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Energy 40 (2012) 358e369

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Energy

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Modeling and optimizing a CHP system for natural gas pressure reduction plant

Sepehr Sanaye*, Amir Mohammadi NasabEnergy Systems Improvement Laboratory (ESIL), Department of Mechanical Engineering, Iran University of Science and Technology (IUST), Narmak, Tehran 16488, Iran

a r t i c l e i n f o

Article history:Received 29 May 2011Received in revised form21 January 2012Accepted 24 January 2012Available online 10 March 2012

Keywords:Pressure reductionNatural gasGenetic algorithmExpander

* Corresponding author. Tel./fax: þ98 21 77240192E-mail address: sepehr@iust.ac.ir (S. Sanaye).

0360-5442/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.energy.2012.01.060

a b s t r a c t

The pressure in the main natural gas transport pipelines should be reduced for proper consumption invicinity of cities. A common procedure of reducing pressure in natural gas station (city gate station, CGS)is using expansion valves, which causes the waste of large amount of exergy (availability). In this papera combined heat and power (CHP) system was used instead which included an expander, gas engines,boilers, a pump and a preheater. A new and relatively quick method for selecting the required number ofgas engine/boiler, and determining their nominal power/heating capacity, as well as the expander effi-ciency are also presented. An objective function named actual annual benefit ($) was defined as the sumof income (from selling electricity) and expenses (such as investment cost, operation and maintenancecosts). Subsequently different parts of the objective function were expressed in terms of 9 decisionvariables. The optimum values of decision variables were obtained by maximizing the objective functionusing genetic algorithm optimization technique. By applying the above procedure for our case study, itwas obtained that two 5.48 (MW) gas engines and one 5.94 (MW) boiler was needed while the paybackperiod was found to be 1.23 (year).

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

The pressure of natural gas in transmission pipelines before citygate stations (CGS) is high (5e7MPa). In order to utilize the potentialenergy of this high-pressure natural gas, power expanders are usedto generate electricity or shaft work during natural gas pressurereduction. A small scale liquefiednatural gas (LNG) plantmay be alsoused in vicinity of pressure reduction plant to use the generatedelectricity to drive the compressors in liquefaction cycle [1,2].

With gas pressure reduction, its temperature drops(JouleeThomson effect), this may cause freezing of watervapor innatural gas which results in pipeline swelling and corrosion. Thesolution is to preheat the natural gas prior to pressure reduction. Inorder to gain evenmore electricity and savings, internal combustion(IC) gas engines may be utilized to drive additional generators andat the same time providing hot water in their water jackets fornatural gas preheating. These equipment are categorized asa combined heat and power (CHP) system (a system which gener-ates electricity and heat simultaneously using a single source offuel). CHP systems play a significant role in efficient usage of energyin industrial and domestic applications. Furthermore, these systemshave less harmful effects on the environment. Properly designedCHP systems may provide a thermal efficiency more than 80% [3].

.

All rights reserved.

Selection of CHP systems has been investigated in some refer-ences [3e11]. In this paper thermal modeling (simulation) ofa combined heat and power (CHP) system shown in Fig. 1 wasperformed. Then by introducing an objective function and selectingnine design parameters, the optimal values of these parameterswere obtained. The selected decision (design) variables for thissystem were: expander efficiency (hex), number (Nbl) and capacity(Hbl) of boilers, number (Nen) and nominal power (Enom,en) of gasengines, the partial load parameter (PL) of gas engines, outlet watertemperature of preheater (T7), mass flow rate of water passingthrough the preheater ( _mw) and outlet natural gas temperature ofexpander (T3).

As a summary the followings are contribution of this paper intothe subject:

� This paper covers thermal modeling of a natural gas pressurereduction stationwith specific group of equipment not coveredin other open literature.

� Optimal design of the natural gas pressure reduction plant withintroducing a new defined objective function, new specificdesign parameters (decision variables) and the correspondinglist of constraints is performed.

