**4. Cost allocation in CPDP utilizing GTCC**

This section develops a mathematical model to evaluate the performance of a typical CPDP using typical GTCC plant and how this performance is affected by parameters such as ambient temperature, compression ratio, air-to-fuel ratio, turbine inlet temperature, and stack temper‐ ature. The fuel consumed by the GT is allocated to each of the products (EP and DW) on the basis of the first and second laws of thermodynamics [30].

Figure 26 shows a schematic diagram of a typical CPDP using GTCC, which is considered as reference plant considered here. The plant's design is based on the data given in Table 4 and 50 o C ambient summer temperature and 600 o C temperature of exhaust gases leaving the GT.


ermally d and fully el type. T y lowerin ual-pressu oximately oiling sec hot gases n dual-pr

y fired. T The singl ng the sta ure desig y unchan ction and s and wa ressure H on refrig

The HRS le-pressu ack tempe gns, lowe nged. A d d generat ater and r HRSG ca geration,

plants or SG can b ure stage erature, a ering stac design p ted steam reduces t an feed th etc.).

r steam t be horizo HRSG h and this r ck tempe parameter m saturat the heat t he steam

turbines ontal or has low requires eratures r of the tion (or transfer turbine

operation

n, three

The fuel

esign is

rature. T ]. plant's de

llow ope

en-cycle

ck temper

re. The p e GT.

and stac

dered her aving the

tack to a

erature,

nt consid gases le


ratio, ai

TCC, whi erature a

h three V

V943A ga

ir-to-fuel

ich is con and 600 o

**Table 4.** Technical specifications of Shuaiba North GTCC power-desalination plant Gas turbines *GE912FA* consumed d by the GT is all located to o each of f the prod ducts (EP P and DW W) on the e basis o of the firs st and sec cond law ws of therm modynam mics [30]

pression

using GT mer tempe

pressure HRSG can feed the steam turbine at a suitable point or it may be used as process

In CPDP, electricity and process heat for desalination are simultaneously produced regardless of gas turbine load; supplementary firing or post-firing (PF) is usually used. In Ras Laffan B CPDP, a very flexible plant design was developed with PF to allow very high thermal power input (maximum 280 MWth) to cope with a wide operational range of GT electrical power and steam production for electricity or desalinated water production. The power island having a total capacity of 1025 MW is equipped with three V943A gas turbines with bypass stack to allow open-cycle operation, three HRSGSs equipped with double PF firing, and two 200 MW range backpressure steam turbines; steam from the power island is fed to four desalination units supplied by Doosan for a total water production of 273,000 m3 per day. Each GT has 310 MW power output at generator terminals, 39.8 % efficiency, and 750 kg/s exhaust gas mass

The HRSGs are of the horizontal gas flow, top supported, natural circulation type, with singlepressure stages, and two-staged supplementary firing. The HRSG steam parameters at full GT load are pressure = 85.4 bar and temperature = 563 °C, 636 t/h nominal, and 703 maximum

The post-firing modified the steam flow as follows: first firing increased the steam flow to nominal 110 t/h and maximum 145 t/h, and second firing increased the steam flow rate to

This section develops a mathematical model to evaluate the performance of a typical CPDP using typical GTCC plant and how this performance is affected by parameters such as ambient temperature, compression ratio, air-to-fuel ratio, turbine inlet temperature, and stack temper‐ ature. The fuel consumed by the GT is allocated to each of the products (EP and DW) on the

Figure 26 shows a schematic diagram of a typical CPDP using GTCC, which is considered as reference plant considered here. The plant's design is based on the data given in Table 4 and

No. of units Fuel type LHV Gross output Ambient temp. Humidity Pressure

No. of units and capacity

3 3 1 % 3×15 MIGD 1 215.7 MW <sup>ο</sup>

HRSG, type: natural circulation Desalination: MSF Steam turbine, ST: BPST

C temperature of exhaust gases leaving the GT.

C 30 % 1.013 bar

Cooling SW temperature

**1**

**19 |** P a g

e

**3** T b v e l w H b a a I ( 2 p H u e T T T i **4** T a c F b

**3.4 He** The HRS bottomin vertical ( efficiency owering would on HRSG is boiling) t area but d at a suitab In CPDP (PF) is us 280 MWt power isl

**eat Reco** SGs utiliz g power Figures 2 y, compa the stea nly decre s the pinc temperatu decreases ble point , electric sually us th) to co land havi

**overy Sy** ze the ho cycle. T 25a–d). A ared to du am pressu ease the ch point ure. The s to a cer t or it ma city and p sed. In R ope with ing a tot

**ystem Ge** ot gases The HRS As given ual-press ure. Low first (low (pp), wh choice o rtain exte ay be use process h Ras Laffa a wide o al capaci

**enerato** leaving SG can b n before, sure HRS wering th w)-stage hich is th of high p ent the H d as proc heat for d an B CPD operation ity of 10

**or (HRSG** the GT be unfire the HRS SG. In sin e steam pressure he tempe pp increa HRSG eff cess steam desalinat DP, a ver nal range 025 MW

**G)** to gener d, supple SG can h ngle-pres pressure e while l erature d ases the m ficiency. m for ind

rate steam ementary have sing ssure HR e lowers leaving t difference mean tem The low dustrial a

m that ca y fired o gle-, dua RSG, high the steam the secon e betwee mperature w-pressur applicatio

an be use r called al-, or trip h efficien m cycle nd state en the ga e differen re (LP) g ons (dryin

ed to op post-fire ple-press ncy is att efficienc condition as leavin nce betw generated ng, desal

erate the ed (PF), sure leve tained by cy. In du ns appro ng the bo ween the h d steam in lination,

es with b

urbine in

nlet temp

ence plan f exhaust

as refere rature of

as turbine

ratio, tu

nsidered C temper

is equipp

ped with

ure, comp

CPDP u ent summ

affected b

by param

meters su

uch as am

mbient te

emperatu

a typical C ambie

gram of a and 50 <sup>o</sup>

atic diag n Table 4

a schem given in

6 shows the data

Figure 26 based on

C

No. of ST Gross capacity, MW

steam for industrial applications (drying, desalination, absorption refrigeration, etc.).

flow rate at 576 °C exhaust gas temperature.

**4. Cost allocation in CPDP utilizing GTCC**

basis of the first and second laws of thermodynamics [30].

3 NG 47,806 kJ/kg 215.5 MW 50 o

C ambient summer temperature and 600 o

HRSG blowdown

steam flow.

156 Desalination Updates

50 o

No. of HRSG Integral type deaerator

nominal 150 t/h and 170 t/h.

Figure 25c c: Ras Laff ffan B HRS SGs [29] **Figure 25.** (a) Vertical and (b) horizontal, HRSG LPEVA arrangement and pinch diagram Figure 25c: Ras Laffan B HRSGs [29] Figure 25d: Ras Laffan longitudinal section, single pressure [29]

nal section

n, single pre

essure [29]

n longitudin

Fig

gure 25d: R

Ras Laffan

**Figure 26.** Mass and heat balance diagram of Shuaiba North GTCC power-desalination plant

#### **4.1. Energy analysis**

An energy analysis, based on the first law of thermodynamics, is given as follows.

#### *4.1.1. Gas Turbine (GT) cycle*

The GT cycle data give 625 o C exhaust gases exit temperature, 50 o C ambient temperature, and 215.5 MW power output for each GT. The isentropic efficiency is 0.85 for the compressor and 0.9 for the turbine. The mechanical efficiency is 0.998 for the turbine and 0.995 for the com‐ pressor.

The used fuel is NG having 47.806 MJ/kg low heating value (LHV) and 12.897 kg/s (45 t/h) flow rate. The airflow rate to each GT is 578.62 kg/s. The air-to-fuel ratio (*A*/*F*) is then 44.86; and the exhaust gases flow rate from each GT is 591.52 kg/s.

The compressor work is

Cogeneration Power-Desalting Plants Using Gas Turbine Combined Cycle http://dx.doi.org/10.5772/60209 159

$$\begin{aligned} W\_c &= m\_a \times \frac{\left(h\_2 - h\_1\right)}{\eta\_{mc}} = 578.62 \times \frac{\left(759.1 - 323.6\right)}{0.995} = 253.2 \text{ MW} \\ Q\_f &= m\_f \times LHV = 12.897 \times 47.806 = 616.55 \text{ MW} \end{aligned}$$

The heat gain by the air in is the combustion chamber

$$Q\_{in} = m\_a \times \left(h\_3 - h\_2\right) = 578.62 \times \left(1724 - 759.1\right) = 558.31 \text{ MW}$$

The turbine work output is

B: Pressure, Bar H: Enthalpy, kJ/kg T: Temperature, <sup>o</sup> C m: mass flow rate, kg/s

**GAS TURBINE GENERATOR (1 OF 3 UNITS)**

> 625.8 T 591.5 m

**4.1. Energy analysis**

pressor.

*4.1.1. Gas Turbine (GT) cycle*

The GT cycle data give 625 o

The compressor work is

GT Comp.

