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Exergy and exergoeconomic evaluation of gas separation process
Journal of Natural Gas Science and Engineering 9 (2012) 86e93
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Exergy and exergoeconomic evaluation of gas separation process B. Ghorbani, G.R. Salehi*, M. Amidpour, M.H. Hamedi Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 August 2011 Received in revised form 23 January 2012 Accepted 7 May 2012 Available online 2 July 2012
Exergy and exergoeconomic analyses for product recovery and separation systems of natural gas plant as well as the refrigeration system required for the plant are carried out. The exergetic and exergoeconomic costs of all process and utility streams are calculated through a systematic method of assigning exergetic cost relations to the streams. The results indicate that the exergetic efficiencies of the Debutanizer, Depropoanizer, and De-ethanizer columns are the lowest. Distillation columns have 64% of the total exergy loss, which is the maximum value of the system components. In the second place, heat exchangers have 15% of the exergy loss. Next there are compressors and expanders which have 13% and 6% of the exergy loss, respectively. It should be noted that the expander is replaced by a choke valve for energy-saving purposes. On the other hand, the results of the exergoeconomic analysis show that the percentage increases in the unit thermoeconomiccosts of the compression and the Demethanizer sections are the highest. This study demonstrates that the exergoeconomic analysis, whose results present cost-based information suggesting potential locations for the process improvement, can provide more information in comparison to the exergy analysis. 2012 Elsevier B.V. All rights reserved.
Keywords: Gas processing Natural gas Exergy Exergoeconomic Analyses
1. Introduction Separation of Methane, Ethane, Propane, and natural gas liquids (NGL) from the natural gas is generally carried out by one of the following alternatives: (i) external refrigeration (ER), (ii) turbo expansion (TE), (iii) JouleeThompson expansion, and (iv) absorption. In many processing schemes, a combination of these is used to improve the energy efficiency or obtain greater recoveries (Mehrpooya et al., 2009). New methods of energy saving have led to the development of analysis techniques based on the second law of thermodynamics and, particularly, the concept of exergy. The exergoeconomic analysis considers the quality of energy (exergy) in allocating the production costs of a process to its products. A general methodology for this kind of analysis was presented by Electric Power Research Institute (Bejan et al., 1996; Kotas, 1985), known as the Total Revenue Requirement method (TRR method). The application of exergoeconomic methods were mostly reported for the analysis of energy conversion systems, such as power plants, cogeneration systems, and refrigeration systems (Mehrpooya et al., 2009), (Luz Silveira et al., 2010; Tona et al., 2010; Khoshgoftar Manesh and Amidpour, 2009; Usón and Valero, 2011; Sayyaadi and Babaelahi, 2010; Ansari et al., 2010; Fabrega et al., 2009; Demirel, 2004; Rivero et al., 2004; Sayyaadi and Saffari, * Corresponding author. Tel.: þ98 9122031671. E-mail address: [email protected] (G.R. Salehi). 1875-5100/$ e see front matter 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jngse.2012.05.001
2009). There are a few reports of applying the exergoeconomic methods on the chemical separation processes (Luz Silveira et al., 2010). This research presents the results of the exergy and exergoeconomic analyses using the TRR method in gas separation process. 2. Process description of the NGL recovery plant After H2S removal, dehydration and mercury removal, the dry sweet gas is routed to the Ethane Recovery Unit 105, where the gas is processed to cope with the process specifications indicated in Table 1. The figures which will be presented in the sequel are indicative only and related to the summer case. They have to be used as a guide but do not represent exact operating conditions or guarantees. 2.1. Gas cooling and expansion Sweet and dry gas coming from the Dehydration and Mercury Guard Unit 104 is first precooled down to 35 C in the Cold Box 105-E-101 against: a Propane stream at medium pressure (Propane at 19.0 C), the cold sales gas coming from Demethanizer Exchanger 105-E-102 (included in Cold Box 105-E-101) at 49 C and going to the Gas/Gas exchanger 104-E-101 at 17.2 C, a withdrawal stream from and to lower section of Demethanizer 105-C-101 (entering and leaving Cold Box at 11.1 C and 16.6 C), a Propane stream at low pressure (propane at 4.1 C), a withdrawal stream from and to
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93 Table 1 Composition of feed stream. Substance
Mole fraction
Nitrogen CO2 Methane Ethane Propane i-butane n-Butane i-pentane i-pentane n-pentane n-hexane n-heptane n-octane
0.035254 0.010001 0.863377 0.055192 0.020372 0.003762 0.005765 0.001761 0.001761 0.001571 0.001367 0.000777 0.000402
medium section of Demethanizer 105-C-101 (entering and leaving Cold Box at 37.5 C and 13.3 C).Fig. 1 At 35 C a major portion of Butane and heavier components are condensed. The liquid phase also contains significant amounts of Methane and Ethane, which must be removed. Then the twophase flow is separated in Feed Flash KO Drum 105-D-101. The liquid is sent under level control, through a flashing valve (about 25% of flashed gas), as a feed stream to the Demethanizer 105-C-101 (at 30.4 bara and 48.4 C downstream the control valve). The gas exiting 105-D-101 is split into two streams: one side stream (at a set flow) is sent to the Demethanizer Exchanger 105-E102, installed in 105-E-101 cold box in which is cooled from 35.0 C down to 84.5 C. This stream is later let down through a flow control valve (30.2 bara and 95.3 C downstream the control valve) and is sent to the top of 105-C-101 as a column reflux to improve C2þ recovery efficiency and light products separation. The main stream, which is let down to 30.4 bara and 67 C before feeding 105-C-101, feeds the Feed Gas Expander 105-X-101. 2.2. Demethanizer and export gas sections The two-phase streams from 105-X-101, 105-D-101 bottom and 105-E-102 enters the Demethanizer 105-C-101, operating at 30 bara at the top, which is a strippereabsorber column that produces sales gas as an overhead and a wide-range liquid as a bottom product.
87
Between the bottom and feed trays, light components are stripped out of the liquid phase and heavy components are absorbed from the gas phase. Between the feed and top trays, the heavier compounds are removed from the gas phase being absorbed by the liquid reflux coming from the Demethanizer Exchanger (included in Cold Box 105-E-101). To minimize the amount of light component in the liquid, a stripping action is provided by means of the low pressure steam used as a heating medium in the Demethanizer Reboiler 105-E-103. Demethanizer bottom temperature is 38.3 C. To lower Demethanizer Reboiler duty and balance the heat input to the column, intermediate withdrawals are provided. They are reheated in the Cold Box by cooling feed to the Demethanizer. Bottom liquid product is sent, by means of Demethanizer Transfer Pumps 105-P101 A/B, under level control resetting a flow control valve as a feed to the De-ethanizer 105-C-102. Gas leaving the top of the Demethanizer at 87.4 C is first heated to 49 C in the Demethanizer Exchanger (included in Cold Box 105-E-101) before being reheated to 17.2 C in the Cold Box and to 34.2 C in the Gas/Gas Exchanger 104-E-101. This gas then feeds the Treated Gas Compressor 105-K101 which will increase the pressure up to 33.7 bara before being exported to the Export Gas Compression and Metering Unit 106. 2.3. De-ethanizer section Demethanizer bottom liquid is sent to the De-ethanizer 105-C102, under level control resetting flow control, by means of Deethanizer Transfer Pumps 105-P-101 A/B (One pump operating and one spare pump). The function of this column, which operates at 30.5 Bara on the top, is to remove Ethane as an overhead vapor stream and yield a bottom product containing all the Propane and heavier components. The overhead of the De-ethanizer is chilled to 8.7 C by the 2.4 C refrigerant in the De-ethanizer Condenser 105-E-105 and the mixed phase is routed to the De-ethanizer Reflux Drum 105-D-102. The pressure control on refrigerant side, that is the temperature control of the refrigerant, is reset by the HC liquid level in the Deethanizer Reflux drum. After separation in the De-ethanizer Reflux Drum, the liquid is pumped under flow control by the De-ethanizer Reflux Pumps 105-P-102 A/B and returned to the top tray of the De-ethanizer as reflux.
Fig. 1. Schematic of gas separation process.
