Vertical ground coupled steam ejector heat pump; thermal-economic modeling and optimization

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Vertical ground coupled steam ejector heat pump; thermal-economic modeling and optimization Sepehr Sanaye*, Behzad Niroomand Energy Systems Improvement Laboratory (ESIL), Department of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran 16488, Iran

article info

abstract

Article history:

A vertical ground coupled steam ejector heat pump is a Ground Coupled Heat Pump (GCHP)

Received 9 June 2009

with closed Vertical Ground Heat eXchanger (VGHX) which utilizes the steam ejector type

Received in revised form

of refrigeration cycle instead of the vapor-compression type.

27 January 2010

This paper presents the modeling and optimizing a Ground-Coupled Steam Ejector Heat

Accepted 5 March 2010

Pump (GC-SEHP) with closed VGHX. The system included two main sections of VGHX and

Available online 27 March 2010

steam ejector heat pump (SEHP), and was optimized by minimizing its total annual cost (TAC) as the objective function. Two optimization techniques (NeldereMead and Genetic

Keywords:

Algorithm) were applied to guarantee the validity of optimization results.

Heat pump

For the given heating/cooling loads as well as for various climatic conditions, the optimum

Ground-water

design parameters of GC-SEHP with closed VGHX were predicted.

Ejector system

Furthermore, the changes in TAC and optimum design parameters with the climatic

Modelling

conditions, cooling/heating capacity, soil type, and number of boreholes were discussed. ª 2010 Elsevier Ltd and IIR. All rights reserved.

Simulation Optimisation Performance

Pompe a` chaleur a` e´jecteur de vapeur couple´e sol-eau : mode´lisation et optimisation thermoe´conomiques Mots cle´s : Pompe a` chaleur ; Sol-eau ; Syste´me a` e´jecteur ; Mode´lisation ; Simulation ; Optimisation ; Performance

1.

Introduction

Ground coupled heat pump is being used as a highly efficient technology for heating and cooling the residential and commercial buildings by exchanging heat with the ground as the thermal source or sink.

GCHPs have less annual energy consumption. Thus, they reduce emissions of greenhouse gases and can be used as a carbon-saving technology. However their initial investment are higher than that for the air source heat pumps due to the costs of ground loop pipes, wells/channel boring and filling, and circulating pump. The limited qualified designers/contractors

* Corresponding author. Tel./fax: þ98 21 77240192. E-mail address: [email protected] (S. Sanaye). 0140-7007/$ e see front matter ª 2010 Elsevier Ltd and IIR. All rights reserved. doi:10.1016/j.ijrefrig.2010.03.004

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VFA

Nomenclature A a1  a9 cAF CEl CFuel CInv cNG CNG COp cp cPipe COP CRF De;Eva DI;i DI;o Dp;GHX E h Hpum i kp kS L LHV M _ m n P Q R s T TW1 TW2 TWi1 TWi2 TAC U v V Vpipe;in

2

cross section area, m constants in computing the equipment cost cost of anti-freeze solution, $/m3 annual cost of power consumption, $/y annual cost of fuel consumption of the system, $/y initial or investment cost per operating years of the system, $/y cost of natural gas, $/m3 annual cost of natural gas consumption of boiler, $/y annual operating cost of system, $/y specific heat, kJ/kg C cost of polyethylene pipe, $/m coefficient of performance capital recovery factor equivalent diameter of the evaporator annulus for estimating hW;Eva;h , m inner diameter of inner pipe of condenser and evaporator, m outer diameter of inner pipe of condenser and evaporator, m GHX nominal pipe diameter, in annual power consumption, kWh/y specific enthalpy, kJ/kg; convection heat transfer coefficient, kW/m2K pump head, Pa interest rate, % thermal conductivity of pipe, kW/(m C) thermal conductivity of soil, kW/(m C) length of heat exchanger, m lower heating value, kJ/kg Mach number mass flow rate, kg/s depreciation time, y pressure, kPa thermal load, kW universal gas constant, kJ/(kg C) specific entropy, kJ/(kg C) annual operating hours, h/y; temperature,  C water temperature at the inlet of heat pump and outlet of the VGHX,  C water temperature at the inlet of the VGHX and outlet of heat pump,  C building circulating water temperature at the inlet of heat pump,  C building circulating water temperature at the outlet of heat pump,  C total annual cost, $/y overall heat transfer coefficient, kW/m2K specific volume, m3/kg velocity, m/s pipe inside volume, m3

W x

volume fraction of the anti-freeze in the intermediate fluid, % power consumption, kW quality

Greek symbols thermal diffusivity of ground, ft2/day aS Dp pressure drop of water flow, Pa g compressibility ratio subsonic diffuser efficiency, % hd mixing chamber efficiency, % hm efficiency of pump motor, % hM primary nozzle efficiency, % hn electric efficiency of circulating pump, % hPum m dynamic viscosity, Pa s r density, kg/m3 s equivalent annual full-load hours, h/y English abbreviations ESIL energy systems improvement laboratory GA genetic algorithm GC-SEHP ground-coupled steam ejector heat pump NM NeldereMead SEHP steam ejector heat pump VGHX vertical ground heat exchanger Subscripts 1, 2, 3, . locations on the cycle 2P 2-phase state a; b; c; d locations inside the ejector AF anti-freeze Boi boiler c cooling mode Con condenser d constant area duct Ej ejector Eva evaporator GHX ground heat exchanger h heating mode HP heat pump i inner pipe M monthly Min minimum Max maximum NG natural gas np cross section of motive stream at exit of converging/diverging nozzle ns cross section of secondary stream at exit of converging/diverging nozzle o outer pipe Pum pump S soil SH superheated state st steam th converging/diverging nozzle throat W water

