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Energy 112 (2016) 420e429

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Energy

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Parameter optimization of dual-pressure vaporization Kalina cyclewith second evaporator parallel to economizer

Zilong Zhu a, Zhi Zhang a, b, Yaping Chen a, *, Jiafeng Wu a

a Key Laboratory of Energy Thermal Conversion and Control of Ministry of Education, School of Energy and Environment, Southeast University, Nanjing,210096, Chinab School of Civil Engineering and Architecture, Anhui Industrial University, Maanshan, Anhui, 243002, China

a r t i c l e i n f o

Article history:Received 2 May 2016Received in revised form20 June 2016Accepted 22 June 2016Available online 5 August 2016

Keywords:Kalina cycleDual-pressure vaporizationPower recovery efficiencyConcentration of solutionParameter optimization

* Corresponding author.E-mail address: ypgchen@sina.com (Y. Chen).

http://dx.doi.org/10.1016/j.energy.2016.06.1080360-5442/© 2016 Elsevier Ltd. All rights reserved.

a b s t r a c t

A modified dual-pressure vaporization Kalina cycle (DPVeKC2) is proposed with the second evaporatorinstalled parallel to the economizer and both are in series after the first evaporator. The merit is to ac-quire higher efficiency by reduced thermal irreversibility in heat transfer between heat source andworking medium. The parameter optimizations were conducted with power recovery efficiency as thecycle performance evaluation index. The calculation conditions are set as that the inlet temperatures ofheat source and cooling water are 400 �C and 25 �C respectively with the constraints such as heattransfer pinch point temperature differences are proper, the maximum evaporation pressure does notexceed 20 MPa, the vapor quality at the turbine outlet is greater than 0.85 and the exhaust temperatureof heat source is not lower than 90 �C. The optimal parameters obtained include concentrations of worksolution and basic solution of 0.5 and 0.3138 respectively, the evaporation dew point temperature of300 �C, the supercool at outlet of economizer of 5 K and the superheating at the second evaporator outletof 75 K respectively. And the corresponding power recovery efficiency of the DPVeKC2 reaches 26.4%,which is 3.4% and 15.2% respectively higher than that of the DPVeKC and the Kalina cycle.

© 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Due to the features of low vapor pressure and large specificvolume of water steam at room temperature, the steam Rankinecycle is not well applicable for power generation driven by wasteheat source. The organic Rankine cycle (ORC) [1] and the Kalinacycle [2,3] are the alternative choices. The Kalina cycle with inex-pensive ammoniaewater mixture as working fluid has been drawnthe attentions by many scholars and experts. With its variableboiling temperature in evaporation process and regeneration heatwith turbine exhaust vapor for desorption before the absorptioncondensation process, the Kalina cycle can match well simulta-neously with the sensible heat source and cooling water, thereforethe heat transfer irreversible losses could be reduced.

Since Kalina proposed the Kalina cycle in 1984, the research andapplications of Kalina cycle have been extended to variety areas [4].Bombarda et al. [5] compared thermodynamic features of Kalinacycle and ORC for heat recovery from diesel engines. Jonnson and

Yan [6] studied the performances of ammoniaewater bottomingcycles for gas engines and gas diesel engines. Nguyen et al. [7]studied power generation from residual industrial heat. Penget al. [8] and Sun et al. [9] respectively applied Kalina cycle forpower generation from solar energy. Mlcak [10], DiPippo [11] andGuzovic et al. [12], Arslan [13] and Coskun et al. [14] conductedrespectively thermodynamic and/or economic analysis of theKalina cycle for power generation from geothermal resources.Singh and Kaushik [15] conducted energy and exergy analysis onKalina cycle for a coal fired steam power plant. Sirko [16] performeda case study of adopting Kalina cycle in a combined heat and powerplant. Zhang et al. [17] and Chen et al. [18] studied an integratedsystem of NH3eH2O Kalina-Rankine cycle that using Kalina cyclefor power generation with high thermal efficiency in non-heatingseasons and the NH3eH2O Rankine cycle for generation both po-wer and heating-water in winter respectively. Hua et al. [19]investigated a power and chilling cycle that generating chillingoutput with some work solution from mid-p-absorber by partiallyevaporating at low pressure based on the triple pressure Kalinacycle. Jing and Zheng [20] investigated a new power and coolingcogeneration cycle with heat source energy cascade utilization.