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The Ethane stream exiting the De-ethanizer Reflux Drum is heated up to 43.2 C by means of liquid Propane at 60 C. A possibility to mix this stream with the Sales Gas upstream the Treated Gas Compressor is provided in the case of off-spec product or upsets in the downstream units. The column is equipped with a De-ethanizer Reboiler 105-E104, which uses low pressure saturated steam as heating medium. The De-ethanizer bottom temperature is of approximately 108.5 C. The liquid hydrocarbons recovered at De-ethanizer bottom (C3þ cut) are sent under the level control resetting a flow control valve to NGL Fractionation Unit 107 for further processing. The operating pressure of the Depropoanizer is set to 22.3 bara to ensure the condensation of the Propane cut in an air cooler. There are 11 actual trays (two pass trays) in the top section, 21 actual trays for the bottom section (four pass trays) plus the bottom draw tray. The operating pressure of the debutanizer is set to 8.2 bara to ensure the condensation of the butane cut in an air cooler. There are 11 actual trays (one pass tray) in the top section, 17 actual trays for the bottom section (two pass trays) plus the bottom draw tray. De-ethanizer bottom liquids are mixed in Unit 107 and are sent to the Depropoanizer. The function of this column, which operates at 22.3 bara is to produce a Propane stream as an overhead liquid stream. The bottom product containing all the Butanes and heavier components feeds the debutanizer. The overhead gas of the Depropoanizer is air-cooled and totally condensed at 60 C in the Depropoanizer Condenser. The liquid Propane product is routed to the Depropoanizer Reflux Drum. Part of the liquid is returned to the top tray of the Depropoanizer as reflux under flow control by the Depropoanizer Reflux Pump. The other part is sent under D-101 level control resetting flow control by the Propane Feed Pump to the Propane treatment Unit, where COS and mercaptans will be removed. The column is equipped with a Depropoanizer Reboiler, which uses LP saturated steam as heating medium. The Depropoanizer bottom temperature is approximately 138 C. The Depropoanizer bottom liquid is sent to the Debutanizer under the level control resetting flow control and mixed with the sour washing C4 cut. The Debutanizer operates at 8.2 bara and is equipped with both a condenser and a reboiler. The overhead gas of the column is air-cooled and totally condensed at 60 C in the Debutanizer Condenser. The liquid Butane product is then routed to the Debutanizer Reflux Drum. One part of the liquid is pumped from the Debutanizer Reflux Drum by the Debutanizer Reflux Pumps and returned under the flow control, to the top tray of the Debutanizer as reflux. The other part is pumped from the Debutanizer Reflux Drum by the Butane feed pumps and cooled by the sea water down to 40 C in the Butane Cooler. After cooling, the Butane is sent to the Butane treatment unit, where Mercaptans will be removed. The Debutanizer Reboiler uses LP saturated steam as heating medium. The Debutanizer bottom temperature is of approximately 130 C. The Debutanizer bottom liquid is pumped to avoid flashing by the condensate circulation pumps before being air-cooled at 60 C. Then the liquid is sent under the Debutanizer level control resetting f the low control, to the stabilization unit to be mixed with stabilized condensates. 3. Exergy analysis Exergy is the maximum available work when some forms of energy are transferred reversibly to a reference system, which is in thermodynamic equilibrium with the surroundings, and has no ability to perform work. Exergy is also a measure of distance of a system from global equilibrium; as the exergy is consumed, the state variables of temperature, pressure, and composition of system approach those of the surroundings. Therefore, the reference state is called the dead state. The total exergy of multicomponent
streams is the sum of its three contributions: the exergy change due to mixing, chemical exergy, and physical exergy, and is expressed by Xtotal ¼ (HH0)T0(SS0), where the subscript 0 indicates the enthalpy, entropy, and temperature of the environment, respectively. The exergy of mixing results from the isothermal and isobaric mixing of streams at the actual process conditions. The chemical exergy is the difference in chemical potentials between the process and reference components in their environmental concentration, temperature, and pressure. The physical exergy is the maximum obtainable amount of shaft work (electrical energy) when a stream is brought from process conditions (T, P) to equilibrium at ambient temperature by a reversible heat exchange. Traditionally, the exergy analysis is based on the overall thermodynamic efficiency that is the ratio of the lost work to the ideal work required for separation. The overall exergy efficiency for distillation is the product of external and internal exergy efficiencies. This external efficiency depends on thermal integration among units, coproduction, and recompression of overhead vapor to be used in the reboiler, while the internal exergy depends on the column internal design, feed composition and state, number of stages, and utility requirements. The results of exergy calculation for all the streams are shown in Tables 2 and 3. After the exergy values streams were calculated for all the process, the fuel-product analysis was carried out to calculate the exergetic efficiency of each equipment. 4. Economic models This method calculates all the costs associated with a project, including a minimum required return on investment. Based on the estimated total capital investment and assumptions for economical, financial, operating, and market input parameters, the total revenue requirement is calculated on a year-by-year basis. Finally, the non-uniform annual monetary values associated with the investment, operating (excluding fuel), maintenance, and the fuel costs of the system being analyzed are levelized; that is, they are converted to an equivalent series of constant payments (annuities) (Fabrega et al., 2009). The series of annual costs concerned with the carrying charges CCj and expenses (FCj and OMCj) for the jth year of a system operation is not uniform. In general, the carrying charges decrease while the fuel costs rise with passing of years of operation (Bejan et al., 1996). A levelized value TRRL for the total annual revenue requirement can be computed by applying a discounting factor and the capital-recovery factor CRF:
TRRL ¼ CRF
n X 1
TRRj 1 þ ieff
j
(1)
Where TRRj is the total revenue requirement in the jth year of system operation, ieff is the average annual effective discount rate (cost of money), and n denotes the system economical life expressed in years. In the case of gas separation plant, the annual total revenue requirement is equal to the sum of the following five annual amounts including the total capital recovery (TCR); minimum return on investment (ROI); electricity cost (FCele); steam cost (FCste); and the operating and maintenance cost (OMC):
TRRj ¼ TCRj þ ROIj þ FCj;ste þ FCj;ele þ OMCj
(2)
For introduction and detailed calculation, the procedures of calculations of TCRj and ROIj are given in Section 8. For applying Eq. (2), it is assumed that each monetary transaction occurs at the end of each year. The capital-recovery factor CRF is given by
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
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Table 2 The results of the exergy analysis of main process stream. Stream
Physical exergy (kj/h)
Chemical exergy (kj/h)
Total exergy (kj/h)
Stream
Physical exergy (kj/h)
Chemical exergy (kj/h)
Total exergy (kj/h)
51 52 53 54 55 56 S56 57 S57 58 59 62 63 64 S68 S69 S76 S77 81 85 86 89 S89 89B 90 90B
238,211,875 249,330,527 8,613,038 152,169,555 8,197,323 185,231,424 260,820,847 182,829,906 261,687,083 11,037,904 11,089,126 190,894,158 6,641,753 4,655,801 452,111 52,360 882,899 8,169,238 8,223,099 3,333,496 2,809,442 1,429,120 915,613 1,482,591 886,340 910,813
7.005Eþ14 7.005Eþ14 1.648Eþ09 1.401Eþ10 1.650Eþ09 6.054Eþ14 2.304Eþ10 1.798Eþ10 2.304Eþ10 3.507Eþ09 3.507Eþ09 1.798Eþ10 1.189Eþ09 2.321Eþ09 4.364Eþ05 1.163Eþ05 2.101Eþ06 7.887Eþ06 4.433Eþ09 2.466Eþ09 2.466Eþ09 1.324Eþ09 2.179Eþ06 1.324Eþ09 1.142Eþ09 1.142Eþ09
7.005Eþ14 7.005Eþ14 1.656Eþ09 1.416Eþ10 1.658Eþ09 6.054Eþ14 2.330Eþ10 1.816Eþ10 2.330Eþ10 3.518Eþ09 3.518Eþ09 1.817Eþ10 1.195Eþ09 2.326Eþ09 8.885Eþ05 1.686Eþ05 2.984Eþ06 1.606Eþ07 4.441Eþ09 2.469Eþ09 2.468Eþ09 1.326Eþ09 3.095Eþ06 1.326Eþ09 1.143Eþ09 1.143Eþ09
91 91B 92 93 S93 S95 S96 S102 S104 S109 S116 S130 143 144 145 146 166 171 244B 244C 247 248 248B 249 250 261
5,342,262 5,478,979 1,383,101 121,887 8,531,784 2,648,691 284,251 28,291 43,726 1,717,856 3926 195,796,680 1,592,190 4904 20,368 419,627 5,453,709 1,371,031 168,063,270 69,618,073 87,449,741 216,228,096 196,692,678 17,657,481 28,210,191 25,295,100
