A techno-economic analysis of geothermal ejector cooling system

Journal Pre-proof A techno-economic analysis of geothermal ejector cooling system Mohammad Habibi, Farid Aligolzadeh, Ali Hakkaki-Fard PII:

S0360-5442(19)32455-7

DOI:

https://doi.org/10.1016/j.energy.2019.116760

Reference:

EGY 116760

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Received Date: 15 August 2019 Revised Date:

10 November 2019

Accepted Date: 11 December 2019

Please cite this article as: Habibi M, Aligolzadeh F, Hakkaki-Fard A, A techno-economic analysis of geothermal ejector cooling system, Energy (2020), doi: https://doi.org/10.1016/j.energy.2019.116760. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier Ltd.

A Techno-Economic Analysis of Geothermal Ejector Cooling System Mohammad Habibi, Farid Aligolzadeh, Ali Hakkaki-Fard* RASES Lab, Department of Mechanical Engineering, Sharif University of Technology, Azadi Ave., Tehran, Iran

Abstract Ground-coupled ejector cooling (GCEC) systems have been introduced to solve the air-coupled ejector cooling (ACEC) systems problems. To date, no research study is dedicated to compare the GCEC and the ACEC systems and determine the relative payback period of the GCEC system vs. the ACEC system. Furthermore, almost all the previous studies simulated the GCEC systems by elementary models. Therefore, a comprehensive simulation is conducted to assess the technoeconomic performance of a GCEC system. The model consists of the ejector and the borehole heat exchanger submodels. The first section of the results compares the ACEC system and the GCEC system during a cooling season. The seasonal coefficient of performance of the GCEC system is 83% higher than that of the ACEC system. The maximum building load per borehole heat exchanger unit length is 12.4, 17.5, and 21.6 W/m when the soil thermal conductivity is 1.40, 2.45, 3.50 W/(m.K), respectively. The second section of the results compares the relative payback period of the GCEC systems vs. the ACEC system for different values of soil thermal conductivities, borehole cost, and natural gas price. The relative payback period of the GCEC system vs. the ACEC system can be as low as five years. Keywords: Ground-coupled ejector cooling system, Air-cooled ejector cooling system, Borehole heat exchanger, Supersonic ejector, Numerical simulation, Relative payback period

*

Corresponding author. E-mail address: [email protected] (A. Hakkaki-Fard). 1

Nomenclature

fluid

working fluid

C

specific heat (kJkg-1s-1)

grout

grout

E

annual building load per borehole depth (GJm-1)

gen

generator

h

enthalpy (Wm-2K-1)

inlet

inlet fluid of borehole

k

thermal conductivity (Wm-1K-1)

outlet

outlet fluid of borehole

L

length (m)

p

pipe

݉ሶ

mass flow rate (kgs-1)

primary

primary flow inlet

Q

heat exchange rate or thermal load (kW)

secondary

secondary flow inlet

r

radius, radial direction (m)

soil

soil, undisturbed soil

R

thermal resistance (m2KW-1)

Abbreviations

t

time (day)

ACEC

air-cooled ejector cooling

T

temperature (K)

BHE

borehole heat exchanger

W

electrical power consumption (kW)

COP

coefficient of performance

DCA

diameter of constant area (mm)

Greek symbols ρ

density (kgm-3)

DISC

discount rate

ω

ejector entrainment ratio

DNE

diameter of nozzle exit (mm)

η

efficiency

GCEC

ground-coupled ejector cooling

GHE

ground heat exchanger

Subscripts b

borehole

GSHP

ground source heat pump

conv

convection

LCA

length of constant area (mm)

cooling

cooling mode

NGIR

natural gas inflation rate

evap

evaporator

NXP

nozzle exit position (mm)

1

Introduction

Nowadays, environmental and energy issues are the major sources of concern for human life [1]. The global demand for energy is continuously increasing due to human population growth and substantial global economic development. This increasing trend in energy consumption leads to world pollution and environmental degradation. Therefore, there is an acute need to substitute conventional energy sources with renewable and sustainable energy sources. In this respect, heat pumps as the only end-use heating/cooling systems with Coefficient of Performance (COP) higher than one have attracted considerable attention [2].

2

On the other hand, one of the promising resources of renewable energy is ground (geothermal). The ground is cooler/warmer than the ambient air in summer/winter; therefore, it can be used as a heat source/sink for heat pumps. The Ground Source Heat Pump (GSHP) is considered as a viable solution for reducing building energy consumption. The GSHP systems have attracted the interest of various researchers because of their availability, high efficiency, and reliability [3]. However, the main drawback of the GSHP systems is their high installation cost [4]. The Ground Heat Exchanger (GHE) is an inseparable part of a GSHP. One of the commonest types of GHE is the Borehole Heat Exchanger (BHE). In a BHE the GHE pipes are buried in boreholes with a depth range of 20 to 150m. In comparison to other GHE types, the BHEs have the best thermal performance and require the least land area. However, their drilling cost is significantly high [5]. Many researchers have studied the thermal performance of BHEs in GSHP systems. For instance, Ikeda et al. [6] analytically studied the performance of a combined air source and GSHP system. They applied optimization methods to find the optimal operating schedule of a hybrid GSHP system. Their proposed operation schedule decreased the operating cost of the heat pump by 12.6% compared to the typical operating schedule. In another study, Zarrella et al. [7] numerically investigated the effect of two different BHE circulation pump control strategies. The first scenario included the constant mass flow rate of the circulating fluid in the BHE, and the second scenario included a variable mass flow rate to maintain a constant circulating fluid temperature difference across the heat pump. Furthermore, they performed their simulations for three different types of BHEs, including single U-tube, double U-tube, and coaxial pipe heat exchangers. Their results demonstrated that the BHE with a constant temperature difference control provides the best thermal performance. Hu et al. [8] carried out a second law analysis to assess and enhance the COP of GSHP under various control scenarios. They found that the best control scenario for the GSHP is using the variable flow in the BHE in which the power consumption of the GHSP in heating and cooling modes is decreased by approximately 60 and 37 %, respectively. On the other hand, vapor-compression cycles are mainly used for air-conditioning and refrigeration. Due to their high COP and reliability, they are considered as the most favorable residential cooling system. However, they run on electricity and are responsible for summer peak electric loads. Thermally driven heat pump systems such as ejector and absorption cooling systems have been studied by many researchers as a potential substitute for conventional vapor-compression systems. The ejector cooling system needs lower initial investment and maintenance costs and has high reliability in comparison with absorption systems [9]. Moreover, they can use low-grade thermal energy sources such as geothermal, solar, or industrial waste heat [10]. Therefore ejector cooling systems as a sustainable alternative to replace conventional cooling systems have