AF

HRSG # 2 HRSG # 3

G

158 Desalination Updates

**215.5 MW**

G

ST **215.7 MW**

IP PROCESS STEAM

2.8 B 158.8 T 2781.5 H 286.08 m

LP PROCESS STEAM

**3 HP EJECTORS**

DESALINATION PLANTS

**3 MSF UNITS**

CONDENSATE PUMPS

> HRSG # 2 HRSG # 3

BRINE HEATERS

> CONDENSATE RETURN FROM DESAL PLANT

13 B 118 T 496.7 H 293.58 m

**STEAM TURBINE GENERATOR (1 UNIT)**

HP

B

87.2 B 142.3 T 603.9 H 10.41 m

B

C exhaust gases exit temperature, 50 o

215.5 MW power output for each GT. The isentropic efficiency is 0.85 for the compressor and 0.9 for the turbine. The mechanical efficiency is 0.998 for the turbine and 0.995 for the com‐

The used fuel is NG having 47.806 MJ/kg low heating value (LHV) and 12.897 kg/s (45 t/h) flow rate. The airflow rate to each GT is 578.62 kg/s. The air-to-fuel ratio (*A*/*F*) is then 44.86; and the

BLOWDOWN 1%

**Figure 26.** Mass and heat balance diagram of Shuaiba North GTCC power-desalination plant

An energy analysis, based on the first law of thermodynamics, is given as follows.

**HEAT RECOVERY STEAN GENERATOR (1 OF 3 UNITS)**

exhaust gases flow rate from each GT is 591.52 kg/s.

75 B 560 T 3550.7 H 293.58 m

> 30.3 B 449.3 T 3342.7 H 7.5 m

> > Drum De-aerator

Make up water

87.2 B 142.3 T 603.9 H 3.47 m

> HRSG # 2 HRSG # 3

BFP

6.8 B 142.3 T 599.3 H 101.33 m

13 B 115.8 T 486.7 H 98.25 m

> 183.1 T 591.5 m

C ambient temperature, and

DUMP CONDENSER

2.8 B 137 T 2734.6 H 2.91 m

CEP

15 B 30 T 127.1 H 3.08 m

13 B 60 T 252.2 H 1.167 m

2.5 B 135 T 2733.1 H 293.58 m

$$\mathcal{W}\_t = m\_g \times \left(h\_3 - h\_4\right)\eta\_w = 591.52 \times \left(1724 - 930.8\right) \times 0.998 = 468.25 \text{ MW}$$

The GT power output is

$$\mathcal{W}\_{GT} = \left(\mathcal{W}\_t - \mathcal{W}\_\varepsilon\right) = 468.25 - 253.2 = 215.05 \text{ MW}$$

The gross GT cycle efficiency based on LHV is

$$
\eta\_{GT} = \frac{W\_{GT}}{Q\_f} = \frac{215.05}{616.55} = 0.35
$$

#### *4.1.2. Heat Recovery Steam Generator (HRSG)*

There are three GTs, three HRSGs, and only one ST. One third (1/3) of feedwater from the steam cycle returns to each HRSG, and the heat gained by this feedwater is equal to that lost by the exhaust gases, then,

$$m\_{\mathcal{g}} \times \mathbb{C}\_p \times \left(T\_4 - T\_{stack}\right) = m\_s \times \left(h\_s - h\_f\right)^2$$

where *T*4 is the exhausted gas temperatures at the GT exit; *T*stack is the HRSG stack exit; *C*<sup>p</sup> is the gases' specific heat (∼1.11 kJ/kgο C); *h*s and *h*<sup>f</sup> are the specific enthalpies in kJ/kg of super‐ heated steam leaving the HRSG and feedwater entering the HRSG, respectively; and *m*s is the steam flow rate from each HRSG. The temperature profile of the hot gases and steam-water temperature in the HRSG is shown in Figure 27.

**Figure 27.** Gas and steam-water temperature profile of the HRSG

The superheated steam temperature *T*s at the HRSG exit is determined by the terminal temperature difference (*T*4 – *T*s) with typical value in the range of 50 <sup>ο</sup> C. The pinch point temperature (pp) difference is defined by the minimum temperature difference between the hot gases *Tp* and the steam saturation temperature, pp = (*T*<sup>p</sup> *– T*sat), say equal to 20 <sup>ο</sup> C.

For the reference plant, mg = 591.5 kg/s, *T*4 = 625.8 <sup>ο</sup> C, and *T*stak = 183 <sup>ο</sup> C, and thus the heat loss from the hot gases is

$$m\_{\mathcal{g}} \times \mathbb{C}\_p \times \left(T\_4 - T\_{\text{stack}}\right) = 591.5 \times 1.11 \times \frac{625 - 183}{1000} = 290.7 \text{ MW}$$

The feedwater is heated from its inlet feed temperature to saturation liquid temperature Tsat, evaporated to saturated steam, and then superheated to Ts.

The steam leaving the three HRSGs is directed to the ST at mass flow rate, 3*m*<sup>s</sup> = 1056.9 t/h (293.58 kg/s) or *m*s = 97.86 kg/s from each HRSG. The heat gain in the

HRSG by water, *Q*HRSG is

$$Q\_{HRSG} = m\_s \times \left(h\_s - h\_f\right) = 97.86 \times \frac{3550.7 - 599.3}{1000} = 288.82 \text{ MW}$$

3*ms* = 1056.9 t/h (293.58 kg/s) or *ms* = 97.86 kg/s from each HRSG. The heat gain in the

#### HRSG by water, is *Q*HRSG

This is almost equal the heat loss by hot gases; and the heat input to the steam cycle, *Q*s, in from the three HRSGs is

$$Q\_{s,in} = \mathfrak{Z}Q\_{HRSG} = \mathfrak{Z} \times \mathfrak{Z}88.82 = 866,46 \text{ MW}$$

#### *4.1.3. Steam cycle*

**Figure 27.** Gas and steam-water temperature profile of the HRSG

For the reference plant, mg = 591.5 kg/s, *T*4 = 625.8 <sup>ο</sup>

from the hot gases is

160 Desalination Updates

HRSG by water, *Q*HRSG is

The superheated steam temperature *T*s at the HRSG exit is determined by the terminal

temperature (pp) difference is defined by the minimum temperature difference between the

*mC TT g p stack MW* - ´´ - = ´ ´ =

The feedwater is heated from its inlet feed temperature to saturation liquid temperature Tsat,

The steam leaving the three HRSGs is directed to the ST at mass flow rate, 3*m*<sup>s</sup> = 1056.9 t/h

3*ms* = 1056.9 t/h (293.58 kg/s) or *ms* = 97.86 kg/s from each HRSG. The heat gain in the

( ) 3550.7 599.3 97.86 288.82 <sup>1000</sup> *Q m hh HRSG s s f MW* - =´- = ´ <sup>=</sup>

C, and *T*stak = 183 <sup>ο</sup>

625 183 591.5 1.11 290.7 1000

hot gases *Tp* and the steam saturation temperature, pp = (*T*<sup>p</sup> *– T*sat), say equal to 20 <sup>ο</sup>

C. The pinch point

C.

C, and thus the heat loss

temperature difference (*T*4 – *T*s) with typical value in the range of 50 <sup>ο</sup>

( ) <sup>4</sup>

(293.58 kg/s) or *m*s = 97.86 kg/s from each HRSG. The heat gain in the

evaporated to saturated steam, and then superheated to Ts.

The steam leaving the three HRSGs is directed to a back-pressure steam turbine (BPST). The steam discharged from the BPST enters the brine heaters of three MSF units.

The throttling condition of the steam inlet to the turbine is 75 bar pressure, 560 <sup>ο</sup> C temperature, and 3,550.7 kJ/kg specific enthalpy. A small part of the expanded steam is extracted from the BPST to operate the steam ejectors of the MSF, at 30.3 bar, 449.3 <sup>ο</sup> C, and 3,342.7 kJ/kg enthalpy, whereas the balance continues to expand and is exhausted to the three MSF units at 2.8 bar, 158.8 <sup>ο</sup> C, and 2,781.5 kJ/kg enthalpy. This steam is desuperheated before entering the MSF units to 2.5 bar, 135 <sup>ο</sup> C, and 2,733.1 kJ/kg enthalpy. The power generated by the BPST is

$$\boldsymbol{W}\_{\rm st} = \left[\sum m\_{in}\boldsymbol{h}\_{in} - \sum m\_{out}\boldsymbol{h}\_{out}\right] \times \boldsymbol{\eta}\_{mech}$$

$$= (293.58 \times 3350.7 - 7.5 \times 3342.7 - 286.07 \times 2781) \times 0.99 / 1000 = 219.4 \text{ MW}$$

The power consumed by the steam cycle pumps in the steam cycle is negligible except that of the boiler feedwater pump (BFP), which can be calculated as follows:

$$\mathcal{W}\_{\rm BFP} = \frac{\upsilon\_f \times (P\_{\rm BFP} - P\_{\rm 68})}{\eta\_{\rm BFP}} = 0.001408 \times (82200 - 680) / (0.8 \times 1000) = 4.3 \text{ MW}$$

The net power generated by the steam turbine is 215.1 MW, and the heat gained by the water in the three HRSGs is 866.46 MW. This gives the ST efficiency as

$$\eta\_{st} = \frac{(W\_{ST} - W\_{BFP})}{Q\_{in}} = \frac{(219.4 - 4.3)}{866.46} = 0.2487$$

This efficiency underestimates the performance of the ST cycle. It does not account for the benefit gained by the steam leaving the ST to the MSF to produce desalted seawater and not expanded to an end condenser.

