**2. GT-air cooling chiller energy analysis**

Figure 1.a shows a schematic of a simple open GT "Brayton cycle" coupled to a refrigeration system. The power cycle consists of a compressor, combustion chamber and a turbine. It is presented by states 1-2-3-4 on the T-S diagram, Fig. 1.b. The cooling system consists of a refrigerant compressor, air cooled condenser, throttle valve and water cooled evaporator. The chilled water from the evaporator passes through a cooling coil mounted at the air compressor entrance, Fig. 1.a. The refrigerant cycle is presented on the T-S diagram, Figure 1.c, by states *a, b, c* and *d*. A fraction of the power produced by the turbine is used to power the refrigerant compressor and the chilled water pumps, as indicated by the dotted lines in Fig. 1.a. To investigate the performance of the coupled GT-cooling system the different involved cycles are analyzed in the following employing the first and second laws of thermodynamics.

### **2.1 Gas turbine cycle**

72 Efficiency, Performance and Robustness of Gas Turbines

and Gajjar *et al* (2003) have presented results of extensive theoretical and experimental studies covering aspects of fogging flow thermodynamics, droplets evaporation, atomizing nozzles design and selection of spray systems as well as experimental data on testing

In the indirect mechanical refrigeration cooling approach the constraint of humidity is eliminated and the air temperature can be reduced well below the ambient WBT. The mechanical refrigeration cooling has gained popularity over the evaporative method and in KSA, for example, 32 GT units have been outfitted with mechanical air chilling systems. There are two approaches for mechanical air cooling; either using vapor compression [Alhazmy (2006) and Elliott (2001)] or absorption refrigerator machines [Yang *et al* (2009), Ondryas *et al* (1991), Punwani (1999) and Kakarus *et al* (2004)]. In general, application of the mechanical air-cooling increases the net power but in the same time reduces the thermal efficiency. For example, Alhazmy *et al* (2004) showed that for a GT of pressure ratio 8 cooling the intake air from 50oC to 40oC increases the power by 3.85 % and reduces the thermal efficiency by 1.037%. Stewart and Patrick (2000) raised another disadvantage (for extensive air chilling) concerning ice formation either as ice crystals in the chilled air or as

Recently, alternative cooling approaches have been investigated. Farzaneh-Gord and Deymi-Dashtebayaz (2009) proposed improving refinery gas turbines performance using the cooling capacity of refinerys' natural-gas pressure drop stations. Zaki *et al* 2007 suggested a reverse Brayton refrigeration cycle for cooling the air intake; they reported an increase in the output power up to 20%, but a 6% decrease in thermal efficiency. This approach was further extended by Jassim *et al* (2009) to include the exergy analysis and show that the second law analysis improvement has dropped to 14.66% due to the components irreversibilities. Khan *et al* (2008) analyzed a system in which the turbine exhaust gases are cooled and fed back to the compressor inlet with water harvested out of the combustion products. Erickson (2003, 2005) suggested using a combination of a waste heat driven absorption air cooling with water injection into the combustion air; the concept

Thermal analyses of GT cooling are abundant in the literature, but few investigations considered the economics of the cooling process. A sound economic evaluation of implementing an air intake GT cooling system is quite involving. Such an evaluation should account for the variations in the ambient conditions (temperature and relative humidity) and the fluctuations in the fuel and electricity prices and interest rates. Therefore, the selection of a cooling technology (evaporative or refrigeration) and the sizing out of the equipment should not be based solely on the results of a thermal analysis but should include estimates of the cash flow. Gareta *et al* (2004) has developed a methodology for combined cycle GT that calculated the additional power gain for 12 months and the economic feasibility of the cooling method. From an economical point of view, they provided straight forward information that supported equipment sizing and selection. Chalker *et al* (2003) have studied the economical potential of using evaporative cooling for GTs in USA, while Hasnain (2002) examined the use of ice storage methods for GTs' air cooling in KSA. Yang *et al* (2009) presented an analytical method for evaluating a cooling technology of a combined cycle GT that included parameters such as the interest rate,

systems for gas turbines up to 655 MW in a combined cycle plant.

solidified layer on air compressors' entrance surfaces.

is named the "*power fogger cycle*".

As seen in Figures 1.a and 1.b, processes 1-2s and 3-4s are isentropic. Assuming the air as an ideal gas, the temperatures and pressures are related to the pressure ratio, *PR*, by:

$$\frac{T\_{2s}}{T\_1} = \frac{T\_3}{T\_{4s}} = \left[\frac{P\_2}{P\_1}\right]^{\frac{k-1}{k}} = PR^{\frac{k-1}{k}}\tag{1}$$

The net power output of a GT with mechanical cooling system as seen in Fig. 1.a is

$$
\dot{\mathcal{W}}\_{net} = \dot{\mathcal{W}}\_t - \left(\dot{\mathcal{W}}\_{comp} + \dot{\mathcal{W}}\_{el,ch}\right) \tag{2}
$$

The first term of the RHS is the power produced by the turbine due to expansion of hot gases;

$$
\dot{\mathcal{W}}\_t = \dot{m}\_t \ c\_{p\chi} \eta\_t \left( T\_\chi - T\_{4s} \right). \tag{3}
$$

Energy, Exergy and Thermoeconomics

*T* 

Fig. 1c. *T-s* diagram for a refrigeration machine

*c* 

(kg*w*/kg*dry air*) (Fig. 1.a) as;

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 75

*Tc*

*d* 

In Eq.3, *mt* is the total gases mass flow rate from the combustion chamber; expressed in terms of the fuel air ratio *<sup>f</sup> <sup>a</sup> f* = *m m* , and the air humidity ratio at the compressor intake

*Te* 

*mt* = *mmm av f* + + = <sup>1</sup> (1 ) *ma* + +

where *hv2* and *hv1* are the enthalpies of saturated water vapor at the compressor exit and

The last term in Eq. 2 ( *Wel ch* , ) is the power consumed by the cooling unit for driving the

*WW W Q*

− + <sup>=</sup> 

<sup>1</sup> (1 ) 1 *t a pg t <sup>k</sup>*

, ( ) *t comp el ch*

*h*

1 3 1

−

 η

= ++ −

The compression power for humid air between states 1 and 2 is estimated from:

inlet states respectively, *mv* is the mass of water vapor = *ma*

refrigeration machine electric motor, pumps and auxiliaries.

The thermal efficiency of a GT coupled to an air cooling system is then;

*cy*

Substituting for *T4s* and *mt* from Equations (1) and (4) into Eq. (3) yields:

*W m fc T*

ω

η

ω

( )( ) *W mc T T m h h comp a pa* = −+ − 21 2 1 *vv v* (5)

ω<sup>1</sup> .

*k*

*PR*

 (7)

ω1 ,

*f* (4)

*b* 

*s* 

*a* 

*bs* 

(6)

Fig. 1a. Simple open type gas turbine with a chilled air-cooling unit

Fig. 1b. T-s diagram of an open type gas turbine cycle

Fig. 1a. Simple open type gas turbine with a chilled air-cooling unit

1

2s 2 4s

*P* = constant

*T* 

Fig. 1b. T-s diagram of an open type gas turbine cycle

*s* 

4

3

Fig. 1c. *T-s* diagram for a refrigeration machine

In Eq.3, *mt* is the total gases mass flow rate from the combustion chamber; expressed in terms of the fuel air ratio *<sup>f</sup> <sup>a</sup> f* = *m m* , and the air humidity ratio at the compressor intakeω1 , (kg*w*/kg*dry air*) (Fig. 1.a) as;

$$
\dot{m}\_t = \dot{m}\_a + \dot{m}\_v + \dot{m}\_f = \dot{m}\_a (1 + a\rho\_l + f) \tag{4}
$$

The compression power for humid air between states 1 and 2 is estimated from:

$$
\dot{\mathcal{W}}\_{coup} = \dot{m}\_a \ c\_{pa} \left( T\_2 - T\_1 \right) + \dot{m}\_v \left( h\_{v2} - h\_{v1} \right) \tag{5}
$$

where *hv2* and *hv1* are the enthalpies of saturated water vapor at the compressor exit and inlet states respectively, *mv* is the mass of water vapor = *ma*ω<sup>1</sup> .

The last term in Eq. 2 ( *Wel ch* , ) is the power consumed by the cooling unit for driving the refrigeration machine electric motor, pumps and auxiliaries.

The thermal efficiency of a GT coupled to an air cooling system is then;

$$\eta\_{cy} = \frac{\dot{\mathcal{W}}\_t - (\dot{\mathcal{W}}\_{comp} + \dot{\mathcal{W}}\_{el,ch})}{\dot{Q}\_h} \tag{6}$$

Substituting for *T4s* and *mt* from Equations (1) and (4) into Eq. (3) yields:

$$\dot{W}\_t = \dot{m}\_a (1 + a\varrho + f) c\_{pg} \,\eta \,\, T\_3 \left(1 - \frac{1}{PR \stackrel{k=1}{\phantom{k=1}}}\right) \tag{7}$$

Energy, Exergy and Thermoeconomics

power ( *Wmotor*

**2.2 Refrigeration cooling system analysis** 

and the pressure drop across the cooling coil, so that:

), the pumps ( *WP*

the refrigerant enthalpy change as

\* \*

*eu m el vo* =ηηη

In this equation,

gain and efficiency.