3

come to the limelight in recent years. Though their significant advantages, they suffer from relatively low COP and working condition restrictions. The ejector is considered as the most critical component of the ejector cooling system as the COP of the system is directly related to the entrainment ratio of the ejector [11]. To date, several researchers have tried to improve the entrainment ratio of the ejector. For example, Carillo et al. [12] used a multi-objective Evolutionary algorithm coupled with a surrogate model based on Computational Fluid Dynamics (CFD) to optimize the shape of a single-phase supersonic ejector. Their optimized ejector had a 35% higher entrainment ratio and 10% higher critical back pressure than the base ejector; however, the base ejector did not have satisfactory performance. Their results also indicated that the diameters of the primary nozzle and mixing section are the most effective parameters on the performance of the ejector. One of the main drawbacks of the ejector cooling system that has hindered their widespread application is that they stop operation as the ambient temperature increases above the corresponding critical back pressure of the ejector [13]. A remedy for this problem is to design an ejector with higher back pressure [14]. However, the entrainment ratio of the ejector and as a result, the COP of the system decreases significantly by increasing its critical condensation temperature (critical exit pressure) [15]. To overcome this problem, in a recent study, Aligolzadeh and Hakkaki-Fard [16] proposed a novel methodology for designing a multi-ejector refrigeration system. Their proposed system has a parallel array of ejectors, and each ejector works within its specific condensing pressure range. They demonstrated that applying a multi-ejector refrigeration system could enhance the seasonal COP of the conventional ejector cooling systems up to 85%. Another feasible approach for enhancing the performance of the ejector cooling system is changing the condensing medium. As mentioned earlier, the ground is cooler than the ambient air during the cooling season. Therefore, replacing the air condenser of a conventional ejector cooling system with a GHE can reduce the condensing pressure of the ejector cooling system. To the best of the authors’ knowledge, only a small amount of research has been dedicated to Ground-Coupled Ejector Cooling (GCEC) systems, limited to introducing this system and cursory evaluation of its performance. For instance, Sanaye and Niroomand [17] introduced the ground-coupled steam ejector heat pump. They applied a simple thermodynamicbased model to evaluate the performance of the ejector and considered a simplified model to evaluate BHE performance. They studied the effect of four different parameters, including climate condition, cooling/heating capacity, soil type, and the number of boreholes on the total annual cost of the system and optimized these parameters. In another study, Alsuhaibani et al. [18] conducted an exergy analysis to evaluate the performance of the geothermal ejector heat pumps under steady-state conditions. They did not simulate the BHE and only assumed a constant heat exchange rate for the BHE. They also

4

determined the performance of the ejector by simple thermodynamics relations. They evaluated the exergy destruction of each component of the system and determined the exergy efficiency of the system. It worth noting that there is another group of studies that applied geothermal energy as the heat source for the generator of the ejector cooling system. For instance, Redo et al. [19] studied applying the geothermal energy as a heat source for the generator of the ejector cooling system. They investigated the effect of various parameters, viz, generator temperature, evaporation temperature, and refrigerant type on the entrainment ratio and COP of the ejector cooling system. However, this type of geothermal ejector cooling system is out of the scope of the present study. According to the aforementioned literature review, the following gaps can be noted regarding GCEC systems: •

No research study is dedicated to a fair comparison between air-cooled ejector cooling (ACEC) systems and groundcoupled ones.

•

No research study is dedicated to determining the relative payback period of the GCEC system vs. the ACEC system.

•

To date, all the research studies of the GCEC system are performed by elementary models denoting that a comprehensive numerical simulation should be performed to predict the performance of the GCEC systems more accurately.

•

Even though some studies have investigated the performance of the GCEC systems, to the best of the authors’ knowledge, there is no study available in the literature to design special ejectors for GCEC systems.

Therefore, in an attempt to fill the gaps as mentioned above, a comprehensive numerical model of the GCEC system is developed. The present model is composed of two coupled submodels; the ejector and the BHE submodels. The ejector submodel is responsible for designing an optimum ejector for predetermined working conditions. The obtained results are divided into two main parts. The first part focuses on a fair comparison between the air-cooled ejector cooling (ACEC) system and ground-coupled one. The second part evaluates the relative payback period of the GCEC systems vs. the ACEC system for different values of soil thermal conductivity, borehole cost, and natural gas price.