#### *4.1.4. Desalination units*

The heating steam mass flow rate to each MSF unit is *m*<sup>s</sup> = 97.86 kg/s (one third of the steam discharged from the ST plus water used for its desuperheating). Each MSF unit produces desalted seawater (DW) at the rate *D* = 15 MIGD (789 kg/s). This gives gain ratio (GR=D/S) equal to mass of DW/heating steam = 789/97.75 = 8.06

The heat consumed by each MSF unit is

$$Q\_{de} = m\_s \times \left(h\_{d,in} - h\_{d,ex}\right) = 97.86 \times \frac{2733.1 - 496.7}{1000} = 277 \text{ MW}$$

where *h*d,in and *h*d,ex are the enthalpy of steam entering the MSF brine heater and its return condensate, respectively.

So, the heat consumed for each 1 m3 of desalted water is qd = = (218.86×1000)/789 = 277 MJ/m3 .

It is more rational to express the heat supplied to the MSF by its real value in terms of me‐ chanical equivalent energy. The turbine work loss due to discharging its steam to brine heater of MSF unit and not expanding to an end condenser can be calculated; if this steam was expanded in low-pressure (LP) turbine to condenser pressure at 10 kPa and dryness fraction of 0.9, its enthalpy would be 2,345.5 kJ/kg, and the produced work is

$$\mathcal{W}\_{dc} = m\_s \times \left(h\_{\text{MFF}} - h\_{cond}\right) = 97.86 \times \frac{2781 - 2345.5}{1000} = 42.7 \text{ MW}$$

This 42.6 MW is equivalent mechanical work *W*de to the heat *Q*de = 218.86 MW supplied to each MSF unit.

Another small amount of steam is extracted from the steam turbine at higher pressure to operate the steam ejectors of each MSF plant at 2.5 kg/s flow rate, 30.3 bar pressure, 449.3 <sup>ο</sup> C temperature, and 3,342.5 kJ/kg enthalpy. If this steam was expanded in a turbine to the condensing pressure of 10 kPa and 90 % dryness fraction, its enthalpy would be 2,345.5 kJ/kg, and its work output is

$$\mathcal{Q}\_{\text{ejector}} = m\_{\text{ejector}} \times \left(h\_{\text{ejector}} - h\_{\text{cond}}\right) = 2.5 \times \frac{3342.5 - 2345.5}{1000} = 2.4925 \text{ MW}$$

So, the work loss by the steam supplied to one 15 MIGD (789 kg/s) is

$$\mathcal{W}\_{th} = \mathcal{W}\_{de} + \mathcal{W}\_{c\text{circ}} = \ 42.6 \ + \ 2.5 = \ 45.1 \ \text{MW}\_{el}$$

and specific work loss is equal to

$$145.100 \text{ kW} / 780 \text{ (kg/s)} = 57.16 \text{ kJ/kg} = 15.9 \text{ kWh/m}^3.1$$

Since the pumping energy of the MSF is in the range of 4 kWh/m3 (14.4 kJ/kg), the total equivalent mechanical energy (counting for pumping and thermal energy) to produce 1 m3 of desalted water is

$$\text{W}\_{\text{eq}} = \text{W}\_{\text{th}} + \text{W}\_{\text{pump}\text{ing}} = 15.9 + 4 \equiv 20 \text{ kWh/m}^3 = 72 \text{ kJ/kg}$$

So, the equivalent mechanical energy required to produce DW at the rate of 45 MIGD (2,367 kg/s) can be calculated as follows:

$$\text{Weq} = 72 \times 2367 \text{ /} 1000 = 170.424 \text{ MW}$$

This 170.424 MW consists of 34.1 MW for pumping energy and 136.34 MW for thermal energy.

The pumping energy of the BFP as well as for the MSF should be subtracted from the total power output of the turbines to become

$$\begin{aligned} \text{Net power output} &= 3 \text{ W}\_{\text{CT}} + \text{W}\_{\text{ST}} - \text{W}\_{\text{pump}} - \text{W}\_{\text{BFP}} \\ &= \left( 3 \times 215.02 \right) + 215.1 - 34.085 \text{ -4.3} = 821.77 \text{ MW} \end{aligned}$$

#### *4.1.5. Total cycle*

.

C

*4.1.4. Desalination units*

162 Desalination Updates

condensate, respectively.

MSF unit.

and its work output is

and specific work loss is equal to

equal to mass of DW/heating steam = 789/97.75 = 8.06

The heat consumed by each MSF unit is

The heating steam mass flow rate to each MSF unit is *m*<sup>s</sup> = 97.86 kg/s (one third of the steam discharged from the ST plus water used for its desuperheating). Each MSF unit produces desalted seawater (DW) at the rate *D* = 15 MIGD (789 kg/s). This gives gain ratio (GR=D/S)

> ( , , ) 2733.1 496.7 97.86 <sup>277</sup> <sup>1000</sup> *Qmh h de s d in d ex MW* - =´ - = ´ =

where *h*d,in and *h*d,ex are the enthalpy of steam entering the MSF brine heater and its return

So, the heat consumed for each 1 m3 of desalted water is qd = = (218.86×1000)/789 = 277 MJ/m3

It is more rational to express the heat supplied to the MSF by its real value in terms of me‐ chanical equivalent energy. The turbine work loss due to discharging its steam to brine heater of MSF unit and not expanding to an end condenser can be calculated; if this steam was expanded in low-pressure (LP) turbine to condenser pressure at 10 kPa and dryness fraction

( ) 2781 2345.5 97.86 42.7

*Wmh h de s MSF cond MW* - =´ - = ´ =

This 42.6 MW is equivalent mechanical work *W*de to the heat *Q*de = 218.86 MW supplied to each

Another small amount of steam is extracted from the steam turbine at higher pressure to operate the steam ejectors of each MSF plant at 2.5 kg/s flow rate, 30.3 bar pressure, 449.3 <sup>ο</sup>

temperature, and 3,342.5 kJ/kg enthalpy. If this steam was expanded in a turbine to the condensing pressure of 10 kPa and 90 % dryness fraction, its enthalpy would be 2,345.5 kJ/kg,

<sup>1000</sup> *Qm hh ejector ejector ejector cond MW* - = ´ - =´ =

42.6 2.5 45.1 MW, *WW W th de ejector* =+ = + =

( ) 3342.5 2345.5 2.5 2.4925

1000

of 0.9, its enthalpy would be 2,345.5 kJ/kg, and the produced work is

So, the work loss by the steam supplied to one 15 MIGD (789 kg/s) is

The fuel energy consumed by the three GT units is

$$Q\_{f,t} = \text{ 3} \times Q\_f = \text{ 3} \times 616.5 = 1849.5 \text{ MW}$$

The total power output from the GTCC is 3 WGT + WST = 645 + 215.1 = 960.1 MW and the GTCC overall efficiency η<sup>t</sup> = 960.1/1849.5 = 0.465.

Again, this efficiency underestimates the performance of the GTCC, since it does not account for the heat gained by the 3 MSF units.

Another term is usually considered and known as the utilization factor (UF):

$$\text{LIF} = \frac{\text{\\$}\,\,\text{W}\_{GT} + \text{W}\_{ST} + \text{Q}\_{\text{dc}}}{\text{Q}\_{f,t}} = \frac{645 + 215.1 + 218.86}{1849.5} = 0.825$$

where *Q*f,t is the only heat added to the three GT cycles.

In fact, the UF overestimates the performance of the CPDP since it adds the work by both GTs and ST (high-quality energy) to heat supplied to the MSF units 3 *Q*de (low-quality energy).

A new modified total efficiency *ηmf* is

$$\eta\_{mf} = \frac{3\mathcal{W}\_{GT} + \mathcal{W}\_{ST} - \mathcal{W}\_{pump} + \mathcal{W}\_{de}}{\mathcal{Q}\_{f,t}} = \frac{(645 + 215.1 - 34.1 + 170.43)}{1849.5} = 0.545$$

So, an energy balance of the given CPDP using GTCC and MSF units shows that *Q <sup>f</sup>* ,*<sup>t</sup>* is supplied to the overall system, which is mainly converted partially to the following main items:


$$\mathcal{Q}\_{\text{staks}} = \mathbf{3} \times \boldsymbol{m}\_g \times \mathbf{C}\_p \times \left( T\_{\text{stack}4} - T\_e \right) = 591.5 \times 1.11 \times \frac{183.1 - 50}{1000} = 262.2 \text{ MW}$$

where *Te* is the ambient temperature.

The balance will be unaccounted energy losses,

$$\begin{aligned} \mathbf{Q}\_{\text{losses}} &= \mathbf{Q}\_f - \mathbf{3}\mathbf{W}\_{GT} - \mathbf{W}\_{ST} - \mathbf{3}\mathbf{Q}\_{d\epsilon} - \mathbf{W}\_{stack} = \\ \mathbf{=1849.4} - 645 - 215.1 - 656.58 - 262.2 &= 70.52 \text{ MW} \end{aligned}$$

Figure 28 shows the energy balance of the given GTCC and MSF units.

**Figure 28.** Energy balance of the given GTCC and MSF units (see online version for colors)

*Q*stack is the largest heat loss and is accounted for about 14 % of the heat input.

The high stack temperature (183 °C) is due to the high feedwater temperature returning back from the MSF desalting units at 142 °C.

If GTCC is chosen without desalting plant, lower feedwater temperature is chosen and the stack temperature when NG without sulfur content was used; *T*stack could be in the order of 100 °C.