η

The subscript *r* indicates refrigerant and

the motor power. For the present analysis

α

electrical and volumetric efficiencies respectively.

condenser in the refrigeration cycle, *Te* and *Tc* respectively as;

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 77

The chilled water from the refrigeration machine is the heat transport fluid to cool the intake air, Fig. 1.a. The chiller's total electrical power can be expressed as the sum of the electric motor

The auxiliary power is estimated as 10% of the compressor power, therefore, 0.1 *W W <sup>A</sup>* <sup>=</sup> *motor* . The second term in Eq. 15 is the pumping power that is related to the chilled water flow rate

The minimum energy utilized by the refrigerant compressor is that for the isentropic compression process (*a-bs*), Fig 1.c. The actual power includes losses due to mechanical transmission, inefficiency in the drive motor converting electrical to mechanical energy and the volumetric efficiency, Dossat (1997). The compressor electric motor work is related to

*W mv P P cw f* = Δ( ) /

*motor*

*W*

) and auxiliary power for fans and control units, ( *WA*

η

( ) *rb a <sup>r</sup>*

*mh h*

*η*

*eu*

η

manufacturers and depends on the type of the compressor, the pressure ratio ( *P P b a* / ) and

Cleland *et al* (2000) developed a semi-empirical form of Equation 17 to calculate the compressor's motor power usage in terms of the temperatures of the evaporator and

η

. The quantities on the right hand side are the compressor mechanical,

*eu* is assumed 85%.

( )

*ra d r*

( ) ( )

<sup>−</sup> <sup>−</sup>

*mh h*

*motor <sup>n</sup> <sup>e</sup>*

*<sup>W</sup> <sup>T</sup> <sup>1</sup> <sup>α</sup> <sup>x</sup> <sup>η</sup> T T* <sup>−</sup> <sup>=</sup>

*c e*

the quality at state *d*, Fig 1.c. The empirical constant is 0.77 for R-22 and 0.69 for R-134a Cleland *et al* (2000). The constant *n* depends on the number of the compression stages; for a simple refrigeration cycle with a single stage compressor *n* = 1. The nominator of Eq. 18 is the evaporator capacity, *Qe r*, and the first term of the denominator is the coefficient of performance of an ideal refrigeration cycle. Equations 2, 5 and 18 could be solved for the power usages by the different components of the coupled GT-refrigeration system to estimate the increase in the power output as function of the air intake conditions. Follows is a thermodynamics second law analysis to estimate the effect of irreversibilities on the power

η

*eu*

is an empirical constant that depends on the type of refrigerant and *x* is

(18)

*W W WW el ch motor P A* , = ++ (15)

*pump* (16)

<sup>−</sup> <sup>=</sup> (17)

*eu* known as the energy use factor;

*eu* is usually determined by

) as:

The turbine isentropic efficiency,η*<sup>t</sup>* , can be estimated using the practical relation recommended by Alhazmy and Najjar (2004):

$$\eta\_t = 1 - \left(0.03 + \frac{PR - 1}{180}\right) \tag{8}$$

Relating the compressor isentropic efficiency to the changes in temperature of the dry air and assuming that the compression of water vapor changes the enthalpy; the actual compressor power becomes;

$$\dot{\mathcal{W}}\_{comp\_{air}} = \dot{m}\_a \left[ c\_{pu} \frac{\mathbf{T}\_1}{\mathbf{n}\_c} \left( P \mathbf{R}^{\frac{k-1}{k}} - \mathbf{1} \right) + o\_1 \left( h\_{v2} - h\_{v1} \right) \right] \tag{9}$$

The compression efficiency,η*<sup>c</sup>* , can be evaluated using the following empirical relation, Alhazmy and Najjar (2004);

$$\eta\_c = 1 - \left(0.04 + \frac{PR - 1}{150}\right) \tag{10}$$

The heat balance in the combustion chamber (Fig. 1.a) gives the heat rate supplied to the gas power cycle as:

$$\dot{Q}\_h = \dot{m}\_f \text{ NCV} \\ \eta\_{avub} = \left(\dot{m}\_a + \dot{m}\_f\right) c\_{pg} T\_3 - \dot{m}\_a c\_{pa} T\_2 + \dot{m}\_v \left(h\_{v3} - h\_{v2}\right) \tag{11}$$

Introducing the fuel air ratio *<sup>f</sup> <sup>a</sup> f* = *m m* and substituting for *T2* in terms of *T1* into Eq.11 yields:

$$\dot{Q}\_{\text{li}} = \dot{m}\_a T\_1 \left[ (1+f)c\_{pg} \frac{T\_3}{T\_1} - c\_{pa} \left( \frac{PR^{\frac{k-1}{k}} - 1}{\eta\_c} + 1 \right) + \frac{a\_1}{T\_1} (h\_{v3} - h\_{v2}) \right] \tag{12}$$

A simple expression for *f* is selected here, Alhazmy *et.al* (2006) as:

$$f = \frac{c\_{p\text{g}}\left(T\_3 - 298\right) - c\_{pa}\left(T\_2 - 298\right) + o\_1\left(h\_{v3} - h\_{v2}\right)}{\text{NCV}\eta\_{cumb} - c\_{p\text{g}}\left(T\_3 - 298\right)}\tag{13}$$

In equation 13, *hv2* and *hv3* are the enthalpies of water vapor at the combustion chamber inlet and exit states respectively and can be calculated from Eq. 14, Dossat (1997).

$$h\_{\overline{v\_{\parallel}}} = 2501.3 + 1.8723 \text{ T}\_{\parallel} \quad \text{j refers to states 2 or 3} \tag{14}$$

The four terms of the gas turbine net power and efficiency in Eq. (6) ( , *W Wt comp* , *Wel ch* , and *Qh* ) depend on the air temperature and relative humidity at the compressor inlet whose values are affected by the type and performance of the cooling system. The chillers' electric power, *Wel ch* , , is calculated in the following account.

### **2.2 Refrigeration cooling system analysis**

76 Efficiency, Performance and Robustness of Gas Turbines

<sup>1</sup> 1 0.03 180 *<sup>t</sup>*

<sup>−</sup> =− +

Relating the compressor isentropic efficiency to the changes in temperature of the dry air and assuming that the compression of water vapor changes the enthalpy; the actual

<sup>T</sup> <sup>1</sup>

*k <sup>k</sup> W m c PR comp a pa v v*

> <sup>1</sup> 1 0.04 150 *<sup>c</sup>*

<sup>−</sup> =− +

The heat balance in the combustion chamber (Fig. 1.a) gives the heat rate supplied to the gas

( ) ( ) *Q m NCV m m c T m c T m h h h f* = =+ − + −

Introducing the fuel air ratio *<sup>f</sup> <sup>a</sup> f* = *m m* and substituting for *T2* in terms of *T1* into Eq.11

*h a1 pg pa v3 v2*

*<sup>T</sup> PR 1 <sup>ω</sup> Q mT 1 f c c 1 hh*

298 298

( ) ( ) *k 1 <sup>k</sup> <sup>3</sup> <sup>1</sup>*

*T η T* <sup>−</sup> <sup>−</sup> = + − ++ −

( ) ( )( )

*pg pa v v comb pg c T cT h h*

In equation 13, *hv2* and *hv3* are the enthalpies of water vapor at the combustion chamber inlet

 *hv,j=* 2501.3+1.8723 *Tj j refers to states 2 or 3* (14)

 ) depend on the air temperature and relative humidity at the compressor inlet whose values are affected by the type and performance of the cooling system. The chillers' electric

3 21 3 2

*1c 1*

*PR*

<sup>−</sup> <sup>=</sup> −+ −

1

c

*PR*

( ) <sup>1</sup>

(9)

ω*h h*

*comb a f pg a pa v v v* 3 2 32 (11)

(12)

( )

298

−− −+ − <sup>=</sup> − − (13)

, *Wel ch* , and

ω

3

12 1

*<sup>c</sup>* , can be evaluated using the following empirical relation,

*<sup>t</sup>* , can be estimated using the practical relation

(8)

(10)

η

η

η *air*

η

η

η

A simple expression for *f* is selected here, Alhazmy *et.al* (2006) as:

power, *Wel ch* , , is calculated in the following account.

*<sup>f</sup> NCV c T*

and exit states respectively and can be calculated from Eq. 14, Dossat (1997).

