PRES22_0231.docx
DOI: 10.3303/CET2294173
Paper Received: 19 May 2022; Revised: 10 June 2022; Accepted: 16 June 2022
Please cite this article as: Pimentel J., Friedler F., 2022, Synthesis of Integrated Vertical Farming Systems with Multiperiodic Resource
Availability, Chemical Engineering Transactions, 94, 1039-1044 DOI:10.3303/CET2294173
CHEMICAL ENGINEERING TRANSACTIONS
VOL. 94, 2022
A publication of
The Italian Association
of Chemical Engineering
Online at www.cetjournal.it
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Copyright © 2022, AIDIC Servizi S.r.l.
ISBN 978-88-95608-93-8; ISSN 2283-9216
Synthesis of Integrated Vertical Farming Systems with
Multiperiodic Resource Availability
Jean Pimentela, Ferenc Friedlerb,*
aBudapest University of Technology and Economics, H-1111 Budapest, Hungary
bSzéchenyi István University, Egyetem tér 1., H-9026 Győr, Hungary
f.friedler@ga.sze.hu
Vertical farming (VF) has been proposed as an approach to decrease the land required for growing agricultural
products. This technique consists of growing produce in vertical orientation within a controlled environment.
However, one of the most significant barriers for its implementation is the uncertain economic feasibility, derived
from the elevated consumption of energy and the high investment costs. A strategy to enhance VF efficiency
proposes its integration with municipal infrastructure, thus establishing closed-loop systems where VF seizes
organic waste, manure, CO2, and excess energy from productive plants and local power stations. Because of
the economic uncertainty of its development, the optimal synthesis of such a closed-loop system (i.e., the
selection and specification of its components, and their connections) is of utmost importance for the
implementation of this strategy. The difficulty of the synthesis task arises from the combinatorial nature of the
problem and the variability of the resources and market conditions in time. This work employs a graph-theoretic
approach for the synthesis of a closed-loop system of VF considering the variability of the resources during
multiple periods of operation. The proposed method relies on the P-graph framework which permits the
identification of the n-best alternatives for the system’s design, employing the properties of the problem’s
structure to enhance the effectiveness of the solution procedure. Consequently, the most cost-effective systems
are identified together with their policy of operation for the different periods. This method constitutes a powerful
tool for the assessment of systems for VF integration that enhance the sustainability of agricultural activity.
1. Introduction
The rapid decrease of the arable land's availability jeopardizes the food safety for humankind, especially,
considering that the world population is expected to increase in about 2 billion people for 2050 (United Nations,
2019). Consequently, ensuring the generation of agricultural products has become a relevant topic for
researchers in numerous areas. Vertical farming (VF) is an interesting alternative for growing crops reducing
the resources consumed in cultivation and harvesting phases; specifically, it is characterized by a low
requirement of the arable land, and it has been proposed as an option for a safer and more reliable food supply
(Despommier, 2011). The reduction of required arable land is a result of employing a vertical orientation for the
crops by stacking layers of growing media in a controlled environment. This is performed in an indoor system
where the relevant growing factors, such as light, temperature, humidity, carbon dioxide (CO2) concentration,
water, and nutrients, are monitored. Figure 1 shows a typical VF installation with artificial UV lighting, which
permits a uniform control of photosynthesis of the plants. Because of the controlled conditions the quality of
produce is uniform and can be guaranteed, since pests, pollutants, and harmful factors are more easily
restrained. Moreover, regardless of the weather, the indoor system permits a consistent production during the
year, which enhances the reliability of the production facilities (SharathKumar et al., 2020) and enhances the
food safety.
VF intensifies the generation of produce by integrating distinct systems in a reduced fraction of land. Therefore,
this kind of systems have a high density of mass and energy per unit of area. Thus, its implementation results
not only in a reduction of the required arable land, but also may derive in a reduction of CO2 and a decrement
of water consumption. Because of these advantages, numerous organizations have shown interest on VF, such
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as the US department of agriculture (Federman, 2021), the association for vertical farming (2017) and
companies such as Tungsram kft. (2021).
Figure 1: Installation of VF in the Netherlands (Bates, 2017)
Despite its advantages, VF still has numerous barriers to overcome as its economic feasibility remains uncertain.