### **5. Exergy analysis**

In fact, the UF overestimates the performance of the CPDP since it adds the work by both GTs and ST (high-quality energy) to heat supplied to the MSF units 3 *Q*de (low-quality energy).

<sup>3</sup> (645 215.1 34,1 170.43) 0.54

+- + + -+ == =

So, an energy balance of the given CPDP using GTCC and MSF units shows that *Q <sup>f</sup>* ,*<sup>t</sup>* is supplied to the overall system, which is mainly converted partially to the following main items: **a.** Total work output by 3 WGT + WST – Wpump - WBFP=3×215+ 215.1- 34.1- 4.3 = 821.7 MW (44.4

**b.** Heat added to 3 MSF units, Qdes,t =3 × Qde = 3×218.86 = 656.58MW (35.51 % of total heat

**c.** The heat rejected to the environment in the form of hot gases leaving the three stacks of

( <sup>4</sup> ) 183.1 50 <sup>3</sup> 591.5 1.11 262.2 <sup>1000</sup> *Q mC T T staks g p stack e MW* - =´ ´ ´ - = ´ ´ =

> 3 3 1849.4 645 215.1 656.58 262.2 70.52 *Q Q W W QW losses f GT ST de stack*

= -- - - =

Figure 28 shows the energy balance of the given GTCC and MSF units.

**Figure 28.** Energy balance of the given GTCC and MSF units (see online version for colors)

=- - - - =

1849.5

*MW*

A new modified total efficiency *ηmf* is

*mf*

h

% net efficiency).

input).

164 Desalination Updates

the HRSGs is

where *Te* is the ambient temperature.

The balance will be unaccounted energy losses,

,

*f t*

*GT ST pump de*

*WWW W Q*

> An exergy analysis, based on the second law of thermodynamics, is conducted here for the cases considered before.

#### **5.1. Compressor**

The exergy destruction (irreversibility) in the compressor can be presented as follows:

$$\mathbf{I}\_{\rm comp} = \mathbf{W}\_{\rm comp} \cdot \mathbf{A}\_{\rm comp}$$

where *A*comp is the increase of flow availability in the air stream across the compressor and equal to

$$A\_{c\text{supp}} = m\_a \times \left[ \left( h\_2 - h\_1 \right) - T\_c (s\_2 - s\_1) \right]^2$$

The second law efficiency of the compressor is expressed as

$$\mathcal{E}\_{\text{comp}} = \frac{A\_{\text{comp}}}{\mathbf{W}\_{\text{comp}}}$$

#### **5.2. Combustion Chamber (cc)**

The main exergy loss (or destruction) of the GT cycle occurs in the combustion chamber (cc) of the GT cycle. An exergy balance in the combustion chamber gives *Ef* = *E3 – E2 + Icc*

The *Ef* , *E2, E3,* and *icc* are the exergies of fuel input, compressed air inlet, combusted gas exit, and exergy destructed (irreversibility), respectively.

*Ef* is almost equal to the mass fuel flow×high heating value (HHV), HHV = 55,530 kJ/kg

For each GT, the value of (*E*3 – *E*2) can be approximated by

$$E\_3 - E\_2 = \left[ m\_g \times \frac{\left[ \left( h\_3 - h\_2 \right) - T\_c \left( s\_3 - s\_2 \right) \right]}{1000} \right] = 426.196 \,\text{MW}$$

Thus, the exergy destruction I*cc* and combustion chamber second law efficiency *εcc* are calculated as

$$I\_{cc} = E\_f - \left(E\_3 - E\_2\right) = 716.17 - 426.19 = 290 \text{ MW}$$

εcc = Exergy gain/Exergy input =426.19/716.17 =0.595

This is much lower than the combustion chamber energy efficiency, ηcc, based on the thermo‐ dynamics first law and is usually assumed equal to 0.99.

#### **5.3. Gas turbine**

An exergy balance around the GT cycle gives

$$E\_1 + E\_f = E\_4 + \mathcal{W}\_{GT} + I\_{GT}$$

*E1 and E4* are the exergy of air inlet to and gases leaving from the GT, respectively, and *IGT* is the exergy destruction in the GT cycle. The values of these terms are calculated as

$$E\_{4-1} = m\_g \times \left[ \left( h\_4 - h\_1 \right) - T\_e \left( s\_4 - s\_1 \right) \right] / 1000 = 159.244 \text{ MW}$$

Since *WGT* = 215 MW, the exergy destruction in the GT cycle is

$$I\_{GT} = E\_f - \left(E\_4 - E\_1\right) - \left(W\_{GT}\right) = 341.4 \text{ MW} \dots$$

This *IGT* (341.4 MW) includes the energy destruction in the combustion chamber (Icc = 290 MW) and the balance = 51.4 MW is the exergy destruction in the cycle components, other than the combustion process.

The exergy difference utilized to produce the *WGT* is (*E*3 – *E*4) = 241.5 MW.

For the three GTs, this exergy difference is 3 ×241.5 = 724.5 MW.

So, the effectiveness of the GT, ε*GT* (without combustion chamber losses), is

$$\varepsilon\_{GT}\left(\text{without combustion energy losses}\right) = 215/241.5 = 0.89$$

and the exergy destruction in the turbine, compressor due to friction is

$$I\_{fric} = E\_3 - E\_4 - W\_{GT} = \begin{pmatrix} 241.5 - 215 \\ \end{pmatrix} = 26.5 \text{MW}.$$

The effectiveness of the GT cycle, when used as simple GT cycle is

*εGT(total) = WGT/Ef* = 215/716.17 = 0.3 which is the same with gross efficiency based on HHV. When GTCC is used, the exergy of the exhaust gases *E*<sup>4</sup> is utilized to generate steam and operate steam turbine, and εGT in a GTCC is

$$
\varepsilon\_{GT} \left( \dot{m} \,\,\,GT \,\,\mathrm{CC} \right) = \frac{W\_{GT} + (E\_4 - E\_1)}{E\_F} = \frac{215 + 159.2}{716.17} = 0.523 \,\,\mathrm{V}
$$

#### **5.4. Heat Recovery Steam Generator (HRSG)**

( 3 2 32 ) ( ) 3 2 426.196MW 1000 *e*

Thus, the exergy destruction I*cc* and combustion chamber second law efficiency *εcc* are

( 3 2 ) 716.17 426.19 290 *cc f I E EE* =- - = - = *MW*

This is much lower than the combustion chamber energy efficiency, ηcc, based on the thermo‐

1 4 *<sup>f</sup> GT GT EE EW I* +=+ +

*E1 and E4* are the exergy of air inlet to and gases leaving from the GT, respectively, and *IGT* is

( 4 1 ) ( ) 341.4 MW. *GT f GT I E EE W* =- - - =

This *IGT* (341.4 MW) includes the energy destruction in the combustion chamber (Icc = 290 MW) and the balance = 51.4 MW is the exergy destruction in the cycle components, other than

ë û ( 4 1 41 ) ( ) / 1000 159.244 MW

the exergy destruction in the GT cycle. The values of these terms are calculated as

*E m h h Ts s* 4 1- =´ -- - = *g e* é ù

The exergy difference utilized to produce the *WGT* is (*E*3 – *E*4) = 241.5 MW.

For the three GTs, this exergy difference is 3 ×241.5 = 724.5 MW.

Since *WGT* = 215 MW, the exergy destruction in the GT cycle is

*h h Ts s*

é ù -- - ë û -= ´ <sup>=</sup>

*g*

*EEm*

εcc = Exergy gain/Exergy input =426.19/716.17 =0.595

An exergy balance around the GT cycle gives

dynamics first law and is usually assumed equal to 0.99.

calculated as

166 Desalination Updates

**5.3. Gas turbine**

the combustion process.

In heat recovery steam generator (HRSG), the heat of hot gases leaving the GT is transferred to feedwater in deaerator, economizer, evaporator, and superheater and the heat transfer in the HRSG.

An exergy balance around the HRSG gives

$$
\Delta E\_s = \Delta E\_w + I\_{\text{HRSG}}
$$

where Δ*Eg* is the exergy loss by the hot gases which is equal to the exergy gain by the water Δ*Ew* plus exergy destruction in one HRSG, I*HRSG*

$$
\Delta E\_g = m\_g \times \left[ \left( C\_p \times \left( T\_4 - T\_{\text{stack}} \right) - T\_c \left( s\_4 - s\_{\text{stack}} \right) \right) \right] = 129.108 \text{ MW}
$$

$$
\Delta E\_w = m\_w \times \left[ \left( h\_s - h\_f \right) - T\_c \left( s\_s - s\_f \right) \right] = 116.438 \text{ MW}
$$

Then, *IHRSG* =(Δ*Eg* −Δ*Ew*) =12.67 *MW* , and the effectiveness of HRSG is εHRSG = <sup>Δ</sup>*Ew* <sup>Δ</sup>*Eg* =0.9

So, the exergy difference gained by water in 3 HRSG = 3 ×116.438 = 349.314 MW, and this is the exergy input to the steam cycle including the three MSF units.