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in some locations is another disadvantage of using these systems (Jenkins et al., 2009; Omer, 2008; Sanaye and Niroomand, 2009). The ejector refrigeration cycle has advantages over vapor compression refrigeration cycle (with working refrigerant such as R-22). The only moveable section of a SEHP system is a pump. No need for lubrication, long operating lifetime, high reliability, low maintenance cost, and little vibration and noise are the other advantages of this system. These systems may utilize solar energy as well as the recovered thermal energy of industrial processes in the boiler section. This fact is important in view of energy savings and emission reduction. Furthermore, due to the fact that water (with high latent heat of vaporization) may be used in these systems as the refrigerant, a lower refrigerant mass flow rate, and smaller pump is required to obtain the same cooling capacity. This is while water is available in many locations, and is environmental friendly with a good thermal conductivity. However, water freezes at low temperatures. Furthermore the COP of the SEHP is smaller than compression and absorption refrigeration systems. With advantages of SEHP system over compression refrigeration cycle, the SEHP system is proposed to be employed with closed VGHX system in this paper. For optimal design of GC-SEHP coupled with VGHX, both SEHP and VGHX systems were modeled. Due to the fact that the ejector has very important duty in the ejector refrigeration system as the thermo compressor (called the heart of the system), its design and operation is very critical. The steam ejector was first modeled by Keenan (Keenan et al., 1950) using a constant pressure assumption in the mixing region of two primary and secondary fluids. That theory was based on the adiabatic flow assumption, (ideal) gas dynamic equations and the steady-state steady-flow conservation equations for energy, momentum, and mass. Munday and Bagster (1977) assumed the separate primary and secondary fluid streams before starting the mixing process (before reaching the secondary fluid velocity to the sonic velocity) and postulated that primary stream does not mix with entrained stream until the onset of secondary fluid choking. The choking and mixing effectively occur at a (hypothetical throat) very end of the converging cone resulting in a transient supersonic mixed stream. He also assumed a complete mixing process before reaching the constantdiameter region as well as existing a normal shock formed in the constant-diameter region to convert the supersonic flow to the subsonic one. The location of normal shock in the constant area pipe was obtained by finding intersection of Fanno and Rayleigh lines. This was while the mixed fluid was compressed to near-zero velocity in the subsonic diffuser (considering the real fluid properties instead of the ideal gas properties). There are many other analytical and experimental studies regarding the steam ejector refrigeration modeling and optimization in which the methods of analysis of the two above mentioned references, as well as conservation equations and the experimental correlations were applied (Eames et al., 1995; Alexis, 2004; Alexis and Rogdakis, 2003; Stinson, 1943; Jackson, 1936; He et al., 2009; Angelino and Invernizzi, 2008; ElDessouky et al., 2002; Pianthong et al., 2007). Grazzini and Rocchetti (2002, 2008) investigated a twostage steam ejector refrigeration cycle. They obtained the

system design parameters such as mass flow rates, dimensions and temperature differences in the heat exchangers using an optimization technique. They studied various objective functions including the cycle COP. Although the literature is very rich on steam ejector refrigeration system and GCHP topics, but using SEHP system with closed VGHX is a new idea presented in this paper. In order to optimal design of a GC-SEHP including SEHP and VGHX, the thermal and economic simulation and optimization of such a system were performed. The modeling procedure of VGHX was based on the method presented in (Sanaye and Niroomand, 2009). The SEHP system was modeled with a new approach based on the Munday theory by deriving and solving the governing system of twelve nonlinear equations. The output results of this model were verified by comparing them with other theoretical and experimental results presented in references (Eames et al., 1995; Alexis, 2004; Alexis and Rogdakis, 2003; Stinson, 1943; Jackson, 1936). To optimize the system, an objective function (the system total annual cost, TAC, including investment and operational costs in this paper) was defined. For the given heating/cooling loads, and various climatic conditions, the optimum values of SEHP design parameters (phase change temperatures in boiler, condenser and evaporator in cooling and heating modes) as well as VGHX optimum design parameters (water temperatures at the inlet and outlet of the buried pipe of VGHX in cooling and heating modes, ground loop pipe diameter, and the number and depth of the boreholes) were estimated. The optimization was performed by minimizing the TAC. To obtain the optimum values of independent parameters, a software program was developed based on the presented model using NeldereMead optimization method. Then, the results of NM method were validated using Genetic Algorithm method using «optiGA ActiveX software package» (Elad Salomons, 2006). Then, the ejector main cross sections at the optimum design point were computed by Keenan theory. Finally the weather (climatic conditions) and soil type effects on the system performance and TAC as well as the changes in TAC with the system capacity and number of boreholes were discussed. Thus, the main objectives of this paper are: optimal design (thermal and economic simulation and optimization) of a GCSEHP including VGHX, computing the ejector main cross sections at the optimum design point, and investigating the effects of weather, soil type, system capacity and number of boreholes on the system performance and TAC. The followings are the groups of new research activities performed in this study:  Introducing the new straight forward application of VGHX with SEHP instead of the common vapor-compression refrigeration cycle.  Proposing a new approach in modeling the SEHP by deriving and solving governing twelve nonlinear equations for obtaining twelve unknowns which guarantees the simultaneous satisfying of all conservation and supplementary equations.  Modeling and optimizing the whole GC-SEHP system by genetic algorithm and NeldereMead techniques with

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Fig. 1 e Tes diagram for steam ejector refrigeration cycle. specific objective function, specific selected design parameters and a list of defined constraints. This approach guaranteed the validity of optimization outputs.

2.

The thermal modeling of SEHP

2.1.

The ejector system

Ejector is a pumping device in SEHP which uses the kinetic energy of a high-pressure fluid (primary or motive fluid) to drive and accelerate a low-pressure fluid (secondary or entrained fluid). After direct mixing process of the two fluids, the mixture leaves the ejector at a pressure between the motive and suction pressures (Keenan et al., 1950). The ejector operation processes are shown in Tes diagram in Fig. 1. Saturated vapor with pressure P1 and temperature Dp;GHX ½in enters the converging-diverging nozzle at point 1 and accelerates to a supersonic flow. In nozzle, the motive fluid expands isentropically to pressure TW1;c ½ C (the pressure at which the secondary fluid reaches the sonic velocity) and reaches the point (as) in Tes diagram. Applying the primary nozzle efficiency, TEva;c ½ C, the actual state of motive fluid is at point (a1). The expansion of the primary fluid causes a low-pressure region at the nozzle exit plane. This drives the secondary fluid from the evaporator into the ejector. This saturated vapor with pressure P2 and temperature T2 enters the ejector at point (2) and expands isentropically to pressure Pcr to reach the sonic velocity. In Munday (Munday and Bagster, 1977) model the mixing process starts when the secondary fluid reaches the sonic velocity (at point a in Fig. 2); then the mixture passes through a constant pressure (Pcr ) process with final state at point (b)

(Fig. 2). Munday computed and showed that the mixed fluid velocity is always supersonic. This supersonic stream compresses isentropically to Pc (the pressure before the shock wave) in (bec) region (Fig. 2) with final actual point at (c) due to existing exit mixing chamber efficiency, hm . The supersonic flow enters the constant-diameter region at point (c). At this stage a normal shock forms in that region due to the ejector back pressure. The strong compression effect of this shock converts the supersonic flow to the subsonic flow, and increases the pressure suddenly to Pd (the pressure after the shock wave). Then, the mixed fluid enters _ 1 ½g=s and expands the subsonic diffuser with pressure m isentropically to P3 at point (3) on Tes diagram (considering hd as diffuser efficiency).

2.2.

The SEHP system

Fig. 3 shows a schematic view of the SEHP system. This system includes evaporator, condenser, expansion valve, refrigerant, ejector, pump, and boiler. The group of boiler-ejector-pump replaces the compressor in a compression refrigeration cycle.

Fig. 2 e Ejector main cross sections.

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2.4.

SEHP model input parameters

The following list includes the input parameters for SEHP model: 1. 2. 3. 4. 5. 6.