2

System configuration

The schematic of the ACEC and GCEC systems are depicted in Figure 1. According to this figure, the ACEC system is composed of six main components, including a generator, an air-cooled condenser, a pump, an evaporator, an expansion valve, and an ejector. The only difference between the ACEC and the GCEC system is that the air-cooled condenser of the ACEC system is replaced by a water-cooled condenser and a geothermal cycle. The geothermal cycle itself is composed of a 5

GHE and a circulating pump. The geothermal cycle exchanges heat with the ejector cooling system through the water-cooled condenser. The GHE type considered in this study is the BHE. Therefore, the GCEC system is composed of two separate cycles, the ejector cooling cycle, and the geothermal cycle. The schematic of the supersonic ejector is depicted in Error! Reference source not found.. According to this figure, the ejector is composed of four main parts, including primary nozzle, suction chamber, mixing section, and diffuser. The ejector has two inlets, i.e., primary and secondary, and one exit. According to Figure 1 and Figure 2, in an ejector cooling cycle, the generator uses a heat source to evaporate the highpressure liquid refrigerant from the pump. Then, the high-pressure vapor (primary flow) enters the primary convergentdivergent nozzle of the ejector. Thus, a supersonic low-pressure vapor leaves the primary nozzle and hence, entrains the vapor from the evaporator (secondary flow). The two flows mix after experiencing several shocks in the mixing section of the ejector. At the end of the constant area mixing section, the mixed flow has low speed and high pressure. As this mixed flow passes the ejector diffuser, its pressure increases even more. The high-pressure high-temperature vapor leaves the ejector and enters the condenser. In the condenser, the flow exchanges heat with the cooling medium and condenses. Ambient air is the cooling medium of the ACEC system, and circulating water of the geothermal cycle is that of the GCEC system. At the condenser exit, the flow splits into two parts. One part goes through the pump, and its pressure increases significantly and then enters the generator. The other part goes through the expansion valve, and after an isenthalpic process, its pressure drops drastically. The low-pressure and low-temperature flow enters the evaporator to create the cooling effect of the cycle.

6

(a)

(b) Figure 1. Schematic view of (a) an air-cooled ejector cooling system (ACEC) and (b) a ground-coupled ejector cooling system (GCEC)

Figure 2. Schematic of a supersonic ejector

3

System design and modeling

In the present study, the ejector cooling cycle model previously developed and validated by Aligolzadeh and Hakkaki-Fard [16] is utilized. This ejector cooling cycle model is coupled with the previously developed and validated BHE model by Habibi and Hakkaki-Fard [20]. Therefore, only the main features and modifications made to the models are outlined. Some general assumptions made in order to develop numerical models include: •

The ACEC and GCEC systems are only used for space cooling.

•

All system components are simulated under quasi-steady-state-steady-flow conditions. 7

•

Thermo-physical properties of materials used in the BHE are considered to be constant.

•

The expansion valve operates in isenthalpic mode.

•

The refrigerant at the ejector secondary flow inlet is considered to be 10 K superheated.

•

The approach temperatures of the condenser and evaporator are respectively considered to be 5 K and 10 K.

•

The refrigerant at the evaporator and the condenser outlets are respectively considered to be saturated vapor and saturated liquid.

•

No pressure-drop occurs in the evaporator, condenser, GHE, and connecting tubes.

•

The ground is assumed to be isotropic medium and homogeneous.

•

At the solid region (soil), only the conduction heat-transfer mechanism is dominant (the advection in the soil is ignored).

•

3.1

All pumps are considered to have constant isentropic efficiency.

Ejector design and modeling

The entrainment ratio of an ejector, ω, is defined as the ratio of the secondary flow (݉ሶୱୣୡ୭୬ୢୟ୰୷ ) to the primary flow mass flux (݉ሶ୮୰୧୫ୟ୰୷ ):

ω=

m& secondary

(1)

m& primary

The COP of the ejector cooling system is defined as the ratio of the cooling load to the thermal energy supplied to the generator [13]:

COP = ω ×

∆hevap

(2)

∆hgen

where ∆ℎ௘௩௔௣ and ∆ℎ୥ୣ୬ denotes the enthalpy difference in the evaporator and generator, respectively. General assumptions considered to develop the supersonic ejector numerical model include: •

Axisymmetric along the x-axis

•

Single-phase compressible flow

•

Steady-state-steady-flow condition

8

The governing equations for the ejector in the cylindrical coordinate system (r, x) include continuity, conservation of momentum, and energy equations. A second-order finite volume method is used for the discretization of the advection and diffusion terms. The SIMPLE algorithm is utilized for pressure-velocity coupling [21]. The real gas Soave-Redlich-Kwong model [22] is applied for the equation of state, and the realizable k-ε model [23] is adopted to model turbulence. Fluid flow inside the ejector is studied in a thin slice along the axis (axisymmetric flow assumption) [24, 25]. It is assumed that the velocity of the fluid at the inlets and the outlet are negligible. Therefore, stagnation pressure and temperature are imposed at the inlets, and stagnation pressure is imposed at the outlet. Solid walls are assumed to be adiabatic with the noslip condition. The periodic boundary condition is used for the two sides of the thin slice that are parallel to the ejector axis. Four different cell numbers (1358, 5704, 17306, 95941) are considered to study grid independency. The developed numerical ejector model has been validated against the experimental study of Hakkaki-Fard et al. [26]. The geometry and dimensions of the ejector which is selected for validating the current numerical models are presented in Figure 3 and Table 1. The inlets and outlet conditions of the ejector used for grid independency and model validation are presented in Table 2. Table 1. Dimensions of the ejector used for validation Axial dimensions (mm)

Radial dimensions (mm)

L1

29.79

D1

60.00

L2

86.00

D2

25.40

L3

315.00

D3

18.00

L4

17.20

D4

7.00

L5

7.75

D5

50.40

LCA

89.00

DNE

9.00

NXP

29.00

DCA

16.62

Table 2. Inlet and outlet conditions of the ejector used for grid independency and model validation Boundary

Pressure (kPa)

Temperature (ºC)

Primary inlet

2633

100

Secondary inlet

350

25

Outlet

600-850

-

9

The grid independence study revealed that for grids with a cell number of 17,306 and higher, the difference between the pressure distribution inside the ejector and also entrainment ratios becomes less than 2%. Therefore, the cell number of 17,306 is used for simulations in this study.