#### **5.5. Steam turbine cycle**

The exergy difference across the ST cycle, ⊗*EST*, is equal to (*Esi* – *Ese*), where *Esi* and *Ese* are the exergy of the steam inlet to the turbine and steam outlet to the MSF units, respectively.

$$\Delta E\_{ST} = \Im \times m\_s \times \left[ \left( h\_{sl} - h\_{se} \right) - T\_e \left( s\_{sl} - s\_{fe} \right) \right] = $$

$$\delta = 3 \times 97.86 \times \left[ \left( 3550.7 - 2781.5 \right) - 323 \left( 6.95 - 7.2 \right) \right] / 1000 = 249.531 \text{ MW}$$

where ssi and sse are the specific entropy of steam at the turbine inlet and outlet, respectively. Then the exergy loss in the ST is

$$I\_{ST} \text{(loss)} = \Delta E\_{ST} - W\_{ST} = \text{249.531 - 215.1 = 34.431 \text{MW}}$$

#### **5.6. Desalination system**

The exergy difference between the discharged steams from the turbine to the condensate from the brine heaters of one MSF unit, ∆*Ede* is as follows:

$$\Delta E\_{dc} = m\_{sd} \times \left[ \left( h\_{d,in} - h\_{d,e} \right) - T\_e \left( s\_{d,in} - s\_{dc} \right) \right] = $$

$$= 97.86 \times \left[ \left( 2783.5 - 496 \right) - \frac{323 \left( 7.2 - 1.52 \right)}{1000} \right] = 39.34 \text{ MW}$$

where msd and (*hd,in* – *hd,e*), *s*d,in, and sde are the steam flow rate to each MSF desalting unit, its specific enthalpy difference between the steam inlet, and its condensate exit from the desalting unit, specific entropy at steam inlet, and specific entropy of its condensate at the exit, respec‐ tively.

So, an exergy balance of the given CPDP using GTCC and MSF units shows that there are unaccounted losses due to steam extracted at moderately high pressure to operate the steam ejectors of the MSF units, and others and can be calculated as follows:

$$E\_{\text{uncort.}} = E\_{f(\text{total})} - W\_{GT(\text{total})} - \Delta E\_{GT(\text{total})} - \Delta E\_{HRSG(\text{total})} - W\_{ST} - \Delta E\_{de(\text{total})} - DE\_{ST} - E\_{rel} \text{ (50)}$$

$$E\_{\text{uncort.}} = 2148.5 - 646.5 - 1024.2 - 38 - 215.7 - 134.56 - 33.83 - 38.85 = 16.85 \text{ MW}$$

#### **5.7. Exergy distribution of the overall GTCC**

Exergy balance of the given CPDP using GTCC and MSF units is conducted for the whole GTCC cycle.

The fuel exergy of the fuel supplied for the three GTs is

$$\mathbf{E}\_{\mathrm{f}(\mathrm{total})} = \mathbf{3} \times \mathbf{m}\_{\mathrm{f}} \times \mathbf{H} \mathbf{H} \mathbf{V} = 2148.5 \text{ MW}$$

This fuel exergy is used to produce the power output power from the three GT= 3× 215 = 646.5 MW.

So, the exergy loss from the GT cycles is

**5.5. Steam turbine cycle**

168 Desalination Updates

Then the exergy loss in the ST is

the brine heaters of one MSF unit, ∆*Ede* is as follows:

**5.6. Desalination system**

.

**5.7. Exergy distribution of the overall GTCC**

The fuel exergy of the fuel supplied for the three GTs is

*unacct*

GTCC cycle.

tively.

The exergy difference across the ST cycle, ⊗*EST*, is equal to (*Esi* – *Ese*), where *Esi* and *Ese* are the exergy of the steam inlet to the turbine and steam outlet to the MSF units, respectively.

D =´ ´ - - - = é ù

where ssi and sse are the specific entropy of steam at the turbine inlet and outlet, respectively.

*ST* ( ) 249.531 215.1 34.431MW *ST ST I loss E W* =D - = - =

The exergy difference between the discharged steams from the turbine to the condensate from

( ) ( )


ejectors of the MSF units, and others and can be calculated as follows:

97.86 [ 2783.5 496 39.34

*de sd d in d e e d in de E m h h Ts s*

D= ´ - - - = é ù

where msd and (*hd,in* – *hd,e*), *s*d,in, and sde are the steam flow rate to each MSF desalting unit, its specific enthalpy difference between the steam inlet, and its condensate exit from the desalting unit, specific entropy at steam inlet, and specific entropy of its condensate at the exit, respec‐

So, an exergy balance of the given CPDP using GTCC and MSF units shows that there are unaccounted losses due to steam extracted at moderately high pressure to operate the steam

( ) ( ) ( ) ( ) . () ( )

2148.5 646.5 1024.2 38 215.7 134.56 33.83 38.85 16.85 *unacct f total GT total GT total HRSG total ST de total ST rej*

*E MW* = - - D - D - -D - - = - - -- - - - =

Exergy balance of the given CPDP using GTCC and MSF units is conducted for the whole

*E E W E E W E DE E*

50

( ) ( )

ë û

1000

,, , 323 7.2 1.52

( ) ( )

=´ ´ - - - = é ù ë û

3 97.86 3550.7 2781.5 323 6,95 7.2 / 1000 249.531 *ST s si se e si fe E m h h Ts s*

3

( ) ( )

ê ú ë û

*MW*

*MW*

$$
\Delta E\_{GT(total)} = \mathfrak{Z} \times I\_{GT} = \mathfrak{Z} \times \mathfrak{Z}
41.4 = 1024.2 \text{ MW}
$$

The exergy destruction in the three HRSG can be calculated as follows:

$$
\Delta E\_{HRSG(total)} = \mathbf{3} \times \ I\_{HRSG} = \mathbf{3} \times \mathbf{12.67} = \mathbf{38} \text{ MW}
$$

The fuel exergy is utilized to produce output power from the steam turbine is

$$W\_{ST} = 1 \times 215.7 = 215.7 \text{ MW}$$

The fuel exergy used to produce 45 MIGD from 3 MSF units is

$$
\Delta E\_{\rm{de(total)}} = \mathbf{3} \times \Delta E\_{\rm{de}} = \mathbf{3} \times \mathbf{3} \mathbf{9}.
\mathbf{34} = \mathbf{134}.
\mathbf{56} \text{ MW}
$$

The exergy destruction in the steam turbine is *IST* =33.83 *MW* and exergy loss to environment through the HRSG stacks can be calculated as follows:

$$E\_{ref} = 3 \times m\_{\%} \times \left[ \frac{\left( h\_{stack} - h\_1 \right) - T\_1 \left( S\_{stuck} - S\_1 \right)}{1000} \right] = $$

$$= 3 \times 591.3 \times \left[ \frac{\left( 458.1 - 323.6 \right) - 323 \left( 6.125 - 5.776 \right)}{1000} \right] = 38.85 \text{ MW}$$

There are unaccounted losses due to steam extracted at moderately high pressure to operate the steam ejectors of the MSF units, and others and can be calculated as follows:

$$\begin{split} E\_{\text{uncact.}} &= E\_{f(\text{total})} - W\_{GT(\text{total})} - \Delta E\_{GT(\text{total})} - \Delta E\_{\text{HRSG(total}} - W\_{ST} - \Delta E\_{\text{def(total})} - D E\_{ST} - E\_{\text{ref}} \\ &= 2148.5 - 646.5 - 1024.2 - 38 - 215.7 - 134.56 - 33.83 - 38.85 = 16.85 \text{ MW} \end{split}$$

**Figure 29.** Grassmann diagram of the GTCC system (see online version for colors)

### **6. Fuel allocation between the EP and DW production**

There are two methods to allocate the fuel between the EP and DW production, while the second is exergy method.

#### **6.1. Work loss method**

The first method is the work loss method. As mentioned, there is work loss due to discharging steam to the MSF units instead of its expansion to the condensing turbine. The CPDP outputs are

3 *WGT* = 646.5 MW by the three GT, *WST* = 215.7 MW by steam turbine, and thermal energy input to the 3 MSFs, 3*Qde* =3×218.68 = 656 MW. It was showed that 3*Qde* causes the loss (or equivalent to) 3 *Wde* = 136.34 MW. The MSF units consume pumping energy at the rate of *W*( *pumping*)= 34.1 MW, which should be deducted from the total power output.

So, the fuel charged to desalination to the total fuel supply should be

#### Cogeneration Power-Desalting Plants Using Gas Turbine Combined Cycle http://dx.doi.org/10.5772/60209 171

$$\text{Fuel}\_{\text{energy to deal.}} = \left(\frac{\mathcal{W}\_{\text{pumping}} + \mathfrak{Z}\mathcal{W}\_{\text{dc}}}{\mathfrak{Z}\mathcal{W}\_{GT} + \mathcal{W}\_{ST} + \mathfrak{Z}\mathcal{W}\_{\text{dc}}}\right) \times \mathcal{Q}\_f = 1$$

$$= \left(\frac{34.1 + 136.34}{646.5 + 215.7 + 136.34}\right) \times 1847.1 = 304.77 \text{ MW}$$

The specific fuel energy charged to produce 1 m3 can be calculated as follows:

$$\text{Specific}\_{\text{fuel energy to deal.}} = \left(\frac{\text{Fuel}\_{\text{energy to deal.}} \times 24 \times 60 \times 60}{45 \text{ MGD} \times 4550 \left(\frac{\text{m}^3}{day}\right)}\right) = 128 \frac{\text{M}}{\text{m}^3}$$

The fuel charged to produce the net power output can be calculated as

$$\text{Fuel}\_{\text{energy to power}} = Q\_f - \text{Fuel}\_{\text{energy to deal.}} = 1847.1 - 304.77 = 1542.3 \text{ MW}$$

#### **6.2. Exergy method**

**Figure 29.** Grassmann diagram of the GTCC system (see online version for colors)

**6. Fuel allocation between the EP and DW production**

second is exergy method.