� The sensitivity analysis of the change in optimal values ofdesign parameters with change in atmospheric conditions, gaspipeline operation conditions (temperature, pressure andnatural gas mass flow rate) and price of fuel and electricity wasinvestigated.

Nomenclature

AAB actual annual benefit ($/year)Ao heat transfer surface area (m2)C capital investment (cost) ($/kW)Cp specific heat at constant pressure (kJ/kg K)E electrical power (kW)H heat rate (kW)i interest rate (%/year)J total number of pollutant emissionsk equipment life cycle (year)LHV fuel lower heating value (kJ/kg)M maintenance cost ($/kW)Nbl number of boilers_m mass flow rate (kg/s)Nen number of enginesnp payback period (year)P pressure (Pa)PL partial load (%)Qf combustion energy (kW)Qreq required heat (kW)R annualized capital investment (cost) ($/kW year)T temperature (K)Uo overall heat transfer coefficient (W/m2 K)

_X mass flow rate of emissions (kg/h)b capital recovery factorg heat capacity ratioh efficiency (%)f cost ($/kW h)sn number of working hours in nth monthDTm log mean temperature difference (K)

Subscriptsbl boilerCHP combined heat and powere electricityem pollutant emissionsexh exhaustf fuelj jth component of pollutant emissionex expandernom nominalw wateren engineng natural gaspu pumpph preheater

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369 359

2. Thermal modeling

As is shown in Fig. 1, the system main equipment consists ofexpander, gas engine, boiler, preheater and pump and the followingrelations were used for thermal modeling of these mentionedequipment. It is noteworthy that the data provided by sellers ofequipment may be directly used in this step alternatively.

2.1. Expander

The inlet natural gas temperature into the expander wasobtained from [11]:

Fig. 1. The schematic diagram of the s

T2 ¼ T3� � �g�1g� (1)

1� hex 1� P3P2

where P2 is the inlet natural gas pressure into the expander whichwas estimated from:

P2 ¼ P1 � DPpreheater (2)

The expander power output was also estimated from:

Wex ¼ _m2ðh2 � h3Þ (3)

tudied pressure reduction station.

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369360

where the enthalpy of expander inlet and outlet methane gas atvarious pressure and temperatures were obtained from the in-house developed database.

2.2. Gas engines

For gas engines, the following relations for partial load werederived from the provided numerical data at nominal load inRefs. [12,13]:

Energy recovered from jacket water_mf ;PL,LHVf

¼ 17:49expð�0:07512ðPLÞÞþ39:36expð�0:002556ðPLÞÞ (4)

For engine thermal efficiency at partial load:

hth;PLhth;nom

¼ �0:0001591ðPLÞ2þ0:024ðPLÞ þ 0:1904 (5)

For engine fuel consumption at partial load:

mf ;PL

mf ;nom¼ 0:2408expð�0:01403ðPLÞÞ

þ 0:03553expð�0:02494ðPLÞÞ (6)

For the exhaust gas enthalpy:

Hexh;PL

mf ;PL¼ 0:001016ðPLÞ2�0:1423ðPLÞ þ 31:72 (7)

For the power output:

Een ¼ Enom;en � PL (8)

It was assumed that for gas engines there was about 3% decreasein efficiency for about each 303 m (z1000 ft) increase in elevation.Power output also decreased 1% for each 5.5 �C (z10 �F) increase inambient temperature [3,12].

Furthermore the stack temperature was assumed to be morethan about 148.8 �C (300 �F) to avoid sulfuric acid productionwhichcauses the stack corrosion [12,14].