Current CFD

Experiment

45 40 35 ω (%)

30 Experiment

25 20 15

Current CFD

10 5 0 550

600

650 700 750 800 Exit pressure (kPa)

850

900

Figure 3. Comparison between the entrainment ratio versus outlet pressure for the current numerical model and experimental results Figure 3 presents the entrainment ratio versus outlet pressure for the current numerical model against the experimental results of Hakkaki-Fard et al. [26]. This figure shows that the developed numerical model has good potential for accurately predicting the entrainment ratio. More details regarding the ejector model and its validation may be found in Ref [16]. Ejectors used in the study are first optimized according to their specific working conditions, and then they are utilized in the ejector cooling system to evaluate the system performance. The objective of this shape optimization is to maximize the entrainment ratio of the ejector while the primary mass flow rate and other boundary conditions are kept constant. The CFD based shape optimization algorithm used in the present study is the one previously proposed by Aligolzadeh and HakkakiFard [16]. Four geometrical parameters, including the diameter of the primary nozzle exit, the diameter of the mixing section, the length of the mixing section, and the primary Nozzle Exit Position (NXP) are chosen as the optimization variables. It should be noted that the other geometrical parameters of ejectors are kept the same as those in Ref. [16]. The pattern-search method [27] is used for optimization. The logic flow chart of the geometrical optimization used in this study is presented in Figure 4. More details regarding the shape optimization of the ejector are available in Ref. [16].

10

Figure 4. The logic flow chart of the geometrical optimization procedure

3.2

Borehole heat exchanger modeling

The thermal load of one BHE (QBHE) can be calculated by the following equation:

 

Q BHE = Q cooling  1 +

+W  pump COP  1

(3)

where, Qcooling represents the amount of building cooling load that can be supplied by one BHE, COP represents the coefficient of performance of the ejector cooling system, and Wpump represents the BHE pump work. The COP of the system is a function of the ejector performance, and the ejector performance is a function of the condensation temperature. Furthermore, the thermal load of one BHE (QBHE) can be calculated by the following equation:

11

Q BHE =

(Tfluid − Tb )L b

(4)

Rb

where, Tfluid represents the arithmetic average of the inlet and outlet water temperatures ((Tinlet+Toutlet)/2), Lb represents the borehole's length, Rb represents the thermal resistance of BHE and can be calculated as follow:

R b = (R conv + R p ) / 2 + R grout

(5)

where, Rconv, Rp, Rgrout, and Tb denote the convective thermal resistance of the circulating fluid, the conductive thermal resistance of the pipe, the thermal resistance of the grout, and the borehole wall temperature, respectively [20]. The borehole wall temperature, Tb, is determined by applying the Infinite Line Source (ILS) method [6, 20]. Moreover, the Duhamel's theorem is utilized to obtain the ground temperature response to the variable BHE thermal load (QBHE) [6, 20]. Furthermore, the spatial superposition method is applied to consider the thermal effect of the adjacent BHEs [6, 20]. Therefore the disturbed ground temperature can be obtained as follows [20]:

T ( r, t ) = Tsoil +

N effective

n

∑∑ j=1

(Q

BHE ,m

m =1

− Q BHE,m−1 ) / L b 4πk soil

 Csoil (r − rj ) 2    4k soil ( t n − t m−1 ) 

Ei 

(6)

where, T(r, t) denotes the disturbed ground temperature, t denotes time, Tsoil denotes the undisturbed ground temperature, n denotes the total number of time steps, QBHE,m denotes the heat exchange rate of the BHE at time-step m, Ei(x) denotes the exponential integral function, Csoil and ksoil denote the specific heat and thermal conductivity of soil and Neffective represents the number of effective adjacent BHEs (that affect the thermal performance of the simulated BHE). In this study, it is assumed that the simulated BHE is located among eight effective BHEs (Neffective=8) in an in-line arrangement, and the distance between them is assumed to be 7m, in accordance with ASHRAE handbook [28]. More details regarding the equation (6) are available in Ref. [20]. Therefore, the borehole wall temperature, Tb, can be obtained using equation (6). The difference between the inlet and the outlet BHE circulating fluid temperature can be obtained by the following equation: & fluid C fluid Tinlet − Toutlet = Q BHE / m

(7)

By using equations (4) and (7), the BHE outlet fluid temperature can be determined as follows: Toutlet =

Q BHE R b Lb

−

Q BHE & fluid C fluid 2m

+ Tb

(8)

To perform a fair comparison between different cases, it is considered that all BHEs comply with the following conditions: (a) The maximum water temperature difference between the inlet and outlet of the BHE is considered to be 5.6 K, as suggested by Kavanagh and Rafferty [29].