Various commercial facilities are operating worldwide in various scales of production, with areas up to 9000 m2
(Kalantari et al., 2018), and numerous projects are expected to be finished in the upcoming years; however, the
landscape remains dynamic with players constantly entering and leaving this line of business (Butturini and
Marcelis, 2019). The elevated initial cost required by the infrastructure and additional costs involved in the
controlled conditions, e.g., energy required for lighting and heating, may lead to not cost-effective operations.
Hence, additional research effort is required to unveil more efficient production techniques, or to generate
strategies for integration of these systems with further enterprises (Banerjee and Adenaeuer, 2014).
Because of this, the strategy of integrating the VF within the municipal infrastructure has been proposed, aiming
at rendering closed-loop systems capable of minimizing the common costs. This strategy consists in merging
systems, such as with the VF productive system, trying to emulate the natural ecosystems that work as closed-
loop schemes; where the waste of some subsystems (or units) is employed as raw material for the others (Al-
Kodmany, 2018). Figure 2 illustrates this concept in a general diagram, where VF may be integrated with
systems of agricultural production, industrial processes, or generators of utilities. For instance, the combination
of VF with an aquaculture system in Figure 2 enables the capacity of recycling the water. There, the fish can
provide a fraction of the nutrients required by the plants whereas the hydroponic vegetables clean the water for
the fish. In these closed-loop agricultural systems, nearly all waste-elements of the farming process, such as
water, sewage, and nutrients, can be harnessed by other units of the network, thereby leading to a close-to-
zero-waste operation. Additionally, the CO2 required by the plants in VF may constitute a sink for the emissions
of other units, thus, not only the land necessary for crops growing is decreased, but also the general footprint of
the global system is reduced. One example of this kind of systems is the VF system named “The Plant”, located
in Chicago (The Plant, 2020). This project intends to improve the energy efficiency of the farm by including
anaerobic digestors, which permits the transformation of organic waste (e.g., organic matter from the farms, or
the aquaculture systems) into biogas to produce power and heat. In this project, the farm is integrated with
aquaculture, anaerobic digestors and production of Kombucha tea (Al-Kodmany, 2018).
However, because of their nature, the demands and availabilities of the products exchanged by the different
subsystems in the closed-loop system may vary with factors such as the seasons and the weather. Although
VF is capable to produce the plants throughout the year, the energy, heating, products required by the
consumers, as well as the prices of raw materials may differ in time. Consequently, for some periods of the year
the systems may be used with a partial capacity to save in costs of labor, operation, and storage. The design of
these closed-loop agricultural systems, as well as the definition of the employed capacity for each period, must
be performed systematically; and their structure needs to be synthesized resorting to algorithmic methods that
generate the most cost-effective integration scheme. The systematic design of structures for closed-loop
productive systems has been previously explored (Pimentel et al., 2021), however, variation of the system’s
conditions with time had not been explored yet.
In this work, the P-graph framework is employed to generate plausible structures for closed-loop agricultural
systems considering plausible variations in time. A multiple period formulation is deployed to represent the
variation of demands, availabilities, and prices for some materials in the network. This type of evaluation
identifies the subsystems (i.e., units) suitable for integration, in addition to the policy of production (i.e., fraction
of the maximal capacity employed for each period) that fulfills the requirements of the market.
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Figure 2: Illustration of closed-loop system for VF
2. Methodology
The P-graph framework is a graph-theoretical approach capable of accelerating the solution of design problems
where the structure of the process is to be determined (i.e., synthesis problems), by resorting to the properties
of the networks that represent them (Friedler et al., 2022). P-graph relies on a bipartite representation where
the units and streams are portrayed as horizontal bars and circles, respectively. Based on this representation,
the framework depicts the network of a process unambiguously, thereby making it suitable for exploiting its
structural properties. Figure 3 shows the closed-loop system of Figure 2 in terms of the P-graph representation.
The streams are substituted by M-type nodes (i.e., circles), and the units are depicted by O-type nodes (i.e.,
horizontal bars). Figure 2 also shows the different sub-types of M-type nodes employed in P-graph
representation.