Nomenclatures

Latin lettersf circulation multipleG mass flow, mass flow in turbine (kg s�1)h specific enthalpy (kJ kg�1)p pressure (MPa)Q heat (kJ kg�1)T, t temperature (K, �C)W power output (kW)x ammonia concentration (kg kg�1)

Greek lettersD differenceh0 power recovery efficiency

hth thermal efficiencyhwh waste heat recovery ratio

Subscriptnumber status point in Fig. 2b basic (concentration)d dilute (concentration)h heat sourceH highH2 second highL lowM midP pumpT turbinew work (concentration)

Z. Zhu et al. / Energy 112 (2016) 420e429 421

Wang et al. [21] performed thermodynamic and parametric anal-ysis of the Kalina cycle. Chen [22] and Hua et al. [23] conductedrespectively thermodynamic analysis on a modified Kalina cycle forbetter cyclic performance. Walraven et al. [24] compared the per-formances of both organic Rankine cycles and the Kalina cycle andconstructed multiepressure evaporation ORC for reclaiming powerfrom lowetemperature geothermal heat source.

Due to the heat absorbing process in the tripleepressure Kalinacycle comprises of three variable temperature sections of liquidsupercool heating, evaporation and vapor superheating, it canmatch well with great temperature difference of sensible heatsource and acquiremore heat from the heat source. It is the suitableform for power generation from high-to-mid temperature sensibleheat source, while the dual-pressure Kalina cycle is suitable forlow-temperature heat source, which has only partial evaporationprocesses with consolidated high-pressure and mid-pressure [25].

It is apparent that the higher temperature heat source usuallyhas greater thermal efficiency as well as economic benefit than thatof the lower one for a power generation cycle system. Thus thehigh-to-mid grade heat source should be placed in the priorityposition in application and exploration for power generation.

With lower thermal irreversibility in both heat transfer pro-cesses of working fluid with the heat source in the evaporator andwith the cooling water in the absorption condenser, the Kalinacycle is of high thermal efficiency. Nevertheless with higher than350 �C heat source, the variation of evaporation temperature seemsnot enough, as simply raising the pressure or superheat in evapo-ration process of work solution might result in higher exhausttemperature or increased heat transfer irreversibility between heatsource and working medium, thus there is still room for furtherimprovement.

The dual-pressure vaporization Kalina cycle (DPVeKC) as shownin Fig. 1a was proposed [26] for this issue. The cycle has a secondevaporator cascading to the first one and some work solutionevaporates at a lower pressure for reclaiming the exhaust heat ofthe heat source from the first evaporator, and the generated steamgoes into the lower pressure section of turbine to expand andproduce power. Thus the heat source is sufficiently utilized and thepower recovery efficiency of the cycle can be raised.

From the heat transfer curve in Fig. 1b it can be seen that thetemperature difference thus the irreversibility of heat transfer be-tween heat source and liquid heating section of workmedium in E1is still great, which is the reason to modify in this paper.

2. Materials and methods

2.1. Schematic of DPVeKC2 system

The typical Kalina cycle includes three different pressure cir-culation sections, the high, low and mid pressure sections, whilethe dual-pressure vaporization Kalina cycle includes four differentpressure circulation sections, the high, low, mid and the secondhigh pressure sections. The second evaporation branch of the dual-pressure vaporization Kalina cycle starts at the outlet of the mid-epeabsorber A2, and a certain percentage of work solution isboosted to the second high pressure by the midepepump P3 andthen enters the second evaporator E2 via the second preheater PH2.The vapor from the second evaporator expands in the lower sectionof the turbine T2.

A modification of dual-pressure vaporization Kalina cycle(DPVeKC2) is proposed with the second evaporator installed par-allel to the economizer i.e. liquid heating section of the first evap-orator and both are in series after the superheating and evaporationsections of the first evaporator, as shown in Fig. 2.

A1dlow-p-absorber; A2dmid-p-absorber; E1dfirst evapo-rator; E2dsecond evaporator; E3deconomizer; P1~P3dpumps;PH1, PH2dpreheaters; Rdrecuperator; Sdseparator; T1,T2dturbines; V1~V5dvalves.