1.970Eþ09 1.970Eþ09 1.324Eþ09 1.142Eþ09 8.179Eþ06 2.539Eþ06 6.765Eþ05 1.182Eþ07 1.182Eþ07 2.385Eþ13 2.132Eþ09 6.054Eþ14 2.385Eþ13 2.132Eþ09 3.221Eþ13 3.221Eþ13 1.970Eþ09 1.324Eþ09 1.401Eþ10 5.804Eþ09 5.804Eþ09 1.798Eþ10 1.798Eþ10 1.446Eþ14 1.606Eþ14 1.606Eþ14
1.975Eþ09 1.975Eþ09 1.326Eþ09 1.326Eþ09 1.671Eþ07 5.188Eþ06 9.608Eþ05 1.184Eþ07 1.186Eþ07 2.385Eþ13 2.132Eþ09 6.054Eþ14 2.385Eþ13 2.132Eþ09 3.221Eþ13 3.221Eþ13 1.975Eþ09 1.326Eþ09 1.417Eþ10 5.873Eþ09 58,912,34,430 1.819Eþ10 1.817Eþ10 1.446Eþ14 1.606Eþ14 1.606Eþ14
n ieff 1 þ ieff CRF ¼ n 1 þ ieff 1
(3)
in which, ieff is the interest rate. If the series of payments for the annual fuel cost FCj is uniform over the time except for a constant escalation rFC (i.e., FCj ¼ FC0 (1 þ rFC)j), then the levelized value FCL of the series can be calculated by multiplying the fuel expenditure FC0 at the beginning of the first year by the constant-escalation levelization factor CELF:
kFC 1 knFC FCL ¼ FC0 CELF ¼ FC0 CRF ð1 kFC Þ
(4a)
Where,
kFC ¼
1 þ rFC and rFC ¼ constant 1 þ ieff
(4b)
The terms rFC and CRF denote the annual escalation rate for the fuel cost and the capital-recovery factor (Eq. (4)), respectively. Accordingly, the levelized annual operating and maintenance costs (OMCL) are given by:
kOMC 1 knOMC OMCL ¼ OMC0 CELF ¼ OMC0 ð1 kOMC Þ
(5a)
Where
kOMC ¼
1 þ rOMC and rOMC ¼ contant 1 þ ieff
(5b)
The term rOMC is the nominal escalation rate for the operating and maintenance costs. Finally, the levelized carrying charges CCL are obtained from the following equation:
CCL ¼ TRRL FCL OMCL
(6)
Table 3 Exergetic efficiency values of all components used in the process of gas separation. Equip. name
Fuel exergy
Product exergy
Prod Ex (Kw)
Fuel Ex(Kw)
˛k %
Cold box
E52 E51
3088.51
3983.55
77.53
E-1 X-1 K-1 E-2 Demethaniser
E56 E57 W E244 E54 E248B Es68 Es69 þ m58(ein e58)
2963.75 2236.9 4953.24 7916.03
4421.12 2963.75 5426.5 8338.54
67.04 75.5 91.28 94.93
V-1 P-1 Demethaniser Depropoanizer Debutanizer P-2 P-3 E-3 E-4
E53 E55 W (Es77 Es76) þ (E144 Es116) þ m64(e59 e64) (Es93 Es89) þ m85(e81 e85) (Es95eEs96) þ m89(e86ee89) þ m90(e86ee90) W W E89B E92 E90B E93
(E77 E76) þ (E144 E116) þ (E77 E76) þ (E144 E116) þ (E77 E76) Es57 Es56 E62 E57 W E247 E244c E248 þ E58 E247 E54 E55$m249 (e249 e256) þ m250(e250 e261) 0 E59 E58 E63 þ E64 E59 þ m63(e63 e59) E91 þ E85 E81 þ m91(e91 e81) E89 þ E90 E86 E89B E89 E89B E90 Es104 Es102 Q(1 T0/T)
0 14.23 1453.63 1215.61 271.87 14.85 6.8 4.29 78
145.57 17.89 4347.86 4139.1 3782.21 19.86 8.35 27.64 219.15
0 79.55 33.43 29.37 7.19 74.8 81.4 15.51 35.59
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The major difference between a conventional economical analysis and an economical analysis conducted as part of a thermoeconomic analysis is that the latter is done at the system component level. The annual carrying charges or capital investment (superscript CI) and operating and maintenance costs (superscript OM) of the total system can be apportioned among the system components according to the contribution of the kth component to the purchased P equipment cost PECtotal ¼ k PECk for the overall system:
CCL PECk CI P Z_ k ¼ s k PECk
(7)
OMCL PECk OM P Z_ k ¼ s PECk
(8)
k
Here, PECk and s denote the purchased-equipment cost of the kth system component and the total annual time (in hours) of system operation at full load, respectively. The term Z_ k represents the cost rate associated with the capital investment and operating and maintenance expenses: CI OM Z_ k ¼ Z_ k þ Z_ k
(9)
5. Thermoeconomic analysis The thermoeconomic analysis uses the unit cost of exergy and cost rates of all the different streams of material and exergy to calculate thermoeconomic variables for each component of the system. Exergetic variables including exergy destruction rate E_ D;K , exergy destruction ratio yD;K , and exergetic efficiency εk are previously determined. 5.1. Thermoeconomic variables Definitions of cost rates of fuel C_ F and product C_ P result from definitions of the fuel and product for calculating the exergetic efficiency. C_ F;K Represents the cost rate of exergy, by which the fuel exergy E_ F;K is supplied for the Kth component of the system, while C_ P;K represents the cost rate related to the product exergy E_ P;K for the same component. Unit average exergy cost of fuel for the Kth component of the system represents the average cost at which the unit fuel exergy is supplied for the Kth component of the system. Thus, we have:
cf ;k ¼ C_ F;K =E_ F;K
(10)
The value of cf ;k depends on the relative situation of the Kth component of the system with respect to the other components. Similarly, the unit cost of the product cp;k is defined as the average cost at which each unit of exergy is supplied by the product of the Kth component of the system:
cp;k ¼ C_ P;K =E_ P;K
(11)
One of the most important parts of the thermoeconomic analysis is determination of cost of exergy destruction for each component of the system. The cost rate C_ D;K associated with the exergy destruction E_ D;K for the Kth component of the system is a hidden cost which can only be revealed by the thermoeconomic analysis. This cost can be evaluated using the cost of the additional fuel required for balancing the exergy destruction rate and producing the same rate of product exergy, E_ P;K :
C_ D;K ¼ cf ;k
E_ D;K
(12)
For most well-designed equipment and system components, the more exergy destruction decreased (efficiency increased); the cost of exergy destruction C_ D;K will be reduced, while at the same time the cost of capital investment ZKCI will increase. In other words, the larger is C_ D;K , the smaller will be Z_ K and vice versa. One of the most interesting aspects of the thermoeconomic analysis is that the exergy destruction cost for a component is estimated and it is compared to the investment cost of that component. This comparison aids the process of decision-making for the changes required for the system. Among all the possible solutions, the solution having the highest efficiency, the lowest specific fuel cost and investment cost ZKCI , resulting in the lowest value of Cp;k , will be opted for. The relative cost difference rk between the average cost of the unit product exergy and unit fuel exergy is obtained by the following relationship:
rk ¼
cp;kCF;K CF;K
¼
Z_ k 1 εk þ εk CF;K E_ P;K
(13)
The above relationship shows that the real sources of cost in the Kth component are: capital investment cost ZKCI , cost of exergy destruction in that component C_ D;K , operational and maintenance cost ZKOM , and exergy destruction C_ L;K . Among these sources of cost, the first two ones are the most prominent and thus used to calculate the exergoeconomic factor. The exergoeconomic factor represents the ratio of the investment cost to the sum of the investment, the exergy destruction, and the lost exergy costs.
fk ¼
Z_ k _Z þ CF;K E_ P;K þ E_ D;K k
(14)
_ Thermoeconomic variables like zCI K and C D;k offer an absolute criterion for the degree of importance of the Kth component, while rk and fk offer relative criteria to evaluate the economical performance of a component. 6. Exergy costing In this section, exergy balance equations are written for each component and the unit cost of exergy is calculated for each stream. The cost of the feed intake of the component No. 105 is taken as zero. Since some of the streams passing the cold box enter the cold box from the Demethanizer column, equations cannot be solved independently for some of the components. To solve these equations, we need to simultaneously solve the cost balance equations for a control volume containing the cold box and the distillation column. These equations which contain 19 equations and 19 unknowns are given in the following and their solution is found using the Matlab software. Table 4 7. Results 7.1. Results of exergy analysis Having evaluated the exergy of the streams, we presented the exergy balance equations for each component, which defined their fuel and product. The exergetic efficiency was evaluated for each component as well. Moreover, the exergy loss and exergy destruction were calculated for all the components. These two values are excellent criteria for assessing the performance of all the components. This is how to identify possible factors increasing the cost of the product and take measures towards eliminating those factors. Theoretically, the exergy loss and exergy destruction are distinct concepts, but herein they both have the same effect. In most
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93 Table 4 Unit exergy cost for each stream.
100
94.9
91
91.3
91
90
Unit cost of exergy ($/TJ)
Stream
Unit cost of exergy ($/TJ)
80
51 52 53 55 244 244B 244C 247 54 81 91 91B 161 85 86
0 10.753 11.025 11.028 11.025 11.022 11.022 11.427 11.022 11.43 33.08 33.715 33.72 11.43 11.432
248 248B 56 57 62 58 59 63 64 89 89B 92 90 90B 93
11.132 11.132 11.132 11.185 15.46 11.132 11.43 41.632 11.43 24.318 25.045 25.854 11.432 11.650 20.962
70
74.8
77.5
74.4
60 50 40 30
33.4
35.6 29.37 23.15 15.5
20 10 0
system components
Fig. 3. Exergy efficiency for system components.
