raising the fish to a certain weight can be
written as
L ¼ K W ðT (cid:0) T ÞþK W þK ;8T > T ð22Þ
1 1 D N 2 D 3 N
where T �T �T and zero otherwise, W is the actual average weight of
0 max D
the individual fish, is the water temperature; T is the empirically determined
0
zero growth temperature (zero appetite); T is the maximum temperature
max
for growing the fish, K are estimates of the costs, and T is the temperature
i N
of the source water. The first term accounts for the costs of heating replaced
water and the second term accounts for other costs which depend on fish
weight W . The third term K is the cost for fingerlings.
D 3
The loss function L associated with the feed depends on both the cost of
2
the food and the cost of waste treatment for the uneaten food.
L ¼ K W GþK W ðG(cid:0) VÞ ð23Þ
2 5 D 24 D
where V and G are dimensionless food variables which are proportional to
food eaten and the food fed, respectively. K is the cost of waste treatment
24
of the uneaten food and K is the cost of food ($/kg), which is calculated as
5
a function of the protein content using the function K ¼δ þδ · DC, where
5 1 2
and DC is the dietary protein (kg protein /kg feed). In the equation, the
intercept represents the non-protein part of the feed and is affected by the
changes in the cost of marketing and processing, as well as by the prices of
other ingredients of the feed. Therefore, the protein cost of the feed is
represented by the slope δ . The coefficients in the equation were estimated
2
from prices of tilapia feeds of different protein contents and correspond to
the values of δ ¼0.112 and δ ¼0.543 as also estimated in Hicks (2015).
1 2
The discount function for the recirculation and water treatment is mainly a
function of the cost allocated to metabolite-induced reduction in fish growth,
heating the water, waste treatment and water pumping. It can be expressed as
follows:
L ¼ K Q ð1(cid:0) RÞðT (cid:0) T ÞþK WaðT (cid:0) T ÞþK Q ð1(cid:0) RÞþK QR
3 11 N 12 A 21 22
ð24Þ
where K are estimates of costs, T is the ambient temperature of the atmos-
ij A
phere (as contrasted to T , which is the natural temperature of source water),
N
and a is an empirically determined exponent. The first term (K ) represents
11
the cost of heating the incoming source water; the second term (K ) repre-
12
sents heat loss to the atmosphere from holding tanks; the fourth term (K )
21
represents costs of pumping water from the source, pre- and post-treatment:
and the last term (K ) represents costs of pumping water through the
22
AQUACULTURE ECONOMICS & MANAGEMENT 9
recirculating system and treating it. It is assumed pump operation and
maintenance costs are proportional to flow rate Q.
A preliminary estimate of the costs allocated to space and maintenance
indicates the cost L , can be represented as
4
(cid:0) �
L ¼ K Wc 1(cid:0) S (cid:0) c=l ð25Þ
4 23 p
where K is an estimate of space and maintenance related costs and γ is an
23
empirically determined exponent. From (Equation 13), the loss function
due to the nutrient supply deficit can be expressed as
L ¼ K �ðE�; (cid:0) ; Þ ð26Þ
5 fert d s
This loss function can be easily implemented as a benefit function in
which the nutrients produced by the fish are considered as an extra revenue
C ¼; �P, where P is the price for (P,N) fertilizer and C is the cost of pro-
f,j j f f f,j
duced fertilizer at time j.
Solution strategies
Having specified the dynamic constraints embedded in equations (5)-(26), the
solution of the optimization problem requires a strategy for dealing with the
large number of potential control variables and free final time. Two solution
strategies were implemented:
1. A multidisciplinary feasible approach (MDF) is applied to solve the
differential equations within the objective function. This approach
implicitly satisfies the constraints, so there is no need to add explicit
equality constraints to the optimization problem. A terminal individual fish
weight W is used as a boundary condition.
F
2. Another optimizing technique also implemented is an indirect method,
which is based on choosing adjoint variables to satisfy the necessary
conditions for an optimal trajectory as suggested by the Pontryagin’s
maximum principle. The Hamiltonian H and the differential equations
for the adjoint variables (costates) kðtÞ ¼ ½k ðtÞ k ðtÞ k ðtÞ�T can be
W N L
written directly.
dW dN dL
H ¼ k þk þk ð27Þ
W N L
dt dt dt
The required conditions for optimality are:
d @H
xðtÞ ¼ ðxðtÞ;uðtÞ;kðtÞ;tÞ ð28Þ
dt @k
d @H
kðtÞ ¼ ðxðtÞ;uðtÞ;kðtÞ;tÞ ð29Þ
dt @x