Figure 3: Representation of closed-loop system in Figure 2 as P-graph
The P-graph framework is employed here as it exploits the structural properties of the synthesis problem to
accelerate its optimization and generates the n-best solutions for it. Such a capability comes from a set of
combinatorial algorithms, which are based on a set of axioms that determine the combinatorial feasibility of a
particular network (Friedler et al., 2022). The method of solution employed here uses two of these algorithms.
First, the algorithm Maximal Structure Generation (MSG) renders a rigorous superstructure (termed as the
maximal structure) by connecting the units specified by the designers. Then, the algorithm Accelerated Branch-
and-Bound (ABB) uses the combinatorial feasibility axioms to accelerate the problem solution by means of the
reduction in the search space, and the simplification of the optimization subproblems (Friedler et al., 2022).
The formulation of synthesis problems involving multiperiod constraints in P-graph was first presented by Heck
et al. (2015). In this formulation, the initial structure for a single period was generated. Thereafter, the nodes
whose conditions change in time (i.e., multiperiodic operation) were replicated as many times as periods were
considered. These nodes represent the activity of the operations in the distinct intervals of time. The nodes
replicated were connected to form the superstructure for the entire operation. Various contributions can be found
in the literature of the implementation of this method in the software P-Graph Studio (P-graph community, 2015),
such as the work of Bertók and Bartos (2018).
This work explores the synthesis of closed-loop systems for VF with integration to municipal infrastructure and
multiperiod operation. Such exploration is illustrated by means of a case study of a closed-loop system where
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the demands of products and the price of raw materials are modified. Initially, the set of units selected to conform
the closed-loop system are specified by the designer, which involves the definition of material balances of the
units and their cost relationships depending on their size. Then, the number of periods to be examined is
determined by evaluating the variation in time of conditions for materials or units selected. Subsequently, the
initial structure is constructed and extended to consider the multiple periods required. Finally, the synthesis
problem posed by the extended structure is solved via algorithm ABB, which generates the installed capacity
and the scheme of operation.
3. Case Study
For illustration, the case study presented by Pimentel et al. (2021) is examined in a more realistic scenario,
considering the change of conditions with time by means of a multiperiod formulation. Here, in addition to the
VF system, seven main units are considered to constitute the structure of the closed-loop system. Figure 4
shows the initial structure for one period with a total of nineteen units, where the eight main units are shown in
green, whereas the auxiliary units are depicted in black. The subsystems represented by the main units account
for the VF system; an electricity production facility; a plant for distribution of district heating; a system for
aquaculture; a biofilter for sending the water to the VF system and a system for valorization of plants generated
in VF. The latter is represented by three units and is considered here as an industrial facility that generates
essential oils (EO) from the plants. In this case. The first unit of this subsystem represents the main process of
extraction and purification of the oils, whereas the other two are complementary processes required for the
correct working of the last. Namely, a combined heat and power cycle, (CHP_unit), proposed to deliver heat
and power to the valorization process; and the industrial wastewater treatment system that removes organic
matter from the water of the process.
These units can be interconnected to exchange energy in the form of power and heat, water, CO2, and materials.
Here it is assumed that the input for WWTP comes only from the facilities that generate valuable products, and
this water is not reused in the system. Furthermore, materials such as the fish, the plants, the added value
products, and the energy are the desired products required by the consumers.
Figure 4: Initial structure for a single period of case study of closed-loop system for VF integration
These units are selected since they are regarded as systems whose inputs or outputs may be seized by VF, or
other members of the closed loop and the structure is created in P-Graph Studio. It is worth noting, that the
estimation of mass balances and costs for the units greatly depend on the characteristics assumed for their
operation. For instance, VF depends on the plant species selected since different species have different yields
and require distinct conditions. The selection of the species may be also considered in the synthesis problem
by including various “VF units” as O-type nodes, where each of them would represent the performance of the
selected crop. Here, the mass and energy balances, and the cost of the units, are estimated as representative
values for illustration retrieved from information available in the literature, naturally, a different case study would
require to re-determine the value of these parameters. For instance, the estimations for cost of large VF facilities
(Banerjee and Adenaeuer, 2014), and technical databases such as Ecoinvent3 in SimaPro®. The evaluation is
performed by dividing the year in four periods of three months each, equivalent to the four seasons of continental
climate. The amount of heating, electricity, and food demanded by the users varies according to their necessities
for each season, whereas the demand of EO (added value product) remains constant (33.75 kg/period).