Fig. 4. Distribution of exergy destruction in system components.
input from the turbine and even if it cannot consume all of its exergy input for increasing the exergy of the stream, there has been great saving in the overall problem. After all, even if an electrical compressor is used, not all of its exergy intake would have resulted in addition of the exergy of the stream. For pressure valves, it should be noted that as these valves have no useful output, their only influence is to reduce the overall output exergy and all of this reduction is actually equal to the amount of the exergy destruction because it associates no useful result or product. Fig. 5 Now, it is time to analyze more closely the most important contribution to the exergy destruction. The pie chart above shows the contribution of each column to the total exergy destruction caused by the distillation columns.
Exergy destruction rate(KW)
components, we assumed adiabatic behavior and thus, the exergy loss is ignored. In the following, diagrams and curves pertaining to the efficiency of each component and its value of the exergy destruction, are illustrated. Figs. 2 and 3 By analyzing the results and comparing exergy destruction for the different components, we can see that the major part of the exergy destruction happens in the distillation columns. The distillation columns of these two units are responsible for more than 64% of wasted exergy (loss and destruction), the reason for which is obvious. The columns consume a lot of exergy in their reboiler, while a large proportion of this heat input is taken back from the system in the condenser at the top of the column and thus, it is lost. Among these columns, the Demethanizer column has the best performance, since, firstly, this column has no condenser and the steam consumption at its reboiler is very small, and secondly, it has a lot of intake streams which make it approach the ideal column. Therefore, it is logically justified for this column to have a larger exergetic efficiency compared to other columns. In the following, a pie chart shows the contribution of each component in the total exergy destruction. Fig. 4 The above pie chart illustrates that after the stage of the distillation columns, which are responsible for 64% of the total exergy destruction, there are heat exchangers causing 15% of the total exergy destruction. Next, the compressor and the expander have considerable exergy destruction shares, i.e., 13% and 6%, respectively. However, it should be noted that the turbo expander set has replaced a big expansion valve, having thus saved a lot of exergy from being destroyed. In this case, the compressor gets its work
exergy efficiency
Stream
81.4
79.5
system components Fig. 2. Exergy destruction for each system component.
Fig. 5. Contribution of each column in exergy destruction of all the columns.
92
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
Table 5 The results of exergoeconomic analysis.
Table 8 Components based on ascending order of F value.
Equipment
Z ($/hr)
Cp ($/Tj)
CF ($/Tj)
CD þ Cl ($/hr)
r (%)
f (%)
Components
F
Demethanizer De-ethanizer Depropoanizer Debutanizer 107-P-100 107-P-101 107-P-102 105-P-101 107-E-100 107-E-101 105-X-101 105-K-101 Cold Box 105-E-102
11.44 18.24 17.37 9.14 0.39 0.36 0.34 0.50 1.05 0.92 51.12 26.45 24.39 2.36
460.98 4909 9782 17446 9206 18052 10195 20480 25.85 13474 9655 2496 677434440 144.8
55.61 4320 1689 1848 8333 8333 8333 8333 0 0 2496 11.022 14717 11.132
0.85 45.01 17.78 6.00 0.11 0.15 0.05 0.11 e e 6.53 0.58 47.42 0.019
þ100 60 þ100 þ100 10.5 þ100 22.3 þ100 e e þ100 þ100 þ100 þ100
99.30 31.50 49.86 60.79 78.01 70.93 88.20 82.06 e e 88.7 99.8 33.96 99.20
De-ethanizer Cold Box De-propanizer De-butanizer
31.5 33.96 49.86 60.79
After complete exergoeconomic analysis of streams, each component can be exergoeconomically analyzed individually. The difference between the relative cost rk and the exergoeconomic cost f is representative of the performance of that component of the system. These values are calculated and listed in Table 5. 8. Conclusions
Table 6 Components, based on their importance. Component
Z ($/hr)þCd ($/hr)
Cold Box De-ethanizer Compressor Depropoanizer Expander Debutanizer Demethanizer 105-E-102
71.81 63.58 57.65 35.47 27.03 15.31 12.29 2.39
As previously stated, the smallest share of the exergy destruction belongs to the Demethanizer column since it is the closest to the ideal state. Moreover, the flow rate of the steam consumed in its reboiler is very small and lacks a condenser, as a result of its low temperature. This column is responsible only for 6 percent of the exergy destruction of columns. The next small exergy destruction occurs in the debutanizer column which is relatively small and has a smaller total feed input\ compared to most other columns. This column causes to produce only 13 percent of the total exergy destruction of the columns. The Largest amount of exergy destruction takes place in De-ethanizer and Depropoanizer columns, whose contribution each is more than 25% of the total exergy destruction. Thus, any small change in efficiencies of these two columns will leads to a magnificent effect on reducing the exergy destruction of the whole system. Four heat exchangers were investigated in the units, and the cold box, which is a special heat exchanger among them, is responsible for more than half of the total exergy destruction of all the heat exchangers. E cold box has a high exergetic efficiency in comparison with the other heat exchangers, which is a proof for its good design. However, since the heat exchanger plays an important role in the entire system and its fuel and product are massive in amount, any change which can cause a small improvement in its performance can lead to great economical benefice.
Table 7 Components, based on their f values. Components
F
Expander Demethanizer 105-E-101 Compressor 107-p-102 105-p-101
99.8 99.3 99.2 88.7 88.2 82.06
In this approach, first the capital cost of the system is estimated. Then, some economical techniques are used to calculate the revenue requirement of the system in dollars per hour and finally, the cost balance equations are written to calculate the unit cost of exergy for each stream. Finally, the exergoeconomic factor is defined and comments are made about the balance between the capital investment and operating costs of the system inflicted by the exergy destruction which have to be compensated by more fuel consumption. There is a distinct algorithm to accomplish the abovementioned results. Based on this algorithm: 1- All the components are put in descending order based on their importance. The importance of each component is known from the magnitude of the sum Z ($/hr)þCd ($/hr). Therefore, this is a way to model the components based on their importance. 2- The exergoeconomic factor is used to find the prominent factor of the cost infliction: a) If the value of f is large, we should check whether it is economically justified to decrease the capital cost of the equipments, because it seems that the capital cost is so high that it has lost its economical justification. b) If f is small, we should try to increase the efficiency even if it yields higher capital cost, since it seems that low efficiency of the system inflicts a high expenditure on the system. Now components are put in a descending order based on their importance, as stated in the above. The factor Z($/hr)þCd($/hr) is ranked for component as below: Table 6 The components are put in descending order based on their importance and respective costs in the system. It can be seen that the cold box was not so seriously distinguished in the exergy analysis but its importance is clearly in the exergoeconomic analysis. In the following, Instruction 2 is performed. The following table shows the components put in order based on their f values. In these components, the capital cost is too high and a simpler, cheaper component can be more economically justified to use: Table 7 The following table shows the components put in ascending order based on their f values. These components are the ones for which low efficiency and high exergy destruction has inflicted a high cost (compared to the capital cost) on the system and thus, these components are not economically justified to operate. Therefore, for these components it should be investigated if there are alternative components with higher quality and
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
efficiency to improve the economical performance of the system. Table 8 The analysis of the exergoeconomic factor shows that the use of the expander and the compressor has inflicted a very high capital cost on the system which does not seem to have proper return of investment and thus, they had better be changed with cheaper equipments. Moreover, the investment carried out for the Methane separation column is extraordinarily high, while its exergy destruction is small. Thus, it appears that a cheaper column can be used instead. However, the De-ethanizer column has a large amount of the exergy destruction and improving its efficiency should be investigated. The cold box also has a similar situation, namely, although its exergy efficiency is large (the result of exergy analysis), it appears that in the case of being technically possible and having access to the required technologies, more investment and more efficiency improvement can be economically justified. The depropaniser column and the debutanizer column are in the next priorities. References Ansari, Kambiz, Sayyaadi, Hoseyn, Amidpour, Majid, 2010. Thermoeconomic optimization of a hybrid pressurized water reactor (PWR) power plant coupled to a multi effect distillation desalination system with thermo-vapor compressor (MED-TVC). Energy.
