Comparative thermodynamic performance study for the design of power and desalting cogeneration technologies in Kuwait

Energy Conversion and Management 185 (2019) 654–665

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Comparative thermodynamic performance study for the design of power and desalting cogeneration technologies in Kuwait Ali H. Abdulrahim, J.N. Chung

T

⁎

Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA

A R T I C LE I N FO

A B S T R A C T

Keywords: Power generation Seawater desalination Dual-purpose plants Cogeneration Gas turbine combined cycle Combined heat and power

This study attempts to answer two questions by developing a thermodynamic mathematical model: which is the optimal energy conversion process, generating power and desalting water independently or coupling power generation with seawater desalination technologies via cogeneration power and desalting plants (CPDP)? How would modifying the plant design affect the performance of a CPDP? Nine different configurations of power and water conversion technologies are modeled and compared with respect to an ideal reversible CPDP using a newly introduced cost-based dimensionless parameter, the power and water gain ratio (PWGR). Results of this study show that producing power using a gas turbine combined cycle (GTCC) and desalting seawater using reverse osmosis (RO) on a stand-alone basis is the most energy efficient for generating power and desalinating water simultaneously. GTCC-RO has the closest PWGR set at 1.470 to the ideal reversible reference plant’s 1.529 PWGR. Modifying the number of gas turbines (GT), steam turbines (ST), and multi-effect distillation (MED) units can improve the performance of the combined cycle heat and power (CCHP) reference plant coupled with MED desalination units.

1. Introduction Seawater desalination technologies are divided into two major categories: thermal and membrane processes [1]. Thermal processes include multistage flash (MSF), multi-effect distillation (MED), and vapor compression (VC). VC desalination plants can be either mechanically (MVC) or thermally driven (TVC). Membrane desalination processes include reverse osmosis (RO) and electrodialysis. The coupling of power production and seawater thermal desalination technologies via dual-purpose cogeneration power and desalting plants (CPDP) plants has long been used in Kuwait due to the shortage of fresh water sources in the country. From the 1970′s up until the mid 2000′s, steam turbine (ST) driven combined heat and power (ST-CHP) plants were coupled with seawater MSF units via the process heat generated in the CHP plant. Low and medium pressure steam is bled from steam turbines for the required MSF intake. Gas turbine combined cycle (GTCC) power plants were adopted in the 2000′s due to their relatively higher thermodynamic efficiency (ηth ) compared to ST power plants. Using an energy and exergy analysis, Ahmadi et al. [2] calculated the ηth of a single 200 MW ST regenerative cycle unit in a power plant in Isfahan, Iran to be 32%. In several studies, Ahmadi et al. [3–5] investigated repowering the same ST plant to a GTCC plant. Significant increases in thermal energy and exergy ⁎

Corresponding author. E-mail address: jnchung@ufl.edu (J.N. Chung).

https://doi.org/10.1016/j.enconman.2019.02.027 Received 23 November 2018; Accepted 11 February 2019 0196-8904/ © 2019 Elsevier Ltd. All rights reserved.

efficiencies were achieved from such repowering. Abuelnuor et al. [6] calculated the ηth to be 38% for a light diesel oil-fired 180 MW GTCC in Sudan. In a study by Ibrahim et al. [7] to reach the optimum thermal performance of Marafiq GTCC (3 GT + 1 ST) in Saudi Arabia, it was found that the highest attained thermal efficiency and power output of the plant reached 61% and 1540 MW respectively. A modeling, simulation, and optimization study by Balku [8] shows that a NG-fired simple combined gas-vapor cycle’s ηth can be increased by 22.55% using optimal design variables. Based on an energy and exergy performance analysis using real operational data of a 119.2 MW GTCC (2 GT + 1 ST) in Turkey, Ersayin et al. [9] found that the energy and exergy efficiencies were 56% and 50.04% respectively. As a result of the higher ηth rates attained in GTCCs in comparison with ST power plants, Kuwait started to commission another CPDP configuration by coupling CCHP plants with their existing MSF units by extracting steam from the steam turbine in the bottom cycle and/or from the heat recovery steam generator (HRSG) units. A study by Ahmadi et al.[10], showed that repowering a CHP system to a CCHP increases the energy, exergy, heat, and total efficiencies significantly. Economic and environmental benefits attained from such repowering are further explored in a latter study by Ahmadi et al.[11] using an energy, exergy, environmental (3E) analysis. Kuwait’s most recently commissioned CPDP in 2015, Az-Zour North (AZN), couples CCHP units

Energy Conversion and Management 185 (2019) 654–665

A.H. Abdulrahim and J.N. Chung

Nomenclature

HRSG IG KWD LHV m MED MIG MIGD MSF MVC MX n NG NGP P PI Pr PR PWGR q Q RO s ST SW SWP T TAC TIT TVC v VC w W WR

Greek Symbols ƞCC ƞgen ƞHRSG ƞs,c ƞs,GT ƞs,P ƞs,ST ƞTH ƞTOP ɣc ε ρ

Efficiency of combustion chambers Efficiency of generators Efficiency of HRSG units Isentropic efficiency of compressors Isentropic efficiency of gas turbines Isentropic efficiency of pumps Isentropic efficiency of steam turbines Thermodynamic Efficiency Thermal efficiency of top cycle Compression ratio Utilization factor Density, kg/m3

Abbreviations A/F AZN CCHP CHP CPDP D DW DWP EP EV FC GOR GT GTCC h HBD HFO

Air-to-fuel ratio Az-Zour North Combined cycle heat and power Combined heat and power Cogeneration power and desalting plants Desalted water production rate, kg/s Desalted water Desalted water price, KWD/Thousand IG Electricity price, KWD/kWh Expansion valve Total fuel cost per second, $/s Desalted water gain ratio Gas turbine Gas turbine combined cycle Enthalpy, kJ/kg Heat balance diagram Heavy Fuel Oil