2.3. Electrical power

Eelec ¼ ðWex þ EenÞ � hgen (9)

2.4. Boiler

Heat capacity of boiler:

Hbl ¼ _mf ;bl � LHV� hbl (10)

2.5. Preheater

The required heat transfer surface area:

Ao ¼ Qreq

Uo,DTm(11)

The required heat transfer rate:

Qreq ¼ _m1ðh2 � h1Þ ¼ _mwcpwðT8 � T9Þ (12)

Log mean temperature difference:

DTm ¼ ðT8 � T2Þ � ðT9 � T1Þln

ðT8 � T2ÞðT9 � T1Þ

(13)

2.6. Pump

The pumping power consumption was estimated from:

Wpu ¼ _mwðp7 � p9Þrwhpu

¼_mw

�Dpph þ Dpen & bl

�rwhpu

(14)

3. Economic considerations and estimating the actual annualbenefit (AAB)

Both thermal and economic analysis should be applied inselection of a CHP system. In economic analysis, the system totalcost included capital, operational and maintenance costs. For esti-mating the annual benefit, the annualized capital cost (R) wascomputed from the total investment cost (C) and capital recoveryfactor (b) which included parameters such as equipment life time(k) and the interest rate (i) [13].

R ¼ b,C (15)

b ¼ ið1þ iÞkð1þ iÞk�1

(16)

The equivalent uniform annual cost (EUAC) was also obtainedfrom the following relation [15]:

EUAC ¼ R� A (17)

where:

A ¼�Salvage value

�$

kW

��"i

ð1þ iÞk�1

#(18)

In order to evaluate the investment (C) and maintenance (M)costs, the following relations were used.

3.1. Expander [15]

C ¼ 1040:6�W�0:354ex

�$

kW

�(19)

M ¼ 0:0055�

$

kW

�(20)

3.2. Gas engine [13]

C ¼ �138:71� ln�Enom;en

�þ 1727:1�

$

kW

�(21)

M ¼ 0:1696� E�0:2nom;en

�1� 0:6875

�E

Enom;en

���$

kW

�(22)

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369 361

3.3. Boiler [13]

C ¼ 205� H�0:13bl

�$

kW

�(23)

M ¼ 0:0027�

$

kW

�(24)

3.4. Preheater [15]

C ¼ 549:56� A0:6691o;ph ð$Þ (25)

M ¼ 0:06� EUACphð$Þ (26)

3.5. Pump [15]

C ¼ 271:64� _mw þ 1094:7ð$Þ (27)

M ¼ 0:06� EUACpuð$Þ (28)

Then a new objective function named actual annual benefit(AAB) was defined as:

AAB ¼X12n¼1

24Een � hgen � fe

zfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflffl{I

þWex � hgen � fe �Wpu � fe

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{II

� _mf � LHV� ff

zfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflffl{III

�XJj¼1

_Xj � fem;j

zfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflffl{IV 35

�sn � ðM þ EUACÞenEnom;en

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{V

� ðM þ EUACÞexWex

zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{VI

� ðM þ EUACÞblHbl

zfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflffl{VII

� ðM þ EUACÞphzfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflffl{VIII

� ðM þ EUACÞpuzfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflffl{IX

(29)

where the definition of terms in ($/hr) and ($/year) in Eq. (29) is asfollows:

I: The income for electricity generated by the gas enginesII: The income for electricity generated by expander minus the

required pumping power (this term exists for both cases ofusing expander with CHP system and expander with onlyboiler system).

III: The cost of natural gas used to preheat natural gas beforeentering expander

IV: The penalty cost of the jth pollutant emission higher thana permitted value

V: Gas engines capital and maintenance costsVI: Expander capital and maintenance costsVII: Boiler capital and maintenance costsVIII: Preheater capital and maintenance costsIX: Pump capital and maintenance costs

_Xj is the mass flow rate of jth pollutant emission higher thana permitted value, and fem,j is the pollutant emission penaltycost of each pollutant gas component. sn is the number ofworking hours of the system in nth month. fe and ff are theprices of selling electricity and purchasing natural gas respec-tively. It was assumed in this paper that whatever electricityproduced in the pressure reduction station could be sold to thegrid.