The four terms of the gas turbine net power and efficiency in Eq. (6) ( , *W Wt comp*

η

The turbine isentropic efficiency,

compressor power becomes;

The compression efficiency,

Alhazmy and Najjar (2004);

power cycle as:

yields:

*Qh*

recommended by Alhazmy and Najjar (2004):

The chilled water from the refrigeration machine is the heat transport fluid to cool the intake air, Fig. 1.a. The chiller's total electrical power can be expressed as the sum of the electric motor power ( *Wmotor* ), the pumps ( *WP* ) and auxiliary power for fans and control units, ( *WA* ) as:

$$
\dot{\mathcal{W}}\_{cl,ch} = \dot{\mathcal{W}}\_{untor} + \dot{\mathcal{W}}\_{p} + \dot{\mathcal{W}}\_{A} \tag{15}
$$

The auxiliary power is estimated as 10% of the compressor power, therefore, 0.1 *W W <sup>A</sup>* <sup>=</sup> *motor* . The second term in Eq. 15 is the pumping power that is related to the chilled water flow rate and the pressure drop across the cooling coil, so that:

$$\dot{\mathcal{W}}\_p = \dot{m}\_{cw} \upsilon\_f \left(\Delta P\right) / \eta\_{pump} \tag{16}$$

The minimum energy utilized by the refrigerant compressor is that for the isentropic compression process (*a-bs*), Fig 1.c. The actual power includes losses due to mechanical transmission, inefficiency in the drive motor converting electrical to mechanical energy and the volumetric efficiency, Dossat (1997). The compressor electric motor work is related to the refrigerant enthalpy change as

$$
\dot{\mathcal{W}}\_{\text{motor}} = \frac{\dot{m}\_r \left(h\_b - h\_a\right)\_r}{\eta\_{cu}} \tag{17}
$$

The subscript *r* indicates refrigerant and η*eu* known as the energy use factor; \* \* η*eu m el vo* =ηηη . The quantities on the right hand side are the compressor mechanical, electrical and volumetric efficiencies respectively. η*eu* is usually determined by manufacturers and depends on the type of the compressor, the pressure ratio ( *P P b a* / ) and the motor power. For the present analysis η*eu* is assumed 85%.

Cleland *et al* (2000) developed a semi-empirical form of Equation 17 to calculate the compressor's motor power usage in terms of the temperatures of the evaporator and condenser in the refrigeration cycle, *Te* and *Tc* respectively as;

$$\dot{W}\_{\text{motor}} = \frac{\dot{m}\_r \left(h\_a - h\_d\right)\_r}{\frac{T\_c}{\left(T\_c - T\_c\right)} \left(1 - a\,\mathrm{x}\right)^n \eta\_{eu}}\tag{18}$$

In this equation, α is an empirical constant that depends on the type of refrigerant and *x* is the quality at state *d*, Fig 1.c. The empirical constant is 0.77 for R-22 and 0.69 for R-134a Cleland *et al* (2000). The constant *n* depends on the number of the compression stages; for a simple refrigeration cycle with a single stage compressor *n* = 1. The nominator of Eq. 18 is the evaporator capacity, *Qe r*, and the first term of the denominator is the coefficient of performance of an ideal refrigeration cycle. Equations 2, 5 and 18 could be solved for the power usages by the different components of the coupled GT-refrigeration system to estimate the increase in the power output as function of the air intake conditions. Follows is a thermodynamics second law analysis to estimate the effect of irreversibilities on the power gain and efficiency.

Energy, Exergy and Thermoeconomics

ϕ

heat to the combustion chamber

Typical values of

*Gas turbine* 

*Chiller compressor*

*Chiller Condenser* 

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 79

( ) 4 4

= ++ <sup>−</sup>

3 3

*W WI eff t t t* , = − (26)

*ref comp r o b a I m T (s s )* = − (27)

(25)

1

*gasturbine a* 1 ω *o pg <sup>g</sup> T P I m f Tc n Rn T P*

for some industrial fuels are given by Jassim *et al,* 2009, the effective

*Q QI eff comb comb comb* , = + (24)

### **3. Exergy analysis**

In general, the expression for the exergy destruction, (Kotas 1995), is.

$$\dot{\mathbf{I}} = \mathbf{T}\_o \left[ \left( \dot{\mathbf{S}}\_{\rm out} - \dot{\mathbf{S}}\_{\rm in} \right) - \sum\_{i=1}^{n} \frac{\dot{\mathbf{Q}}\_i}{\mathbf{T}\_i} \right] \ge 0 \tag{19}$$

and the exergy balance for any component of the coupled GT and refrigeration cooling cycle (Fig.1) is expressed as;

$$
\dot{E}\_{in} + \dot{E}^Q = \dot{E}\_{out} + \dot{V}\dot{V} + \dot{I} \tag{20}
$$

Various amounts of the exergy destruction terms due to irreversibility for each component in the gas turbine and the proposed air cooling system are given in final expressions, Table 1. Details of derivations can be found in Jassim, *et al* (2005 & 2009) and Khir *et.al* 2007.

( ) <sup>n</sup>

<sup>Q</sup> IT S S 0

and the exergy balance for any component of the coupled GT and refrigeration cooling cycle

Various amounts of the exergy destruction terms due to irreversibility for each component in the gas turbine and the proposed air cooling system are given in final expressions, Table 1. Details of derivations can be found in Jassim, *et al* (2005 & 2009) and Khir *et.al* 2007.

( ) 2 2

= + <sup>−</sup>

1 *comp air a 1 o pa <sup>a</sup> T P I m <sup>ω</sup> Tc n Rn*

( )

1 ω

1

*T S o o* Δ = rate of exergy loss in combustion or reaction ( ) 1 = ×× − *m f NCV <sup>a</sup>*

1

*comb chamber a o o o pa a*

*I mT T S*

( )

1 ω

1 1

*W WI eff comp comp comp* , = + (22)

ϕ

(23)

*T P* 

(21)

3 3

*o o*

2 2

*o o*

*pg g*

*T P f c n Rn T P*

= + Δ + − 

+ + − −

*T P c n Rn T P*

= −− ≥

o out in

i

(19)

*<sup>Q</sup> E E E WI in* += ++ *out* (20)

i 1 i

<sup>=</sup> T

In general, the expression for the exergy destruction, (Kotas 1995), is.

**3. Exergy analysis** 

(Fig.1) is expressed as;

 *Air Compressor*

Air compressor process 1-2, Fig. 1-b

 *Combustion chamber* 

,

Energy, Exergy and Thermoeconomics

,sup *P evap I*

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 81

*sw*

(33)

*evap evap evap III* Δ Δ = + (34)

*evap evap sat evap II I* ΔΔ Δ = + (35)

*P evap sat I* <sup>Δ</sup> ,

( ) *<sup>T</sup> a d*

The refrigerant flow in the evaporator is divided into two regimes saturation(two phase) and superheated regions. The two phase (saturation) region, and superheated vapor region for which the exergy destruction due to flow pressure losses in each region are ,

<sup>Δ</sup> see Khir *et al* 2007. The exergy destruction rate is the sum of the thermal and

*T P*

*PP P*

Table 1. Exergy destruction terms for the individual components of the GT and coupled

The increase in the power output due to intake air cooling will add to the revenue of the GT plant but will partially offset by the increase of the annual payments associated with the installation, personnel and utility expenditures for the operation of that system. For a cooling unit that includes a water chiller, the increase in expenses include the capital installments for the chiller, ( ) *<sup>c</sup> Cch* , and cooling coil, ( ) *<sup>c</sup> Ccc* . The annual operation expenses is a function of the operation period, *op t* , and the electricity rate. If the chiller consumes electrical power *Wel ch* , and the electricity rate is *Cel* (\$/kWh) then the total annual expenses

op t

0

total investment gives the annual payment necessary to payback the investment after a

The chiller's purchase cost may be estimated from venders data or mechanical equipment cost index; this cost is related to the chiller's capacity, *Qe r*, (kW). For a particular chiller size and method of construction and installation; the capital cost is usually given by

> *<sup>c</sup> C Q ch ch e r* = α

el el,ch

( )

,

C W dt *cc c C aC C total ch cc* = ++ (\$/y) (36)

, which when multiplied by the

*<sup>m</sup>* , of the chiller capital

(37)

α

*n n i1 i 1i 1* <sup>+</sup> <sup>=</sup> + −

, ,sup

*h h I m T (s s ) <sup>T</sup>* <sup>Δ</sup> <sup>−</sup> = −−

*evap r o a d*

pressure loss terms for both regimes (Eqs. 34 and 35) as,

In equation 36, the capital recovery factor *<sup>c</sup> <sup>a</sup>* ( )

For simplicity, the maintenance expenses are assumed as a fraction,

cost, therefore, the total chiller cost is expressed as;

cooling chilled water unit, see Figs 1.a-1.c

**4. Economics analysis** 

can be expressed as:

specified period (*n)*.

manufacturers in the following form;

$$\dot{I}\_{cond}^{\Delta T} = \dot{m}\_r \ T\_o \left[ (\mathbf{s}\_c - \mathbf{s}\_b) + \frac{(h\_b - h\_c)}{T\_o} \right] \tag{28}$$

The condenser flow is divided into three regions: superheated vapor region, two phase (saturation) region, and subcooled liquid region for which the exergy destruction due to flow pressure losses in each region are ,sup *P cond I* <sup>Δ</sup> , , *P cond sat I* <sup>Δ</sup> and , *P cond sub I* <sup>Δ</sup> . (Jassim *et al* 2005)

$$
\dot{I}\_{coul}^{\Lambda^p} = \dot{I}\_{coul,sup}^{\Lambda^p} + \dot{I}\_{cond,sat}^{\Lambda^p} + \dot{I}\_{cond,sub}^{\Lambda^p} \tag{29}
$$

$$
\dot{I}\_{cond} = \dot{I}\_{cond}^{\Delta T} + \dot{I}\_{cond}^{\Delta P} \tag{30}
$$

$$\dot{I}\_{evap}^{\Delta T} = \dot{m}\_r \ T\_o \left[ (\mathbf{s}\_a - \mathbf{s}\_d) - \frac{(h\_a - h\_d)}{T\_{sw}} \right] \tag{33}$$