Saturation temperature in boiler (TBoi ) Saturation temperature in evaporator (TEva ) Saturation temperature in condenser (TCon ) Primary nozzle efficiency (hn ) Mixing chamber efficiency (hm ) Subsonic diffuser efficiency (hd )

2.5. Fig. 3 e Schematic view of the steam ejector refrigeration cycle.

The motive steam with high pressure and temperature enters the ejector (1). By converting the thermal energy of steam into the kinetic energy in the converging-diverging nozzle, the flow becomes supersonic with low-pressure region at the primary nozzle exit plane. This causes to derive the low-pressure refrigerant from the evaporator (2) into the nozzle (and to decrease the evaporator pressure) as well as to increase the evaporation of refrigerant in evaporator while absorbing heat. Then, the primary and secondary fluids mix and the resulting mixed fluid leaves the ejector and enters the condenser (3) after compressing in diffuser. After condensing the refrigerant vapor in the condenser (4), a part of the saturated liquid is sent to the evaporator (5) by passing through the expansion valve, and the rest is sent to the boiler (6) by a pump.

2.3.

The SEHP thermal modeling

As shown in Fig. 1, the primary flow (saturated steam) and the secondary flow (water vapor in evaporator), enter the ejector from boiler and evaporator, with temperatures T1 ¼ TBoi and T2 ¼ TEva respectively. The mixed fluid leaves the ejector and enters the condenser with pressure P3 (saturation pressure at TCon ). The following simplifying assumptions were made: 1. The primary and secondary fluids are saturated and have the same molecular weight and ratio of specific heats. 2. The kinetic energy at the inlets of primary and secondary (suction) ports as well as at the diffuser exit is negligible. 3. At the entrance of the cylindrical mixing tube, the suction fluid velocity reaches the speed of sound (choking condition). 4. The mixing between steam and water vapor occurs at a constant pressure process. 5. The ejector flow is one-dimensional and at steady state conditions. 6. The process is adiabatic. 7. Losses such as wall friction and boundary layer separation were introduced by applying isentropic efficiencies to the primary nozzle, diffuser and mixing chamber.

Outputs of SEHP model

According to the Tes diagram of the SEHP (Fig. 1), there are following twelve unknown parameters in this system which are the SEHP model output and should be computed: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

_ 1 ). Refrigerant mass flow rate in boiler (m _ 2 ). Refrigerant mass flow rate in evaporator (m _ 3 ). Refrigerant mass flow rate in condenser (m Fluid temperature at the ejector exit plane (T3 ). Mixed fluid quality at point “b” (xb ). Mixed fluid velocity at point “b” (Vb ). Fluid pressure at point “c” (Pc ). Fluid quality at point “c” (xc ). Fluid velocity at point “c” (Vc ). Fluid pressure at point “d” (Pd ). Fluid temperature at point “d” (Td ). Fluid velocity at point “d” (Vd ).

2.6.

Governing system of nonlinear equations in SEHP

Twelve nonlinear equations are required for obtaining twelve above mentioned unknowns. While eleven equations are the same in both cooling and heating modes, the twelfth equation in cooling and heating system operation modes is as follows: In cooling mode, the indoor water flows through the evaporator (QEva;c ¼ Qc ), where Qc is heat transfer rate between refrigerant and indoor water in evaporator in cooling mode, thus: _ 2;c ðh2;c  h5;c Þ ¼ Qc m

(1)

In heating mode, the indoor water flows through the condenser (QCon;h ¼ Qh ); where Qh is heat transfer rate between refrigerant and indoor water in condenser in heating mode, thus: _ 3;h ðh3;h  h4;h Þ ¼ Qh m

(2)

Therefore to satisfy all conservation and supplementary equations and to compute the twelve unknown parameters, the following twelve equations are derived (Munday and Bagster, 1977; Rao and Singh, 1988; Kouremenos et al., 1998): _1þm _2¼m _3 m

(I)

_ 1 h1 þ m _ 2 h2 ¼ m _ 3 hSH fP3 ; T3 g m


(II)

_1 þm _ 1 Va1 þ m _ 2 Va2 ¼ m _ 2 Vb m

(III)

h2P fPcr ; xb g þ 0:5Vb2 ¼ hSH fP3 ; T3 g

(IV)

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hm ¼

h2P fPcr ; xb g  h2P fPc ; sb g h2P fPcr ; xb g  h2P fPc ; xc g

(V)

h2P fPc ; xc g þ 0:5Vc2 ¼ hSH fP3 ; T3 g

(VI)

hSH fPd ; Td g þ 0:5Vd2 ¼ hSH fP3 ; T3 g

(VII)

Vc Vd ¼ v2P fPc ; xc g vSH fPd ; Td g

(VIII)

Pc þ

Vc2 Vd2 ¼ Pd þ v2P fPc ; xc g vSH fPd ; Td g

hd ¼

hSH fPd ; Td g  hSH fP3 ; sd g hSH fPd ; Td g  hSH fP3 ; T3 g

(X)

P3 ¼ Pd

g=ðg1Þ  h ðg  1ÞVd2 1þ d 2gRst Td

(XI)

(IX)

In cooling mode: _ 2 ðh2  h5 Þ ¼ Qc m

3.2. (XII-h)

The above system of non-linear equations was solved by Newton’s method (Kelley, 1987). The ejector geometry was defined based on the optimum operating conditions (the design point). In the next step the system off-design conditions were predicted based on the ejector main cross sections (Fig. 2). Knowing the values of these cross sections, the lengths of the ejector sections were determined based on the relations and procedure recommended in reference (ASHRAE, 1979).

3.

The thermal modeling of GC-SEHP

A schematic diagram of the studied system is shown in Fig. 4. Letters “c” and “h” show the flow lines in cooling and heating modes, respectively. The followings are the general specifications of the studied GC-SEHP and VGHX:  The refrigeration cycle is a steam ejector type with the simplifying assumptions presented in the SEHP thermal modeling.  Evaporator and condenser are double-pipe heat exchangers in which the refrigerant and water flow through the pipe and annulus respectively.  The U-shaped polyethylene pipe is used in the well.

3.1.

Design and input parameters

3.1.1.

Design parameters

3. TW2;c : GC-SEHP outlet water temperature in cooling mode,  C. 4. TW2;h : GC-SEHP outlet water temperature in heating mode,  C. 5. TEva;c : Phase change temperature in the evaporator in cooling mode,  C. 6. TEva;h : Phase change temperature in the evaporator in heating mode,  C. 7. TCon;c : Phase change temperature in the condenser in cooling mode,  C. 8. TCon;h : Phase change temperature in the condenser in heating mode,  C. 9. TBoi;c : Phase change temperature in the boiler in cooling mode,  C. 10. TBoi;h : Phase change temperature in the boiler in heating mode,  C. 11. Dp;GHX : VGHX nominal pipe diameter, in., (0.75, 1, 1.25, 1.5 in.).