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Bejan, A., Tsatsaronis, G., Moran, M., 1996. Thermal Design and Optimization. J. Wiley. Demirel, Y., 2004. Thermodynamic Analysis of Separation Systems. Chemical and Biomolecular Engineering Research and Publications. Fabrega, F.M., Rossi, J.S., d’Angelo, J.V.H., 2009. Exergetic analysis of the refrigeration system in ethylene and propylene production process. Energy. Khoshgoftar Manesh, M.H., Amidpour, M., 2009. Multi-objective thermoeconomic optimization of coupling MSF desalination with PWR nuclear power plant through evolutionary algorithms. Desalination. Kotas, T.J., 1985. The Exergy Method of Thermal Plant Analysis. Butterworths, London. Luz Silveira, Jose, et al., 2010. A contribution for thermoeconomic modelling: a methodology. Applied Thermal Engineering. Mehrpooya, M., Gharagheizi1, F., Vatani, A., 2009. Thermoeconomic analysis of a large industrial propane refrigeration cycle used in NGL recovery plant. International Journal of Energy Research. Rivero, Ricardo, Rendon, Consuelo, Gallegos, Salvador, 2004. Exergy and exergoeconomic analysis of a crude oil combined distillation unit. Energy 29, 1909e1927. Sayyaadi, Hoseyn, Babaelahi, M., 2010. Thermoeconomic optimization of a cryogenic refrigeration cycle for re-liquefaction of the LNG boil-off gas. International Journal of Refrigeration. Sayyaadi, Hoseyn, Saffari, Arash, 2009. Thermoeconomic optimization of multi effect distillation desalination systems. Applied Energy. Tona, Cesare, Raviolo, Paolo Antonio, Pellegrini, Luiz Felipe, de Oliveira Jr., Silvio, 2010. Exergy and thermoeconomic analysis of a turbofan engine during a typical commercial flight. Energy. Usón, Sergio, Valero, Antonio, 2011. Thermoeconomic diagnosis for improving the operation of energy intensive systems: comparison of methods. Applied Energy.
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Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse
Exergy and exergoeconomic evaluation of gas separation process B. Ghorbani, G.R. Salehi*, M. Amidpour, M.H. Hamedi Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 17 August 2011 Received in revised form 23 January 2012 Accepted 7 May 2012 Available online 2 July 2012
Exergy and exergoeconomic analyses for product recovery and separation systems of natural gas plant as well as the refrigeration system required for the plant are carried out. The exergetic and exergoeconomic costs of all process and utility streams are calculated through a systematic method of assigning exergetic cost relations to the streams. The results indicate that the exergetic efficiencies of the Debutanizer, Depropoanizer, and De-ethanizer columns are the lowest. Distillation columns have 64% of the total exergy loss, which is the maximum value of the system components. In the second place, heat exchangers have 15% of the exergy loss. Next there are compressors and expanders which have 13% and 6% of the exergy loss, respectively. It should be noted that the expander is replaced by a choke valve for energy-saving purposes. On the other hand, the results of the exergoeconomic analysis show that the percentage increases in the unit thermoeconomiccosts of the compression and the Demethanizer sections are the highest. This study demonstrates that the exergoeconomic analysis, whose results present cost-based information suggesting potential locations for the process improvement, can provide more information in comparison to the exergy analysis. 2012 Elsevier B.V. All rights reserved.
Keywords: Gas processing Natural gas Exergy Exergoeconomic Analyses
1. Introduction Separation of Methane, Ethane, Propane, and natural gas liquids (NGL) from the natural gas is generally carried out by one of the following alternatives: (i) external refrigeration (ER), (ii) turbo expansion (TE), (iii) JouleeThompson expansion, and (iv) absorption. In many processing schemes, a combination of these is used to improve the energy efficiency or obtain greater recoveries (Mehrpooya et al., 2009). New methods of energy saving have led to the development of analysis techniques based on the second law of thermodynamics and, particularly, the concept of exergy. The exergoeconomic analysis considers the quality of energy (exergy) in allocating the production costs of a process to its products. A general methodology for this kind of analysis was presented by Electric Power Research Institute (Bejan et al., 1996; Kotas, 1985), known as the Total Revenue Requirement method (TRR method). The application of exergoeconomic methods were mostly reported for the analysis of energy conversion systems, such as power plants, cogeneration systems, and refrigeration systems (Mehrpooya et al., 2009), (Luz Silveira et al., 2010; Tona et al., 2010; Khoshgoftar Manesh and Amidpour, 2009; Usón and Valero, 2011; Sayyaadi and Babaelahi, 2010; Ansari et al., 2010; Fabrega et al., 2009; Demirel, 2004; Rivero et al., 2004; Sayyaadi and Saffari, * Corresponding author. Tel.: þ98 9122031671. E-mail address: [email protected] (G.R. Salehi). 1875-5100/$ e see front matter 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jngse.2012.05.001
2009). There are a few reports of applying the exergoeconomic methods on the chemical separation processes (Luz Silveira et al., 2010). This research presents the results of the exergy and exergoeconomic analyses using the TRR method in gas separation process. 2. Process description of the NGL recovery plant After H2S removal, dehydration and mercury removal, the dry sweet gas is routed to the Ethane Recovery Unit 105, where the gas is processed to cope with the process specifications indicated in Table 1. The figures which will be presented in the sequel are indicative only and related to the summer case. They have to be used as a guide but do not represent exact operating conditions or guarantees. 2.1. Gas cooling and expansion Sweet and dry gas coming from the Dehydration and Mercury Guard Unit 104 is first precooled down to 35 C in the Cold Box 105-E-101 against: a Propane stream at medium pressure (Propane at 19.0 C), the cold sales gas coming from Demethanizer Exchanger 105-E-102 (included in Cold Box 105-E-101) at 49 C and going to the Gas/Gas exchanger 104-E-101 at 17.2 C, a withdrawal stream from and to lower section of Demethanizer 105-C-101 (entering and leaving Cold Box at 11.1 C and 16.6 C), a Propane stream at low pressure (propane at 4.1 C), a withdrawal stream from and to
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93 Table 1 Composition of feed stream. Substance
Mole fraction
Nitrogen CO2 Methane Ethane Propane i-butane n-Butane i-pentane i-pentane n-pentane n-hexane n-heptane n-octane
0.035254 0.010001 0.863377 0.055192 0.020372 0.003762 0.005765 0.001761 0.001761 0.001571 0.001367 0.000777 0.000402
medium section of Demethanizer 105-C-101 (entering and leaving Cold Box at 37.5 C and 13.3 C).Fig. 1 At 35 C a major portion of Butane and heavier components are condensed. The liquid phase also contains significant amounts of Methane and Ethane, which must be removed. Then the twophase flow is separated in Feed Flash KO Drum 105-D-101. The liquid is sent under level control, through a flashing valve (about 25% of flashed gas), as a feed stream to the Demethanizer 105-C-101 (at 30.4 bara and 48.4 C downstream the control valve). The gas exiting 105-D-101 is split into two streams: one side stream (at a set flow) is sent to the Demethanizer Exchanger 105-E102, installed in 105-E-101 cold box in which is cooled from 35.0 C down to 84.5 C. This stream is later let down through a flow control valve (30.2 bara and 95.3 C downstream the control valve) and is sent to the top of 105-C-101 as a column reflux to improve C2þ recovery efficiency and light products separation. The main stream, which is let down to 30.4 bara and 67 C before feeding 105-C-101, feeds the Feed Gas Expander 105-X-101. 2.2. Demethanizer and export gas sections The two-phase streams from 105-X-101, 105-D-101 bottom and 105-E-102 enters the Demethanizer 105-C-101, operating at 30 bara at the top, which is a strippereabsorber column that produces sales gas as an overhead and a wide-range liquid as a bottom product.
87
Between the bottom and feed trays, light components are stripped out of the liquid phase and heavy components are absorbed from the gas phase. Between the feed and top trays, the heavier compounds are removed from the gas phase being absorbed by the liquid reflux coming from the Demethanizer Exchanger (included in Cold Box 105-E-101). To minimize the amount of light component in the liquid, a stripping action is provided by means of the low pressure steam used as a heating medium in the Demethanizer Reboiler 105-E-103. Demethanizer bottom temperature is 38.3 C. To lower Demethanizer Reboiler duty and balance the heat input to the column, intermediate withdrawals are provided. They are reheated in the Cold Box by cooling feed to the Demethanizer. Bottom liquid product is sent, by means of Demethanizer Transfer Pumps 105-P101 A/B, under level control resetting a flow control valve as a feed to the De-ethanizer 105-C-102. Gas leaving the top of the Demethanizer at 87.4 C is first heated to 49 C in the Demethanizer Exchanger (included in Cold Box 105-E-101) before being reheated to 17.2 C in the Cold Box and to 34.2 C in the Gas/Gas Exchanger 104-E-101. This gas then feeds the Treated Gas Compressor 105-K101 which will increase the pressure up to 33.7 bara before being exported to the Export Gas Compression and Metering Unit 106. 2.3. De-ethanizer section Demethanizer bottom liquid is sent to the De-ethanizer 105-C102, under level control resetting flow control, by means of Deethanizer Transfer Pumps 105-P-101 A/B (One pump operating and one spare pump). The function of this column, which operates at 30.5 Bara on the top, is to remove Ethane as an overhead vapor stream and yield a bottom product containing all the Propane and heavier components. The overhead of the De-ethanizer is chilled to 8.7 C by the 2.4 C refrigerant in the De-ethanizer Condenser 105-E-105 and the mixed phase is routed to the De-ethanizer Reflux Drum 105-D-102. The pressure control on refrigerant side, that is the temperature control of the refrigerant, is reset by the HC liquid level in the Deethanizer Reflux drum. After separation in the De-ethanizer Reflux Drum, the liquid is pumped under flow control by the De-ethanizer Reflux Pumps 105-P-102 A/B and returned to the top tray of the De-ethanizer as reflux.