12

(b) The maximum difference between the outlet water temperature of the BHE and the undisturbed ground temperature is considered to be 12 K, as suggested by Kavanagh and Rafferty [29]. To meet the two constraints mentioned above, the maximum building cooling load per BHE unit length (W/m) and mass flow rate of the circulating water per unit building cooling load (kg/s.W) are determined by trial and error. The mathematical model of BHEs is developed in MATLAB environment. The experimental result of Yoon et al. [30] is used for verifying the developed BHE model. Yoon et al. [30] carried out a Thermal Response Test (TRT) for 48 h on a BHE. The main parameters and material properties of their experiment are listed in Table 3 and Table 4. Table 3. Main parameters of Yoon et al. [30] experimet Parameters

Value

Internal pipe diameter

1.6 cm

External pipe diameter

2.0 cm

Borehole depth

50 m

Borehole diameter

15 cm

Shank spacing

6~7 cm

Initial ground Temperature

16.44 ℃

Flow rate

7~8 lpm

Table 4. Material properties of Yoon et al. [30] experiment Thermal conductivity (W.m-1.K-1)

Specific heat capacity (J.kg-1.K-1)

Density (kg.m-3)

2.239

1134

2237

Grout (Bentonite)

0.9

380

1580

Pipe (Polybutylene)

0.38

525

955

Water

0.57

4200

1000

Material Soil (Averaged)

Figure 5 compares the experimentally obtained and the calculated outlet water temperature over time. As shown in this figure, the predicted outlet water temperatures are in good congruence with those reported by Yoon et al. [30].

13

34 Inlet

Temperature (℃)

32 30

Outlet, Experiment

28 26 Outlet, Present study

24

Inlet Outlet, Experiment Outlet, Present study

22 20 18 0

500

1000

1500 2000 Time (h)

2500

3000

Figure 5. Comparison of the calculated BHE outlet temperature against the experiment results of Yoon et al. [30] Figure 6 illustrates the logic flow chart of the proposed GCEC system model.

Figure 6. The logic flow chart of the GCEC system model

14

4

Initial and Operating Costs

In order to perform the economic analysis of the ACEC and GCEC systems, the relative payback period of the GCEC system vs. the ACEC system is evaluated. Some general assumptions made to calculate the relative payback period of the systems include: •

Maintenance costs are not considered.

•

It is assumed that a gas burner supplies the generator energy; therefore, the gas consumption cost of the systems is considered.

The initial costs of the different components of the studied systems are taken from the current market prices [31, 32], as listed in Table 5. The initial cost of the evaporator and expansion valve is assumed to be identical for all cases. According to Table 5, although the initial cost of individual components is different for each system, the total initial cost of both systems is the same. Therefore, it is rational to assume that the costs of the ejector cooling system are identical for all cases and therefore ignored in the Relative Payback Period (RPP) evaluation. Hence, only the installation expenses of the BHE are considered as the initial cost, which mainly includes pipe and excavation costs. Table 5. Initial costs of the studied ejector cooling systems System type

Component

Capacity (kW)

Price ($)

System type

Component

Capacity (kW)

Price ($)

ACEC

Air-condenser

12.9

4000

GCEC

Water-condenser

7.9

5527

Generator

10.9

4500

Generator

5.9

2500

-

-

-

BHEs pump

0.2

400

Total

8500

8427

The RPP of GCEC system vs. the ACEC system can be obtained by the following relation [33, 34]: y  E building  1 1 1 + NGIR     = ∑  COP − COP  ηboiler PNG ,0  1 + DISC     y =1  L total  ACEC GCEC  RPP

COSTBHE

(9)

where, Ebuilding represents the annual building cooling energy demand (GJ), Ltotal represents total required borehole length (m), COPACEC and COPGCEC represent the seasonal COPs of the ACEC and the GCEC systems, respectively. Also, ηboiler represents the boiler efficiency that is assumed to be 0.733 [35] in this study, and COSTBHE represents the BHE cost per unit BHE length ($/m). It worth noting that BHE drilling cost depends on many different factors such as soil type and processes 15

and components used to drill the BHE. In this study, four different values viz. 20, 30, 40, and 50 $/m are considered as BHE cost. Moreover, PNG,0 represents the natural gas price of year zero ($/GJ). The current gas prices vary around the world, approximately between 3 and 9 $/GJ [36]. Therefore, three different values viz. 4, 6, 8 $/GJ are considered as natural gas prices. NGIR represents the Natural Gas Inflation Rate, which is considered to be 3.45 % [37], and DISC represents the discount rate and is considered to be 3 % here.

5

Case studies

As already noted, this work aims to evaluate the techno-economic performance of the GCEC system and compares it with the ACEC system. It is assumed that considered systems are used for space cooling of a residential building located in Tehran, Iran (representing an arid climate region). The considered building has a volume of 8×6×2.7m3 and a window-wall ratio of 15.9%. The building cooling load of the building is calculated by EnergyPlus software [38]. Figure 7 illustrates the ambient air temperature and the calculated building cooling load of the simulated building [38, 39]. The average ambient air temperature of Tehran is 17.2 ℃. The calculated nominal (maximum) hourly building cooling load is 2 kW with annual building cooling energy demand of 2,273 kWh.

Building cooling load

40

4.0

35

3.5

30

3.0

25

2.5

20

2.0

15

1.5

10 5

1.0

0

0.5

-5 0

800

1600

2400

3200 4000 4800 5600 Time (h) Figure 7. Ambient air temperature and building cooling load of the simulated building

Cooling load (kW)

Ambient temperature (℃)

Ambient air temperature

0.0 6400

The working fluid of the ejector cooling system is considered to be R-134a, and the circulating fluid of the geothermal cycle is considered to be water. Moreover, it is considered that the evaporating temperature of the system is 15 °C; therefore, the temperature and pressure of the secondary flow of the ejector are 25°C and 488.7 kPa, respectively. Furthermore, the temperature and pressure of the primary flow of the ejector are 100°C and 2633 kPa, respectively. In this study, it is

16

presumed that the borehole diameter, internal pipe diameter, external pipe diameter, and shank spacing are 0.15, 0.032, 0.04, and 0.09 m, respectively. Table 6 presents the thermal and physical properties of the material used in this study. Table 6. Thermal and physical characteristic of the material used in this study Density