(XII-c)

In heating mode: _ 3 ðhSH fP3 ; T3 g  h4 Þ ¼ Qh m

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The following 11 independent parameters are design parameters: 1. TW1;c : GC-SEHP inlet water temperature in cooling mode,  C. 2. TW1;h : GC-SEHP inlet water temperature in heating mode,  C.

System operating related input parameters

1. Cooling and heating loads (Qc and Qh ), kW. 2. Total running time in a year (T) in heating and cooling modes, h/y. 3. Equivalent full-load hours (Pd ½Pa) in heating and cooling modes, h/y. 4. Building circulating water temperature: - Condenser inlet water temperature in heating mode (TWi1;h ),  C. - Evaporator inlet water temperature in cooling mode (TWi1;c ),  C. 5. Depreciation time (n), y. 6. Interest rate (i), %. 7. Soil properties: The soil properties include the annual mean temperature (TS ), heat conductivity (kS ), and heat transfer coefficient (US ). kS was determined based on the density, humidity, and composition of the soil. The heat exchange between VGHX wall and the ground (a thermal conduction problem), depends on the thermophysical characteristics of the soil such as the humidity, density and temperature of dry soil. These thermal properties of soil may be measured or appropriate references such as (GeoSource Heat Pump Handbook, 1993) may be referred to. The next step is to obtain the soil yearly mean temperature. The ground temperature down to the depth of 5e6 meters is affected by the sun thermal fluxes, temperature changes of the air, and rainfalls. However, for the depths between 15 and 25 meters, the soil yearly mean temperature is approximately constant with one or two degrees different from the annual mean temperature of the air. In deeper distances, the temperature increases with depth which affects the fluxes resulting from the geothermal energy with an approximate constant gradient equal to 30  C/km. Due to the fact that for VGHX system, the sub-surface ground temperature does not vary significantly during a year, the ground temperature was estimated using the mean annual surface soil temperature (TS ) (Kasuda and Archenbach, 1965).

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Fig. 4 e A schematic view of the studied GC-SEHP with VGHX.

Among the mentioned system operating related parameters, the ground temperature (TS ) estimated using the mean annual air temperature is directly related to the weather conditions. Furthermore, cooling and heating loads, total annual running hours and equivalent full-load hours in heating and cooling modes are the other involved weather parameters.

- Heat conductivity of VGHX pipe wall (kp;GHX ), kW/(mK). - The layout of VGHX borehole network (series or parallel). 5. Efficiencies of ejector elements: - Primary nozzle efficiency (hn ), %. - Mixing chamber efficiency (hm ), %. - Subsonic diffuser efficiency (hd ), %.

3.3.

3.4.

Equipment related input parameters

1. VGHX Pump specifications: - Pump efficiency (hPum ), %. - Pump motor electrical efficiency (hM ), %. 2. Condenser specifications: - Inner and outer diameter (DI;i;Con and DI;o;Con ) of condenser inner pipe, m. - Heat conductivity (kp;Con ) of condenser inner pipe, kW/ (mK). 3. Evaporator specifications: - Inner and outer diameter (DI;i;Eva and DI;o;Eva ) of evaporator inner pipe, m. - Heat conductivity (kp;Eva ) of evaporator inner pipe, kW/ (mK). 4. VGHX specifications:

Refrigerant and water mass flow rates

_ 1 ), The mass flow rates of refrigerant (steam) in boiler (m _ 3 ) were computed by _ 2 ), and condenser (m evaporator (m solving the mentioned system of nonlinear equations. Properties of water flow in GHX including thermal conductivity (kW ½kW=ðmKÞ), dynamic viscosity (mW ½Pa s), density (rW ½kg=m3 ), and specific heat (cp;W ½kJ=kg K) were obtained from tables of water properties provided by reference (Shames, 2003) at mean temperature of GHX inlet and outlet water in cooling and heating modes (TW;c andTW;h ). The underground water in GHX flows through evaporator in heating (QW;h ¼ QEva;h ) and condenser in cooling (QW;c ¼ QCon;c ) modes, where QCon;c and QEva;h are heat transfer rate between refrigerant and outdoor water in cooling and heating modes, respectively.

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Using the first law of thermodynamics and considering zero rate of work crossing the boundaries of the control volume, the ground water mass flow rate in heating _ W;c ½kg=s) modes were computed _ W;h ½kg=s) and cooling (m (m from Eqs. (3) and (4): QEva;h cp;W  ðTW1;h  TW2;h Þ

(3)

QCon;c ¼ cp;W  ðTW2;c  TW1;c Þ

(4)

_ W;h ¼ m

_ W;c m

WVGHXPum;h ¼

_ W;h  HPum;h m rW;h  hPum;h

(5)

WVGHXPum;c ¼

_ W;c  HPum;c m rW;c  hPum;c

(6)

And for circulating pump:  WVGHXPum ¼ Max WVGHXPum;c ; WVGHXPum;h

3.10. 3.5.

3.6. VGHX arrangement (number and depth of boreholes) Based on the VGHX model presented in reference (Sanaye and Niroomand, 2009), the number (Nb ) and depth (Lb ) of boreholes were estimated. The inputs and outputs of VGHX model are as follows:

Inputs of VGHX model

1. VGHX inlet water temperature (TW2 ) in cooling and heating modes. 2. VGHX outlet water temperature (TW1 ) in cooling and heating modes. _ W ) in cooling and heating 3. Ground water mass flow rate (m modes. 4. Annual operating hours (T ) in cooling and heating modes. 5. Equivalent annual full-load hours (s) in cooling and heating modes. 6. VGHX required heat transfer rate (QGHX ) in cooling and heating modes. 7. Annual average temperature of soil (TS ). 8. Overall heat transfer coefficient of soil (US ). 9. Thermal conductivity of GHX pipe (KP ; GHX). 10. Nominal diameter of GHX pipe (Dp;GHX ).

3.8.

(7)

Overall coefficient of performance (COP)

The evaporator and condenser lengths

The values of evaporator and condenser lengths were computed based on the method presented in reference (Sanaye and Niroomand, 2009) while using water as the refrigerant.

3.7.

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Outputs of VGHX model

1. Number of boreholes of VGHX (Nb ). 2. Depth of boreholes of VGHX (CEj ¼ 2122 $).

The overall values of COP in heating and cooling modes of GCSEHP operation are estimated from: COPGC-SEHP;h ¼

Qh WGHXPum;h þ WEjPum;h þ QBoi;h

(8)

COPGC-SEHP;c ¼

Qc WGHX Pum;c þ WEj Pum;c þ QBoi;c

(9)

4.

Optimizing the GC-SEHP system

The design of GC-SEHP system was implemented by defining an objective function (the total cost) and using two different optimization techniques to find the optimum design parameters.

4.1.

Objective function

An objective function (the total annual cost of GC-SEHP system) named TAC was defined as: TAC ¼ CInv þ COp

(10)

where: CInv : Initial investment cost for yearly system operation, $/y; COp : Annual operating cost of GC-SEHP system, $/y.