The refrigerant flow in the evaporator is divided into two regimes saturation(two phase) and superheated regions. The two phase (saturation) region, and superheated vapor region for which the exergy destruction due to flow pressure losses in each region are , *P evap sat I* <sup>Δ</sup> , ,sup *P evap I* <sup>Δ</sup> see Khir *et al* 2007. The exergy destruction rate is the sum of the thermal and pressure loss terms for both regimes (Eqs. 34 and 35) as,

$$
\dot{I}\_{cvap} = \dot{I}\_{cvap}^{\Lambda T} + \dot{I}\_{cvap}^{\Lambda P} \tag{34}
$$

$$
\dot{I}\_{evap}^{\Lambda p} = \dot{I}\_{evap,sat}^{\Lambda p} + \dot{I}\_{evap,sup}^{\Lambda p} \tag{35}
$$

Table 1. Exergy destruction terms for the individual components of the GT and coupled cooling chilled water unit, see Figs 1.a-1.c

### **4. Economics analysis**

80 Efficiency, Performance and Robustness of Gas Turbines

( ) *<sup>T</sup> b c*

The condenser flow is divided into three regions: superheated vapor region, two phase (saturation) region, and subcooled liquid region for which the exergy destruction due to

> *P cond sat I*

,sup , ,

*T P*

<sup>Δ</sup> , ,

*PP P P cond cond cond sat cond sub II I I*

( )( ) 1 o1 1 ss *cooling coil a <sup>o</sup> out I mT Q* = + −+ ω

*h h I m T (s s ) <sup>T</sup>* <sup>Δ</sup> − = −+

*o*

<sup>Δ</sup> and ,

(28)

*P cond sub I*

ΔΔ Δ Δ = ++ (29)

*cond cond cond III* Δ Δ = + (30)

(31)

[ ] exp *ro d c I m T (s s )* = − (32)

<sup>Δ</sup> . (Jassim *et al* 2005)

*cond r o c b*

*P cond I*

flow pressure losses in each region are ,sup

*Chiller cooling coil*

*Expansion valve*

*Refrigerant evaporator*

The increase in the power output due to intake air cooling will add to the revenue of the GT plant but will partially offset by the increase of the annual payments associated with the installation, personnel and utility expenditures for the operation of that system. For a cooling unit that includes a water chiller, the increase in expenses include the capital installments for the chiller, ( ) *<sup>c</sup> Cch* , and cooling coil, ( ) *<sup>c</sup> Ccc* . The annual operation expenses is a function of the operation period, *op t* , and the electricity rate. If the chiller consumes electrical power *Wel ch* , and the electricity rate is *Cel* (\$/kWh) then the total annual expenses can be expressed as:

$$\mathbf{C}\_{\text{total}} = a^c \left[ \mathbf{C}\_{\text{ch}}^c + \mathbf{C}\_{\text{cc}}^c \right] + \int\_0^{t\_{\text{op}}} \mathbf{C}\_{\text{el}} \dot{\mathbf{W}}\_{\text{el,ch}} \, \mathbf{d}t \tag{36}$$

In equation 36, the capital recovery factor *<sup>c</sup> <sup>a</sup>* ( ) ( ) *n n i1 i 1i 1* <sup>+</sup> <sup>=</sup> + − , which when multiplied by the

total investment gives the annual payment necessary to payback the investment after a specified period (*n)*.

The chiller's purchase cost may be estimated from venders data or mechanical equipment cost index; this cost is related to the chiller's capacity, *Qe r*, (kW). For a particular chiller size and method of construction and installation; the capital cost is usually given by manufacturers in the following form;

$$\mathbf{C}\_{ch}^{c} = \mathbf{a}\_{ch}^{\prime} \ \dot{\mathbf{Q}}\_{e,r} \tag{37}$$

For simplicity, the maintenance expenses are assumed as a fraction, α *<sup>m</sup>* , of the chiller capital cost, therefore, the total chiller cost is expressed as;

Energy, Exergy and Thermoeconomics

ω ω

the air, *m m w ao* = − ( )

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 83

( ) 1 , ( ) *Q m h h mh mc T T cc a o w w cw w eff cc chwr chws* = −− =

where, *mcw* is the chilled water mass flow rate and *mw* is the rate of water extraction from

compared to the first and can be neglected, McQuiston *et al* (2005).

Fig. 2. Temperature levels for the three working fluids, not to scale

Fig. 3. Moist air cooling process before GT compressor intake

ε− (44)

<sup>1</sup> . The second term in equation 44 is usually a small term when

$$\mathbf{C}\_{ch}^{\epsilon} = \alpha\_{ch} \left( \mathbf{1} + \alpha\_{m} \right) \dot{Q}\_{\epsilon, r} \qquad \text{(\\$)}\tag{38}$$

Similarly, the capital cost of a particular cooling coil is given by manufacturers in terms of the cooling capacity that is directly proportional to the total heat transfer surface area ( *Acc* , m2) Kotas (1995) as;

$$\mathbf{C}\_{\alpha}^{\circ} = \mathcal{B}\_{\alpha} \left( A\_{\alpha} \right)^{w} \qquad \text{ (\\$)}\tag{39}$$

In equation 39, β*cc* and *m* depend on the type of the cooling coil and material. For the present study and local Saudi market, β*cc* = 30000 and *m* = 0.582 are recommended (York Co consultation, 2009). Substituting equations 38 and 39 into Eq. 36, assuming for simplicity that the chiller power is an average constant value and constant electricity rate over the operation period, the annual total expenses for the cooling system become;

$$\mathbf{C}\_{\text{total}} = a^{\varepsilon} \left[ \alpha\_{\text{ch}} \left( \mathbf{1} + \alpha\_{\text{m}} \right) \dot{Q}\_{\varepsilon,r} + \mathcal{B}\_{\text{cl}} \left( A\_{\text{cc}} \right)^{\text{m}} \right] + t\_{\text{op}} \mathbf{C}\_{\text{cl}} \dot{W}\_{\text{cl,ch}} \tag{40} \tag{40}$$

In Eq. 40 the heat transfer area *Acc* is the parameter used to evaluate the cost of the cooling coil. Energy balance on both the cooling coil and the refrigerant evaporator, taking into account the effectiveness factors for the evaporator, *eff er* , ε , and the cooling coil, *eff cc* , ε, gives

$$A\_{cc} = \frac{\dot{Q}\_{cc}}{\mathcal{U}\Delta T\_m F \varepsilon\_{\text{eff,cc}}} = \frac{\dot{Q}\_{e,r} \,\mathcal{E}\_{c\text{fl},cr}}{\mathcal{U}\Delta T\_m F} \tag{41}$$

Where, *U* is the overall heat transfer coefficient for chilled water-air tube bank heat exchanger. Gareta*, et al* (2004) suggested a moderate value of 64 W/m2 K and 0.98 for the correction factor *F*.

Figure 2, illustrates the temperature variations in the combined refrigerant, water chiller and air cooling system. the mean temperature difference for the cooling coil (air and chilled water fluids) is;

$$
\Delta T\_m = \frac{\left(T\_o - T\_{\text{chuv}}\right) - \left(T\_1 - T\_{\text{chus}}\right)}{\ell m \left(\left(T\_o - T\_{\text{chuv}}\right) \Big/ \left(T\_1 - T\_{\text{chus}}\right)\right)}\tag{42}
$$

Equations 39 and 41 give the cooling coil cost as,

$$\mathbf{C}\_{cc}^{c} = \mathcal{B}\_{cc} \left( \frac{\dot{\mathbf{Q}}\_{cc}}{\mathcal{U} \Delta T\_{w} F} \right)^{m} \tag{43}$$

where, *Qcc* is the thermal capacity of the cooling coil. The atmospheric air enters at *To* and ω*<sup>o</sup>* and leaves the cooling coil to enter the air compressor intake at *T*1 and *ω<sup>1</sup>* , Fig.1.a. Both *T*<sup>1</sup> and *ω1* depend on the chilled water supply temperature (*Tchws*) and mass flow rate, *mcw* . When the outer surface temperature of the cooling coil falls below the dew point (corresponding to the partial pressure of the water vapor) the water vapor condensates and leaves the air stream. This process may be treated as a cooling-dehumidification process as illustrated in Figure 3. Steady state heat balance of the cooling coil gives;

(\$) (38)

(\$) (39)

*cc* = 30000 and *m* = 0.582 are recommended (York Co

, and the cooling coil, *eff cc* ,

− − (42)

(43)

ε

, gives

(41)

( ) , 1 *<sup>c</sup> C Q ch ch m e r* = + α

( ) *<sup>c</sup> <sup>m</sup> C A cc cc cc* = β

β

operation period, the annual total expenses for the cooling system become;

αα

*cc*

*<sup>Q</sup> <sup>A</sup> U TF*ε

<sup>=</sup> <sup>Δ</sup>

account the effectiveness factors for the evaporator, *eff er* ,

Equations 39 and 41 give the cooling coil cost as,

m2) Kotas (1995) as;

In equation 39,

correction factor *F*.

water fluids) is;

where, *Qcc*

ω

β

present study and local Saudi market,

*C a total*

 α

Similarly, the capital cost of a particular cooling coil is given by manufacturers in terms of the cooling capacity that is directly proportional to the total heat transfer surface area ( *Acc* ,

consultation, 2009). Substituting equations 38 and 39 into Eq. 36, assuming for simplicity that the chiller power is an average constant value and constant electricity rate over the