The payback period is the time taken for the total initialinvestment of a product to be recovered by the total accumulatedsavings. The payback period was estimated from [16]:

ðInvestment Cost of EquipmentÞð$Þþ ðOperation & Maintenance Cost of EquipmentÞ

��

$year

��ð1þ iÞnp�1ið1þ iÞnp

� ðAnnual BenefitÞ�

$year

��ð1þ iÞnp�1ið1þ iÞnp

¼ 0 (30)

where:

Investment Cost of Equipment

¼ CenEnom;en þ CexWex þ CblHbl þ Cph þ Cpu (31)

Operation & Maintenance Cost of Equipment

¼X12n¼1

h_mf LHVff þWpu�fe

i�snþMenEnom;enþMexWex

þMblHblþMphþMpu (32)

Annual Benefit ¼X12n¼1

hEen � hgen � fe þWex � hgen � fe

i� sn

(33)

4. Optimization (objective function, design parameters andconstraints)

4.1. Objective function and the system design parameters (decisionvariables)

In this study, the actual annual benefit AAB ($), explained inSection 3 (Eq. (29)), was considered as the objective function. Thegoal was to maximize AAB. Nine design parameters or decisionvariables for the optimization process are expander efficiency (hex),number of boilers (Nbl), power of boilers (Hbl), number of engines(Nen), nominal power of gas engines (Enom,en), the partial loadparameter of gas engines (PL), outlet water temperature ofpreheater (T7), mass flow rate of water passing through preheater( _mw) and outlet natural gas temperature of expander (T3).

4.2. The constraints

The constraints of this problem are a set of environmental,economic and mechanical limitations. The list of constraints isgiven in Table 1.

4.3. Genetic algorithm

The optimization problem consists of optimizing (i.e. mini-mizing or maximizing) an objective, with a number of inequality or

Table 1The range of variation of design parameters.

Constrains Reason

0.5 � hex � 0.9 Commercial availability0 � _mw � 40 (kg/s) Commercial availability0 � Nen � 5 Limitation in investment sources0.5 � Enom,en � 6 (MW) Commercial availability0 � Nbl � 5 Limitation in investment sources0.5 � Hbl � 6 (MW) Commercial availability5 � T7 � 70 (�C) Typical range of values of engine

water jacket cooling inlet temperatureT3 � 5 (�C) To avoid freezing of water vapor in natural

gas and pipeline swelling and corrosionT8 � 140 (�C) To avoid hot water boiling in preheaterTexh � 148.8 (�C) To avoid production of corrosive acids

from gas engine exhaust

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369362

equality constraints. GAs are semi-stochastic methods, based on ananalogy with Darwin’s laws of natural selection [17].

4.3.1. Stochastic uniform selectionStochastic uniform lays out a line in which each parent corre-

sponds to a section of the line of length proportional to its expec-tation. The algorithm moves along the line in steps of equal size,one step for each parent. At each step, the algorithm allocatesa parent from the section it lands on. The first step is a uniformrandom number less than the step size.

4.3.2. ElitismElite count specifies the number of individuals that are guar-

anteed to survive to the next generation. Elite count must bea positive integer less than or equal to Population size.

4.3.3. Crossover and mutationUniform crossover and random uniformmutation are employed

to obtain the offspring population, Qt1. The integer-based uniformcrossover operator takes two distinct parent individuals andinterchanges each corresponding binary bits with a probability,0 < pc � 1. Following crossover, the mutation operator changeseach of the binary bits with a mutation probability, 0 < pm < 0.5.

5. Case study

Modeling and optimization of pressure reduction station at thenorth east of Iran with 850 km distance from the capital (Tehran)

Fig. 2. Variation of inlet natural gas tempera

was performed and the results of this case study are reported here.Fig. 1 illustrates the schematic diagram of the analyzed pressurereduction plant. An expander, gas engines, boilers, preheater andpump are the main equipment in this plant. The task of the CHPsystem in natural gas pressure reduction station is to produceelectricity and heat when the natural gas pressure reduces at thecity gate station (CGS). Natural gas enters the stations withtemperature, pressure and mass flow rates shown in Figs. 2e4 withthe desired 17 (bars) as the outlet pressure.