Fig. 1. Schematic of gas separation process.
88
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
The Ethane stream exiting the De-ethanizer Reflux Drum is heated up to 43.2 C by means of liquid Propane at 60 C. A possibility to mix this stream with the Sales Gas upstream the Treated Gas Compressor is provided in the case of off-spec product or upsets in the downstream units. The column is equipped with a De-ethanizer Reboiler 105-E104, which uses low pressure saturated steam as heating medium. The De-ethanizer bottom temperature is of approximately 108.5 C. The liquid hydrocarbons recovered at De-ethanizer bottom (C3þ cut) are sent under the level control resetting a flow control valve to NGL Fractionation Unit 107 for further processing. The operating pressure of the Depropoanizer is set to 22.3 bara to ensure the condensation of the Propane cut in an air cooler. There are 11 actual trays (two pass trays) in the top section, 21 actual trays for the bottom section (four pass trays) plus the bottom draw tray. The operating pressure of the debutanizer is set to 8.2 bara to ensure the condensation of the butane cut in an air cooler. There are 11 actual trays (one pass tray) in the top section, 17 actual trays for the bottom section (two pass trays) plus the bottom draw tray. De-ethanizer bottom liquids are mixed in Unit 107 and are sent to the Depropoanizer. The function of this column, which operates at 22.3 bara is to produce a Propane stream as an overhead liquid stream. The bottom product containing all the Butanes and heavier components feeds the debutanizer. The overhead gas of the Depropoanizer is air-cooled and totally condensed at 60 C in the Depropoanizer Condenser. The liquid Propane product is routed to the Depropoanizer Reflux Drum. Part of the liquid is returned to the top tray of the Depropoanizer as reflux under flow control by the Depropoanizer Reflux Pump. The other part is sent under D-101 level control resetting flow control by the Propane Feed Pump to the Propane treatment Unit, where COS and mercaptans will be removed. The column is equipped with a Depropoanizer Reboiler, which uses LP saturated steam as heating medium. The Depropoanizer bottom temperature is approximately 138 C. The Depropoanizer bottom liquid is sent to the Debutanizer under the level control resetting flow control and mixed with the sour washing C4 cut. The Debutanizer operates at 8.2 bara and is equipped with both a condenser and a reboiler. The overhead gas of the column is air-cooled and totally condensed at 60 C in the Debutanizer Condenser. The liquid Butane product is then routed to the Debutanizer Reflux Drum. One part of the liquid is pumped from the Debutanizer Reflux Drum by the Debutanizer Reflux Pumps and returned under the flow control, to the top tray of the Debutanizer as reflux. The other part is pumped from the Debutanizer Reflux Drum by the Butane feed pumps and cooled by the sea water down to 40 C in the Butane Cooler. After cooling, the Butane is sent to the Butane treatment unit, where Mercaptans will be removed. The Debutanizer Reboiler uses LP saturated steam as heating medium. The Debutanizer bottom temperature is of approximately 130 C. The Debutanizer bottom liquid is pumped to avoid flashing by the condensate circulation pumps before being air-cooled at 60 C. Then the liquid is sent under the Debutanizer level control resetting f the low control, to the stabilization unit to be mixed with stabilized condensates. 3. Exergy analysis Exergy is the maximum available work when some forms of energy are transferred reversibly to a reference system, which is in thermodynamic equilibrium with the surroundings, and has no ability to perform work. Exergy is also a measure of distance of a system from global equilibrium; as the exergy is consumed, the state variables of temperature, pressure, and composition of system approach those of the surroundings. Therefore, the reference state is called the dead state. The total exergy of multicomponent
streams is the sum of its three contributions: the exergy change due to mixing, chemical exergy, and physical exergy, and is expressed by Xtotal ¼ (HH0)T0(SS0), where the subscript 0 indicates the enthalpy, entropy, and temperature of the environment, respectively. The exergy of mixing results from the isothermal and isobaric mixing of streams at the actual process conditions. The chemical exergy is the difference in chemical potentials between the process and reference components in their environmental concentration, temperature, and pressure. The physical exergy is the maximum obtainable amount of shaft work (electrical energy) when a stream is brought from process conditions (T, P) to equilibrium at ambient temperature by a reversible heat exchange. Traditionally, the exergy analysis is based on the overall thermodynamic efficiency that is the ratio of the lost work to the ideal work required for separation. The overall exergy efficiency for distillation is the product of external and internal exergy efficiencies. This external efficiency depends on thermal integration among units, coproduction, and recompression of overhead vapor to be used in the reboiler, while the internal exergy depends on the column internal design, feed composition and state, number of stages, and utility requirements. The results of exergy calculation for all the streams are shown in Tables 2 and 3. After the exergy values streams were calculated for all the process, the fuel-product analysis was carried out to calculate the exergetic efficiency of each equipment. 4. Economic models This method calculates all the costs associated with a project, including a minimum required return on investment. Based on the estimated total capital investment and assumptions for economical, financial, operating, and market input parameters, the total revenue requirement is calculated on a year-by-year basis. Finally, the non-uniform annual monetary values associated with the investment, operating (excluding fuel), maintenance, and the fuel costs of the system being analyzed are levelized; that is, they are converted to an equivalent series of constant payments (annuities) (Fabrega et al., 2009). The series of annual costs concerned with the carrying charges CCj and expenses (FCj and OMCj) for the jth year of a system operation is not uniform. In general, the carrying charges decrease while the fuel costs rise with passing of years of operation (Bejan et al., 1996). A levelized value TRRL for the total annual revenue requirement can be computed by applying a discounting factor and the capital-recovery factor CRF:
TRRL ¼ CRF
n X 1
TRRj 1 þ ieff
j
(1)
Where TRRj is the total revenue requirement in the jth year of system operation, ieff is the average annual effective discount rate (cost of money), and n denotes the system economical life expressed in years. In the case of gas separation plant, the annual total revenue requirement is equal to the sum of the following five annual amounts including the total capital recovery (TCR); minimum return on investment (ROI); electricity cost (FCele); steam cost (FCste); and the operating and maintenance cost (OMC):
TRRj ¼ TCRj þ ROIj þ FCj;ste þ FCj;ele þ OMCj
(2)
For introduction and detailed calculation, the procedures of calculations of TCRj and ROIj are given in Section 8. For applying Eq. (2), it is assumed that each monetary transaction occurs at the end of each year. The capital-recovery factor CRF is given by
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
89
Table 2 The results of the exergy analysis of main process stream. Stream
Physical exergy (kj/h)
Chemical exergy (kj/h)
Total exergy (kj/h)
Stream
Physical exergy (kj/h)
Chemical exergy (kj/h)
Total exergy (kj/h)
51 52 53 54 55 56 S56 57 S57 58 59 62 63 64 S68 S69 S76 S77 81 85 86 89 S89 89B 90 90B
238,211,875 249,330,527 8,613,038 152,169,555 8,197,323 185,231,424 260,820,847 182,829,906 261,687,083 11,037,904 11,089,126 190,894,158 6,641,753 4,655,801 452,111 52,360 882,899 8,169,238 8,223,099 3,333,496 2,809,442 1,429,120 915,613 1,482,591 886,340 910,813
7.005Eþ14 7.005Eþ14 1.648Eþ09 1.401Eþ10 1.650Eþ09 6.054Eþ14 2.304Eþ10 1.798Eþ10 2.304Eþ10 3.507Eþ09 3.507Eþ09 1.798Eþ10 1.189Eþ09 2.321Eþ09 4.364Eþ05 1.163Eþ05 2.101Eþ06 7.887Eþ06 4.433Eþ09 2.466Eþ09 2.466Eþ09 1.324Eþ09 2.179Eþ06 1.324Eþ09 1.142Eþ09 1.142Eþ09
7.005Eþ14 7.005Eþ14 1.656Eþ09 1.416Eþ10 1.658Eþ09 6.054Eþ14 2.330Eþ10 1.816Eþ10 2.330Eþ10 3.518Eþ09 3.518Eþ09 1.817Eþ10 1.195Eþ09 2.326Eþ09 8.885Eþ05 1.686Eþ05 2.984Eþ06 1.606Eþ07 4.441Eþ09 2.469Eþ09 2.468Eþ09 1.326Eþ09 3.095Eþ06 1.326Eþ09 1.143Eþ09 1.143Eþ09
91 91B 92 93 S93 S95 S96 S102 S104 S109 S116 S130 143 144 145 146 166 171 244B 244C 247 248 248B 249 250 261