( ) () , , <sup>1</sup> *<sup>c</sup> <sup>m</sup>*

In Eq. 40 the heat transfer area *Acc* is the parameter used to evaluate the cost of the cooling coil. Energy balance on both the cooling coil and the refrigerant evaporator, taking into

,

Where, *U* is the overall heat transfer coefficient for chilled water-air tube bank heat exchanger. Gareta*, et al* (2004) suggested a moderate value of 64 W/m2 K and 0.98 for the

Figure 2, illustrates the temperature variations in the combined refrigerant, water chiller and air cooling system. the mean temperature difference for the cooling coil (air and chilled

<sup>Δ</sup>*Tm* <sup>=</sup> ( )( )

*c cc cc cc*

*<sup>Q</sup> <sup>C</sup>*

β

illustrated in Figure 3. Steady state heat balance of the cooling coil gives;

( ) ( )( ) 1 1

*m*

is the thermal capacity of the cooling coil. The atmospheric air enters at *To* and

*U TF*

<sup>=</sup> <sup>Δ</sup>

*<sup>o</sup>* and leaves the cooling coil to enter the air compressor intake at *T*1 and *ω<sup>1</sup>* , Fig.1.a. Both *T*<sup>1</sup> and *ω1* depend on the chilled water supply temperature (*Tchws*) and mass flow rate, *mcw* . When the outer surface temperature of the cooling coil falls below the dew point (corresponding to the partial pressure of the water vapor) the water vapor condensates and leaves the air stream. This process may be treated as a cooling-dehumidification process as

*m*

*o chwr chws o chwr chws*

*TT TT nT T T T* − −−

*m eff cc*

*cc*

ε

*Q*

<sup>=</sup> *er e* , , *ff er*

 β*ch m e r cc cc o Q A tCW <sup>p</sup> el el ch* = ++ +

*cc* and *m* depend on the type of the cooling coil and material. For the

(\$/y) (40)

*m*

*U TF* ε

Δ

$$
\dot{Q}\_{cc} = \dot{m}\_a \left( h\_o - h\_1 \right) - \dot{m}\_w \, h\_w = \dot{m}\_{cw} c\_w \, c\_{\text{eff,cc}} \left( T\_{c\text{hvar}} - T\_{\text{chw}} \right) \tag{44}
$$

where, *mcw* is the chilled water mass flow rate and *mw* is the rate of water extraction from the air, *m m w ao* = − ( ) ω ω<sup>1</sup> . The second term in equation 44 is usually a small term when compared to the first and can be neglected, McQuiston *et al* (2005).

Fig. 2. Temperature levels for the three working fluids, not to scale

Fig. 3. Moist air cooling process before GT compressor intake

Energy, Exergy and Thermoeconomics

economics analysis).

intake (*T1* and

cooling system:

**5.2 Exrgetic efficiency** 

and

to total rate of exergy input( ) *Ein*

**5.1 First law efficiency** 

ω

**5. Evaluation criteria of GT-cooling system** 

*PGR*

*TEC*

η

as;

and heat terms in Table 1, can be expressed in the following forms,

proposed in AlHazmy *et al* (2006) is defined as

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 85

In order to evaluate the feasibility of a cooling system coupled to a GT plant, the performance of the plant is examined with and without the cooling system. In the present study it is recommended to consider the results of the three procedures (energy, exergy and

In general, the net power output of a complete system is given in Eq. 2 in terms of , *WW W t comp* , and *el ch* . The three terms are functions of the air properties at the compressor

present analysis considers the "*power gain ratio*" (*PGR*), a broad term suggested by AlHazmy *et al* (2006) that takes into account the operation parameters of the GT and the associated

*net without cooling*

For a stand-alone GT, *PGR* = 0. Thus, the *PGR* gives the percentage enhancement in power generation by the coupled system. The thermal efficiency of the system is an important parameter to describe the input-output relationship. The *thermal efficiency change factor* (*TEC*)

*cy without cooling*

Exergetic efficiency is a performance criterion for which the output is expressible in terms of exergy. Defining the exergetic efficiency ηex , as a ratio of total rate of exergy output ( ) *Eout*

*out*

*in E <sup>η</sup> <sup>E</sup>* <sup>=</sup>

The exergy balance for the gas turbine and the water chiller system, using the effective work

In analogy with the energy efficiency the exergetic efficiency for a GT-refrigeration unit is:

*ex*

 η

<sup>−</sup> = ×

100% *net withcooling net without cooling*

100% *cy withcooling cy without cooling*

, , ,

, , ,

η

*W W*

*W*

<sup>1</sup> ), which in turn depend on the performance of the cooling system. The

(50)

<sup>−</sup> = × (51)

*EW W W out eff t eff comp eff Chiller* =− − ,, , (53)

*EQ Q in eff comb eff cc* = − , , (54)

(52)

In equation 44 the enthalpy and temperature of the air leaving the cooling coil (*h1* and *T1*) may be calculated from;

$$h\_1 = h\_o - \mathbb{C}F\left(h\_o - h\_s\right) \tag{45}$$

$$T\_1 = T\_o - \mathbb{C}F\left(T\_o - T\_s\right) \tag{46}$$

The contact factor *CF* is defined as the ratio between the actual air temperature drop to the maximum, at which the air theatrically leaves at the coil surface temperature *Ts* = *Tchws* and 100% relative humidity. Substituting for *h1* from Eq. 45 into Eq. 44 and use Eq. 41 gives;

$$\dot{Q}\_{e,r} = \frac{\dot{m}\_a \left\lfloor \text{CF} \left( h\_o - h\_{\text{clus}} \right) - \left( o\_o - o\_1 \right) h\_w \right\rfloor}{\mathcal{E}\_{\text{eff},cr} \ \mathcal{E}\_{\text{eff},cc}} \tag{47}$$

Equations 40 through 47 give the chiller and cooling coil annual expenses in terms of the air mass flow rate and properties. The total annual cost function is derived from Eq. 40 as follows.

### **4.1 Annual cost function**

Combining equations 40 and 41, substituting for the cooling coil surface area, pump and auxiliary power gives the total annual cost in terms of the evaporator capacity*Qer* , as,

$$\mathbf{C}\_{total} = \begin{bmatrix} a^c \left[ \alpha\_{ch} \left( 1 + \alpha\_{w} \right) \dot{\mathbf{Q}}\_{cr} + \mathcal{J}\_{cc} \left( \frac{\dot{\mathbf{Q}}\_{cr} \mathcal{E}\_{\text{eff},cr} \,\mathcal{E}\_{\text{eff},cc}}{U \Delta T\_{m} F} \right)^m \right] + \\\\ t\_{op} \,\dot{\mathbf{Q}}\_{cr} \,\mathbf{C}\_{cl} \left[ \left( \frac{1.1 \left( T\_c - T\_s \right)}{T\_c \left( 1 - \alpha x \right)^n \eta\_{cu}} \right) + \left( \frac{\mathcal{E}\_{\text{eff},cr} \,\nu\_f \left( \Delta P \right)}{c\_{p,w} \,\Delta T\_{c,w} \eta\_{pump}} \right) \right] \end{bmatrix} \tag{48}$$

The first term in Eq. 48 is the annual fixed charges of the refrigeration machine and the surface air cooling coil, while the second term is the operation expenses that depend mainly on the electricity rate. If the water pump's power is considered small compared to the compressor power, the second term of the operation charges can be dropped. If the evaporator capacity *Qer* is replaced by the expression in Eq. 47, the cost function, in terms of the primary parameters, becomes;

$$\begin{aligned} \text{C}\_{\text{total}} &= \left[ \frac{\dot{m}\_{s} \left[ \text{CF} \left( h\_{\text{b}} - h\_{\text{dus}} \right) - \left( \alpha\_{\text{b}} - \alpha\_{\text{l}} \right) h\_{w} \right]}{\mathcal{E}\_{\text{eff},w} \, \mathcal{E}\_{\text{eff},w}} \right] \Bigg| \begin{aligned} &a^{c} \\ &\left[ \left( \frac{\dot{m}\_{s} \left( 1 + \alpha\_{w} \right) + \beta\_{c} \left( \frac{\mathcal{E}\_{\text{eff},w} \, \mathcal{E}\_{\text{eff},w}}{\text{UI} \, \Delta T\_{w} \text{F}} \right)^{n}}{\left( \text{I} \, \text{av}\_{\text{eff},w} \right) - \left( \alpha\_{\text{b}} - \alpha\_{\text{l}} \right) h\_{w}} \right]^{n+1} \Bigg] \\ &+ t\_{op} \, \mathcal{C}\_{\text{cl}} \left[ \left( \frac{\mathcal{I} \, \text{I} \, \text{I} \, \text{T}\_{c} - \text{T}\_{c}}{\left( \text{T}\_{c} \right) \left( \text{I} - \text{ax} \right) \, \text{\eta}\_{\text{av}}} \right) + \left( \frac{\mathcal{E}\_{\text{eff},w} \, \mathcal{V}\_{\text{f}} \left( \Delta P \right)}{\mathcal{E}\_{\text{pr},w} \, \Delta T\_{w} \text{F}\_{\text{th},w}} \right) \right] \end{aligned} \tag{49}$$

## **5. Evaluation criteria of GT-cooling system**

In order to evaluate the feasibility of a cooling system coupled to a GT plant, the performance of the plant is examined with and without the cooling system. In the present study it is recommended to consider the results of the three procedures (energy, exergy and economics analysis).