Table 2 details the composition of the natural gas flowing intothe station with 99% methane.

The electricity and fuel cost (for natural gas with LHV (fuel lowerheating value) about 47,966 kJ/kg) are 0.067 ($/kW h) and 0.07($/m3), respectively. The penalty cost of emissions in this case studywas assumed to be negligible. sn was assumed to be the number ofworking hours in nth month. The values of equipment life time (k)and interest rate (i) were considered to be 15 years and 10%,respectively. The salvage value was 20% of initial capital cost [13].

6. Discussion and results

6.1. Model verification

To verify the modeling results, the simulation output wascompared with the corresponding reported results given in litera-ture. The comparison of our modeling results and the corre-sponding values from Ref. [18], for the same input values is shownin Table 3.

In Ref. [18] the expander generated power output from pressurereduction process was obtained without preheating the natural gasentering the expander. Therefore our modeling results withoutpreheating were used for the comparison. The mean differencevalue in this comparison was 4.8% as is shown in Table 3.

6.2. Modeling and optimization results

The flowchart of developedmodeling and optimization computerprogram for system shown in Fig. 1, is demonstrated in Fig. 5.

The optimum values of design parameters using genetic algo-rithm optimization technique are presented in Table 4. In additionthe selected technical specifications for system equipment(preheater heat transfer surface area as well as expander and pumppower) at the optimum design point as well as its correspondingAAB values are shown in Table 5.

ture during a year at north east station.

Fig. 3. Variation of inlet natural gas pressure (P1) to the north east station during a year.

Fig. 4. Variation of inlet natural gas mass flow rate to the north east station during a year.

Table 3Comparison of present work modeling result and corresponding values at Ref. [14].

Month Present work Present work Ref. [14] Diff. [%]

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369 363

Fig. 6 shows the total generated electric power by expander andengines at the optimum system design point mentioned in Table 4.Furthermore Fig. 7 compares the generated heat by engines andboiler at the optimum design point (Table 4) and its comparisonwith the required heat load at the station. Fig. 7 shows that gasengine(s) and boiler(s) were successful in providing the requiredheat load.

Table 2Natural gas composition at north east natural gas pressure reductionstation.

Component Percent mole fraction (%)

CH4 98.64C2H6 0.593C3H8 0.065C4H10 0.049C5H12 0.026CO2 0.055N2 0.428C6þ 0.125Total 100.00

It was assumed that at all months of the year the gas enginesprovided heat load just up to 5% more than that was required fornatural gas preheating.

with preheating without preheating

Wex Wex Wexa& [14]

January 13.45 8.95 8.27 8.27February 12.24 7.19 6.53 10.05March 10.4 6.03 5.60 7.68April 8.94 5.38 5.07 6.18May 4.05 2.47 2.40 2.92June 3.85 2.38 2.20 8.18July 4.38 2.76 2.67 3.50August 4.5 2.84 2.73 3.90September 4.81 2.98 2.80 6.43October 6.38 3.89 4.00 �2.75November 11.29 6.81 6.80 0.15December 13.45 8.45 8.13 3.89

a Present work without preheating.

Input• Ambient conditions• Economic parameters• Condition of inlet and outlet flows

GA selects decision variable

T2 and Qreq

Could the selected number of boilers and engines satisfy the Qreq?

Thermodynamic properties at all state points

Yes

Are the constrains met?

AAB

No

Yes

No

Fig. 5. Flowchart of the modeling and optimization computer program.

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369364

6.2.1. The effect of energy prices on optimum values of designparameters and operating variables

Results show that with the specified prices of electricity andnatural gas (given in Section 5), using two gas engines and one

Table 4The optimum values of design parameters (decision variables) for our case study during

Design parameters Optimum values of design parameters

hex 0.8Nen 2Enom,en (MW) 5.48E6PL (for 12 months) 100 100 99 96 0Nbl 1Hbl (MW) 5.941 5.042 2.51 0.5 4.664_mw (kg/s) (for 12 months) 31.50 28.25 23.42 19.45 9.03T7 (K) (for 12 months) 285.35 278.22 278.21 288.54 290.2T3 (K) (for 12 months) 278.83 294.18 289.08 284.01 289.29

boiler were more economical than other cases. Fig. 8 compares theAAB values when applying expander with CHP system (engine andboiler) or expander with just boiler system at the system optimumdesign point mentioned in Table 4. However, in case of 75% lower

12 months of a year.