Heat recovery steam generator Imperial gallons Kuwaiti Dinars Lower heating value, kJ/kg Mass flow rate, kg/s Multi-effect distillation Millions of imperial gallons Millions of imperial gallons per day Multistage flash Mechanical vapor compression Mixing Chamber Number of units Natural gas Natural gas price, $/ft3 Pressure, kPa Pump I Relative Pressure Total revenue generated per second from power, $/s Power and water gain ratio Heat per unit mass, kJ/kg Heat, MW Reverse osmosis Entropy, kJ/(kg.K) Steam turbine Seawater Seawater pumps Temperature, K (unless stated otherwise) Total annual cost Gas turbine inlet temperature, °C Thermal vapor compression Specific volume, m3/kg Vapor compression Work per unit mass, kJ/kg Power, MW Total revenue generated per second from water, $/s

The main objective of this study is to develop a mathematical model based on the 1st law of thermodynamics to compare the performance of nine different options for the production of power and desalted seawater in Kuwait using conventional and newly introduced cost-based comparison parameters. In power and/or heat plants, evaluating the thermodynamic performance of each plant type is clearly defined via comparing conventional metrics such as the thermodynamic efficiency, utilization factor, and heat generation rate of each plant. However, in CPDPs, two useful outputs are produced (electricity and desalted water from two different sources: fuel and seawater) which can make conventional metric’s values misleading in assessing the actual performance of CPDPs.

with an improved thermal desalting conversion technology, MED, which generally has a higher desalted water gain ratio (GOR) than MSF. In recent years, Kuwait also commissioned stand-alone GTCC plants to produce power only and stand-alone RO plants to produce water only i.e. produce power and desalt seawater independently. RO plants are electrically-operated and no low/medium pressure steam is needed to operate them. Several studies performed energy and exergy analysis-based models on different configurations of CPDPs. Darwish et al. [12] presents a comprehensive description of the system components in a CCHP-MSF using Kuwait’s Shuaibah North as a reference plant and develops a mathematical model to assess the plant’s fuel consumption A thermoeconomic performance analysis was performed by Hanafi et al. [13] on a CCHP-TVC cogeneration plant. In a comparative case study by Lianying et al. [14], a mixed integer nonlinear programming model was used to optimize the total annual costs in the cogeneration of power and water using a top-to-bottom approach. In another study and using real operational data of Sabiya’s GTCC plant and Al-Jubail TVC-MED desalination plant in Saudi Arabia, Almutairi et al. [15] performs a detailed exergy-based analysis to assess the major sources of irreversibility’s in their proposed cogeneration plant. In an attempt to reduce the dependence on fossil fuels for power generation, several research studies explore hybridizing conventional power generation technologies with renewable and sustainable energy systems. Ahmadi et al. [16] investigated the integration of solar energy with an existing fossil fuel-fired power plant by replacing high-pressure feed water preheaters with a solar farm.

2. Modelling of CPDP systems An ideal reversible power and desalination plant resembling of AZN’s design is empirically modeled (Ideal Case). AZN is a natural gasfired CCHP-MED with a total power capacity of 1648 MW and a total desalination capacity of 107 MIGD. The plant is composed of five 228 MW GT units coupled with five HRSG units. Steam generated from the 5 HRSG units are fed into two 254 MW ST units. Medium and lowpressure heat is bled from the HRSG and ST units respectively to feed the ten 10.7 MIGD MED units. The base case is modeled using physical operating data collected from AZN’s heat balance diagrams including the fuel type and heating value, ambient conditions, and turbines’ inlet temperatures. Case 1 is generated by mimicking the AZN plant. The system 655

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2.2. Desalination units

components’ efficiencies of Case 1 are estimated such that the thermophysical properties at each state point in the cycles are within 5% from the values in AZN’s HBD. Changes are made to the system’s components such as replacing the MED units with RO units to generate other cases for comparison. In this case, the plant will be converted from a CCHP-MED (Case 1) to a GTCC-RO plant (Case 3 in this study). A total of nine cases will be studied. The chemical to mechanical to electrical energy and water conversion pathways for the nine cases are illustrated in Fig. 1. The nine cases are modeled to achieve the same power and fresh water export rates as Case 1 using the same ambient and operating conditions, fuel type and heating value, and system component’s efficiencies for all cases to ensure an impartial comparison. For all cases, the ambient air temperature (Tamb) is set at 34 °C, ambient air pressure (Pamb) is equal to 101.3 kPa, and the fuel type is natural gas (NG) with a lower heating value (LHV) of 47,969 kJ/kg and a density ( ρNG ) equal to 0.8 kg/m3.

MED units’ intakes are superheated steam and seawater (SW) and the MED units’ output are desalted water (DW) and condensate (mCOND). For the reference case of this study, multiplying DMED by nMED gives the plant’s total DW production (DPROD) equal to 107 MIGD. It is assumed that the SW mass flow rate (mSW) is equal to the mass flow rate of DW (mDW) which is equal to DMED. It was also assumed that the density of SW (ρSW ) is equal to the density of DW ( ρDW ) which are both assumed equal to 1000 kg/m3. DMED is converted to kg/s as follows: 6 3 kg 1D ⎞⎛ 1 × 10 ⎞⎛ 0.00455 m ⎞ × ρDW ⎛ ⎞ DMED = 10.7MIGD⎛ 3 24 60 60 1 1 m × × s M IG ⎠⎝ ⎝ ⎝ ⎠ ⎠⎝ ⎠ ⎜

⎟⎜

= 563.5 kg / s

⎟

(1)

The two forms of steam consumed in the desalination process are LP steam (mLP) and MP steam (mMP). The MED unit consumes electrical power (Wdesal) only to operate the seawater pumps (SWP) as shown in Fig. 2. SW is pumped into the MED unit with a pumping energy per unit mass (wSWP) at 14.4 kJ/kg as approximated in [12]. Wdesal in the reference model and the seawater pumps’ electrical power per MED unit (WSWP) are calculated using the relation:

2.1. Modelling approach A top-to-bottom modelling approach was undertaken where the power and fresh water production and export rates are set as input parameters and the objective function was to find the required fuel consumption rate to achieve the defined outputs. Darwish et al. [12] performed a similar 1st Law analysis on Shuaiba North, another CPDP configuration in Kuwait (CCHP-MSF) using a bottom-to-top approach. For the development of the reference model, AZN is modelled by splitting the CPDP plant into three cycles: desalination cycle, top cycle, and bottom cycle. The reference plant system has 31 state points as shown in Fig. 2. First, the MED desalination cycles are modelled followed by the power cycle. The power cycle is composed of two subsystems: top cycle and bottom cycle. Since the bottom cycle depends on the low pressure (LP) and medium pressure (MP) steam supply rates being consumed in the MED plant to generate desalted water, modelling the MED plant first is important to find these mass flow rates. For each process, several assumptions and operating parameters are defined. The reference model’s input parameters are tabulated in Table 1.