### **5.1 First law efficiency**

84 Efficiency, Performance and Robustness of Gas Turbines

In equation 44 the enthalpy and temperature of the air leaving the cooling coil (*h1* and *T1*)

The contact factor *CF* is defined as the ratio between the actual air temperature drop to the maximum, at which the air theatrically leaves at the coil surface temperature *Ts* = *Tchws* and 100% relative humidity. Substituting for *h1* from Eq. 45 into Eq. 44 and use Eq. 41 gives;

,

*e r*

*Q*

( )( ) <sup>1</sup>

ω ω

− −− <sup>=</sup> (47)

, ,

*m*

ε ν

is replaced by the expression in Eq. 47, the cost function, in terms of

( )

 αβ

*ch m cc <sup>m</sup> <sup>c</sup>*

1

α

1 1

*op el n*

*c e eff er f*

ε ε

*T T P*

*p w ch w pump e eu*

*T x c T*

+ + <sup>+</sup> <sup>Δ</sup> <sup>=</sup> <sup>−</sup> <sup>Δ</sup> <sup>+</sup> <sup>−</sup> <sup>Δ</sup>

, , ,

, , *a o chws o w*

*eff er eff cc*

*m CF h h h*

ε ε

Equations 40 through 47 give the chiller and cooling coil annual expenses in terms of the air mass flow rate and properties. The total annual cost function is derived from Eq. 40 as

Combining equations 40 and 41, substituting for the cooling coil surface area, pump and

( ) ( )

The first term in Eq. 48 is the annual fixed charges of the refrigeration machine and the surface air cooling coil, while the second term is the operation expenses that depend mainly on the electricity rate. If the water pump's power is considered small compared to the compressor power, the second term of the operation charges can be dropped. If the

α η

, , , ,

*t C*

*eff er eff cc eff er eff cc*

*a o chws o w a o chws o w*

 − −− − −− <sup>=</sup> 

*a m CF h h h m CF h h h*

*c er eff er eff cc*

 β

*<sup>Q</sup> a Q U TF*

auxiliary power gives the total annual cost in terms of the evaporator capacity*Qer*

1.1 1

*op er el n*

*ch m er cc*

( )

1

αα

*t QC*

( )( )

ε ε ω ω

( ) <sup>1</sup> *o os h h CF h h* =− − (45)

( ) *T T CF T T* <sup>1</sup> =− − *o os* (46)

( )

η

( )( )

ε ε

+ + <sup>×</sup>

*c e eff,*

, ,

*eff er eff cc*

*U TF*

Δ

ω ω *m*

( )

*1.1 T T ε*

*e eu*

*T 1 αx η*

−

ε ε

( )( )

<sup>−</sup> + +

*m*

, as,

(48)

1

+

(49)

−

*m*

( ) *er f p,w ch,w p ν ΔP c ΔT η*

may be calculated from;

follows.

**4.1 Annual cost function** 

evaporator capacity *Qer*

*total*

*C*

the primary parameters, becomes;

*total*

*C*

In general, the net power output of a complete system is given in Eq. 2 in terms of , *WW W t comp* , and *el ch* . The three terms are functions of the air properties at the compressor intake (*T1* andω<sup>1</sup> ), which in turn depend on the performance of the cooling system. The present analysis considers the "*power gain ratio*" (*PGR*), a broad term suggested by AlHazmy *et al* (2006) that takes into account the operation parameters of the GT and the associated cooling system:

$$PGR = \frac{\dot{\mathcal{W}}\_{\text{net, without cooling}} - \dot{\mathcal{W}}\_{\text{net, without cooling}}}{\dot{\mathcal{W}}\_{\text{net, without cooling}}} \times 100\,\% \tag{50}$$

For a stand-alone GT, *PGR* = 0. Thus, the *PGR* gives the percentage enhancement in power generation by the coupled system. The thermal efficiency of the system is an important parameter to describe the input-output relationship. The *thermal efficiency change factor* (*TEC*) proposed in AlHazmy *et al* (2006) is defined as

$$TEC = \frac{\eta\_{cy, without cooling} - \eta\_{cy, without cooling}}{\eta\_{cy, without cooling}} \times 100\% \tag{51}$$

### **5.2 Exrgetic efficiency**

Exergetic efficiency is a performance criterion for which the output is expressible in terms of exergy. Defining the exergetic efficiency ηex , as a ratio of total rate of exergy output ( ) *Eout* to total rate of exergy input( ) *Ein* as;

$$
\eta\_{ex} = \frac{\dot{E}\_{out}}{\dot{E}\_{in}} \tag{52}
$$

The exergy balance for the gas turbine and the water chiller system, using the effective work and heat terms in Table 1, can be expressed in the following forms,

$$
\dot{E}\_{\text{out}} = \dot{\mathsf{V}}\_{\text{eff},t} - \dot{\mathsf{V}}\_{\text{eff,comp}} - \dot{\mathsf{V}}\_{\text{eff,Chiller}} \tag{53}
$$

and

$$
\dot{E}\_{in} = \dot{Q}\_{\text{eff,comb}} - \dot{Q}\_{\text{eff,cc}} \tag{54}
$$

In analogy with the energy efficiency the exergetic efficiency for a GT-refrigeration unit is:

Energy, Exergy and Thermoeconomics

**6. Results and discussion** 

20

25

30

35

*Ambient Temp.*

*RH %*

40

**Ambient Temp. [C]**

45

50

55

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 87

The performance of the GT with water chiller cooler and its economical feasibility are

longitude 38o E) where a HITACH FS-7001B model GT plant is already connected to the main electric grid. Table 2 lists the main specs of the selected GT plant. The water chiller capacity is selected on basis of the maximum annual ambient temperature at the site. On August 18th, 2008, the dry bulb temperature (DBT) reached 50oC at 14:00 O'clock and the relative humidity was 84% at dawn time. The recorded hourly variations in the DBT (*To*) and *RHo* are shown in Figure 4 and the values are listed in Table 2. Eq. 47 gives the evaporator capacity of the water chiller (Ton Refrigeration) as function of the DBT and *RH*. Figure 5 shows that if the chiller is selected based on the maximum DBT = 50oC and RH = 18%, (the data at 14: O'clock), its capacity would be 2200 Ton. Another option is to select the chiller capacity based on the maximum *RHo* (*RHo* = 0.83 and *To* = 28.5oC, 5:00 data), which gives 3500 Ton. It is more accurate, however, to determine the chiller capacity for the available climatic data of the selected day and determine the maximum required capacity, as seen in Fig. 6; for the weather conditions at Yanbu City, a chiller capacity of 4200 Ton is selected it is the largest chiller capacity ( ) *Qe r*, to handle the worst scenario as shown in Fig. 6.

Fig. 4. Ambient temperature variation and *RH* for 18th of August 2008 of Yanbu Industrial City

**hour [hr]**

0 2 4 6 8 10 12 14 16 18 20 22 24

Equations 45 and 46 are employed to give the air properties leaving the cooling coil, assuming 0.5 contact factor and a chilled water supply temperature of 5oC. All thermophysical properties are determined to the accuracy of the Engineering Equation Solver (EES)

*out out els withcooling without cooling* = − *E E C dt* (61)

N and

0

0.2

0.4

*RHo [%]*

0.6

0.8

1

*Revenueeff* ( ) () ()

investigated. The selected site is the Industrial City of Yanbu (Latitude 24o 05'

0

*op t*

$$\eta\_{c\mathbf{x},c} = \frac{\dot{\mathcal{W}}\_{\rm eff,t} - \dot{\mathcal{W}}\_{\rm eff,comp} - \dot{\mathcal{W}}\_{\rm eff,hiller}}{\dot{\mathcal{Q}}\_{\rm eff,courb} - \dot{\mathcal{Q}}\_{\rm eff,cc}} \tag{55}$$

For the present analysis let us define dimensionless terms as the e*xergetic power gain ratio*  (*PGRex*) and *exergetic thermal efficiency change* (*TECex*):

$$\text{PGR}\_{\text{ex}} = \frac{\left(\dot{E}\_{\text{out}}\right)\_{\text{withcooling}} - \left(\dot{E}\_{\text{out}}\right)\_{\text{without cooling}}}{\left(\dot{E}\_{\text{out}}\right)\_{\text{without cooling}}} \times 100\text{ }\% \tag{56}$$

and

$$TEC\_{cc} = \frac{\eta\_{cc,c} - \eta\_{cc,nc}}{\eta\_{cc,nc}} \times 100\,\%\tag{57}$$

Equations 50, 51, 56 and 57 can be easily employed to appraise the changes in the system performance, but they are not sufficient for a complete evaluation of the cooling method, the economics assessement of installing a cooling system follows.