0 0 0 0 67 99 100

4.248 4.803 4.919 5.598 0.5 2.913 5.928.51 9.95 10.29 11.16 14.00 25.55 30.31

294.36 298.16 299.26 293.70 291.74 285.76 280.46287.31 291.58 292.57 295.03 285.68 291.5 290.42

Table 5Technical specifications for the selected system equipment at the system optimum design point as well as its corresponding AAB values.

Dependent operating parameters Ao (m2) preheater heattransfer surface area

Wpu (W) pump power Wex (MW) expander power AAB ($)

The technical specificationsfor the system equipment andits corresponding AAB value

5.34E7 3.52E3 13.45 5.28E6

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369 365

electricity prices, it was more economical to use boilers instead ofgas engines.

Tables 6 and 7 provide the results of analyzing the sensitivity ofthe numerical values of optimum design variables with change inprice of electricity and fuel (natural gas) respectively. Since thestation inlet pressure, temperature and mass flow rate of naturalgas change in various months of the year, the results in Tables 6 and7 are computed based on yearly average values of inlet pressure(P1 ¼ 5.33 MPa), inlet temperature (T1 ¼ 286.8 K) and inlet massflow rate (33.25 kg/s) of natural gas. Table 8 shows the optimumvalues of design parameters at these operating conditions.

Fig. 6. The electricity generated by expander and gas engines in natural gas pressure redu

Fig. 7. The generated heat by gas engines and boiler in comparison with the required heatpoint mentioned in Table 4.

6.2.2. The effect of inlet natural gas condition on the optimumvalues of design parameters and operating variables

Fig. 9 shows the generated power output of the expander (Wex)at the system optimum design point for yearly average values ofinlet gas pressure (P1 ¼ 5.33 MPa), inlet gas mass flow rate(M ¼ 33.25 kg/s), and inlet gas temperature (T1 ¼ 286.8 K). Theexpander power output increases with increasing the amount ofthe yearly average inlet gas pressure (P1) from about 2 to 5 (MPa).The expander power output then shows a very mild decrease withfurther increase of yearly average inlet pressure (Fig. 9). Withincreasing the station average inlet gas pressure (P1), the expander

ction station during a year at the optimum system design point mentioned in Table 4.

in natural gas pressure reduction station during a year at the optimum system design

Fig. 8. AAB values of expander with CHP system (engines þ boiler) or expander with just boiler system at natural gas pressure reduction station during a year at the systemoptimum design point mentioned in Table 4.

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369366

inlet gas pressure (P2) and temperature (T2) increase (Eqs. (1) and(2)). It was observed that for about P1 ¼ 5 MPa, T2 had itsmaximum allowable value (T2 � T8 � 140 �C to avoid hot waterboiling in preheater, 140 �C was the saturated temperature ofengine cooling water at about 360 kPa). Therefore with furtherincrease in P1>5MPa andwhile P2 increases, T2 remained constantat 140 �C. In this situation the natural gas enthalpy h2 as well as theexpander power output had a mild decrease.

For the same above explained reason, with increase in stationyearly average inlet gas pressure (P1) more than about 5 MPa theoptimumvalue of expander efficiency also decreased as is shown inFig. 10.

Since the station yearly average inlet gas temperature andstation average inlet mass flow rate are not exist in Eq. (1), hex wasindependent of these two parameters (Fig. 10).