Wdesal = WSWP =

mSW × wSWP = 8. 113 MW 1000

(2)

In AZN, mMP at a pressure of 1600 kPa is drawn from HRSG units for desalination. This steam is used for the ejectors in the MED unit to generate the required vacuum in different sections of the unit [1]. mMP is not recovered, and make-up water is fed into the plant’s deaerator to compensate the lost steam. In the reference case, mMP over the total steam supply is set equal to 4.9112% based on AZN’s HBD. The majority of the steam supply, mLP at a pressure of 291 kPa is bled from the ST units and is used for the multiple effect distillation process. This LP steam is recovered as condensate at a pressure of 1200 kPa and fed into the plant’s deaerator at state condition (28) in the bottom cycle. The gain ratio (GOR) of a thermal desalination plant is a metric used to determine how efficient the plant is producing desalted water based on the total amount of thermal energy consumed. In MSF units, the

Fig. 1. The nine energy and water conversion pathways cases to generate electricity and desalted water in Kuwait are illustrated. 656

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Fig. 2. System diagram of the reference model.

the same pumping electrical power requirement as MED units. The MSF units’ modeling is equivalent to MED units except for the lower GOR i.e. more heating steam is needed in MSF unit which will negatively impact the performance of the power block. For Cases 3, 6, and 9, DW is produced using RO units which require electrical power as the only form of energy i.e. mMP and mLP are equal to zero in RO units and the power block needs to produce more power to compensate the additional electrical power consumption in the RO units. The reported average energy consumption of RO units ranges from 3.7 to 8 kWh/m3. For a typical 24,000 m3/day seawater RO unit (approximately equivalent to DRO = 278 kg/s), the consumption ranges from 4 to 6 kWh/m3 [1]. For the RO cases modeled in this study the following parameters are used:

GOR is relatively lower than in MED units. More specifically in the Arab Gulf countries, the GOR ranges between 8 and 10 kgdistillate/kgsteam for MSF plants and 8–12 for MED plants [1]. Based on Darwish et al.’s [12] energy analysis on SHN, the GOR of MSF units were calculated to be 8.06. Kotb [17] developed a numerical model for the design of a MSF system to be coupled with a 650 MW power plant in Suez City, Egypt using the Red Sea’s seawater and calculated a GOR of 8.76 for a 28 flashing stages MSF system with D equal to 2229 kg/s. In this study, the MED’s GOR is defined as an input parameter in the system equal to 10.598 and mLP, mMP are calculated using the following relations:

mMP = 0.049112 × (mMP + mLP )

GOR =

D mMP + mLP

(3)

• Number of RO units (n ) is equal to 20. • RO unit capacity is equal to 280.4 kg/s

(4)

RO

For Cases 2, 5, and 8, the MSF unit’s GOR is set equal to 8.76 with 657

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following equation:

Table 1 Reference model top and bottom cycle input parameters.

ηs, c =

Desalination Cycle Desalted water production rate per MED unit (DMED) Number of MED units (nMED) MED unit desalted water gain ratio (GORMED) Top Cycle Net electric power generated per gas turbine (Wgen,GT) Number of GT units (nGT) Number of HRSG units (nHRSG) Compression ratio (ɣc) GT inlet temperature (TIT) Temperature of air and exhaust gases leaving HRSG stack (Tstack) Bottom Cycle Net electric power generated per steam turbine (Wgen,ST) Number of ST units (nST) Pressure of water leaving deaerator (P6) Pressure of water entering HRSG unit (P10) Pressure of water leaving the dump condenser (P26) Steam Turbine Inlet Temperature (T18) Temperature of Make-up water (T31)

10.7 MIGD

isentropic work h − h1 = 2s actual work h2 − h1

T2 and s2 are functions of h2 and are calculated using [18]. T3 = TIT and isobaric heat addition is assumed in the combustion chamber i.e. P3 = P2. At state 3, h3, s3, and Pr3 are functions of T3 and are interpolated from [18]. The expansion ratio in the gas turbine is assumed equal to the compression ratio in the compressor and the pressure and relative pressure at state 4 are calculated using the following relationship:

10 10.60 228.0 MW 5 5 17.21 1,340 °C 164.4 °C

γc =

P3 Pr = 3 P4 Pr4

254 MW

ηs, GT = 2 170 kPa 10,052 kPa 26.60 kPa 546.0 °C 40.00 °C

wnet , TOP = wGT − wC = (h3 − h4 ) − (h2 − h1)

ηgen =

mair =

RO

equal to 18 kJ/kg (5 kWh/m3).

(9)

(10)

Wgen, GT Wnet , GT

(11)

Wnet , GT = m1 = m2 = m3 = m4 = m5 (ASA) wnet , TOP

(12)

Therefore, the compressor and gas turbine power consumption and production are equal to:

The power required to operate one RO unit (WRO) is calculated using the following equation: (5)

Compressor Power Consumption, Wc = (mair × wc )/1000

(13)

GT Power Production, WGT = (mair × wGT )/1000

(14)

The heat gain of air per unit mass in the combustion chamber (qin,TOP), heat available for HRSG unit from GT exhaust air per unit mass (qHRSG,TOP), heat input per gas turbine unit (Qin,GT), and heat available for bottom cycle per HRSG unit (QHRSG,TOP) are calculated as follows:

2.3. Top cycle – GT units As shown in Fig. 2, there are five state conditions in the top cycle. The top cycle calculations are valid for Cases 1 to 6 in our comparison study. Several idealizations and assumptions were made to calculate the required fuel intake in the top cycle. The Air Standard Assumption (ASA) was used in the steady-state model with air considered an ideal gas. Filtering and cooling of ambient air before entering the compressor is neglected in this study. Friction and heat losses to the surroundings from system components are accounted for by assigning efficiencies to each system component in cases 1 to 9. Pressure drops in the pipelines are neglected. A step-by-step guide is presented in this paper to determine the NG consumption in the actual top cycle. First, T1 and P1 are assumed equal to the ambient temperature and pressure, respectively. Other thermodynamic properties including relative pressure (Pr), enthalpy (h), and entropy (s) at state 1 are functions of T1 and P1 and are calculated using a MATLAB code by Miller [18] which interpolates thermodynamic values using the standard thermodynamic air tables that follow the ideal gas law. The pressure and relative pressure at state2 are found using the following formulas:

P Pr γc = 2 = 2 P1 Pr1

actual work h − h4 = 3 isentropic work h3 − h4s

T4 and s4 are functions of h4 and are interpolated from air tables [18]. At the HRSG stack exit: T5 = Tstack, P5 = Pamb, and h5, s5 are functions of T5 and are interpolated from [18]. The net -work per unit mass in the top cycle (wnet,TOP), net mechanical power produced per gas turbine (Wnet,GT), mass flow rate of air (mair), and mass flow rate at each state are calculated using the following equations:

• Total desalted water exported from RO unit is equal to the total MED units’ DW export value. • Electrical energy consumed per unit mass of desalted water (w ) is

WRO

(8)

T4s and h4s are functions of Pr4 and are estimated by [18]. h4 is calculated using the following formula:

6.420% of mass flow rate of steam leaving ST is fed into deaerator. 0.792% of water leaving deaerator is bled from Pump I to cool MP steam and Pump I raises water pressure to 4042 kPa for cooling MP steam (P7) and 14278 kPa for the HRSG units (P8).

D × wRO = RO 1000

(7)

qin, TOP = h3 − h2

(15)

qHRSG, TOP = h4 − h5

(16)

Qin, GT = mair × qin, TOP

(17)

QHRSG, TOP = mair × qHRSG, TOP

(18)

Finally, the air-to-fuel ratio (A/F), thermal efficiency of the top cycle (ηTOP), and the mass flow rate of natural gas per GT unit (mNG,TOP) are calculated using the following equations:

Qin, GT = (mNG, TOP × LHV ) ηCC A/F =

ηTOP =

mair mNG, TOP

(19)

(20)

Wgen, GT Qin, GT

(21)

The ambient temperature effects on the fuel consumption of the top cycle was assessed by simulating the top cycle mathematical model using hourly temperature data from a 2011 weather file for Az-Zour, Kuwait.

(6)

The isentropic temperature (T2s) and enthalpy (h2s) at state 2 are functions of Pr1 and are estimated using [18]. h2 is calculated using the 658

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m6 = m24 + m30 + m31

2.4. Bottom cycle – ST units

0.792% of water mass flow rate is used for cooling the MP steam and the mass balance of PI and HRSG yields:

State points 6 to 31 represent the bottom cycle as shown in Fig. 2 with water/steam being the working fluid of the cycle. Several assumptions were introduced to assist modelling the bottom cycle. Ideal throttling is assumed in all expansion valves and isobaric heat addition in the HRSG units. Using a similar methodology as the top cycle, thermophysical properties at each state point are calculated using a MATLAB code by Holmgren [19] which interpolates thermodynamic values using the standard thermodynamic steam tables and system components’ mass and energy balances. To avoid redundancies, only the required equations and mass/energy balances used for modeling the bottom cycle are presented in this paper.

=

(39)

m8 = m10 = m11 = m12 + m16 nHRSG

(40)

m = 18 nST

(41)

m17 = m16 × nHRSG

Finally, the mass balance of mixing chamber II (MXII) unit returns the remaining mass flow rates:

m14 = m15 − m7 = m13 = m12 × nHRSG

(42)

2.4.3. Mass flow rate of NG in bottom cycle After obtaining the water/steam mass flow rates at each state, the remaining thermodynamic properties at each state condition in the bottom cycle and the mass flow rate of NG feeding the bottom cycle (mNG,HRSG) in the HRSG unit are found by performing an energy balance on the mixing chambers, expansion valves, deaerator, and HRSG units. Mixing Chambers: (43)

v26 × (P27 − P26) wPII

MXII: m15 h15 = m7 h7 + m14 h14

(44)

(22)

wPI ,(ii) = h8 − h6

(24)

wPI = wPI ,(i) + wPI ,(ii)

(25)

wPII = h27 − h26

(26)

Deaerator:

m6 h6 = m30 h30 + m24 h24 + m31 h31

actual turbine work w h − h19 = ST = 18 isentropic turbine work wST , s h18 − h19s

wnet , bottom = wST − wPI − wPII

(45)

Expansion Valves:

EVI: h13 = h14

(46)

EVII: h22 = h24

(47)

EVIII: h23 = h25

(48)

EVIV: h29 = h30

(49)

(27)

EVV: h9 = h10

(50)

(28)

HRSG Units: In the HRSG units, additional firing of NG is used to assist the heat received from the top cycle to reach the defined steam turbine inlet temperature’s enthalpy. The heat gain of steam per unit mass in the HRSG (qin,HRSG) and the additional NG mass flow rate of the bottom cycle (mNG,HRSG) is calculated via an energy balance on the HRSG unit as follows:

Steam Turbines:

m19 =

m 7 + m8 = m 6

MXI: m29 h29 = m27 h27 + m28 h28

(23)

ηgen =

(38)

isentropic pump work v × (P7 − P6) v × (P8 − P6) = 6 = 6 actual pump work wPI ,(i) wPI ,(ii)

wPI ,(i) = h 7 − h6

ηs, ST =

m7 = m6 × 0.007920

m9 =

2.4.1. Mass flow rate of steam at turbine exit First, the pumps and steam turbines are evaluated with the objective of finding the mass flow rate of steam at the turbine exit (m19) from the power over work per unit mass relationship as derived for the mass flow rate of air at the gas turbine exit in the top cycle. Pumps: A small amount of water is bled from Pump I for cooling the MP steam drawn from the HRSG unit as intake for the desalination plant. Pump I and Pump II’s work per unit mass and enthalpies are found using the following equations:

ηs, P =

(37)

Wgen, ST Wnet , ST

(29)