Heat capacity

Thermal conductivity

Viscosity

(kg.m-3)

(J.kg-1.K-1)

(W.m-1.K-1)

(Pa.s) × 105

Water

997.1

4183

0.59

89.05

Pipe (PVC)

950.0

2300

0.50

-

Soil

2723.0

837

1.40, 2.45, 3.50 [28]

-

Grout

-

-

2.50

-

Material

In order to design a suitable ejector for each ejector cooling system, it is essential to determine the critical condensation temperature of the system. The critical condensation temperature of the system is obtained by determining the maximum condensation temperature of the system during its operation period. The maximum condensation temperature depends on the condensing medium temperature. The ambient air and the circulating water of the geothermal cycle are the condensing mediums of the ACEC and the GCEC systems, respectively. According to Figure 7, the maximum ambient temperature of Tehran is about 38 ℃. Therefore, as it is considered that the condensation temperature of the air-cooled condenser to be 5 K higher than the ambient temperature, the maximum condensation temperature of the ACEC system would be 43 ℃. The undisturbed ground temperature of Tehran is 17.2 ℃. According to section 3.2, the maximum water temperature difference between the inlet and outlet of the BHE is considered to be 5.6 K, and the maximum difference between the outlet water temperature of the BHE and undisturbed soil temperature is considered to be 12 K. Furthermore, the condensation temperature of water-cooled condenser is considered to be 5 K higher than the mean circulating water temperature of the BHE. Therefore, the maximum condensation temperature of the GCEC system would be 37℃ (17.2+12+5.6/2+5=37).

17

6

Results and discussions

This section provides the simulation results of the ACEC and the GCEC systems. This section is divided into two main parts; the first of which presents a fair comparison between the ACEC and GCEC systems. The second part evaluates the relative payback period of the GCEC system vs. the ACEC system for different values of soil thermal conductivity, borehole cost, and natural gas price.

6.1

Designed ejectors

As already mentioned in section 5, the critical condensation temperature of the air-cooled and ground-coupled condensers are 43 ℃ and 37 ℃, respectively. By performing the ejector design procedure, ejectors “A” and “B” are designed and optimized for the maximum entrainment ratio. The geometrical parameters of ejector “A” and “B” are presented in Table 7. Furthermore, the coefficient of performance of ejector “A” and “B” are presented in Figure 8. Table 7. The geometrical parameters of the designed ejectors

Ejector

Critical condensation temperature (℃)

LCA (mm)

NXP (mm)

DNE (mm)

DCA (mm)

A

43

30.13

12.70

3.40

4.74

B

37

34.90

10.23

3.46

5.52

18

Ejector B

Ejector A

0.40 0.35 0.30

Critical temperature=37 ℃

COP

0.25 0.20 0.15 Critical temperature=43 ℃

0.10 0.05 0.00 10

15 20 25 30 35 40 Condensation temperature (℃)

45

Figure 8. Operating curves of the designed ejectors

6.2

Air-cooled ejector cooling system

The condensation temperature and the coefficient of performance of the ACEC system with ejector A are illustrated in Figure 9. As presented in this figure, the COP of the ejector cooling system strongly depends on the condensation temperature. It can be noted that, while the condensation temperature varies from 17 to 43 ℃, the COP of the ACEC system only varies from 0.184 to 0.196. This small change in the system COP can be attributed to the function of the ejector. The entrainment ratio of the ejector is approximately constant as the condensation temperature is equal or less than its critical condensation temperature, so the same trend is also observed for the COP. The seasonal COP of the ACEC system with the ejector A is 0.1877.

19

COP

44

0.213

36

0.208

28

0.203

20

0.198

12

0.193

4

0.188

-4 0

6.3

800

1600

2400

3200 4000 4800 5600 Time (h) Figure 9. Condensation temperature and COP of the ACEC system

COP

Condensation temperature (℃)

Condensation temperature

0.183 6400

Ground-coupled ejector cooling system

By substituting the air-cooled condenser with the geothermal cycle, the GCEC system is obtained. As mentioned before, the ejector B is designed as an appropriate ejector for the GCEC system. However, to investigate the effect of utilizing a suitable ejector in the GCEC system, the performance of the GCEC system with both ejectors A and B is investigated. Figure 10 illustrates the COP and the condensation temperature of the GCEC system with ejector A. According to the figure, the maximum COP occurs at the beginning of the cooling season when the building load is low, and the soil near the BHE is not disturbed. By increasing the building load, the soil temperature is intensively disturbed, and the COP of the GCEC system is affected. Therefore, the minimum COP occurs in the middle of the cooling season when the building cooling load is maximum. At the end of the cooling season, because of the heat stored near the BHE during the cooling season, the soil near the borehole is warmer than the undisturbed soil. Therefore, although the building load is low, the COP of the system is not as high as the beginning of the cooling season. By coupling the BHE with the ejector cooling system, the condensation temperature of the system is significantly reduced. According to Figure 10, the maximum condensation temperature of the GCEC system is approximately 37℃. Although the maximum condensation temperature of the GCEC system is approximately 6℃ lower than that of the ACEC system, the performance of the GCEC system with ejector A is not significantly better than the ACEC system. The seasonal COP of the GCEC system is 0.189, which is only 0.7 % higher than the seasonal COP of the ACEC system. Therefore, the low condensation temperature, without an appropriate ejector, does not enhance the COP of an ejector cooling system.