**6.1. Work loss method**

170 Desalination Updates

are

There are two methods to allocate the fuel between the EP and DW production, while the

The first method is the work loss method. As mentioned, there is work loss due to discharging steam to the MSF units instead of its expansion to the condensing turbine. The CPDP outputs

3 *WGT* = 646.5 MW by the three GT, *WST* = 215.7 MW by steam turbine, and thermal energy input to the 3 MSFs, 3*Qde* =3×218.68 = 656 MW. It was showed that 3*Qde* causes the loss (or equivalent to) 3 *Wde* = 136.34 MW. The MSF units consume pumping energy at the rate of

*W*( *pumping*)= 34.1 MW, which should be deducted from the total power output.

So, the fuel charged to desalination to the total fuel supply should be

The aim of combining the 3 MSF units with the GTCC is to supply these units with its heat needs, 3 *Qde* =3×218.68=656 MW. The exergy difference across the three MSF units is 3∆ *Ede* = 134.56 MW and represents the exergy consumed by the desalting system.

The pumping work *W*( *pumping*)= 34.1 MW and work loss due to extraction of steam to the MSF steam ejector (2.4925 MW) should be added to 3∆ *Ede* to become 171.15 MW

This almost the same work was charged to the desalting units in the method of lost work, and there is no need to repeat the share of desalting in the fuel energy again.

It is clear that both methods give very close results, but the first method is easier and under‐ standable by practitioner engineers.

#### **6.3. Desalinated water cost**

Since all combined cycle power plants in Kuwait were dual fuel (i.e., can be operated either by natural gas or heavy oil), the cost of desalinated water is evaluated in this section based on the current oil and natural gas prices. Hence, the desalinated water produced by this plant will be estimated based on two different types of fuel as follows:

The oil price is 60 \$/bbl and the low heating value of the oil is LHVoil = 42229 kJ/kg; so, the energy content in 1 barrel of oil (density of 900 kg/m3 ) can be calculated as follows:

<sup>1</sup> barrel=0.159 *<sup>m</sup>*<sup>3</sup> ×900 *kg <sup>m</sup>* <sup>3</sup> ×42299 *kJ kg* =6. 04 GJ; so, the oil price per GJ will be \$9.33/GJ

$$\text{The desired water cost} = \text{Specific}\_{\text{fuel energy to deal.}} \frac{Gf}{m^3} \times \text{fuel price} \frac{\\$}{Gf}$$

$$\text{The desalinated water cost} = 0.128 \frac{Gf}{m^3} \times 9.33 \frac{\\$}{Gf} = 1.272 \frac{\\$}{m^3}$$

When the gas price is \$2/MMBTU which is equivalent to 1.895 \$/GJ and LHVNG= 47806 kJ/kg.

$$\text{The desalinated water cost} = 0.128 \frac{GJ}{m^3} \times 1.895 \frac{\ $}{GJ} = 0.243 \frac{\$ }{m^3}$$

The following assumption is assumed for the analysis: steady state operation.

### **7. Sensitivity analysis**

The developed equations were used to evaluate the performance of the reference CPDP using the GTCC in this section. A simplified schematic diagram of plant is shown in Figure 30, while state point conditions of the model are given in Table 5.

The model was tested against the available data of Al-Shuaiba CCPP, and the results showed good agreements as shown in Table 4. This model can also be used for simulation and/or parametric studies of the plants in order to evaluate its performance. A sensitivity analysis is carried out to investigate the effects of some combined cycle parameters on the overall efficiency, specific fuel energy to desalination, as well as the desalinated water cost. The selected parameters are ambient air temperature, compression ratio, and air-to-fuel ratio, turbine inlet temperature, and stuck temperature.

**Figure 30.** A simplified schematic diagram of Al-Shuaiba combined cycle power plant model

Cogeneration Power-Desalting Plants Using Gas Turbine Combined Cycle http://dx.doi.org/10.5772/60209 173


**Table 5.** State point conditions of the model

fuel energy to desal. 3

*GJ*

= ´=

= ´

\$ The desalinated water cost Spesific fuel price

\$ \$ The desalinated water cost 0.128 9.33 1.272

When the gas price is \$2/MMBTU which is equivalent to 1.895 \$/GJ and LHVNG= 47806 kJ/kg.

\$ \$ The desalinated water cost 0.128 1.895 0.243 *GJ*

The developed equations were used to evaluate the performance of the reference CPDP using the GTCC in this section. A simplified schematic diagram of plant is shown in Figure 30, while

The model was tested against the available data of Al-Shuaiba CCPP, and the results showed good agreements as shown in Table 4. This model can also be used for simulation and/or parametric studies of the plants in order to evaluate its performance. A sensitivity analysis is carried out to investigate the effects of some combined cycle parameters on the overall efficiency, specific fuel energy to desalination, as well as the desalinated water cost. The selected parameters are ambient air temperature, compression ratio, and air-to-fuel ratio,

6

The following assumption is assumed for the analysis: steady state operation.

state point conditions of the model are given in Table 5.

turbine inlet temperature, and stuck temperature.

1 4 mg

**3 × GT**

2 3 c=0.88 t =0.88

Fuel m*<sup>f</sup>*

> P4 T4

**Figure 30.** A simplified schematic diagram of Al-Shuaiba combined cycle power plant model

**7. Sensitivity analysis**

172 Desalination Updates

ma P1 T1 3 3

3 3

*m m GJ* = ´=

*m m GJ*

*m GJ*

11

5

9

HP G

7 8

3 × M

S

F

10

**3 × HRSG**

*GJ*



**Table 6.** Mathematical model results against actual plant

combined cycle

combined cycle

0.450

0.455

0.460

0.465

0.470

0.475

0.480

0.485

0.450

0.455

0.460

0.465

0.470

0.475

0.480

0.485

0.490

The effect of ambient air temperature on the fuel allocation between the electric power and desalinated seawater production is presented in Figure 31. It shows that as the ambient air temperature increases, the allocated fuel to the electric power decreases, and this led to increase the allocated fuel to desalination. Figure 32 shows the effect of ambient temperature on the combined cycle efficiency at different compression ratios. It is clear that the cycle efficiency is the highest at maximum pressure ratio and minimum ambient temperature. On the other hand, the effect of air-to-fuel ratio is limited as shown in Figure 33.

Figure 34 shows the effect of ambient and turbine inlet temperatures (TIT) on the specific fuel energy to desalination. It shows that the specific fuel energy to desalination increases at high ambient temperatures, while it decreases at higher turbine inlet temperatures.

Figure 31. The effect of air ambient temperature to fuel allocation between the electric power and desalinated seawater production **Figure 31.** The effect of air ambient temperature to fuel allocation between the electric power and desalinated seawater production

Figure 32. The effect of ambient temperature on the combined cycle efficiency at different compression ratios

rp=15 rp=17.5 rp=20

rp=15 rp=17.5 rp=20

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

Figure 33. The effect of air-to-fuel ratio on the combined cycle efficiency at different compression ratios

Air to fuel ratio, A/F 36 38 40 42 44 46 48 50 52 54 56 58 Figure 31. The effect of air ambient temperature to fuel allocation between the electric power and desalinated seawater production

Fuel energy to power, MW

Fuel energy to power, MW

1560

1565

1570

1575

1580

1585

1590

1595

1565

1570

1575

1580

1585

1590

1595

280 290 300 310 320 330 340

Ambient temperature, T1 (K)

Fuel energy to D Fuel energy to P

Fuel energy to D Fuel energy to P

Fuel energy to desalination, MW

Fuel energy to desalination, MW

255

260

255

0.485

260

265

265

270

270

275

275

280

280

285

285

290

290

**Model Actual Operating and design conditions**

2.5 2.5 Steam flow rate to ejector, kg/s 30 30 Inlet pressure to ejector, bar 450 449.3 Inlet temperature to ejector, o

46.66 46.7 Combined cycle efficiency, %

the effect of air-to-fuel ratio is limited as shown in Figure 33.

**Table 6.** Mathematical model results against actual plant

174 Desalination Updates

Fuel energy to desalination, MW

255

combined cycle

production

combined cycle

0.450

0.455

0.460

0.465

0.470

0.475

0.480

0.485

0.450

0.455

0.460

0.465

0.470

0.475

0.480

0.485

0.490

260

265

270

275

280

285

290

GTCC

The effect of ambient air temperature on the fuel allocation between the electric power and desalinated seawater production is presented in Figure 31. It shows that as the ambient air temperature increases, the allocated fuel to the electric power decreases, and this led to increase the allocated fuel to desalination. Figure 32 shows the effect of ambient temperature on the combined cycle efficiency at different compression ratios. It is clear that the cycle efficiency is the highest at maximum pressure ratio and minimum ambient temperature. On the other hand,

Figure 34 shows the effect of ambient and turbine inlet temperatures (TIT) on the specific fuel energy to desalination. It shows that the specific fuel energy to desalination increases at high

> Fuel energy to D Fuel energy to P

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

**Figure 31.** The effect of air ambient temperature to fuel allocation between the electric power and desalinated seawater

ambient temperatures, while it decreases at higher turbine inlet temperatures.