5,342,262 5,478,979 1,383,101 121,887 8,531,784 2,648,691 284,251 28,291 43,726 1,717,856 3926 195,796,680 1,592,190 4904 20,368 419,627 5,453,709 1,371,031 168,063,270 69,618,073 87,449,741 216,228,096 196,692,678 17,657,481 28,210,191 25,295,100
1.970Eþ09 1.970Eþ09 1.324Eþ09 1.142Eþ09 8.179Eþ06 2.539Eþ06 6.765Eþ05 1.182Eþ07 1.182Eþ07 2.385Eþ13 2.132Eþ09 6.054Eþ14 2.385Eþ13 2.132Eþ09 3.221Eþ13 3.221Eþ13 1.970Eþ09 1.324Eþ09 1.401Eþ10 5.804Eþ09 5.804Eþ09 1.798Eþ10 1.798Eþ10 1.446Eþ14 1.606Eþ14 1.606Eþ14
1.975Eþ09 1.975Eþ09 1.326Eþ09 1.326Eþ09 1.671Eþ07 5.188Eþ06 9.608Eþ05 1.184Eþ07 1.186Eþ07 2.385Eþ13 2.132Eþ09 6.054Eþ14 2.385Eþ13 2.132Eþ09 3.221Eþ13 3.221Eþ13 1.975Eþ09 1.326Eþ09 1.417Eþ10 5.873Eþ09 58,912,34,430 1.819Eþ10 1.817Eþ10 1.446Eþ14 1.606Eþ14 1.606Eþ14
n ieff 1 þ ieff CRF ¼ n 1 þ ieff 1
(3)
in which, ieff is the interest rate. If the series of payments for the annual fuel cost FCj is uniform over the time except for a constant escalation rFC (i.e., FCj ¼ FC0 (1 þ rFC)j), then the levelized value FCL of the series can be calculated by multiplying the fuel expenditure FC0 at the beginning of the first year by the constant-escalation levelization factor CELF:
kFC 1 knFC FCL ¼ FC0 CELF ¼ FC0 CRF ð1 kFC Þ
(4a)
Where,
kFC ¼
1 þ rFC and rFC ¼ constant 1 þ ieff
(4b)
The terms rFC and CRF denote the annual escalation rate for the fuel cost and the capital-recovery factor (Eq. (4)), respectively. Accordingly, the levelized annual operating and maintenance costs (OMCL) are given by:
kOMC 1 knOMC OMCL ¼ OMC0 CELF ¼ OMC0 ð1 kOMC Þ
(5a)
Where
kOMC ¼
1 þ rOMC and rOMC ¼ contant 1 þ ieff
(5b)
The term rOMC is the nominal escalation rate for the operating and maintenance costs. Finally, the levelized carrying charges CCL are obtained from the following equation:
CCL ¼ TRRL FCL OMCL
(6)
Table 3 Exergetic efficiency values of all components used in the process of gas separation. Equip. name
Fuel exergy
Product exergy
Prod Ex (Kw)
Fuel Ex(Kw)
˛k %
Cold box
E52 E51
3088.51
3983.55
77.53
E-1 X-1 K-1 E-2 Demethaniser
E56 E57 W E244 E54 E248B Es68 Es69 þ m58(ein e58)
2963.75 2236.9 4953.24 7916.03
4421.12 2963.75 5426.5 8338.54
67.04 75.5 91.28 94.93
V-1 P-1 Demethaniser Depropoanizer Debutanizer P-2 P-3 E-3 E-4
E53 E55 W (Es77 Es76) þ (E144 Es116) þ m64(e59 e64) (Es93 Es89) þ m85(e81 e85) (Es95eEs96) þ m89(e86ee89) þ m90(e86ee90) W W E89B E92 E90B E93
(E77 E76) þ (E144 E116) þ (E77 E76) þ (E144 E116) þ (E77 E76) Es57 Es56 E62 E57 W E247 E244c E248 þ E58 E247 E54 E55$m249 (e249 e256) þ m250(e250 e261) 0 E59 E58 E63 þ E64 E59 þ m63(e63 e59) E91 þ E85 E81 þ m91(e91 e81) E89 þ E90 E86 E89B E89 E89B E90 Es104 Es102 Q(1 T0/T)
0 14.23 1453.63 1215.61 271.87 14.85 6.8 4.29 78
145.57 17.89 4347.86 4139.1 3782.21 19.86 8.35 27.64 219.15
0 79.55 33.43 29.37 7.19 74.8 81.4 15.51 35.59
90
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
The major difference between a conventional economical analysis and an economical analysis conducted as part of a thermoeconomic analysis is that the latter is done at the system component level. The annual carrying charges or capital investment (superscript CI) and operating and maintenance costs (superscript OM) of the total system can be apportioned among the system components according to the contribution of the kth component to the purchased P equipment cost PECtotal ¼ k PECk for the overall system:
CCL PECk CI P Z_ k ¼ s k PECk
(7)
OMCL PECk OM P Z_ k ¼ s PECk
(8)
k
Here, PECk and s denote the purchased-equipment cost of the kth system component and the total annual time (in hours) of system operation at full load, respectively. The term Z_ k represents the cost rate associated with the capital investment and operating and maintenance expenses: CI OM Z_ k ¼ Z_ k þ Z_ k
(9)
5. Thermoeconomic analysis The thermoeconomic analysis uses the unit cost of exergy and cost rates of all the different streams of material and exergy to calculate thermoeconomic variables for each component of the system. Exergetic variables including exergy destruction rate E_ D;K , exergy destruction ratio yD;K , and exergetic efficiency εk are previously determined. 5.1. Thermoeconomic variables Definitions of cost rates of fuel C_ F and product C_ P result from definitions of the fuel and product for calculating the exergetic efficiency. C_ F;K Represents the cost rate of exergy, by which the fuel exergy E_ F;K is supplied for the Kth component of the system, while C_ P;K represents the cost rate related to the product exergy E_ P;K for the same component. Unit average exergy cost of fuel for the Kth component of the system represents the average cost at which the unit fuel exergy is supplied for the Kth component of the system. Thus, we have:
cf ;k ¼ C_ F;K =E_ F;K
(10)
The value of cf ;k depends on the relative situation of the Kth component of the system with respect to the other components. Similarly, the unit cost of the product cp;k is defined as the average cost at which each unit of exergy is supplied by the product of the Kth component of the system:
cp;k ¼ C_ P;K =E_ P;K
(11)
One of the most important parts of the thermoeconomic analysis is determination of cost of exergy destruction for each component of the system. The cost rate C_ D;K associated with the exergy destruction E_ D;K for the Kth component of the system is a hidden cost which can only be revealed by the thermoeconomic analysis. This cost can be evaluated using the cost of the additional fuel required for balancing the exergy destruction rate and producing the same rate of product exergy, E_ P;K :
C_ D;K ¼ cf ;k
E_ D;K
(12)
For most well-designed equipment and system components, the more exergy destruction decreased (efficiency increased); the cost of exergy destruction C_ D;K will be reduced, while at the same time the cost of capital investment ZKCI will increase. In other words, the larger is C_ D;K , the smaller will be Z_ K and vice versa. One of the most interesting aspects of the thermoeconomic analysis is that the exergy destruction cost for a component is estimated and it is compared to the investment cost of that component. This comparison aids the process of decision-making for the changes required for the system. Among all the possible solutions, the solution having the highest efficiency, the lowest specific fuel cost and investment cost ZKCI , resulting in the lowest value of Cp;k , will be opted for. The relative cost difference rk between the average cost of the unit product exergy and unit fuel exergy is obtained by the following relationship:
rk ¼
cp;kCF;K CF;K
¼
Z_ k 1 εk þ εk CF;K E_ P;K
(13)
The above relationship shows that the real sources of cost in the Kth component are: capital investment cost ZKCI , cost of exergy destruction in that component C_ D;K , operational and maintenance cost ZKOM , and exergy destruction C_ L;K . Among these sources of cost, the first two ones are the most prominent and thus used to calculate the exergoeconomic factor. The exergoeconomic factor represents the ratio of the investment cost to the sum of the investment, the exergy destruction, and the lost exergy costs.
fk ¼
Z_ k _Z þ CF;K E_ P;K þ E_ D;K k
(14)
_ Thermoeconomic variables like zCI K and C D;k offer an absolute criterion for the degree of importance of the Kth component, while rk and fk offer relative criteria to evaluate the economical performance of a component. 6. Exergy costing In this section, exergy balance equations are written for each component and the unit cost of exergy is calculated for each stream. The cost of the feed intake of the component No. 105 is taken as zero. Since some of the streams passing the cold box enter the cold box from the Demethanizer column, equations cannot be solved independently for some of the components. To solve these equations, we need to simultaneously solve the cost balance equations for a control volume containing the cold box and the distillation column. These equations which contain 19 equations and 19 unknowns are given in the following and their solution is found using the Matlab software. Table 4 7. Results 7.1. Results of exergy analysis Having evaluated the exergy of the streams, we presented the exergy balance equations for each component, which defined their fuel and product. The exergetic efficiency was evaluated for each component as well. Moreover, the exergy loss and exergy destruction were calculated for all the components. These two values are excellent criteria for assessing the performance of all the components. This is how to identify possible factors increasing the cost of the product and take measures towards eliminating those factors. Theoretically, the exergy loss and exergy destruction are distinct concepts, but herein they both have the same effect. In most
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93 Table 4 Unit exergy cost for each stream.