Wnet , ST wnet , bottom

(30)

qin, HRSG = h11 − h10

2.4.2. Mass balance of bottom cycle Second, a mass balance is conducted for all the state points in the bottom cycle to evaluate the mass flow rate at each state. Since LP steam directed to the desalination plant is recovered as condensate and 6.42% of mass flow rate of steam leaving ST is fed to deaerator:

(51)

Qin, HRSG = ηHRSG × LHV × mNG, HRSG = m10 (h10 − h11) − QHRSG, TOP (52)

m m19 = 20 nST

(31)

Finally, the total MP (QMP) and LP (QLP) heat gain in the desalination plants, and heat rejection in the dump condenser (Qout) are calculated as follows:

m21 = mLP × nMED = m28

(32)

QMP = nMED × mMP × qMP = nMED × mMP × (h15 − h31)

(53)

m22 = m20 × 0.0642 = m24

(33)

QLP = nMED × mLP × qLP = nMED × mMP × (h21 − h28)

(54)

m23 = m20 − m21 − m22 = m25 = m26 = m27

(34)

Qout = m26 × qout = m26 × (h25 − h26)

(55)

(35)

2.5. CPDP performance summary

Conducting a mass balance on mixing chamber I (MXI) unit:

m27 + m28 = m29 = m30

Since all MP steam lost to desalination plant is recovered as makeup water and performing a mass balance on the deaerator:

m31 = mMP × nMED = m15

To assess the overall performance of the CPDP, the total electrical power produced and consumed by the plant (Wgen,total), total desalted water produced and consumed by the plant per second (Dtotal), and total

(36) 659

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natural gas consumed by the plant per second (mNG,total) are computed. These parameters are calculated as follows:

Wgen, total = [(nGT × Wgen, GT ) + (nST × Wgen, ST )] − [ndesal × Wdesal]

(56)

Dtotal = (ndesal × Ddesal ) − (ndesal × mMP )

(57)

mNG, total = (nGT × mNG, TOP ) + (nHRSG × mNG, HRSG )

(58)

The utilization factor of the plant (ε) is a conventional parameter used to measure the overall efficiency in cogeneration CHP plants and is calculated as follows:

ε=

PR,

$ = Wgen, total × EP s

(63)

WR,

$ = Dtotal × DWP s

(64)

FC ,

$ = mNG, total × NGP s

(65)

PWGR =

PR + WR FC

(66)

Wgen, total + QLP + QMP (nGT × Qin, GT ) + (nHRSG × Qin, HRSG )

(59)

2.6. CPDP comparison

Usually, the thermodynamic performance of cogeneration heat and power plants is evaluated based on this parameter. However, the utilization factor does not differentiate between the quality of energy produced since ε combines electrical energy (high grade energy) and process heat in the form of thermal energy (low grade energy) over the total fuel thermal energy produced from NG (low grade energy). The utilization factor cannot necessarily be a true assessment of “how efficient the plant is” in producing high quality commodities from lower quality commodities. A new cost-based dimensionless parameter, PWGR is introduced to effectively assess “what we get for what we put in”. PWGR measures the total revenue generated per second from power and water minus the total costs per second of in-house power and water consumption (PR and WR) over the total fuel cost in the plant per second (FC) using the electricity price (EP), desalted water price (DWP), and NG price (NGP). Historically, electricity and fresh water prices were highly subsidized at a rate of 0.002 KWD/kWh and 0.800 KWD/Thousand IG. In 2017, the Ministry of Electricity and Water in Kuwait, MEW set new electricity and water tariffs on a sectoral basis for all sectors except the private residential sector [20]. Table 2 lists the current electricity and water tariffs by sector and the load distribution consumption for electrical installations in 2016. In this study, EP and DWP were assumed to be 0.00529 KWD/kWh and 1.462 KWD/Thousand IG, respectively, based on a weighted average of sectoral load consumption percentages for electrical installation in 2016. As for NGP, the price is assumed constant and estimated to be $2.99 /1000 ft3 based on the Henry Hub NG spot price annual average in 2017 [21]. Price conversions for calculating EP, DWP, NGP and the PR, WR, FC, and PWGR calculations are as follows:

Cases 1 to 9 are modelled such that they export the same amount of power and fresh water from the plant as the reference ideal reversible model. The desalination technologies are compared first followed by the overall CPDP performance comparison. Other parametric studies are performed to assess the impact of the number of GT, HRSG, ST, and MED units on the performance of the reference plant. Desalination units are sized such that all desalination technologies’ DW export values are the same amount as that of the reference model. As a result, the DW production rate for each technology is different. Since the GOR in MSF plants is lower than MED plants, the total steam supply required for the MSF plant and the total fuel consumption in the coupled power plant is relatively higher. In RO plants, the steam supply mass flow rates are set to zero since no thermal energy is consumed in RO plants and the power consumption includes both the power required to operate the seawater pumps and the RO plant itself. As a result of the higher electrical consumption in the RO plants, the power capacity in the power plant is increased in Cases 3, 6, and 9 to achieve the same power export values as the reference model. In Case 3, there is an option to increase either the GT or the ST capacity. Two subcases are analyzed to assess the impact of increasing the GT or ST power production: Case 3a increases GT power production and Case3b increases ST power production. For Cases 4 and 5, the bottom cycle is different from the reference model since there are no ST units and the bottom cycle exists solely for the production of MP and LP steam. As a result, the state points are different, and the bottom cycle system diagram is illustrated in Fig. 3 for Cases 4 and 5. The temperature and pressure of LP steam is assumed the same as in Case 1 and the mass flow rate in the cycle is calculated based on the mLP instead of the mass flow rate exiting the steam turbine as in the reference model. Coupling of the top cycle model with the RO plant model generates Case 6 and coupling the bottom cycle model with the MED/MSF models generate Case 7 and 8 respectively. Many CPDPs in Kuwait follow Case 8 with some operating modifications such as using reheat and regenerative cycles. In addition to NG, heavy fuel oil (HFO) is another fuel commonly used in Kuwait for firing ST-CHP plants. As for Case 9, the bottom cycle model is coupled with the RO plant. HRSG units are replaced with boilers for cases 7–9. An advantage of Cases 7–9 is that ambient conditions have minimal effect on the performance of power and fresh water production since the working fluid in the cycle is water/steam only.