C

Figure 32. The effect of ambient temperature on the combined cycle efficiency at different compression ratios

rp=15 rp=17.5 rp=20

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

Figure 33. The effect of air-to-fuel ratio on the combined cycle efficiency at different compression ratios

Air to fuel ratio, A/F 36 38 40 42 44 46 48 50 52 54 56 58

C

Fuel energy to power, MW

1560

rp=15 rp=17.5 rp=20

1565

1570

1575

1580

1585

1590

1595

789 789 Distillate output, kg/s 2.5 2.5 Inlet pressure to MSF, bar 135 135 Inlet temperature to MSF o

Figure 32. The effect of ambient temperature on the combined cycle efficiency at different compression ratios **Figure 32.** The effect of ambient temperature on the combined cycle efficiency at different compression ratios

Ambient temperature, T1 (K)

Figure 32. The effect of ambient temperature on the combined cycle efficiency at different compression ratios

Figure 31. The effect of air ambient temperature to fuel allocation between the electric power and desalinated seawater production Figure 33. The effect of air-to-fuel ratio on the combined cycle efficiency at different compression ratios Figure 33. The effect of air-to-fuel ratio on the combined cycle efficiency at different compression ratios **Figure 33.** The effect of air-to-fuel ratio on the combined cycle efficiency at different compression ratios

110

115

120

125

130

135

TIT=1300 K TIT=1350 K TIT=1400 K

Figure 34. The effect of ambient temperature on the specific fuel energy to desalination at different turbine inlet temperatures **Figure 34.** The effect of ambient temperature on the specific fuel energy to desalination at different turbine inlet tem‐ peratures Although the effect of steam turbine inlet pressure on the specific fuel energy to desalination is negligible, it will

fuel charged for thermal energy would be 269.75 or 113 MJ/m3.

slightly be affected by the types of fuel as shown in Figure 37.

On the other hand, the effect of stack temperatures on the heat rejection into environment as well as on the exergy destruction of HRSG is depicted in Figure 35. It is clear that as the stack temperatures increases, the heat rejection

Figure 35. The effect of stack temperatures on the heat rejection into environment as well as on the HRSG exergy destruction

260

Heat rejection in to the environment from stucks, MW240 Exergy destruction in one HRSG, MW26 Figure 35. The effect of stack temperatures on the heat rejection into environment as well as on the HRSG exergy destruction **Figure 35.** The effect of stack temperatures on the heat rejection into environment as well as on the HRSG exergy de‐ struction

I HRSG

Tstucks, K 360 380 400 420 440 460 480

14

16

18

20

22

24

On the other hand, the effect of stack temperatures on the heat rejection into environment as well as on the exergy destruction of HRSG is depicted in Figure 35. It is clear that as the stack temperatures increases, the heat rejection into the environment will increase and consequently the exergy destruction in HRSG will decrease.

Figure 34. The effect of ambient temperature on the specific fuel energy to desalination at different turbine inlet temperatures On the other hand, the effect of stack temperatures on the heat rejection into environment as well as on the exergy destruction of HRSG is depicted in Figure 35. It is clear that as the stack temperatures increases, the heat rejection The main real problem by this plant is the high stack temperature of 183 o C because the high feedwater returns from the MSF desalting units at 135 o C. If the stack temperature is reduced to 110 o C, the heat gained by the water in the HRSG temperature is increased to 16.5 %, and the ST output would increase to 251.32 MW. The difference between this ST output and actual output of 215.7 by the ST or 35.62 should be charged as well to the desalting process. Again for net efficiency of 44 %, the fuel energy of 80.955 MW should be added to the 188.8 MW calculated before, or the fuel charged for thermal energy would be 269.75 or 113 MJ/m3 .

The main real problem by this plant is the high stack temperature of 183 oC because the high feedwater returns from the MSF desalting units at 135 oC. If the stack temperature is reduced to 110 oC, the heat gained by the water in the Although the effect of steam turbine inlet pressure on the specific fuel energy to desalination is negligible, it will slightly be affected by the types of fuel as shown in Figure 37.

into the environment will increase and consequently the exergy destruction in HRSG will decrease.

Qstucks I HRSG

into the environment will increase and consequently the exergy destruction in HRSG will decrease.

HRSG temperature is increased to 16.5 %, and the ST output would increase to 251.32 MW. The difference between this ST output and actual output of 215.7 by the ST or 35.62 should be charged as well to the desalting process. Again

> Qstucks I HRSG

Figure 35. The effect of stack temperatures on the heat rejection into environment as well as on the HRSG exergy destruction

Heat rejection in to the environment from stucks, MW

Heat rejection in to the environment from stucks, MW

fuel charged for thermal energy would be 269.75 or 113 MJ/m3.

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

**Figure 34.** The effect of ambient temperature on the specific fuel energy to desalination at different turbine inlet tem‐

fuel charged for thermal energy would be 269.75 or 113 MJ/m3.

slightly be affected by the types of fuel as shown in Figure 37.

TIT=1300 K TIT=1350 K TIT=1400 K

TIT=1300 K TIT=1350 K TIT=1400 K

Specific fuel energy to desalination, MJ/m3

peratures

Exergy destruction in one HRSG, MW

struction

14

16

18

20

22

24

26

28

30

14

16

18

20

22

24

26

28

30

Exergy destruction in one HRSG, MW

105

110

115

120

125

130

135

105

110

115

120

125

130

135

Specific fuel energy to desalination, MJ/m3

176 Desalination Updates

slightly be affected by the types of fuel as shown in Figure 37.

Tstucks, K 360 380 400 420 440 460 480

**Figure 35.** The effect of stack temperatures on the heat rejection into environment as well as on the HRSG exergy de‐

Tstucks, K 360 380 400 420 440 460 480 **Figure 36.** The effect of steam turbine inlet pressure on the specific fuel energy to desalination at different types of fuel

. 36Figure The effect of steam turbine inlet pressure on the specific fuel energy to desalination at different types of fuel

Figure 37. The effect of ambient temperature on the specific fuel energy to desalination at different types of fuel

Figure 38. The effect of fuel energy price on the desalinated water cost at different ambient temperatures

Fuel energy price, \$/GJ 0 2 4 6 8 10 12 14 16 18 20 22

desalinated water is strongly affected by the fuel type as shown in Figure 39.

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

100

Desalinated water cost, \$/m3

0.0

0.5

1.0

1.5

2.0

2.5

3.0

105

110

115

120

125

Figure 38 shows the effect of ambient temperature on the specific fuel energy to desalination when different types of fuel are used. Since there is a large difference in price per unit of energy between oil and natural gas, the cost of

> T1 = 50 o C

> T1 = 15 o C

Figure 35. The effect of stack temperatures on the heat rejection into environment as well as on the HRSG exergy destruction Specific fuel energy to desalnation, MJ/m3 130 135 Fuel oil Natural gas Figure 38 shows the effect of ambient temperature on the specific fuel energy to desalination when different types of fuel are used. Since there is a large difference in price per unit of energy between oil and natural gas, the cost of desalinated water is strongly affected by the fuel type as shown in Figure 39.

Specific fuel energy to desalination, MJ/m3

Specific fuel energy to desalination, MJ/m3

130

Fuel oil Natural gas

Fuel oil Natural gas

> Fuel oil Natural gas

Steam turbine inlet pressure, Psteam (kPa) 4000 5000 6000 7000 8000 9000 10000

Steam turbine inlet pressure, Psteam (kPa) 4000 5000 6000 7000 8000 9000 10000

. 36Figure The effect of steam turbine inlet pressure on the specific fuel energy to desalination at different types of fuel

. 36Figure The effect of steam turbine inlet pressure on the specific fuel energy to desalination at different types of fuel

fuel are used. Since there is a large difference in price per unit of energy between oil and natural gas, the cost of

desalinated water is strongly affected by the fuel type as shown in Figure 39. Figure 37. The effect of ambient temperature on the specific fuel energy to desalination at different types of fuel **Figure 37.** The effect of ambient temperature on the specific fuel energy to desalination at different types of fuel

Figure 38. The effect of fuel energy price on the desalinated water cost at different ambient temperatures

Fuel energy price, \$/GJ 0 2 4 6 8 10 12 14 16 18 20 22

Figure 38. The effect of fuel energy price on the desalinated water cost at different ambient temperatures **Figure 38.** The effect of fuel energy price on the desalinated water cost at different ambient temperatures 0.0

Figure 38 shows the effect of ambient temperature on the specific fuel energy to desalination when different types of Figure 39. The effect of steam turbine inlet pressure on the fuel energy allocated to DW at different types of fuel **Figure 39.** The effect of steam turbine inlet pressure on the fuel energy allocated to DW at different types of fuel

#### **8. Conclusion 8. Conclusion**

and natural gas.