### **5.3 System profitability**

To investigate the economic feasibility of retrofitting a gas turbine plant with an intake cooling system, the total cost of the cooling system is determined (Eq. 32 or Eq. 33). The increase in the *annual* income cash flow from selling the additional electricity generation is also calculated. The annual exported energy by the coupled power plant system is;

$$E\left(k\text{V\!\!\!/}\text{\!\!\!n\text]}\right) = \int\_0^{t\_{op}} \dot{V}\_{\text{net}} dt\tag{58}$$

If the gas turbine's annual electricity generation without the cooling system is *Ewithout cooling* and the cooling system increases the power generation to *Ewith cooling*, then the net increase in revenue due to the addition of the cooling system is:

$$\text{Net revenue} = \left(\mathbf{E}\_{\text{with cooling}} - \mathbf{E}\_{\text{without cooling}}\right) \mathbf{C}\_{\text{ds}} \tag{59}$$

The profitability due to the coupled power plant system is defined as the increase in revenues due to the increase in electricity generation after deducting the expenses for installing and operating the cooling system as:

$$\text{rofitability} \equiv (E\_{\text{with cooling}} - E\_{\text{without cooling}})C\_{\text{ds}} - C\_{\text{total}} \tag{60}$$

The first term in Eq. 60 gives the increase in revenue and the second term gives the annual expenses of the cooling system. The profitability could be either positive, which means an economical incentive for adding the cooling system, or negative, meaning that there is no economical advantage, despite the increase in the electricity generation of the plant.

For more accurate evaluation the irreversibility of the different components are taken into consideration and an effective revenue *(Revenue)eff* is defined by;

$$Reverune\_{\rm eff} = \int\_0^{t\_{\rm TF}} \left( \dot{E}\_{\rm out} \right)\_{\rm without cooling} - \left( \dot{E}\_{\rm out} \right)\_{\rm without cooling} \right) \mathbf{C}\_{ds} \, dt \tag{61}$$

### **6. Results and discussion**

86 Efficiency, Performance and Robustness of Gas Turbines

*WW W Q Q*

For the present analysis let us define dimensionless terms as the e*xergetic power gain ratio* 

− = ×

*out without cooling*

*ex,nc*

Equations 50, 51, 56 and 57 can be easily employed to appraise the changes in the system performance, but they are not sufficient for a complete evaluation of the cooling method, the

To investigate the economic feasibility of retrofitting a gas turbine plant with an intake cooling system, the total cost of the cooling system is determined (Eq. 32 or Eq. 33). The increase in the *annual* income cash flow from selling the additional electricity generation is

0

*Net revenue* = ( ) *EE C with cooling without cooling els* − (59)

If the gas turbine's annual electricity generation without the cooling system is *Ewithout cooling* and the cooling system increases the power generation to *Ewith cooling*, then the net increase in

The profitability due to the coupled power plant system is defined as the increase in revenues due to the increase in electricity generation after deducting the expenses for

rofitability = ( ) *E E CC with cooling without cooling els total* − − (60)

The first term in Eq. 60 gives the increase in revenue and the second term gives the annual expenses of the cooling system. The profitability could be either positive, which means an economical incentive for adding the cooling system, or negative, meaning that there is no

For more accurate evaluation the irreversibility of the different components are taken into

economical advantage, despite the increase in the electricity generation of the plant.

consideration and an effective revenue *(Revenue)eff* is defined by;

*op t E (kWh) W dt* <sup>=</sup> *net*

also calculated. The annual exported energy by the coupled power plant system is;

*η*

− − <sup>=</sup> <sup>−</sup>

() ()

*E E*

*E*

*η η TEC*

*ex*

*ex,c*

η

(*PGRex*) and *exergetic thermal efficiency change* (*TECex*):

*PGR*

and

**5.3 System profitability** 

*ex*

economics assessement of installing a cooling system follows.

revenue due to the addition of the cooling system is:

installing and operating the cooling system as:

*eff,t eff,comp eff,chiller*

(55)

(56)

<sup>−</sup> = × (57)

(58)

*eff,comb eff,cc*

( ) 100% *out out withcooling without cooling*

100% *ex,c ex,nc*

The performance of the GT with water chiller cooler and its economical feasibility are investigated. The selected site is the Industrial City of Yanbu (Latitude 24o 05' N and longitude 38o E) where a HITACH FS-7001B model GT plant is already connected to the main electric grid. Table 2 lists the main specs of the selected GT plant. The water chiller capacity is selected on basis of the maximum annual ambient temperature at the site. On August 18th, 2008, the dry bulb temperature (DBT) reached 50oC at 14:00 O'clock and the relative humidity was 84% at dawn time. The recorded hourly variations in the DBT (*To*) and *RHo* are shown in Figure 4 and the values are listed in Table 2. Eq. 47 gives the evaporator capacity of the water chiller (Ton Refrigeration) as function of the DBT and *RH*. Figure 5 shows that if the chiller is selected based on the maximum DBT = 50oC and RH = 18%, (the data at 14: O'clock), its capacity would be 2200 Ton. Another option is to select the chiller capacity based on the maximum *RHo* (*RHo* = 0.83 and *To* = 28.5oC, 5:00 data), which gives 3500 Ton. It is more accurate, however, to determine the chiller capacity for the available climatic data of the selected day and determine the maximum required capacity, as seen in Fig. 6; for the weather conditions at Yanbu City, a chiller capacity of 4200 Ton is selected it is the largest chiller capacity ( ) *Qe r*, to handle the worst scenario as shown in Fig. 6.

Fig. 4. Ambient temperature variation and *RH* for 18th of August 2008 of Yanbu Industrial City

Equations 45 and 46 are employed to give the air properties leaving the cooling coil, assuming 0.5 contact factor and a chilled water supply temperature of 5oC. All thermophysical properties are determined to the accuracy of the Engineering Equation Solver (EES)

Energy, Exergy and Thermoeconomics

during 18th August 2008 operation

temperature is 45.2oC, and 34% *RH*.

0

2000

4000

6000

8000

10000

**Chiller Cooling Capacity [TR]**

12000

14000

16000

18000

Hour *To*

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 89

0 33.4 0.38 19.2 0.64 12 44.0 0.33 24.5 0.64 1 32.6 0.44 18.8 0.70 13 45.2 0.34 25.1 0.66 2 31.7 0.8 18.35 0.99 14 50.0 0.18 27.5 0.43 3 30.5 0.77 17.75 0.98 15 47.0 0.25 26.0 0.53 4 29.0 0.76 17.0 0.99 16 45.9 0.30 25.45 0.61 5 28.5 0.84 16.75 0.97 17 43.0 0.37 24.0 0.69 6 30.0 0.83 17.5 0.99 18 43.0 0.24 24.0 0.50 7 32.2 0.79 18.6 0.96 19 37.9 0.45 21.45 0.76 8 35.1 0.67 20.05 0.99 20 37.4 0.40 21.2 0.69 9 38.0 0.51 21.5 0.84 21 37.6 0.33 21.3 0.60 10 40.2 0.35 22.6 0.64 22 37.1 0.34 21.05 0.61 11 43.3 0.37 24.15 0.69 23 36.8 0.32 20.90 0.58

Table 3. The ambient conditions and the cooling coil outlet temperature and humidity

Fig. 5. Dependence of chiller cooling capacity on the climatic conditions

20 25 30 35 40 45 50 55 60

*RH=100%*

*80%*

*60 %*

*40 % 20 %*

*Ta,o [C]*

Solution of Equations 50 and 51, using the data in Table 3, gives the daily variation in *PGR* and *TEC,* Figure 7. There is certainly a potential benefit of adding the cooling system where there is an increase in the power output all the time, the calculated average for the design day is 12.25 %. The *PGR* follows the same pattern of the ambient temperature; the increase in power of the GT plant reaches a maximum of 15.46 %, with a little change in the plant thermal efficiency. The practical illustrative application indicates that a maximum decrease in the thermal efficiency change of only 0.391 % occurs at 13:00 PM when the air

*oC RHo T1 oC RH1* Hour *To oC RHo T1 oC RH1*


software [Klein and Alvarado 2004]. The result show that the cooling system decrease the intake air temperature from *To* to *T1* and increases the relative humidity to *RH1* (Table 3).

Table 2. Range of parameters for the present analysis

software [Klein and Alvarado 2004]. The result show that the cooling system decrease the intake air temperature from *To* to *T1* and increases the relative humidity to *RH1* (Table 3).