4.2. The annual capital or investment cost of GC-SEHP system (CInv ) The annual capital cost of the system (CInv ) is: CInv ¼ CRF  CEj þ CEj Pum þ CBoi þ CEva þ CCon þ CGHX þ CGHX Pum
þ CAF (11) where: CRF, the capital recovery factor, was computed from:

3.9.

Pumping power consumption CRF ¼

The required pumping head (HPum ) was estimated by computing the sum of losses in heat pump (DpHP ) and GHX (DpGHX ) as well as considering roughly 50% as an overestimate to compensate for the losses in fittings. The pumping power consumption in heating and cooling modes are (Kakac and Liu, 2002):

i n 1  ði þ 1Þ

(12)

i and n are annual interest rate and years of the system operation, respectively. The relations and methods used to compute the costs of GC-SEHP components are presented in references (Peters et al., 2002; Rohsenow et al., 1998).

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4.3.

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The annual operating cost of GC-SEHP system (COp )

4.4.

The system annual operating cost includes the annual boiler maintenance cost and annual cost of energy consumption of boiler, ejector pump, and VGHX circulating pump: COp ¼ CFuel þ CMain

The following constraints were applied in optimization procedure: 1. TW2;h > 0 C: To prevent freezing of the water in evaporator. 2. TWi1;c  TEva;c > 10 C: To guarantee the proper heat exchange between the chilled water and the refrigerant in evaporator in cooling mode. 3. TCon;h  TWi1;h > 10 C: To guarantee the proper heat exchange between the hot water and refrigerant in condenser in heating mode.

(13)

where: CFuel : Annual cost of fuel consumption of the system, $/y: CFuel ¼ CEl þ CNG

(14)

where: CEl : Annual cost of power consumption of GC-SEHP system, $/y: CEl ¼ CEl;M  12

(15)

4.5.

CEl;M is the monthly electricity cost computed based on the average monthly electricity consumption (E=12) referring to the tariff of domestic electricity consumption. The annual electricity consumption of the system (E [kW h/y]) is: E ¼ EEj Pum þ EGHX Pum

where: EEj Pum : Annual energy consumption of the ejector pump, kW h/y: (17)

EGHX Pum : Annual energy consumption of VGHX circulating pump, kW h/y: EGHX Pum ¼ Tc  WGHX Pum;c þ Th  WGHX Pum;h

The optimization by NeldereMead method

NeldereMead method (NM) is one of the direct numerical search methods to find the local extermums of multivariate functions used for optimization (finding the minimum value of the objective function). For two variables, this method is a pattern search that compares function values at the three vertices of a triangle. The worst vertex, where the function is largest, is rejected and replaced with a new vertex. A new triangle is formed and the search is continued. The process generates a sequence of triangles (which might have different shapes), for which the function values at the vertices get smaller and smaller. The size of the triangles is reduced and the coordinates of the minimum point are found. The algorithm is stated using the term simplex (a generalized triangle in N dimensions) and will find the minimum of a function of N variables. This method is computationally compact, and thus, had a relatively good convergence and fast run time (Nelder and Mead, 1965). The followings are implemented to optimize the objective function by NM method:

(16)

EEj Pum ¼ sc  WEj Pum;c þ sh  WEj Pum;h

Constraints

(18)

CNG : Annual cost of the boiler natural gas consumption, $/y: sc  QBoi;c þ sh  QBoi;h CNG ¼ cNG  3600  (19) LHVNG  rNG CMain : Annual maintenance cost of boiler, $/y, was computed referring to (Peters et al., 2002).

Table 1 e Comparison between the results of presented SEHP model and the theoretical results computed by references (Eames et al., 1995; Alexis, 2004) and experimental data given by references (Alexis and Rogdakis, 2003; Stinson, 1943; Jackson, 1936) PBoi ½bar

3.6 2.3 2.7 6 8 8 11.05 11.05 11.05 7.9 7.9 7.9 7.9 7.9

TCon TEva 

½ C

25 29.5 31.9 50 50 45 37.4 38.5 39.6 33.6 43.1 38.8 32.9 42.5



½ C

5 7.5 10 4 6 4 11.3 17.6 22.3 15.6 12.8 15.6 10 15.6

hn

hm

hd

½% ½% ½%

85 85 85 90 90 90 70 70 70 70 70 70 70 70

95 95 95 80 80 80 80 80 80 80 80 80 80 80

85 85 85 90 90 90 80 80 80 80 80 80 80 80

Present work COP

_2 m _1 m

_1 QEva =m ½kJ=kg

0.7610 0.5078 0.5163

COP

_2 m _1 m

_ 1 ½kJ=kg QEva =m

Diff. [%]

Ref. Ref. Ref. (Alexis Ref. Ref. (Eames (Alexis, and Rogdakis, (Stinson, (Jackson, et al., 1995) 2004) 2003) 1943) 1936) 0.7812 0.5052 0.5299

0.43 0.51 0.56

0.45 0.52 0.58 1754 2050 2217 2135 1259 1715 1883 1457

1609 2007 2275 2170 1190 1700 1900 1400

2.6 0.5 2.6 4.4 1.9 3.4 9 2.1 2.5 1.6 5.8 0.9 0.9 4.1

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Table 2 e The list of system operating conditions, soil properties and the specifications of equipment for ESIL case study. TS ¼ 16  C US ¼ 12 W=ðm2  CÞ hs ¼ 75% hel ¼ 80% hPum ¼ 80% hM ¼ 80% DI;i;Con ¼ 0:0318 m DI;o;Con ¼ 0:0348 m kp;Con ¼ 0:398 kW=ðm  CÞ DI;i;Eva ¼ 0:0318 m DI;o;Eva ¼ 0:0348 m kp;Eva ¼ 0:398 kW=ðm  CÞ kp;GHX ¼ 0:3979 W=ðm  CÞ

Qc ¼ 16 kW Qh ¼ 16 kW Tc ¼ 1320 h=y Th ¼ 1225 h=y sc ¼ 500 h=y sh ¼ 580 h=y TWi1;h ¼ 15 C TWi2;h ¼ 20 C TWi1;c ¼ 30  C TWi2;c ¼ 20  C n ¼ 15 y i ¼ 10% kS ¼ 2:4 W=ðm  CÞ

1. Choosing n þ 1 initial points, each point with n components. These components are in fact the independent variables of the system: fPj ðkÞjj ¼ 1; .; n þ 1; k ¼ 1; .; ng. 2. Choosing the maximum number of trials to prevent the algorithm from getting involved in perpetual loop. 3. A criterion named the tolerance which is the acceptable difference between the best and the worst points in NeldereMead method was considered to be 0.1. Due to the mentioned non-equality constraints of design parameters, the numerical value of the objective function was not acceptable in some specific conditions. In this situation NM method could not proceed to obtain the next set of values closer to optimum design parameters. Therefore a modification was developed to enable the method work for an optimization problem with non-equality constraints.