100
94.9
91
91.3
91
90
Unit cost of exergy ($/TJ)
Stream
Unit cost of exergy ($/TJ)
80
51 52 53 55 244 244B 244C 247 54 81 91 91B 161 85 86
0 10.753 11.025 11.028 11.025 11.022 11.022 11.427 11.022 11.43 33.08 33.715 33.72 11.43 11.432
248 248B 56 57 62 58 59 63 64 89 89B 92 90 90B 93
11.132 11.132 11.132 11.185 15.46 11.132 11.43 41.632 11.43 24.318 25.045 25.854 11.432 11.650 20.962
70
74.8
77.5
74.4
60 50 40 30
33.4
35.6 29.37 23.15 15.5
20 10 0
system components
Fig. 3. Exergy efficiency for system components.
Fig. 4. Distribution of exergy destruction in system components.
input from the turbine and even if it cannot consume all of its exergy input for increasing the exergy of the stream, there has been great saving in the overall problem. After all, even if an electrical compressor is used, not all of its exergy intake would have resulted in addition of the exergy of the stream. For pressure valves, it should be noted that as these valves have no useful output, their only influence is to reduce the overall output exergy and all of this reduction is actually equal to the amount of the exergy destruction because it associates no useful result or product. Fig. 5 Now, it is time to analyze more closely the most important contribution to the exergy destruction. The pie chart above shows the contribution of each column to the total exergy destruction caused by the distillation columns.
Exergy destruction rate(KW)
components, we assumed adiabatic behavior and thus, the exergy loss is ignored. In the following, diagrams and curves pertaining to the efficiency of each component and its value of the exergy destruction, are illustrated. Figs. 2 and 3 By analyzing the results and comparing exergy destruction for the different components, we can see that the major part of the exergy destruction happens in the distillation columns. The distillation columns of these two units are responsible for more than 64% of wasted exergy (loss and destruction), the reason for which is obvious. The columns consume a lot of exergy in their reboiler, while a large proportion of this heat input is taken back from the system in the condenser at the top of the column and thus, it is lost. Among these columns, the Demethanizer column has the best performance, since, firstly, this column has no condenser and the steam consumption at its reboiler is very small, and secondly, it has a lot of intake streams which make it approach the ideal column. Therefore, it is logically justified for this column to have a larger exergetic efficiency compared to other columns. In the following, a pie chart shows the contribution of each component in the total exergy destruction. Fig. 4 The above pie chart illustrates that after the stage of the distillation columns, which are responsible for 64% of the total exergy destruction, there are heat exchangers causing 15% of the total exergy destruction. Next, the compressor and the expander have considerable exergy destruction shares, i.e., 13% and 6%, respectively. However, it should be noted that the turbo expander set has replaced a big expansion valve, having thus saved a lot of exergy from being destroyed. In this case, the compressor gets its work
exergy efficiency
Stream
81.4
79.5
system components Fig. 2. Exergy destruction for each system component.
Fig. 5. Contribution of each column in exergy destruction of all the columns.
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B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
Table 5 The results of exergoeconomic analysis.
Table 8 Components based on ascending order of F value.
Equipment
Z ($/hr)
Cp ($/Tj)
CF ($/Tj)
CD þ Cl ($/hr)
r (%)
f (%)
Components
F
Demethanizer De-ethanizer Depropoanizer Debutanizer 107-P-100 107-P-101 107-P-102 105-P-101 107-E-100 107-E-101 105-X-101 105-K-101 Cold Box 105-E-102
11.44 18.24 17.37 9.14 0.39 0.36 0.34 0.50 1.05 0.92 51.12 26.45 24.39 2.36
460.98 4909 9782 17446 9206 18052 10195 20480 25.85 13474 9655 2496 677434440 144.8
55.61 4320 1689 1848 8333 8333 8333 8333 0 0 2496 11.022 14717 11.132
0.85 45.01 17.78 6.00 0.11 0.15 0.05 0.11 e e 6.53 0.58 47.42 0.019
þ100 60 þ100 þ100 10.5 þ100 22.3 þ100 e e þ100 þ100 þ100 þ100
99.30 31.50 49.86 60.79 78.01 70.93 88.20 82.06 e e 88.7 99.8 33.96 99.20
De-ethanizer Cold Box De-propanizer De-butanizer
31.5 33.96 49.86 60.79
After complete exergoeconomic analysis of streams, each component can be exergoeconomically analyzed individually. The difference between the relative cost rk and the exergoeconomic cost f is representative of the performance of that component of the system. These values are calculated and listed in Table 5. 8. Conclusions
Table 6 Components, based on their importance. Component
Z ($/hr)þCd ($/hr)
Cold Box De-ethanizer Compressor Depropoanizer Expander Debutanizer Demethanizer 105-E-102
71.81 63.58 57.65 35.47 27.03 15.31 12.29 2.39
As previously stated, the smallest share of the exergy destruction belongs to the Demethanizer column since it is the closest to the ideal state. Moreover, the flow rate of the steam consumed in its reboiler is very small and lacks a condenser, as a result of its low temperature. This column is responsible only for 6 percent of the exergy destruction of columns. The next small exergy destruction occurs in the debutanizer column which is relatively small and has a smaller total feed input\ compared to most other columns. This column causes to produce only 13 percent of the total exergy destruction of the columns. The Largest amount of exergy destruction takes place in De-ethanizer and Depropoanizer columns, whose contribution each is more than 25% of the total exergy destruction. Thus, any small change in efficiencies of these two columns will leads to a magnificent effect on reducing the exergy destruction of the whole system. Four heat exchangers were investigated in the units, and the cold box, which is a special heat exchanger among them, is responsible for more than half of the total exergy destruction of all the heat exchangers. E cold box has a high exergetic efficiency in comparison with the other heat exchangers, which is a proof for its good design. However, since the heat exchanger plays an important role in the entire system and its fuel and product are massive in amount, any change which can cause a small improvement in its performance can lead to great economical benefice.
Table 7 Components, based on their f values. Components
F
Expander Demethanizer 105-E-101 Compressor 107-p-102 105-p-101
99.8 99.3 99.2 88.7 88.2 82.06
In this approach, first the capital cost of the system is estimated. Then, some economical techniques are used to calculate the revenue requirement of the system in dollars per hour and finally, the cost balance equations are written to calculate the unit cost of exergy for each stream. Finally, the exergoeconomic factor is defined and comments are made about the balance between the capital investment and operating costs of the system inflicted by the exergy destruction which have to be compensated by more fuel consumption. There is a distinct algorithm to accomplish the abovementioned results. Based on this algorithm: 1- All the components are put in descending order based on their importance. The importance of each component is known from the magnitude of the sum Z ($/hr)þCd ($/hr). Therefore, this is a way to model the components based on their importance. 2- The exergoeconomic factor is used to find the prominent factor of the cost infliction: a) If the value of f is large, we should check whether it is economically justified to decrease the capital cost of the equipments, because it seems that the capital cost is so high that it has lost its economical justification. b) If f is small, we should try to increase the efficiency even if it yields higher capital cost, since it seems that low efficiency of the system inflicts a high expenditure on the system. Now components are put in a descending order based on their importance, as stated in the above. The factor Z($/hr)þCd($/hr) is ranked for component as below: Table 6 The components are put in descending order based on their importance and respective costs in the system. It can be seen that the cold box was not so seriously distinguished in the exergy analysis but its importance is clearly in the exergoeconomic analysis. In the following, Instruction 2 is performed. The following table shows the components put in order based on their f values. In these components, the capital cost is too high and a simpler, cheaper component can be more economically justified to use: Table 7 The following table shows the components put in ascending order based on their f values. These components are the ones for which low efficiency and high exergy destruction has inflicted a high cost (compared to the capital cost) on the system and thus, these components are not economically justified to operate. Therefore, for these components it should be investigated if there are alternative components with higher quality and
B. Ghorbani et al. / Journal of Natural Gas Science and Engineering 9 (2012) 86e93
efficiency to improve the economical performance of the system. Table 8 The analysis of the exergoeconomic factor shows that the use of the expander and the compressor has inflicted a very high capital cost on the system which does not seem to have proper return of investment and thus, they had better be changed with cheaper equipments. Moreover, the investment carried out for the Methane separation column is extraordinarily high, while its exergy destruction is small. Thus, it appears that a cheaper column can be used instead. However, the De-ethanizer column has a large amount of the exergy destruction and improving its efficiency should be investigated. The cold box also has a similar situation, namely, although its exergy efficiency is large (the result of exergy analysis), it appears that in the case of being technically possible and having access to the required technologies, more investment and more efficiency improvement can be economically justified. The depropaniser column and the debutanizer column are in the next priorities. References Ansari, Kambiz, Sayyaadi, Hoseyn, Amidpour, Majid, 2010. Thermoeconomic optimization of a hybrid pressurized water reactor (PWR) power plant coupled to a multi effect distillation desalination system with thermo-vapor compressor (MED-TVC). Energy.
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