1. Introduction
Greenhouses are a technology used to produce food in areas where the weather and pollution can be negative factors during the harvest process. Greenhouses also reduce the water demand. The use of fossil fuels for greenhouse heating represents a high amount of greenhouse gas emissions into the environment. In this sense, the scientific community aware of this problem has made different proposals for sustainable technologies to meet the thermal and electrical demand of conventional greenhouses.
In 2018, Hassen et al. [
1] carried out an analysis of the performance of a GHP connected to a novel conical GHE for heating a greenhouse in northern Tunisia. To carry out this research, the authors installed the GHP, the GHE, and the appropriate instrumentation to obtain experimental data. This study was made with the purpose of contributing to the resolution of the excessively cold temperatures during the night inside the greenhouse located in the north of Tunisia. Its greenhouse GHP system ensured an amount of heat equivalent to 692,208 kW, which corresponded to a temperature increase of 3 °C inside the greenhouse, with an optimal flow of 0.6 kg/s. In addition, the performance coefficients of the GHP and the system corresponded to 3.93 and 2.64, respectively.
In a different study, Ahmed O. [
2] made a predictive model and an extensive numerical simulation of a microgrid for smart energy monitoring and management in a greenhouse. The author was motivated to achieve the net-zero energy goal in greenhouses by means of a predictive algorithm capable of capturing the complex interaction between microclimate variables within the greenhouse and the development of plantations in any other greenhouse. The results showed that the control algorithm responded effectively to the control of heating, ventilation, and air conditioning operations, to monitor the ideal temperature of crops without using the electrical network, guaranteeing compliance with the objective of net-zero energy in greenhouses.
In another study, Mehdi M. et al. [
3] designed and simulated a solar-geothermal system for heating a greenhouse. The authors carried out the simulation in the TRNSyS software to evaluate the performance of the system for a whole year, using refrigerant R-134A, R407C, and R410A as working fluids. The authors wanted to find a solution in which the soil recovers during the winter to prevent the COP of the system from decreasing due to high heat extraction from the soil when the thermal load is maximum. According to the results, the authors managed to increase the COP value by 0.6 compared to the system without subsoil preheating.
In New Zealand, Mariana de P. et al. [
4] carried out an experimental analysis of the performance of six greenhouses heated with GHP. To obtain the experimental data, calorimeters were installed at the outlet of the vertical wells with concentric tubes to evaluate the heat gain of the GHE. The area where the greenhouses were installed was close to the native tribes of the region, and the study and expansion of the greenhouses directly benefitted the region. The results obtained from the heat gain of the geothermal well proved to be up to 4.5 times more than what was calculated, which implied that the greenhouses could be expanded and thus benefit the native community of the region.
In another relevant study, Mehmet E. et al. [
5] developed an experimental study of different heat sources for greenhouse heating, such as biogas, solar energy, and geothermal energy. The installation and instrumentation of an experimental hybrid biogas greenhouse were carried out, including GHP with slinky-type GHEs and solar collectors for the supply of heat during the winter. The authors intended to demonstrate that heat sources such as biogas, solar energy, and geothermal energy can efficiently supply the energy needed for heating greenhouses in Eastern Turkey. It was concluded that the combination of biogas, solar energy, and geothermal energy has favorable results in the performance of greenhouses in Eastern Turkey and guarantees the autonomy of the system during the winter season.
Hassen B. et al. [
6] conducted an experimental study to evaluate the performance of a novel conical GHE for cooling greenhouses under climatic conditions in Tunisia. A GHE array with a novel conical shape was designed, installed, and tested at a depth of 3 m. Performance analysis of the GHP and system showed a maximum COP of 4.25 and 3.25, respectively.