4.6.

The optimization by genetic algorithm method

Genetic Algorithm is also a general-purpose search method and non-deterministic optimization technique based upon the principles of evolution observed in nature. It combines selection, crossover, and mutation operators with the goal of finding the best solution to a problem. GAs mimic the process of evolution by natural selection. Potential solutions are repeatedly graded on fitness and combined to produce new, potentially better, solutions. GAs search for the optimal solution until a specified termination criterion is met. They are suitable for optimization of difficult functions in reasonable time (Goldberg, 1989). The following important properties were considered in GA optimization algorithm:

Table 3 e Properties and cost of U-shaped polyethylene pipe (type SDR 11). Nominal diameter of U-shaped pipe [in] 0.75 1 1.25 1.5

Inner diameter [m]

Outer diameter [m]

Equivalent diameter [ft]

½cent=m

Price

0.0218 0.0274 0.0345 0.0394

0.0267 0.0334 0.0422 0.0483

0.15 0.18 0.22 0.25

21.55 28.02 40.95 62.5

Table 4 e Comparison between the optimum design values obtained by NM and GA optimization methods for ESIL case study. Parameter

TBoi;h ½ C TEva;h ½ C TCon;h ½ C TW1;h ½ C TW2;h ½ C TBoi;c ½ C TEva;c ½ C TCon;c ½ C TW1;c ½ C TW2;c ½ C Dp;GHX ½in TAC ½$=y

1. 2. 3. 4. 5. 6.

Optimization methods NM

GA

134.9 3.1 41.5 5.6 4.1 162.6 16.6 38.4 30.6 35.2 1.5 1581.5

145.5 3.2 26.7 5.6 3.9 164.6 15.9 40.9 31.7 39.7 1.5 1476.7

Difference (%)

7.8 3.1 55.4 0 5.1 1.2 4.4 6.1 3.5 11.3 0 7.1

Number of generations: 2000. Size of population: 100. Elitism was allowed. Mutation type: Randomly. Mutation probability: 10%. Crossover probability: 95%.

5. Developed software for modeling and optimization of GC-SEHP system (GC-SEHP Designer) For performing the massive design computations and timeconsuming optimization process of GC-SEHPs, a software program was designed in Energy Systems Improvement Laboratory (ESIL) and was developed in Visual Basic 6 based on the presented model using NeldereMead mathematical optimization method to obtain the optimum values of independent parameters in GC-SEHP design.

Table 5 e The optimum values of the ejector design parameters for ESIL case study (results of solving the governing system of twelve nonlinear equations at the system optimum design point obtained using NM optimization method). Parameter

_ 1 ½g=s m _ 2 ½g=s m _ 3 ½g=s m T3 ½ C xb Vb ½m=s Pc ½Pa xc Vc ½m=s Pd ½Pa Td ½ C Vd ½m=s

Operating mode Cooling

Heating

9.4 6.8 16.2 361.1 0.906 880.3 1.3 0.915 26.7 7 349.6 207.1

3.5 2.8 6.3 346 0.911 860.6 0.6 0.925 25.5 3.1 334.5 207.6

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6.2.

Table 6 e The optimum values of ejector main cross sections for ESIL case study. Ath ¼ 0:1 cm2 Ad ¼ 20:1 cm2

The verification of the VGHX model was completely investigated in reference (Sanaye and Niroomand, 2009) and the validity of VGHX model results was evaluated by comparing the model output with the results of several other procedures and with numerical data provided in several references.

Anp ¼ 3:4 cm2 Ans ¼ 475:2 cm2

6.3.

Table 7 e The optimum values of effective parameters in objective function for ESIL case study. CFuel ¼ 533 $=y CMain ¼ 47:5 $=y COp ¼ 580:5 $=y CEj ¼ 2122 $ CBoi ¼ 135:3 $ CEva ¼ 778:3 $ CCon ¼ 957:2 $ CEj Pum ¼ 56:9 $ CGHX Pum ¼ 225:3 $

The results of NM method were validated using Genetic Algorithm technique using «optiGA ActiveX software package» (Elad Salomons, 2006). The code consists of 7700-line (about 550 kB), 5 forms and 93 functions. The equations presented in reference (Thomas Irvine and Liley, 1984) were used to compute the thermodynamic properties of steam. The software input included the required data to model and design GC-SEHP with VGHX as well as to optimize the values of independent parameters.

Discussion and results

6.1.

Verification of the SEHP model

A case study

After validation of GC-SEHP model, as a current working project with Iranian Fuel Conservation Organization (IFCO), a GC-SEHP system was designed using GC-SEHP Designer which is going to be installed and tested on campus. The system operating conditions, the soil properties (Iranian Meteorological Organization, 2001), and the specifications of equipment are listed in Table 2. The regional cost of polyethylene pipe per meter (cPipe ) is presented in Table 3. The price of electricity was obtained from the tariff of domestic electricity consumption in Tehran (Iran ministry of energy, 2008). A series of parallel boreholes in GHX with 20 ft separation distance were selected. The optimum values of design (independent) parameters by NM and GA methods are listed in Table 4. Total Annual Cost (TAC, $/y), temperatures ( C), and the GHX pipe diameter (inch) are included in this table. As is shown in Table 4, there is an acceptable agreement (7.1% percent points difference in TAC values and 9% percent points mean difference in design parameters) when NM and GA optimization techniques were applied. The ejector design parameters, including steam mass flow rates in boiler, evaporator, and condenser and the steam properties at various sections of the ejector, at optimum design point were obtained by solving the governing system of twelve nonlinear equations. These values are presented in Table 5. The values of the ejector main cross sections were computed and are listed in Table 6. The numerical values of effective terms in the objective function at the optimum design point are listed in Table 7.

Nb ¼ 4 Lb ¼ 108:7 m CGHX ¼ 2541:6 $ CAF ¼ 0 CRF ¼ 0:1627 CIn ¼ 896:2$=y COPc ¼ 0:65 COPh ¼ 1:67

6.

Verification of the VGHX model

To verify the results obtained from the recommended model for SEHP, the modeling output were compared with the theoretical and experimental results presented in references (Eames et al., 1995; Alexis, 2004; Alexis and Rogdakis, 2003; Stinson, 1943; Jackson, 1936). The numerical results for various studied parameters are compared in Table 1. The difference percent points in this comparison were acceptable in our engineering analysis.