Additionally, the price of the gas is also assumed to change in time, to illustrate the possibility of examining
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scenarios with variability in the price of raw materials. Table 1 shows the value of the key materials, whose
parameters vary throughout the year. With these conditions, the multiperiod formulation of the P-graph
framework is employed via software P-Graph Studio to identify the optimal maximum capacities of the units,
and the policy of operation for the four seasons in various alternative solutions. Initially, the algorithm MSG
identifies the maximal structure for the four periods, which comprises 95 operating unit nodes, and 165 material
nodes.
Table 1: Demands and changes of prices for the four periods considered in the case study
Material Electricity Fish Heating Natural gas Plants
Period name Demand (kWh) Demand (kg) Demand(kWh) Price (USD/m3) Demand (kg)
Winter 4500 50 27000 0.0540 65
Spring 2500 50 10000 0.0499 41
Summer 9500 30 8000 0.0540 30
Fall 3500 20 15000 0.0457 25
Subsequently, the algorithm ABB identifies the maximum capacity of the units, and their policy of operation for
each period in the form of the partial work capacity. Figure 5 illustrates the policy of operation for the 12 months
of the year for the main units in the best network identified, i.e., the scheme of operation for the best solution
found. Since the problem was modelled for 4 periods, each group of three consecutive months exhibits the same
value in the Figure 5. This figure shows that units such as aquaculture and district heating are operated at partial
capacity for months 7 to 12, and 4 to 12, respectively. On the other hand, the production of EO and the water
treatment are always operated at total capacity as they are related to the demand of EO (assumed invariant in
this case study).
Figure 5: Policy of operation for the main units included in the best solution identified by algorithm ABB for the
four periods in Case Study
As illustrated in Figure 5 biofilter is not included in the best solution. This because of the low price assumed for
the fresh water, however, its inclusion becomes advantageous if this parameter increases in 27 %. The electricity
producer is not included either, consequently, the system’s power is independent from external providers and
is satisfied uniquely by the CHP, whose policy of operation is related to the variation of the electricity demand.
The heat required is produced by both the CHP and the district heating. The latter is fully employed during the
first period (winter), then, it is operated at 70 %, 56 %, and 78 % of its capacity for the next periods, following
the behavior of the heating requirement. Additionally, VF generates the totality of plants required for the demand,
and for the manufacture of EO. This unit is always operated above 97% alongside its auxiliary units. In this
solution no CO2 is purchased as the entire amount required is produced within the network. Also, the aquaculture
operates at full capacity for the first half of the year, and then it decreases to 60 % and 40 % for the last periods,
as a response to the behavior assumed for the fish demand in the case study.
This network presents a total annualized cost of 44,087 USD. The algorithm ABB renders the same information
for the best 100 solutions in less than 3 seconds, resulting in annual operating costs between 44,087 and 46,771
USD. Therefore, a diverse range of solutions, including the optimal and some near-optimal alternatives that are
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close in profit, can be identified in short time. These structures can provide additional insights about the problem
to be solved, and can exhibit useful features such as reliability, robustness, or resilience.
4. Conclusions
The multiperiod formulation of the P-graph has been implemented to determine the best network of closed-loop
systems integrating vertical farming considering variation of conditions with time. The framework permits the
unambiguous modelling of the problem by means of the bipartite representation of P-graph, which enables the
combinatorial handling of the problem. The capability of the framework is demonstrated by means of a case
study of 19 plausible units for the construction of an integrated system for enhancement of sustainability. The
methodology successfully determines the maximum capacity to be installed for the design of the network, as
well as the scheme of operation of the selected units all over the year. Therefore, the formulation employed
constitutes a powerful design tool for closed-loop systems, considering the changes of conditions during the
time of operation.
Acknowledgments
The research presented in this paper was partially funded by the “National Laboratories 2020 Program – Artificial
Intelligence Subprogram – Establishment of the National Artificial Intelligence Laboratory (MILAB) at Széchenyi
István University (NKFIH-870-21/2020)” project.
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PRES22_0355.pdf
Synthesis of Integrated Vertical Farming Systems with Multiperiodic Resource Availability