*Ambient air***,** *Fig. 4*

*Gas Turbine, Model HITACH-FS-7001B*

Volumetric air flow rate 250 m3s-1at NPT Fuel net calorific value, *NCV* 46000 kJ kg-1

*<sup>t</sup>* 0.88

*Generator* 

*Water Chiller* 

85%

Evaporating temperature, *Te T TD chws e* − oC

η*eu*

*Cooling Coil* 

*Economics analysis* 

85%

*<sup>m</sup>* 10% of *<sup>c</sup> Cch*

Ambient air temperature, *To* 28—50 oC Ambient air relative humidity, *RHo* 18% → 84%

Pressure ratio, *P2/P1* 10

Electrical efficiency 95% Mechanical efficiency 90%

Refrigerant R22

Superheat 10 K Condensing temperature, *Tc* To + TDc K Condenser design temperature difference *TDc* 10 K Evaporator design temperature difference TDe 6 K Subcooling 3 K Chilled water supply temperature, *Tchws* 5 oC

ε

Contact Factor, CF 50%

Interest rate *i* 10% Period of repayment (Payback period), *n* 3 years

Electricity rate, *Cel* (Eqs. 33&34) 0.07 \$/kWh Cost of selling excess electricity, *Cels* (Eqs. 40&41) 0.07-0.15 \$/kWh

Hours of operation per year, *op t* 7240 h/y

Net power, ISO Site power

Turbine efficiency,

Turbine inlet temperature *T3*

Air Compressor efficiency

Combustion efficiency

η

Chiller evaporator effectiveness, *eff er* ,

Cooling coil effectiveness *eff cc* ,

The maintenance cost,

α*ch*

Chiller compressor energy use efficiency,

ε

α

Table 2. Range of parameters for the present analysis

η*c*

η*comb* **Parameter Range** 

52.4 MW 37 MW 1273.15 K

0.82 0.85

85% 172 *\$/kW*


Table 3. The ambient conditions and the cooling coil outlet temperature and humidity during 18th August 2008 operation

Solution of Equations 50 and 51, using the data in Table 3, gives the daily variation in *PGR* and *TEC,* Figure 7. There is certainly a potential benefit of adding the cooling system where there is an increase in the power output all the time, the calculated average for the design day is 12.25 %. The *PGR* follows the same pattern of the ambient temperature; the increase in power of the GT plant reaches a maximum of 15.46 %, with a little change in the plant thermal efficiency. The practical illustrative application indicates that a maximum decrease in the thermal efficiency change of only 0.391 % occurs at 13:00 PM when the air temperature is 45.2oC, and 34% *RH*.

Fig. 5. Dependence of chiller cooling capacity on the climatic conditions

Energy, Exergy and Thermoeconomics

result indicate the importance of the second law analysis.

*PGRex*

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 91

Figure 8. shows that the power increase for the worst day of the year that varies between 7% to 10.4% (average 8.5%) and the thermal efficiency drops by a maximum of 6 %. These

Fig. 8. Variation of gas turbine exergetic *PGRex* and *TECex* during 18th August operation

0 2 4 6 8 10 12 14 16 18 20 22 24

(Fig. 7). The variations in *Ctotal* are due to the changes in *Qev*

to 0.15 \$/kWh, nearly double the base tariff.

of the excess electricity generation is higher than the base rate of 0.07 \$/kWh.

( <sup>1</sup> , , *T T o o* ω andω

0

2

4

6

*PGR*

 *%*

8

10

*ex*

12

14

16

18

Based on the daily variation of the ambient conditions on August 18th, assuming different values for selling the electricity (*Cels*), Eq. 59 gives the hourly revenues needed to payback the investment after a specified operation period (selected by 3 years)*.* The different terms in Equations 49 and 59 are calculated and presented in Figure 9. The effect of the climate changes is quite obvious on both the total expenses (Fig. 9) and the GT net power output

**hour [hr]**

*TECex*

same figure, which shows clearly the potential of adding the cooling system. Figure 9 indicates that selling the electricity to the consumers at the same base price (*C C els el* = = 0.07 \$/kWh) makes the cooling system barley profitable. The profit increases directly with the cost of selling the electricity. This result is interesting and encourages the utilities to consider a time-of-use tariff during the high demand periods. The profitability of the system, being the difference between the revenues and the total cost, is appreciable when the selling rate

Economy calculations for one year with 7240 operation hours and for different electricity selling rates are summarized in Table 4. The values show that there is always a net positive profit starting after the payback period for different energy selling prices. During the first 3 years of the cooling system life, there is a net profit when the electricity selling rate increases

<sup>1</sup> ). The revenue from selling additional electricity is also presented in the

in Eq. 49 that depends on




*TEC*

 *%*

*ex*


0.0

2.0

Fig. 6. Chiller capacity variation with the climatic conditions of the selected design day

On basis of the second law analysis the exergetic power gain ratio *PGRex* is still positive meaning that there is increase in output power but at a reduced value than that of the energy analysis.

Fig. 7. Variation of gas turbine *PGR* and *TEC* during 18th August operation

Fig. 6. Chiller capacity variation with the climatic conditions of the selected design day

Fig. 7. Variation of gas turbine *PGR* and *TEC* during 18th August operation

0 2 4 6 8 10 12 14 16 18 20 22 24

**hour [hr]**



0

TEC [%]

0.5

*TEC [%]*

1

1.5

2

energy analysis.

0

2

4

6

8

10

*PGR [%]*

*PGR [%]*

12

14

16

18

0

4204

**Chiller Capacity [TR]**

On basis of the second law analysis the exergetic power gain ratio *PGRex* is still positive meaning that there is increase in output power but at a reduced value than that of the

0 2 4 6 8 10 12 14 16 18 20 22 24

**hour [hr]**

Figure 8. shows that the power increase for the worst day of the year that varies between 7% to 10.4% (average 8.5%) and the thermal efficiency drops by a maximum of 6 %. These result indicate the importance of the second law analysis.

**hour [hr]**

Fig. 8. Variation of gas turbine exergetic *PGRex* and *TECex* during 18th August operation

Based on the daily variation of the ambient conditions on August 18th, assuming different values for selling the electricity (*Cels*), Eq. 59 gives the hourly revenues needed to payback the investment after a specified operation period (selected by 3 years)*.* The different terms in Equations 49 and 59 are calculated and presented in Figure 9. The effect of the climate changes is quite obvious on both the total expenses (Fig. 9) and the GT net power output (Fig. 7). The variations in *Ctotal* are due to the changes in *Qev* in Eq. 49 that depends on ( <sup>1</sup> , , *T T o o* ω andω<sup>1</sup> ). The revenue from selling additional electricity is also presented in the same figure, which shows clearly the potential of adding the cooling system. Figure 9 indicates that selling the electricity to the consumers at the same base price (*C C els el* = = 0.07 \$/kWh) makes the cooling system barley profitable. The profit increases directly with the cost of selling the electricity. This result is interesting and encourages the utilities to consider a time-of-use tariff during the high demand periods. The profitability of the system, being the difference between the revenues and the total cost, is appreciable when the selling rate of the excess electricity generation is higher than the base rate of 0.07 \$/kWh.

Economy calculations for one year with 7240 operation hours and for different electricity selling rates are summarized in Table 4. The values show that there is always a net positive profit starting after the payback period for different energy selling prices. During the first 3 years of the cooling system life, there is a net profit when the electricity selling rate increases to 0.15 \$/kWh, nearly double the base tariff.

Energy, Exergy and Thermoeconomics

irreversibility is the highest.

decrease in thermal efficiency.

**8. Nomenclatures** 

*CF* contact factor *E* energy kWh

output power of the plant and increased revenues.

*Acc* Cooling coil heat transfer area, m2 *<sup>c</sup> Ccc* capital cost of cooling coil (\$)

*<sup>c</sup> Cch* capital cost of chiller (\$) *Cel* unit cost of electricity, \$/kWh *<sup>p</sup> c* specific heat of gases, kJ/kg K

*EES* engineering Equation Solver

*i* interest rate on capital

*hv* specific enthalpy of water vapor in the air, kJ/kg

**7. Conclusions** 

(TEC).

Analysis of Water Chiller Cooler for Gas Turbines Intake Air Cooling 93

Figure 10 shows the effect of irreversibilities on the economic feasibility of using an air cooling system for the selected case. The effective revenue Eq. 61 ( ) Re *eff venue* that can be accumulated from selling the net power output is reduced by 41.8% as a result of irreversibilities. The major contribution comes from the water chiller, where the

There are various methods to improve the performance of gas turbine power plants operating under hot ambient temperatures far from the ISO standards. One proven approach is to reduce the compressor intake temperature by installing an external cooling system. In this paper, a simulation model that consists of thermal analysis of a GT and coupled to a refrigeration cooler, exergy analysis and economics evaluation is developed. The performed analysis is based on coupling the thermodynamics parameters of the GT and cooler unit with the other variables as the interest rate, life time, increased revenue and profitability in a single cost function. The augmentation of the GT plant performance is characterized using the power gain ratio (PGR) and the thermal efficiency change term

The developed model is applied to a GT power plant (HITACHI FS-7001B) in the city of Yanbu (20o 05" N latitude and 38o E longitude) KSA, where the maximum DBT has reached 50oC on August 18th, 2008 The recorded climate conditions on that day are selected for sizing out the chiller and cooling coil capacities. The performance analysis of the GT shows that the intake air temperature decreases by 12 to 22 K, while the PGR increases to a maximum of 15.46%. The average increase in the plant power output power is 12.25%, with insignificant change in plant thermal efficiency. The second law analysis show that the exergetic power gain ratio drops to an average of 8.5% with 6% maximum

In the present study, the profitability resulting from cooling the intake air is calculated for electricity rates between 0.07 and 0.15 \$/kWh and a payback period of 3 years. Cash flow analysis of the GT power plant in the city of Yanbu shows a potential for increasing the

Fig. 9. Variation of hourly total cost and excess revenue at different electricity selling rate


Table 4. Annual net profits out of retrofitting a cooling system to a GT, HITACHI FS-7001B at Yanbu for different product tariff and 3 years payback period

Fig. 10. Effect of irreversibility on the revenue, *Cels* = 0.07 \$/kWh

Figure 10 shows the effect of irreversibilities on the economic feasibility of using an air cooling system for the selected case. The effective revenue Eq. 61 ( ) Re *eff venue* that can be accumulated from selling the net power output is reduced by 41.8% as a result of irreversibilities. The major contribution comes from the water chiller, where the irreversibility is the highest.