**Nomenclature** 

. 36Figure The effect of steam turbine inlet pressure on the specific fuel energy to desalination at different types of fuel

. 36Figure The effect of steam turbine inlet pressure on the specific fuel energy to desalination at different types of fuel

Figure 37. The effect of ambient temperature on the specific fuel energy to desalination at different types of fuel

Figure 37. The effect of ambient temperature on the specific fuel energy to desalination at different types of fuel

Figure 38. The effect of fuel energy price on the desalinated water cost at different ambient temperatures

Figure 38. The effect of fuel energy price on the desalinated water cost at different ambient temperatures

T1 = 50 o C

fuel are used. Since there is a large difference in price per unit of energy between oil and natural gas, the cost of

T1 = 15 o C

T1 = 50 o C

T1 = 15 o C

Fuel energy price, \$/GJ 0 2 4 6 8 10 12 14 16 18 20 22

Fuel energy price, \$/GJ 0 2 4 6 8 10 12 14 16 18 20 22

**Figure 38.** The effect of fuel energy price on the desalinated water cost at different ambient temperatures

desalinated water is strongly affected by the fuel type as shown in Figure 39.

**Figure 37.** The effect of ambient temperature on the specific fuel energy to desalination at different types of fuel

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

desalinated water is strongly affected by the fuel type as shown in Figure 39.

Ambient temperature, T1 (K) 280 290 300 310 320 330 340

Steam turbine inlet pressure, Psteam (kPa) 4000 5000 6000 7000 8000 9000 10000

Steam turbine inlet pressure, Psteam (kPa) 4000 5000 6000 7000 8000 9000 10000

Specific fuel energy to desalination, MJ/m3

Specific fuel energy to desalination, MJ/m3

Specific fuel energy to desalnation, MJ/m3

178 Desalination Updates

Specific fuel energy to desalnation, MJ/m3

Desalinated water cost, \$/m3

Desalinated water cost, \$/m3

0.0

1.0

0.5

0.0

0.5

1.5

1.0

2.0

1.5

2.5

2.0

3.0

2.5

3.0

100

110

100

105

105

115

110

120

115

125

120

130

125

135

130

135

Fuel oil Natural gas

Fuel oil Natural gas

> Fuel oil Natural gas

> Fuel oil Natural gas

> > A general overview on the CPDP using GTCC is presented including description and analysis of the GTCC component. Energy and exergy analyses, based on the first and second laws of thermodynamics, respectively, were conducted on CPDP using GTCC connected with MSF desalting system. The concept of work loss due to exhausting steam from the ST at higher pressure and temperatures compared to end condenser condition was introduced and calculated. The exergy at different points of both GT and ST cycles and HRSG and the exergy destructions in several components were calculated. The main exergy loss was found in the GT combustion chambers. The fuel energy allocation between the desalting process and power production was conducted, based on the work loss and exergy methods. Both methods gave almost the same results. The main problem detected from the design of the given plant the high stack temperature of 183 oC of the HRSG to match that of high feedwater returning from the MSF desalting units at 135 oC. In GTCC using condensing turbines and NG with no sulfur, the typical HRSG stack temperature is 100 oC. The decrease of the stack temperature is reduced from 183 oC to 100 oC, which would increase the heat gain A general overview on the CPDP using GTCC is presented including description and analysis of the GTCC component. Energy and exergy analyses, based on the first and second laws of thermodynamics, respectively, were conducted on CPDP using GTCC connected with MSF desalting system. The concept of work loss due to exhausting steam from the ST at higher pressure and temperatures compared to end condenser condition was introduced and calculated. The exergy at different points of both GT and ST cycles and HRSG and the exergy destructions in several components were calculated. The main exergy loss was found in the GT combustion chambers. The fuel energy allocation between the desalting process and power production was conducted, based on the work loss and exergy methods. Both methods gave almost the same results. The main problem detected from the design of the given plant the high stack temperature of 183 o C of the HRSG to match that of high feedwater returning from the MSF desalting units at 135 o C. In GTCC using condensing turbines and NG with no sulfur, the typical HRSG stack temperature is 100 o C. The decrease of the stack temperature is reduced from 183 o C to 100 o C, which would increase the heat gain by the HRSG and ST work output about 19 %. This means that ST work output would be 256.6 MW. The difference between this ST output and actual output of 215.7 by the ST or 40.9 MW should be charged to also to the

> > > a specific exergy, kJ/kg

BPST back pressure steam turbine

F seawater feed flow rate, kg/s

GCC Gulf Cooperation Countries

GTCC gas-steam turbine combined cycle

CPDP cogeneration power-desalting plant

ECST extraction condensing steam turbine

D distillate output flow rate, kg/s or MIGD

GR gain ratio, distillate D per heating steam S, D:S

B brine flow, kg/s

DP desalting plant

EP electric power

FH feed heater

GT gas turbine

DW desalted seawater

BH brine heater

before, or the fuel charged for thermal energy would be 281.82 MW or 119 MJ/m3.

by the HRSG and ST work output about 19 %. This means that ST work output would be 256.6 MW. The difference between this ST output and actual output of 215.7 by the ST or 40.9 MW should be charged to also to the desalting process. Again, for net efficiency of 44 %, the fuel energy of 92.94 MW should be added to the 188.8 MW calculated

Sensitivity analysis shows that the pressure ratio, inlet air temperature, turbine inlet temperature, and stack temperature have a significant role in the combined cycle performance. It shows also that the cost of desalinated water is strongly affected by the fuel type because there is a large difference in price per unit of energy between oil

A stream availability, mass flow rate×specific exergy, kW or MJ

desalting process. Again, for net efficiency of 44 %, the fuel energy of 92.94 MW should be added to the 188.8 MW calculated before, or the fuel charged for thermal energy would be 281.82 MW or 119 MJ/m3 .

Sensitivity analysis shows that the pressure ratio, inlet air temperature, turbine inlet temper‐ ature, and stack temperature have a significant role in the combined cycle performance. It shows also that the cost of desalinated water is strongly affected by the fuel type because there is a large difference in price per unit of energy between oil and natural gas.

### **Nomenclature**



#### **Greek letters**

desalting process. Again, for net efficiency of 44 %, the fuel energy of 92.94 MW should be added to the 188.8 MW calculated before, or the fuel charged for thermal energy would be

Sensitivity analysis shows that the pressure ratio, inlet air temperature, turbine inlet temper‐ ature, and stack temperature have a significant role in the combined cycle performance. It shows also that the cost of desalinated water is strongly affected by the fuel type because there

is a large difference in price per unit of energy between oil and natural gas.

A stream availability, mass flow rate×specific exergy, kW or MJ

281.82 MW or 119 MJ/m3

180 Desalination Updates

**Nomenclature**

a specific exergy, kJ/kg

BPST back pressure steam turbine CPDP cogeneration power-desalting plant D distillate output flow rate, kg/s or MIGD

ECST extraction condensing steam turbine

GR gain ratio, distillate D per heating steam S, D:S

F seawater feed flow rate, kg/s

GCC Gulf Cooperation Countries

h specific enthalpy, kJ/kg H heat rate (3,600/h), kJ/kWh HHV fuel high heating value, kJ/kg

GTCC gas-steam turbine combined cycle

HRSG heat recovery steam generator

L latent heat of vaporization, kJ/kg

IP intermediate pressure

B brine flow, kg/s BH brine heater

DP desalting plant DW desalted seawater

EP electric power

FH feed heater

GT gas turbine

HP high pressure

kWh 3,600 kJ/s

.


#### **Subscripts**


### **Author details**

M.A. Darwish, H.K. Abdulrahim\* , A.A. Mabrouk and A.S. Hassan

\*Address all correspondence to: habdelrehem@qf.org.qa

Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar

#### **References**


[5] Bob Shepard, Gas turbines technologies for electric generation, Power Plant Primer - Combustion Turbines - IEEE Mississippi Section, http://www.ieeems.org/Meetings/ presentations/MS3-ASME%20Gas%20Turbine%20Technologies%20Presentation.ppt

**Subscripts**

182 Desalination Updates

b boiler or brine bd blowdown stream cw cooling seawater

*e* extracted steam e environment

pp power plant r reheat

**Author details**

**References**

g saturated vapor properties

M.A. Darwish, H.K. Abdulrahim\*

9\_SGT65000F.pdf

2014-10-12\_PGME\_8000H.pdf

kompendium\_power\_Bolland.pdf

d desalting unit, discharge vapor, or distillate

f saturated liquid properties, feed heaters, or fuel

\*Address all correspondence to: habdelrehem@qf.org.qa

of gas turbines in Kuwait, Energy 33 (2008) 571–588

gy.siemens.com/nl/pool/hq/energy-topics/technical-papers/

, A.A. Mabrouk and A.S. Hassan

[1] Mohamed A. Darwish, Hassan K. Abdulrahim, Anwar B. Amer, On better utilization

[2] John Xia, Rick Antos, (W501F) 3 Million hours fleet operational experience, POWER-GEN International 2006 – Orlando, FL, November 28-30, 2006, http://www.ener‐

[3] Armin Städtler, Meeting the Middle East Energy Demand with the Proven 8000H Series, Power-Gen Middle East, Abu Dhabi, 2014-10-12, http://www.ener‐

[4] Olav Bolland, Thermal power Generation, (2014), http://folk.ntnu.no/obolland/pdf/

gy.siemens.com/co/pool/hq/energy-topics/pdfs/en/gas-turbines-power-plants/

Qatar Environment and Energy Research Institute, Qatar Foundation, Doha, Qatar


Ishak, Development of low NOx liquid fuel burner, Faculty of Mechanical Engineer‐ ing, Universiti Teknologi Malaysia 2005, http://eprints.utm.my/539/1/LAPOR‐ AN\_AKHIR\_IRPA\_74069.pdf