6.4. Investigating the effects of design parameters on costs and operation of GC-SEHPs The effects of various parameters such as the climate condition, heat pump capacity (heating, Qh, loads), soil type, and

Table 8 e The specifications of climatic regions. Region 1 2 3 4 5 6 7

Qc =Qh

Tc ½h=y

Th ½h=y

sc ½h=y

sh ½h=y

Qc ½kW

Qh ½kW

TS ½ C

0.125 0.25 0.5 1 2 4 8

300 540 900 1350 1800 2160 2400

2400 2160 1800 1350 900 540 300

120 216 360 540 720 864 960

960 864 720 540 360 216 120

4 7.2 12 18 24 28.8 32

32 28.8 24 18 12 7.2 4

10 13 16 19 22 25 28

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Table 9 e The optimum design parameters of GC-SEHP obtained from NM and GA methods in 7 climatic regions. Region Method TBoi;c 1

TEva;c

TCon;c

TW1;c

TW2;c

Dp;GHX 1.5 1.5 1.5 1.5 1.25 1.25 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

NM GA NM GA NM GA NM GA NM GA NM GA NM GA

136.7 166.7 135.1 164.3 149.7 168.5 166.6 165.7 182 167.3 176.1 167 167.7 166.9

14.9 15.1 7.4 17.5 12.3 13.9 10.4 15.8 4.4 17 16.5 16.8 17.1 15.8

43.8 47.2 38.5 40.3 40.4 36.9 42.9 44.6 48.9 49 51.6 48.1 59.7 50.2

28.1 27.6 17.5 19.1 19.8 20.4 30.9 31.2 35.5 39.4 31.3 32.6 37.1 39

40.8 33.8 28.3 24.7 34.1 29.5 40.5 42.3 46.4 46.5 46.4 46.6 53.9 47.5

Region

Method

TBoi;h

TEva;h

TCon;h

TW1;h

TW2;h

1

NM GA NM GA NM GA NM GA NM GA NM GA NM GA

113.6 102.6 159.8 138.4 143.7 152.3 143.4 157.9 146.7 137.2 132.4 115.9 109 122.1

1.9 2.7 2.1 2.8 2.1 2.2 4.3 3.5 4.5 5 3.8 5.1 3.4 4.6

32.6 35.4 37.2 41 33.2 29.9 30.4 32 31.4 37 33.7 29.6 38.5 37.7

4 4.4 5.6 5.5 7.1 6.5 11.2 10.3 14 15 17.4 21.2 18.7 18.9

2.4 2.8 3.1 2.9 3 2.7 8.8 7.8 10 13.1 6.6 19.1 7.8 18.1

2 3 4 5 6 7

2 3 4 5 6 7

TAC 2365.5 2364.1 1934 1877.4 1657 1545.7 1773 1695.1 2413.2 2247.7 3088.2 3027.2 3989.9 3719.6

number of boreholes of VGHX (Nb ) on GC-SEHP operation and cost have been studied in this section. In this section, the economic inputs and equipment specifications were obtained from Table 2.

6.4.1.

The climate

To investigate the effect of climate (tropical, temperate, and cold) on GC-SEHP operation, first a criterion was defined which depends on parameters such as cooling to heating load ratio

Table 10 e The direction of change in values of TAC for the first climate region in comparison with the second one (in parenthesis). Regions to be compared

TS

Qc

Qh

Temperate (vs. tropical) Temperate (vs. cold)

lower

lower

higher

higher

higher

lower

LGHX a

TACb

e

lower

lower

lower

lower

lower

CAF

a Ref. (Sanaye and Niroomand, 2009). b Ref. (Sanaye and Niroomand, 2009), Eqs. (11) and (10).

(the ratio of equivalent full-load operating hours in cooling and heating modes), and the ground temperature. Seven climatic regions were considered: Three regions (No. 1 to 3) represent the cold climate, one region (No. 4) represents the temperate climate, and three regions (No. 5 to 7) represent the tropical climate. To be able to compare the results in various climates, sum of heating and cooling loads was considered to be 36 kW, while sum of operating hours in heating and cooling modes was considered to be 2700 h/y. Furthermore, the ratio of cooling and heating loads was assumed to be equal to the ratio of system operating hours in cooling and heating modes (Geothermal Heat Pump Design Manual, 2002). The specifications of climatic regions are shown in Table 8. The optimization results of GC-SEHP in seven mentioned climatic regions (including the value of objective function and design parameters) were obtained using NM and GA methods as is shown in Table 9. The values of TAC, temperatures, and the GHX pipe diameter are given in units of $/y,  C and inch, respectively. The maximum difference value between TAC results obtained from NM and GA in seven regions was 7.4% and the maximum difference points between design parameters obtained from NM and GA in seven regions was 14.4%. The values of the total annual cost at the optimum design point in various climatic regions are shown in Fig. 5. The average value of the total annual cost at the optimum design points in cold climate, was obtained as average optimum values of TAC in regions No. 1 to 3 ($1929.1). The average value of the total annual cost at the optimum design point in temperate climate was also

3800 1.5

3000

1.3

2600

1.1

COP

Total annual cost, $/y

1.7

3400

COPc COPh

0.9

2200 0.7

1800

0.5

1400

0.3

0

1

2

3

4

5

6

7

Climatic region Fig. 5 e The average TAC values at the optimum design points in the three climatic regions.

0

1

2

3

4

5

6

7

Climatic region

Fig. 6 e The optimum COP values in cooling and heating modes in various climatic regions.

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24

Steam mass flow rate, kg/s

2900

Total annual cost, $/y

2600 2300 2000 1700 1400

m1,c m1,h

20

m2,c m2,h

16 12 8 4

1100 800

0

5

10

15

20

25

30

35

5

10

System capacity, kW Fig. 7 e Change in the TAC value at the optimum design point with system capacity (TAC½$=y[80:123Q½kW D293:96).

obtained as the optimum value of TAC in region No. 4 ($1695.1) (therefore the value and average value was the same). Finally, the average value of the total annual cost at the optimum design points in tropical climates was obtained as average optimum values of TAC in regions No. 5 to 7 ($2998.2). Thus, with employing GC-SEHP in temperate climate, the lowest average value for TAC was obtained. The average value of TAC in temperate climate was 13.8% lower than that for the cold climate and 76.9% lower than that for the tropical climate. As mentioned before, the major part of the TAC value in GC-SEHPs belonged to the investment cost for GHX and GHX length. Regions located in temperate climate have higher TS and lower QEva;h values than that of the corresponding values in the regions located in cold climates. Therefore, the value of LGHX (and thus TAC) in temperate climate is smaller than the corresponding values in cold climates. Similarly, regions located in temperate climate have a lower TS and QCon;c than that for the corresponding values in the regions located in tropical climates. Therefore, the value of LGHX (and thus TAC) in temperate climate is smaller than tropical climate. The above results are summarized in Table 10. The overall values of COP for GC-SEHP in heating and cooling modes (COPh and COPc ) in various climatic regions computed at optimum design points are shown in Fig. 6. Results indicate that

20

25

30

35

Fig. 9 e Change in the ejector input mass flow rates in cooling and heating modes (kg/s) with the system capacity (kW).

the maximum values of COP in both heating and cooling modes occurred in temperate climate. In the temperate climate, the values of COPh and COPc were 23% and 24.9% greater than their corresponding mean values in cold climates, respectively. Also, in the temperate climate, the mean values of COPh and COPc were 20.2% and 10.3% greater than their corresponding mean values in tropical climates, respectively. Therefore, GC-SEHP system operates with the minimum average value of TAC and the maximum value of overall COP in the temperate climate.