A numerical analysis of the long-term energy supply of a greenhouse using renewable energy sources was performed by Saeed M. et al. [
7] a mathematical model of a microgrid and an interconnected microgrid were analyzed to evaluate the performance of the system and optimize it when considering the deviation of renewable energies. The authors wanted to find the perfect mix between the production of renewable energy, the number of storage units, and the capacity of the backup system that minimizes costs in the microgrid mode and maximizes remuneration in the interconnected mode. The results show that under certain climatic conditions in the Makran region, the combination of different renewable energies in the microgrid can cause an unjustified technical-economic proposal, that is, that the investment and maintenance costs could make the system unsustainable.
Alexandros S. et al. [
8] developed a numerical analysis of a greenhouse that used photovoltaic energy, hydrogen, and geothermal energy for heating during the winter season. The mathematical model analyzed was of a photovoltaic array connected to an electrolyzer that, during the day, generated hydrogen, which was stored in a tank, and during the night, that hydrogen was consumed by a fuel cell to generate electricity to supply energy to a GHP with vertical GHEs for heating a tunnel greenhouse. The overall efficiency of the greenhouse heating system with renewable energy was 11%. Additionally, Issam M. et al. [
9] presented a numerical-experimental analysis of a greenhouse air conditioning system that uses groundwater in direct-indirect evaporative cooling equipment in the desert climate of Baghdad. The authors proposed a mathematical model that describes the thermal load of refrigeration in the greenhouse and the instrumentation in the greenhouse to obtain experimental data. It was possible to increase the efficiency of the direct or indirect evaporative cooling system up to 108% of the efficiency of the conventional system by using subsoil water as the cooling fluid. A different strategy to control the climate with an evaporation system with natural ventilation connected to a brackish water well was presented by Hacene M. et al. [
10] In turn, this system allowed desalination of water for irrigation use in the greenhouse. The regions of the Middle East and North Africa have very little drinking water, but they do have brackish water and sources of geothermal energy. For this reason, the authors were motivated to propose a seawater desalination system and greenhouse air conditioning. A similar study presented by Youngguk S. et al. [
11] analyzed a GHP greenhouse air-conditioning system in areas near highways in South Korea. The authors proposed a mathematical model that described the performance of GHP under climatic conditions in South Korea. Similarly, an experimental greenhouse was installed to validate the mathematical model. This study was carried out with the intention of being able to effectively predict the return on investment of greenhouses heated with GHP and compare them with conventional heating systems. This study showed that the experimental COP of the system varied between 3.4 and 3.6, compared to a design COP value of 3.7. Erdem C. et al. [
12] presented a state-of-the-art focus on energy-saving strategies and air conditioning in greenhouses. The study focused on different technologies for photovoltaic modules, solar collectors, thermal energy storage systems, GHPs, lighting, and insolation in greenhouses. The intention of the authors was to show a broad overview of cutting-edge technology that improves greenhouse performance and reduces greenhouse gas emissions, as well as energy consumption and operating costs. The study showed that, in general, the use of greenhouse air conditioning strategies with renewable energies reduces the return on investment between 4 and 8 years, depending on the technology used.
In summary, the lines of research for greenhouse air conditioning using renewable energies focus mainly on geothermal energy and solar energy. Mexico is a world leader in the use of geothermal energy for electricity generation; however, this contrasts with the direct use of geothermal heat, which has received less attention. This is despite having large resources of medium and low enthalpy distributed throughout the country. However, applications of GHPs in tropical or semi-tropical climates are few. Within Mexico, only two industrial-type applications are known: balneology, in most regions of the country, and a district heating system for offices, workshops, and laboratories in the Los Azufres geothermal field (Romo J. et al. [
13]). Approximately 73.7% of Mexico’s area is classified as arid or semi-arid zones, which represents a potential for developing applications of this technology suitable for the particular conditions of the country. In particular, the performance of slinky-type systems should be characterized since, due to the soil conditions in these regions, it is easier in technological and economic terms to make trenches than to drill. Nowadays, there is no simulation tool with the specific parameters of the country’s regions since climatic conditions can easily reach 50 °C and remain in that temperature band for a long period of the day, especially in extreme climate zones. Climatic conditions can also reach very low temperatures in winter. An area of research opportunity was found for simulation tools that allow the performance of GHP systems with slinky-type GHE to be predicted. The purpose of this study is to obtain and validate, through experimentation, a simulation tool using the TRNSyS software of a greenhouse air conditioning system in arid zones in northwestern Mexico. This tool allows forecasting the performance of GHE systems under very high and low-temperature climatic conditions. Additionally, the performance of the geothermal air conditioning system will be analyzed with the intention of evaluating and determining if the installed capacity in the experimental greenhouse meets the thermal demand.