KWD 5. 29 × 10−3 ⎡ $1 1 kW ⎤⎡ 1 h ⎤⎡ ⎤ −3 kWh ⎣ KWD 0. 300 ⎦ ⎣ 3600 s ⎦ ⎣ 1 × 10 MW ⎦ $4. 898 × 10−3 = (60) MJ

EP =

3 KWD 1. 462 ⎡ $1 1 IG ⎤⎡ ⎤ × 1 ⎡m ⎤ 1000 IG ⎣ KWD 0. 300 ⎦ ⎣ 0. 00455 m3 ⎦ ρDW ⎢ kg ⎣ ⎥ ⎦ 3 − $1. 071 × 10 = kg

DWP =

NGP =

$2. 99 ⎡ 35. 3147 ft 3 ⎤ 1 ⎡ m3 ⎤ $ 0. 1320 = × 3 3 ⎥ ⎢ ⎥ ρNG ⎢ 1000 ft ⎣ 1m kg kg ⎦ ⎣ ⎦

(61)

(62)

Table 2 Load consumption percentages for electrical installations during 2016 – input data from [22], electricity and water tariffs by sector in Kuwait-input data from [20]. Sector

Load Consumption Percentages for Electrical Installations during 2016

Electricity Tariff (KD/kWh)

Water Tariff (KD/Thousand IG)

Agriculture Industrial Commercial Investment Buildings Government Private

3% 6% 11% 16% 10% 54%

0.003–0.005 0.003–0.005 0.005 0.005 0.025 0.002

0.75–1.25 0.75–1.25 2 2 4 0.8

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Fig. 3. Bottom cycle system diagram for Cases 4 and 5.

3. Results and discussion

desalination processes. As a result, CPDP plants coupled with MED and MSF desalination systems produce an additional 26.1 kg/s and 31.7 kg/ s of DW respectively for the make-up water. The total DW production rate for each desalination system to export the same rate as AZN’s DW is shown in Fig. 6b).

The ideal reversible CCHP-MED reference case is designed such that the total power (1566.9 MW) and desalted water (5608.7 kg/s) export rates are identical to AZN’s power and fresh water export values. The thermophysical properties at each state point in the reversible reference system were used to ultimately compute the system’s performance parameters for comparison with the other power and water conversion technologies. Case 1 is then modelled as a more accurate representation of AZN’s CCHP-MED plant configuration. System components’ efficiencies shown in Table 3 were calculated such that the mass flow rate, pressure, temperature, enthalpy, and entropy at each state point in the system were within 5% of the published values in AZN’s HBD. The system components’ efficiencies are applied to all of the following cases in this study. Case 1′s thermophysical properties at each state point are reported in Table 4. When comparing the reversible cycle (Ideal) with the actual CCHPMED cycle (Case 1), the thermal efficiency in the top cycle dropped from 54.48% to 37.09% due to the inclusion of the polytropic efficiencies of the compressors, combustion chambers, and GT in the model. Furthermore, the inclusion of other system components’ efficiencies in the bottom cycle reduced the utilization factor of the CPDP plant from 85.53% to 78.24% as shown in Fig. 4. Assuming a constant power demand, Case 1′s top cycle is simulated for one calendar year on an hourly basis. The simulation results showed that the total NG consumption rate in the top cycle varied from 65 to 69 kg/s depending on the ambient temperature as shown in Fig. 5. The electric power requirements for the investigated desalination technologies are shown in Fig. 6a). The seawater pumps’ electric power requirement ranged from 80.77−81.14 MW depending on the desalination technology. As opposed to MED and MSF, RO desalination plants only require electric power as the sole form of energy input. The total electric power consumption of RO systems was calculated to be 124.0% more than the power consumption in MED plants. In MED and MSF desalination plants, the DW production rate is higher than the DW export rate since desalted water is fed in the bottom cycle as make-up water to recover the lost MP steam in the thermal

3.1. CPDP comparison The gross electrical power generated for all the cases studied are shown in Fig. 7a). CPDP plants coupled with RO desalination plants (Cases 3a, 3b, 6, and 9) produce the highest electrical power to compensate for the lost power utilized in the RO plants. When compared with Case 1′s 1648 MW electric power production, the RO coupled CPDP configurations have to generate an additional 6.104% of electric power. The top cycle electric power production ranges between 65.20% and 70.95% of the total power produced in combined cycle cases (Cases Ideal, 1, 2, 3a, and 3b). Thermal energy generated in the HRSG units drives the ST units in the bottom cycle and account for the remaining electric power production. Cases 4, 5, 6 generate power via GT units only and Cases 7, 8, and 9 via ST units only. CPDP plants coupled with thermal desalination technologies (Cases Ideal, 1, 2, 4, 5, 7, and 8) require thermal energy in the form of low and medium pressure steam for desalination. The thermal energy required for these cases is shown in Fig. 7b). The thermal energy consumption rate of CCHP plants (Cases Ideal, 1, and 2) ranged between 1215 MW Table 3 System component’s efficiencies. Component Isentropic Efficiency Isentropic Efficiency Isentropic Efficiency Isentropic

661

efficiency of compressors (ƞs,c) of combustion chamber (ƞcc) efficiency of GT units (ƞs,GT) of generators (ƞgen) efficiency of pumps (ƞs,P) of HRSG units (ƞHRSG) efficiency of ST units (ƞs,ST)