20

COP

38

0.204

34

0.201

30

0.198

26 0.195 22

COP

Condensation temperature (℃)

Condensation temperature

0.192

18

0.189

14 10 0

0.186 3200 4000 4800 5600 6400 Time (h) Figure 10. Condensation temperature and COP of the GCEC system with ejector A 800

1600

2400

In order to illustrate how the proposed system model works, the two applied constraints are evaluated. Therefore, the difference between the inlet and outlet water temperatures of the BHE (Tinlet-Toutlet) and the difference between the outlet water temperature of the BHE and the undisturbed soil temperature are demonstrated in Figure 11 and Figure 12, respectively. According to these figures, the maximum temperature difference between the inlet and outlet fluid temperature and the maximum difference between the outlet water temperature of the BHE and the undisturbed soil temperature are 5.6 and 12 K, respectively. Therefore the applied constraints are completely satisfied. According to Figure 12, at the end of the cooling season, the soil in the vicinity of the BHE is approximately 2.75 K warmer than the undisturbed soil, which is due to

6

Temperature difference (K)

Temperature difference (K)

the thermal performance of the BHE during the cooling season.

5 4 3 2 1 0 0

800 1600 2400 3200 4000 4800 5600 6400

12 10 8 6 4 2 0 0

Time (h) Figure 11. The difference between the inlet and outlet water temperatures of the BHE (Tinlet-Toutlet)

800 1600 2400 3200 4000 4800 5600 6400

Time (h) Figure 12. The difference between the outlet water temperature of the BHE and the undisturbed soil temperature

In order to enhance the performance of the GCEC system, it is essential to utilize ejector B with critical condensation temperature of 37 ℃. The calculated hourly COP values of the GCEC system and the corresponding condensation

21

temperatures of the system are illustrated in Figure 13. According to this figure, the COP of this GCEC system is significantly higher than the previous GCEC system with ejector A. The seasonal COP of this GCEC system is 0.343 that is 83% higher than the seasonal COP of the ACEC system. Therefore, utilizing BHEs, along with an appropriate ejector, can significantly enhance the thermal performance of an ejector cooling system.

38

0.375

34

0.37 0.365

30

0.36

26

0.355 22

0.35

18

0.345

14

0.34

10 0

6.4

COP

COP

Condensation temperature (℃)

Condensation temperature

0.335 3200 4000 4800 5600 6400 Time (h) Figure 13. Condensation temperature and COP of the GCEC system with ejector B 800

1600

2400

Comparison of different types of ejector cooling systems

The calculated maximum building cooling load per BHE unit length (the nominal building cooling load that can be supplied by one meter of the BHE) of each of the studied ejector cooling systems, for different values of soil thermal conductivity, are presented in Table 8. According to this table, by increasing the soil thermal conductivity, the maximum building cooling load per BHE unit length increases. This increase can be attributed to the fact that by reducing the thermal resistance of the soil, the higher amount of heat can be transferred to the soil. When soil thermal conductivity is increased from 1.40 W/(m.K) to 2.45 W/(m.K), the maximum building cooling load per BHE unit length is enhanced by about 41 %. Moreover, increasing soil thermal conductivity from 2.45 W/(m.K) to 3.50 W/(m.K) results in an approximately 24 % improvement in the maximum building cooling load per BHE unit length. Furthermore, according to Table 8, the maximum building cooling load per BHE unit length of the GCEC system with ejector B is approximately 60% higher than that of the GCEC system with ejector A. This can be attributed to the fact that the GCEC system with ejector B rejects more heat through the condenser, than the GCEC system with ejector A, per unit building cooling load. Therefore, by substituting the ejector A, with ejector B, not only the energy consumption of the GCEC system is reduced, but also a smaller BHE is needed. Moreover, according to Table 8, the mass flow rate of the circulating

22

water per unit building cooling load of the GCEC system with ejector A is approximately 60% higher than that of the GCEC system with ejector B. Therefore, for supplying equal building cooling load, the geothermal circulation pump power consumption of the GCEC system with ejector A is significantly higher than that of the GCEC system with ejector B. Table 8. Seasonal COP, the mass flow rate of the circulating water per unit building cooling load, and the maximum cooling load per unit length of the BHE for different ejector cooling systems Maximum building cooling load per unit length System type

Ejector

COPseasona

per unit building cooling load

(or the nominal building cooling load that can be supplied by one meter of the BHE)

(kg/(s.kW))

ACEC

A

0.188

-

GCEC

A

0.189

GCEC

B

0.343

6.5

of the BHE (W/m)

Mass flow rate of the circulating water

ksoil=1.40

ksoil=2.45

ksoil=3.50

W/(m.K)

W/(m.K)

W/(m.K)

-

-

-

0.272

7.7

10.9

13.6

0.169

12.4

17.5

21.6

Cost analysis

The calculated Relative Payback Period (RPP) of the GCEC system vs. the ACEC system is presented in this section. It should be noted that the cost analysis is performed for the GCEC system with ejector B. The natural gas price, the BHE cost, and soil thermal conductivity are the three key parameters in determining the RPP. Therefore, in this study, the RPP of the GCEC system are determined for three different values of natural gas price including 4, 6, and 8 $/GJ, four different values of BHE cost including 20, 30, 40, and 50 $/m, and three different values of soil thermal conductivity including 1.40, 2.45, and 3.50 W/m.K. It should be noted that the BHE pipe (polyethylene) has a lifetime of 50 years; therefore, the lifetime of the BHE is approximately 50 years [40]. The RPP of the GCEC system vs. the ACEC system as a function of natural gas price, borehole cost, and soil thermal conductivity is presented in Figure 14. According to this figure, the natural gas price, borehole cost, and soil thermal conductivity, significantly affect the RPP of the GCEC system vs. the ACEC system. According to Figure 14 (a), the RPP of the GCEC system vs. the ACEC system with a natural gas price of 4$/GJ varies between 15 to 65 years. If the borehole cost is less than 35$/m, the RPP can be less than 30 years. According to Figure 14 (b), the RPP of the GCEC system vs. the ACEC system for a natural gas price of 6$/GJ varies between 10 to 45 years. With a natural gas price of 6$/GJ, if the soil thermal conductivity is higher than 2.1 W/m.K and the borehole cost is less than 27.5$/m at the same time, the RPP can be less than 15 years. Moreover, if the soil thermal conductivity is less than 2.8 W/m.K, and the borehole cost is higher than 27.5 $/m at the same time, the RPP is more than 30 years. According to Figure 14 (c), when the natural gas price is 7 $/GJ, 23