6.2.3. The effect of inlet natural gas condition on AABWith rising the yearly average inlet gas temperature, there was

a small decrease in the optimum AAB values (Fig. 11) due to the factthat the required heat load, Qreq, decreased which resulted inrunning the gas engines with lower power outputs (electricitygeneration) which provided lower heat load as well. This decreased

Table 6The change (in percentage) of the numerical values of optimum design parameters givengas (sensitivity analysis).

Change in the numericalvalues of design parameters

Variation in price of natural gas

�75% �50%

Dhex=hex 0.10 0.29DNen=Nen 0.00 0.00DEnom;en=Enom;en �0.14 0.00DpL=pL �3.13 �3.13D _mw= _mw 0.07 0.09DT7=T7 �0.15 �0.20DNbl=Nbl NA* NADðDTmÞ=DTm �32.07 �42.69DHbl=Hbl NA NADWex=Wex 0.33 0.60DQreq=Qreq 0.42 0.56DAph=Aph 47.82 75.47DWpu=Wpu 0.69 0.92DðAABÞ=AAB 55.84 31.84

NA*: Due to zero number of selecting boilers (Nb ¼ 0), this term was not applicable.

the income from selling electricity as well as decreasing of AABvalues.

Furthermore Fig. 12 shows the optimum amount of AAB foryearly average values of inlet natural gas pressure between 2 and 6(MPa) for various values of yearly average inlet gas mass flow rates.The optimum values of AAB increased substantially from 2 to 5(MPa) (due to increase in electricity production) with a very milddecrease between 5 and 6 (MPa) (as described in Section 6.2.2).

Finally with increasing the yearly average inlet gas mass flowrate, the station power output (Eq. (3)) as well as AAB increased(Fig. 13). With increasing the yearly average inlet gas pressure, AABreached its maximum value at P1 about 5 (MPa).

6.2.4. Economic analysisResults showed that the application of expander with CHP

system (gas engine and boiler) for natural gas preheating provided5.28 � 106 ($) as actual annual benefit while the application ofexpander with just boiler system for natural gas preheatingprovided 4.31 � 106 ($) as actual annual benefit (Fig. 8). The esti-mated payback period for the mentioned ranges of inlet gas massflow rate and inlet gas pressure also changed from0.77 to 1.07 years(Fig. 14).

in Table 8 as well as operating dependent parameters with change in price of natural

�25% þ25% þ50% þ75%

0.17 0.18 0.17 �1.800.00 0.00 0.00 50.000.00 0.00 0.00 �20.16�2.08 �2.08 �2.08 �14.580.05 0.06 0.05 0.06�0.12 �0.13 �0.11 �0.13NA NA NA NA�24.30 �26.86 �24.09 �27.29NA NA NA NA0.34 0.38 0.34 �1.640.32 0.35 0.31 0.3532.52 37.21 32.15 38.020.55 0.60 0.51 0.6014.21 �36.23 �61.30 �90.71

Table 8Optimum values of design parameters (decision variables) for the average values of natural gas mass flow rate ð _m1 ¼ 33:25 kgÞ, inlet pressure (P1 ¼ 5.33 MPa), and inlettemperature (T1 ¼ 286.8 K) during a year.

Design parameters hex Nen Enom,en PL Nbl Hbl _mwðkg=sÞ T7 (K) T3 (K)

Optimum values ofdesign parameters

0.89 2 6 96 0 0 19.47 288.17 278.15

Table 7The change (in percentage) of the numerical values of optimum design parameters given in Table 8 as well as operating dependent parameters with change in price ofelectricity (sensitivity analysis).