(%) 84.90 94.60 87.86 97.98 90.00 99.80 93.00

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where it merely consumed an additional 4.042% per unit time than the ideal case. The total NG consumption rate ranged from 67.79 to 134.1 kg/s for all cases. The ST-CHP-MSF (Case 8) plant consumed the highest NG per unit time to export the same power and fresh water export rates as AZN. In combined cycle cases (Cases Ideal, 1, 2, and 3b), additional NG is fired in the HRSG units. No additional NG firing in HRSG is needed for Case 3a as the top cycle excess heat (Qhrsg,TOP = 302.1 MW) is sufficient to supply the bottom cycle’s required heat input (Qin,bottom = 274.5 MW). In ST-CHP plants, NG is fired in boilers only and NG is fired in the top cycle’s combustion chambers only in the GT-CHP plants. The utilization factors of the CPDP cases are displayed in Fig. 9a). Excluding the Ideal case, the CCHP-MSF plant (Case 2) had the highest utilization factor. This performance parameter is misleading since it measures the total energy output over the total energy input without factoring in the quality and use of the energy output. Even though GTCC-RO’s (Case 3a and 3b) utilization factor is significantly lower than those of the CCHP plants (Cases 1 and 2), they consumed the lowest fuel per unit time to generate the required power and DW export rates. To further demonstrate the superiority of GTCC plants, they had the lowest total fuel cost per unit time to operate the CPDP as shown in Fig. 9b). Total fuel cost per unit time in Case 3b is 9.73 $/s whereas Case 2′s total fuel cost per unit time is 10.41 $/s. The PWGR values of all cases compared in this research are displayed in Fig. 10. The PWGR parameter is introduced such that all CPDP plants can be compared regardless of the power and fresh water export rates. From a thermodynamic perspective and using the same operating and ambient conditions for all cogeneration technologies studied, it can be concluded that producing power in a GTCC configuration and desalting seawater using RO desalination plants is the most energy efficient cogeneration system. Comparing CCHP-MSF (Case 2) with CCHP-MED (Case 1), MSF is a less efficient seawater desalination technology than MED (lower GOR) therefore the capacity of the desalination plant and the amount of total steam supply is relatively larger. As a result, QMP and QLP are higher in MSF coupled plants. Since QMP and QLP are higher, the utilization factor of the plant is higher. However, from an energy conversion efficiency point of view and using the PWGR parameter, CCHP-MED plants are slightly more efficient than CCHP-MSF plants by 0.4545%. Since there are no ST units in GT-CHP plants, heat input requirements in the bottom cycle are drastically lower and therefore the HRSG units are reduced to 1 unit only. The rate of heat supply available from the top cycle is 312 MW, whereas the rate of process heat produced in the bottom cycle for the desalination plant only needs to provide 35.89 MW. Because of not fully utilizing this excess available heat, the PWGR is much lower in Case 4 than those in Cases 1–3. Swapping the MED units with MSF units in Case 5 would slightly deteriorate the performance in the plant due to the lower GOR in MSF desalination. Surprisingly, coupling thermal desalination processes with GT-CHP plants (Cases 4 and 5) is more efficient than producing power and DW independently using GT and RO stand-alone systems (Case 6). Case 6′s PWGR is lower than those of Cases 4 and 5. This was not the case when comparing Cases 3a and 3b vs. Cases 1 and 2 and Case 9 vs. Cases 7 and 8. In Cases 6, 7, and 8 the PWGR values are all less than unity which implies that the CDPD plant is losing money on a continuous basis since the running cost of fuel and water per unit time is higher than the revenues generated from power and water per unit time. The power and water subsidies costs in Kuwait play a pivotal role in the profitability of the plants.

Table 4 Thermophysical properties at each state in Case 1′s model. State

m (kg/s)

h (kJ/kg)

T (K)

P (kPa)

s (kJ/kg-K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31

607.1 607.1 607.1 607.1 607.1 683.1 5.410 677.6 135.5 135.5 135.5 4.140 20.70 20.70 26.11 131.4 656.9 328.5 328.5 656.9 505.6 42.18 109.2 42.18 109.2 109.2 109.2 505.6 614.8 614.8 26.11

307.4 760.7 1773 936.8 439.1 483.2 487.7 499.7 499.7 499.7 3491.4 3491.4 3491.4 3491.4 2869.1 3491.4 3491.4 3491.4 2679.7 2679.7 2679.7 2679.7 2679.7 2679.7 2679.7 277.8 279.1 360.3 345.9 345.9 167.5

307.2 744.0 1613 903.4 437.6 388.3 388.7 389.8 389.8 390.5 819.2 819.2 819.2 781.8 502.6 819.2 819.2 819.2 405.6 405.6 405.6 405.6 405.6 388.3 370.2 339.5 339.6 359.0 355.5 355.7 313.2

101.3 1743 1743 101.3 101.3 170.0 4042 14,278 14,278 10,052 10,052 10,052 10,052 1600 1600 10,052 10,052 10,052 291.0 291.0 291.0 291.0 291.0 170.0 26.60 26.60 1200 1200 1200 170 7.384

1.726 2.639 3.534 2.853 2.083 1.475 1.476 1.480 1.480 1.491 6.743 6.743 6.743 7.565 6.576 6.743 6.743 6.743 6.894 6.894 6.894 6.894 6.894 7.132 7.978 0.9103 0.9134 1.143 1.103 1.106 0.5724

Fig. 4. The top cycle’s thermal efficiency and the system’s utilization factor of the Ideal case and Case 1.

and 1516 MW. Amongst these cases, per unit time, the ideal MEDcoupled plant consumed the least and the MSF-coupled consumed the highest due to the lower gain ratio. ST-CHP plants’ (Cases 7 and 8) thermal energy consumption rate ranges between 1134 MW and 1407 MW which is relatively lower than CCHP plants. Since the bottom cycle is solely responsible for generating the desired desalination thermal energy in Cases 4 and 5, the required thermal energy is significantly lower than the other cases. Thermal energy consumption rates ranged between 45.20 MW and 54.74 MW for GT-CHP plants. Amongst all the power and fresh water cogeneration technologies studied, the Ideal CCHP-MED consumed the lowest NG per unit time as shown in Fig. 8. As expected, the total NG consumption rate in the Ideal case was calculated to be 11.51% less than the NG consumption rate reported in AZN’s HBD since all system components were assumed reversible in the reference case. The GTCC-RO case with the ST unit capacity increased to 304.3 MW (Case 3b) had the closest total NG consumption rate to the ideal case

3.2. Number of units effect on thermodynamic performance Changing the number of GT, ST, and desalination units in the system results in various output and input energy and water rates. The PWGR parameter is used to assess the impact on the power and desalting 662

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Fig. 5. Case 1′s top cycle total NG mass flow rate as a function of ambient temperature on an hourly-basis from January to December 2011 at Az-Zour, Kuwait.