3. Mathematical Model
The mathematical model that describes the performance of the linear GHE used in this study was based on the programming found in the buried pipeline simulation module of the TRNSyS 2017 library. The simulation module consists of a subroutine model of buried pipes in 3 finite dimensions that calculate the dissipation or absorption of heat in the subsoil with water as the working fluid.
The liquid in the tube was modeled as an axial series of isothermal liquid nodes. The mass of the liquid nodes was taken into account in the model, but the assumption was made that the pipe wall material and insulation were massless. Similarly, the assumption was made that the pipe was surrounded by soil whose thermal conductivity, density, and specific heat were known.
Figure 8 shows the diagram of radial and axial nodes of the subsoil surrounding the pipe.
The volume of cylindrical soil surrounding the tube is called the near field. The temperature of the nodes in the near field is affected by the energy transferred with the pipe. The near field is, in turn, surrounded by the far field, which is assumed to be a sink or source of infinite energy. In other words, the energy transfer with the far field does not result in a temperature change in the far field. Temperatures in the far field are governed only by depth and time of year. The energy balance at any node in the soil is shown in Equation (1).
If a node is contained entirely within the near field and is bounded neither by the far field nor by the pipe wall, its energy balance is made up of purely conductive terms. The equations for
and
are:
The first term of each equation represents the energy transfer in the radial direction. The second represents the energy transfer in the circumferential direction, and the third represents the energy transfer in the axial direction. The resistors (each of which is written in the form (Δx/kA) are:
For a fluid node, there are three basic terms in the energy balance. Energy is transferred in and out of the node due to fluid flow, the energy is transferred due to axial conduction between fluid nodes, and energy is transferred between the fluid and the pipe wall. The energy transfer due to flow takes the form:
The energy flux due to axial conduction takes the form:
The flow of energy between the fluid and the wall depends on the mass flow rate of the fluid in the pipe. The Reynolds and Prandtl numbers are calculated as:
The Nusselt number is then calculated as:
The internal convection coefficient is as follows:
The general equation of the energy transferred between the fluid node and the pipe wall node can finally be written as:
where
Finally, the efficiency in the cooling mode of the GHP is calculated with the following equation:
5. Conclusions
In this study, the results of a simulation supported by experimental data to analyze the performance of a greenhouse operating with a geothermal heat pump located in Mexico in an arid zone were presented. The study was conducted during a complete year to include the heating and cooling mode performance while tomatoes were harvested. The results show that the average deviation of the simulator for the geothermal heat exchanger (GHE) outlet temperature corresponded to a value of 2.77% and 3.7% for the EER of the GHP. The average error percentage of the GHE outlet temperature with a flow of 1, 2, and 3 GPM corresponded to 0.4%, 1.84%, and 2.82%, respectively. The deviation for the EER with a flow of 1, 2, and 3 GPM corresponded to 0.5%, 2.9%, and 7.7%, respectively. According to the results, the critical hours in the heating mode were in the range from 5:00 to 7:00. The critical hours in the cooling mode were in the range of 13:00 to 15:00. The months of April and October are the transition months, that is, the months in which the predominance of one of the modes of operation changes. The months of July and December are the months with the highest electricity consumption for cooling and heating, respectively. The installed capacity of GHP in the experimental greenhouse meets the thermal demand of the enclosure. However, it is recommended that for areas similar to those in the study, the number of hours of operation be reduced in the last 2 weeks of July and the first 2 weeks of August due to subsoil heat saturation.