6.4.2. Heat pump capacity (heating, Qh , and cooling, Qc , loads) The effect of heat pump cooling/heating capacity on the optimal value of TAC is shown in Fig. 7. Results show that the TAC values approximately change linearly (TAC½) with capacity due to increasing CGHX (Eq. (11)) and TAC value (Eq. (10)). It is note worthy that the VGHX length (LGHX) approximately changes linearly with the heat pump cooling/heating capacity as shown in Fig. 8. The effect of heat pump capacity on the ejector inlet mass flow rate in cooling and heating modes is shown in Fig. 9. _ 2 increase with _ 1 and m Results show that the values of m capacity (Eqs. XII-c and XII-h).

35

Cross section area, cm²

500 450

VGHX Length, m

15

System capacity, kW

400 350 300 250

Ath × 100 Ad

30

Anp

25

Ans × 0.01

20 15 10

200

5

150

0

100 5

10

15

20

25

30

System capacity, kW

Fig. 8 e Change in the GHX length (m) with the system capacity (kW).

35

5

10

15

20

25

30

35

System capacity, kW Fig. 10 e Change in the ejector main cross sections (m2) with the system capacity (kW).

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285

1525

GHX Length, m

Total annual cost, $/y

1550

1500 1475 1450 1425

280

275

270

1400 Damp clay Saturated sand

Dry clay

Dry sand

Damp loam

265

Dry loam

0

1

Soil type

Soil type

Loose dry soil traps air and is less effective for the heat transfer required in VGHX of GC-SEHP system than the moist packed soil. Low-conductive soil may require as much as 50% more loops than a proper high-conductive soil (Enertran, 2007). The heat transfer coefficient (US ) is a good single criterion for showing the effect of soil properties. Change in TAC value at the optimum design point with the soil type is shown in Fig. 11. These results were obtained based on heat transfer coefficient of various soil types given in Table 11 assuming the run time equal to 70%. Results show that soil types with bigger US have lower optimal TAC (200% bigger US decreases the TAC for 8.7% points). Furthermore increasing theUS value, decreases the LGHX , and thus the TAC value. Therefore, considering the fact that dry loam has the lowest value of heat transfer coefficient, installation of GCSEHP in regions with this soil type is not recommended. On the other hand, the damp clay has the best heat transfer coefficient, and is the most proper soil type for VGHX of GCSEHP system. Therefore, the general rule in this case is: “The

Table 11 e Soil types heat transfer coefficient (US ½kW=m2 K) (GeoSource Heat Pump Handbook, 1993).

Damp clay Saturated sand Dry clay Dry sand Damp loam Dry loam

4

5

6

7

8

9

10

Run time (%) 100

90

80

70

0.0119 0.0114 0.0102 0.0085 0.0062 0.0040

0.0131 0.0125 0.0108 0.0091 0.0068 0.0043

0.0142 0.0136 0.0119 0.0102 0.0074 0.0045

0.0153 0.0148 0.0131 0.0114 0.0080 0.0051

Fig. 12 e Change in GHX length with the number of boreholes.

wetter, the better”; because dampness increases the thermal conductivity of soils; which increases the VGHX effectiveness. The overall values of COPh and COPc at the optimum design points for various soil types specified in Fig. 11, were computed to be about 1.1 and 0.6 respectively, meaning that change in theUS value does not change the optimal overall values of COPh andCOPc , noticeably. By increasing theUS , it was observed that theLGHX , the pressure loss in GHX (DpGHX ), the required pumping head (HPum ), and the pumping power consumption (WGHX; Pum ) (equations 5 and 6) decrease. Based on equations (8) and (9), this can increase the overall value of COP, however, for our case studies, the heating and cooling loads (Qc and Qh ) and the heat transfer rate in boiler (QBoi ) were the dominant parameters in computing the overall value of COP. This shows that decreasing the pumping power consumption didn’t affect the COP value considerably.

6.4.4.

Number of boreholes of GHX (Nb )

Fig. 12 shows the change in the GHX length with the number of boreholes. As shown in this figure, there is an approximate linear relation between the number of boreholes and the GHX length. With increasing the number of boreholes, the water mass flow rate as well as convection heat transfer coefficient decrease in each well. Therefore, with choosing a number of

1725

Total annual cost, $/y

The effect of heat pump capacity on the ejector design cross sections is also shown in Fig. 10. Results show thatAth ,Ad , Anp , and Ans (Fig. 2) increase with capacity. These results are obtained _ 1 with capacity) and based on Eqs. XII-c and XII-h (increasing m _ 1 as well as relations given in (Alexis, 2004) among Ath and m among design cross section areas (Ath, Ad, Anp and Ans).

Soil type

3

Number of boreholes

Fig. 11 e Change in TAC value at the optimum design points with the type of soil assuming run time [ 70%.

6.4.3.

2

1720 1715 1710 1705 1700 1695 1690

0

1

2

3

4

5

6

7

8

9

10

Number of parallel boreholes Fig. 13 e Change in the TAC values with the number of boreholes.

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boreholes instead of a single one (Nb > 1), the length of each borehole (Lb ) is bigger than the multiplication of a single well depth (Lsingle well ) and N1b (Lb > N1b Lsingle well ). Thus, the total GHX length (LGHX ¼ Nb  Lb ) is bigger than the pipe length of a single well (LGHX > Lsingle well ). It means that increasing the number of boreholes increases the GHX length. Change in the TAC values with the number of parallel boreholes is shown in Fig. 13. It can be observed that the TAC values increase slightly with increasing the number of boreholes. In fact, increasing the GHX length with the number of parallel boreholes leads to increase the cost of GHX and TAC.

7.

Conclusions

A new application of SEHP with VGHX was introduced. A new approach in modeling the SEHP by deriving and solving governing twelve nonlinear equations was proposed. A thermaleconomic optimal design method was presented to obtain the various optimum design parameters of a GC-SEHP system with VGHX using two optimization techniques (NM and GA) to guarantee the validity of optimization results. The results showed:  GC-SEHP has the smallest mean TAC value and maximum overall COP value in temperate climates in comparison with cold and tropical climates.  The TAC values approximately change linearly with capacity.  The optimum values of ejector input mass flow rates increase with capacity.  The optimum values of ejector main cross sections increase with capacity.  By increasing the US value, the optimal TAC value decreases. This may be also reached by dampening the soil adjacent to VGHX of GC-SEHP which increases its effectiveness.  The optimal overall COP value does not change considerably by changing the US value.  Increasing the number of boreholes increases the length of GHX. This leads to increase the TAC value.

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