Fig. 6. a) Electric power requirement and b) DW production rate (kg/s) of each desalination technology to export 5608.7 kg/s of desalted water.

Fig. 7. a) Electrical power production of the CPDP cases to export 1566.9 MW of electric power and 5608.7 kg/s of desalted water. b) Thermal energy consumption rates of CPDP cases coupled with thermal desalination technologies.

While keeping the ST constant at 2 units in the CCHP-MED plant, the number of GT and HRSG units are varied to assess the impact on the PWGR (Fig. 11). Increasing the number of GT/HRSG units improves the PWGR of the plant when the coupled MED units are lower than 7 units and vice versa. If 7 MED units are coupled with the CCHP plant, the PWGR is the same for all cases regardless of the number of GT units involved as shown in Fig. 11. As for varying the ST units, the PWGR is also dependent on the number of MED units coupled as shown in Fig. 12. When the CCHP is coupled with the maximum allowable MED units, increasing the number of ST units generally increases the PWGR. The PWGR increases by 3.220% and 5.301% when increasing the number of ST units from the existing 2 to 3 and 4 respectively (Fig. 12) if the maximum number of MED units are coupled. If the number of MED units is fixed at the

performance of CPDP plants when changing the number of units coupled with the system. Case 1′s (CCHP-MED) configuration is composed of 5 GT units coupled with 5 HRSG units, 2 ST units (5-5-2), and 10 MED units. Different cases were studied on Case 1 to assess the impact of changing the number of GT, ST, and MED units. Increasing the number of MED units improves the performance of the system as shown in Figs. 11 and 12. However, there is an upper limit on the number of MED units that can be coupled with the CCHP plant. The upper limit is dependent on the amount of steam leaving the ST units. Consequently, increasing the number of ST units increases the maximum allowable MED units to be coupled with the process heat and power plant. The PWGR of the 5-5-2 plant increases by 7.756% when increasing the number of MED units from the existing 10 units to the maximum 12 units. 663

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Fig. 10. The PWGR factor for the nine CPDP cases.

Fig. 8. NG Consumption Rates for the nine CPDP cases.

existing 10 units, the 5-5-2 configuration generates the highest PWGR. In summary, the number of units comparison results show that there is potential to improve the CCHP-MED plant’s economic performance by modifying the number of GT, ST, and MED units and that the PWGR can be an effective performance indicator for the design of CPDP plants. The number of GT, ST, and MED units can have a significant effect on the profitability of the plant. 4. Conclusions This study compared the performance of several independent and coupled conventional power and desalination technologies in Kuwait using a thermodynamic mathematical model. Keeping the same power and desalted water export rates for all plants, the various conversion technologies’ fuel, energy, and water consumption rates were compared with those of a reference reversible ideal CCHP-MED model that had a PWGR of 1.529 and required a total NG mass flow rate equal to 67.79 kg/s. Based on the comparison results, GTCC-RO plants were closest to the ideal reversible reference model in terms of PWGR values and are considered the most energy efficient. Their fuel consumption rate is only 4.04% more than that of the reference reversible case. The optimal GTCC-RO plant also had the highest PWGR (3.86% less than the reference case) and the coupled ST-CHP-MSF CPDP had the lowest PWGR (49.4% less than the reference case) among the cases compared in this study. If CCHP-MED coupled plants were converted to independent GTCC-RO plants, savings on fuel consumption can reach up to 10.19%. In an attempt to improve the performance of CCHP-MED plants, the number of GT, ST, and MED units were modified to assess the effects on the PWGR of the plant. The PWGR is increased if the maximum allowable number of MED units is allowed to be coupled with the CCHP plant. The performance of the CPDP plant is increased if the number of

Fig. 11. Modifying the number of GT, HRSG, and MED units’ effect on PWGR.

ST units increases only if the maximum amount of MED units is coupled with process heat and power plant. As for varying the number of GT units, a positive or negative effect on the performance of the plant is achieved depending on the number of MED units coupled with the system. For future research, the developed thermodynamic models of the various CPDP types presented in this paper can be used as a base for evaluating the performance of the proposed new plants to assess the effects of ambient conditions and seasonality of power demand. Such effects usually play a pivotal role in the actual performance of the plants. The ambient temperature variations can influence the performance of GT-driven plants and its effects can be on both the top and bottom cycles. Also, the seasonality of the power demand can also influence the required fuel consumption as the peak power demand in winter months is much lower than that for the summer months in

Fig. 9. a) Utilization factor and b) total fuel cost per unit time for the nine CPDP cases. 664

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Fig. 12. Modifying the number of ST and MED units’ effect on the PWGR.

Kuwait. This study only analyzed the effects of ambient temperature on the top cycle where the NG mass flow rate feeding the top cycle hovered between 65 and 69 kg/s when simulating Case 1. The developed empirical model could be used for other studies to assess the performance of power and desalination plants by fuel type and availability, heat content, and cost. Including alternative desalination technologies such as TVC and MVC desalination plants in the comparative analysis will also widen the scope of comparison. The cost-based comparison of this study only considered the fuel, electricity, and fresh water cost in Kuwait. Other economic factors such as capital expenditure, operation, and maintenance costs of system components can further contribute to the evaluation of the feasibility of changing or modifying system components. Additionally, studies identifying opportunities for renewable/sustainable energy-use in CDPDs to aid the fresh water and power production and diversify the fuel intake. Sustainable options include firing synthetic gas produced from biomass or waste to diversify fuel intake and reduce the cost of NG fuel and/or using solar energy to reduce the fossil fuel dependence of the CPDPs in Kuwait.

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Acknowledgements This research was partially supported by the Andrew H. Hines, Jr./ Progress Energy Endowment Fund. Ali H. Abdulrahim acknowledges Kuwait Institute for Scientific Research (KISR) for funding his graduate studies and research. The authors would like to thank (a) Fahad Alzuabi, Technical Engineer at Shamal Az Zour Al Oula and (b) Mike Wood from the Ministry of Electricity & Water for the valuable data provided to conduct this research. Competing interest statement The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. Funding statement This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. References [1] Al-Karaghouli A, Kazmerski LL. Energy consumption and water production cost of conventional and renewable-energy-powered desalination processes. Renew Sustain

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