the RPP is approximately less than 34 years. If the borehole cost is less than 37 $/m, the RPP can be less than 15 years. The least RPP is five years, which is for the case with a natural gas price of 8$/GJ, borehole cost of 20 $/m, and soil thermal conductivity of 3.5 W/m.K.

Relative payback period (year)

65 60 55 50 45 40 35 30 25 20 15

55-60 45-50 35-40 25-30 15-20

50 40 30

1.4

Relative payback period (year)

PNG,0=8 $/GJ

35 30 25 50

20 15

40

10

30 20 3.5

Borehole cost ($/m)

(b) PNG,0=6 $/GJ 30-35

25-30

20-25

15-20

10-15

5-10

35 30 25 20 15

50

10

40

5

30

1.4 2.45 Soil conductivity (W/m.k)

20 3.5

(c) PNG,0=8 $/GJ

7

40

2.45 Soil conductivity (W/m.k)

(a) PNG,0=4 $/GJ

35-40 25-30 15-20

45

1.4

Borehole cost ($/m)

20 2.45 Soil conductivity (W/m.k) 3.5

40-45 30-35 20-25 10-15

PNG,0=6 $/GJ

Relative payback period (year)

60-65 50-55 40-45 30-35 20-25

PNG,0=4 $/GJ

Borehole cost ($/m)

Figure 14. Relative payback period of the GCEC system vs. the ACEC system as a function of natural gas price, borehole cost, and soil thermal conductivity

Conclusion

In this study, a comprehensive numerical simulation has been performed in order to evaluate the techno-economic performance of the air-cooled ejector cooling (ACEC) and ground-coupled ejector cooling (GCEC) systems. The proposed model is first utilized to evaluate the performance of the GCEC system during a cooling season. Furthermore, the relative

24

payback period of the GCEC systems vs. the ACEC system for different values of soil thermal conductivity, borehole cost, and natural gas price is studied. To put it concisely, the results of this study can be expressed as follows: •

The seasonal COP of the GCEC system with ejector A is 0.189, that is only 0.7% higher than that of the ACEC system. However, when a proper ejector (ejector B) is designed for the GCEC system, the seasonal COP reaches to 0.343, that is 83% higher than the ACEC system.

•

The maximum building cooling load per BHE unit length of the GCEC system with ejector B is approximately 61% higher than that of the GCEC system with ejector A. Furthermore, the maximum building cooling load per BHE unit length has been investigated for three different values of soil thermal conductivity. When the soil thermal conductivity is increased from 1.40 W/(m.K) to 2.45 W/(m.K), the maximum building cooling load per BHE unit length is enhanced by about 41 %. Moreover, increasing the soil thermal conductivity from 2.45 W/(m.K) to 3.50 W/(m.K) results in an approximately 24 % improvement in the maximum building cooling load per BHE unit length.

•

The Relative Payback Period (RPP) of the GCEC system vs. the ACEC system has been investigated for different values of soil thermal conductivity, borehole cost, and natural gas price. The RPP of the GCEC system vs. the ACEC system with a natural gas price of 4 $/GJ is lower than 30 years if the BHE cost is lower than 25 $/m. With a natural gas price of 6 $/GJ, if the soil thermal conductivity is higher than 2.1 W/m.K and the BHE cost is lower than 27.5 $/m at the same time, the RPP can be less than 15 years. When the natural gas price is 8 $/GJ, the RPP is approximately less than 34 years. Moreover, the least RPP is five years, which is for the case with a natural gas price of 8$/GJ, borehole cost of 20 $/m, and soil thermal conductivity of 3.5 W/m.K.

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27

Highlights: The performance of the ACEC and GCEC systems are evaluated during a cooling season. A proper ejector (ejector B) is designed for the GCEC system. The seasonal COP of the GCEC system is 83% higher than that of the ACEC system. The RPP of the GCEC vs. the ACEC system is analyzed for different parameters. The RPP of the GCEC vs. the ACEC system can be as low as five years.

We wish to confirm that there are no known conflicts of interest associated with this publication and there has been no significant financial support for this work that could have influenced its outcome. We confirm that the manuscript has been read and approved by all named authors and that there are no other persons who satisfied the criteria for authorship but are not listed. We further confirm that the order of authors listed in the manuscript has been approved by all of us. We confirm that we have given due consideration to the protection of intellectual property associated with this work and that there are no impediments to publication, including the timing of publication, with respect to intellectual property. In so doing we confirm that we have followed the regulations of our institutions concerning intellectual property. We understand that the Corresponding Author is the sole contact for the Editorial process (including Editorial Manager and direct communications with the office). He is responsible for communicating with the other authors about progress, submissions of revisions and final approval of proofs. We confirm that we have provided a current, correct email address which is accessible by the Corresponding Author and which has been configured to accept email from [email protected]

MOHAMMAD HABIBI, FARID ALIGOLZADEH, ALI HAKKAKI-FARD.

November 6, 2019.