Change in the optimumvalues of design parameters andoperating dependent parameters

Variation in price of electricity

�75% �50% �25% þ25% þ50% þ75%

Dhex=hex �1.01 �0.48 �0.17 0.27 0.29 0.21D _mw= _mw �0.31 �0.15 �0.05 0.09 0.10 0.12DNen=Nen �100 0.00 0.00 50.00 50.00 50.00DEnom;en=Enom;en �100 0.00 0.00 �21.55 �24.59 �21.42DNbl=Nbl NA* NA NA NA NA NADHbl=Hbl NA NA NA NA NA NADT7=T7 0.69 0.33 0.11 �0.19 �0.23 �0.25DpL=pL �100 �3.13 �4.17 �14.58 �11.46 �14.58DWex=Wex �2.03 �0.97 �0.33 0.56 0.64 0.59DQreq=Qreq �1.90 �0.90 �0.31 0.53 0.64 0.70DðDTmÞ=DTm 145.33 68.81 23.72 �40.49 �48.40 �53.23DAph=Aph �60.01 �41.30 �19.43 68.93 95.02 115.33DWpu=Wpu �0.31 �0.15 �0.05 0.09 0.11 0.11DðAABÞ=AAB �89.08 �65.16 �33.78 30.79 63.09 95.84

NA*: Due to zero number of selecting boilers (Nb ¼ 0), this term is not applicable.

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369 367

Fig. 14 shows that the payback period decreases withincreasing the yearly average natural gas mass flow rate for lessthan about 30 kg/s. This was due to increase in expander powergeneration and more income from selling electricity. For yearlyaverage inlet natural gas mass flow rate more than 30 kg/s theoptimum number of gas engines increased from 2 to 3 for all P1values. Therefore the investment cost as well as the paybackperiod increased. With further increase in yearly average inlet gasmass flow rate (while the number of selected gas engines remain

Fig. 9. Values of electric power generated by the expander (Wex) at the systemoptimum design point for yearly average values of inlet natural gas pressure P1 (MPa)and inlet gas mass flow rate M (kg/s), As well as for yearly average inlet gas temper-ature of T1 ¼ 286.8 K.

unchanged) and rising power generation and income from sellingelectricity, the payback period decreased again (except forP1 ¼ 6 MPa). For P1 ¼ 6 MPa, with selecting the fourth gas engineboth investment cost and payback period increased, thereforepayback period did not show any fall.

Furthermore by increasing the price of selling electricity or bydecreasing the natural gas cost, it was observed that the paybackperiod became shorter for a specific yearly average inlet gascondition.

Fig. 10. Optimum values of expander efficiency (hex) for yearly average values inletnatural gas pressure P1 (MPa) and inlet gas mass flow rateM (kg/s), as well as for yearlyaverage inlet gas temperature of T1 ¼ 286.8 K.

Fig. 11. Optimum values of AAB ($) for yearly average values of inlet natural gastemperature (K) and various values of inlet gas mass flow rates M (kg/s) as well as foryearly average inlet gas pressure P1 ¼ 5.33 MPa.

Fig. 12. Optimum values of AAB ($) for yearly average values of inlet natural gaspressure P1 (MPa) and inlet gas mass flow rates M (kg/s) as well as for yearly averageinlet gas temperature of T1 ¼ 286.8 K.

Fig. 13. Optimum values of AAB ($) for yearly average values of inlet natural gas massflow rates (kg/s) and inlet gas pressure, P1 (MPa) as well as for yearly average inlet gastemperature of T1 ¼ 286.8 K.

Fig. 14. The values of payback period (year) at the system optimum design point foryearly average values of inlet natural gas mass flow rates (kg/s) and inlet gas pressureP1 (MPa) as well as for yearly average inlet gas temperature of T1 ¼ 286.8 K.

S. Sanaye, A. Mohammadi Nasab / Energy 40 (2012) 358e369368

7. Conclusions

A new and relatively quick method for selecting the size and thenumber of equipment at natural gas pressure reduction plant wasintroduced. The method considered both economic and thermalanalysis of the system. The optimum design parameters wereobtained by introducing and maximizing a new defined objectivefunction named actual annual benefit. The maximum amount ofAAB was reached for our case study when two gas engines withEnom,en ¼ 5.48 (MW), a preheater with heat transfer surface areaequal to Ao ¼ 53,480 (m2), pump power Wpu ¼ 3522 (W) and anexpander powerWex ¼ 13.45 (MW) were used. The payback periodof about 1.23 years was estimated for the above plant at theoptimum design point (Table 4).

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