The evaporation of work solution with either high pressure orsecond high pressure comprises liquid-heating, evaporation andvapor-superheating sections. The work solution (point 10) from themid-p-absorber split to two streams, the majority is pumped to thehigh pressure (point 11) by the highepepump P2, and then it ispreheated (point 12) by the dilute solution from the separatorbefore entering the economizer E3 and evaporator E1 in series. Thehigh temperature/pressure work solution vapor (point 15) from theevaporator E1 expands and generates work in the turbine T1. Thestate points 13, 130 and 14 are respectively the outlet state of E3,bubble and dew points during evaporation in E1, while h4, h3 andh2 are respectively corresponding points at the heat source side.The minority work solution from the midepeabsorber is pumpedto the second high pressure (point 20) by themidepepump P3, andit is then preheated (point 21) by the rich vapor solution (point 400)from the separator in the second preheater PH2 before entering thesecond evaporator E2. The produced work solution vapor (point 25)from the E2 generates work in the lower section of the turbine T2.The state points 22 and 23 are respectively the bubble and dewpoints during the second high pressure evaporation in E2, while h6

R

A1A2

P1

P2

PH2

S

E1

E2

V2

V1

P3

PH1

V4heat source

coolingwatercooling

water

12

3

4

4"

4'

6 718

17

16

89

1011

20

2415

12

h1

h7

h4

21

V3

13

14

2223

h6h5

h3

h2

c1

c2

c3c4

5

R

A1A2

P1

P2

PH2

S

E1

E2

V2

V1

P3

PH1

V4heat source

coowacooling

water

12

3

4

4"

4'

6 718

17

16

89

1011

20

2415

12

hhhhhhhhhh1

hhhhhhhhhhhhhh7

h4

21

V3

13

14

2223

h6h5

h3

h2

c

c

c3c4

5

(a)

(b)

0

50

100

150

200

250

300

350

400

0 0.2 0.4 0.6 0.8 1Q ·Q 0

-1

t /°

C

heat resource

work solution inevaporator E1

work solution inevaporator E2

Fig. 1. Dual-pressure vaporization Kalina cycle (DPVeKC). (a) Schematic diagram, and (b) heat transfer curves of evaporation with heat source.

Z. Zhu et al. / Energy 112 (2016) 420e429422

Z. Zhu et al. / Energy 112 (2016) 420e429 423

and h5 are respectively corresponding points at the heat sourceside. And h7 is the outlet point of heat source for both E2 and E3. Inall of these heat exchangers the work solution flows in counter-current direction with the heat source.

2.2. Model for DPVeKC2

The inlet and outlet parameters of each component of theDPVeKC2 are labeled subscripts consistent to the state points in theFig. 2 in the following discussion. Table 1 shows the calculationmodel of DPVeKC2 with the principal of energy and mass conser-vation laws neglecting the pressure and heat dissipation losses ineach component as well as connecting pipes. The engineeringcalculation software EES was adopted to calculate themodel as wellas the state points of the cycle.

Note: f () stands for function; G, kg s�1, and G stand for the flowrate and the relative flow rate to the total turbine flow rate, Gwithout subscript is the total turbine flow rate,¼ G16; the subscripth and c stand for heat source and cooling water respectively; thesubscript number stands for the state point shown in Fig. 2. hT andhp are respectively the isentropic efficiencies of turbine and pumps,taken values of 0.85 and 0.75 respectively; and the subscript sstands for the isentropic process of turbine or pump.

P3

P2

A2

E1

E2 E3

PH2

14

13'

h2

h3

2322

h5h6

h7h7

13h4

h1

4"

10

20

2112

5

9

11

1524

V5

c3

c4

P3

P2

A2

E1

E2 E3

PH2

14

13'

h2

h3

h5h6

h7h7

13h4

h1

4"

10

20

2112

5

9

11

1524

V5

c3

c4

A1—low-p-absorber; A2—mid-p-absorbevaporator; E3—economizer; P1~P3

R—recuperator; S—separator; T1,

Fig. 2. Schematic of modified dual-pressure

2.3. Evaluation index

The thermal efficiency hth is the ratio of the net power generatedin the cycle system over the heat absorbed in the evaporators:

hth ¼ Wnet

Qh¼ Wnet

ðQhE1 þ QhE3 þ QhE2Þ(27)

The thermal efficiency is not a complete criterion indicator forwaste heat recovery system, because high thermal efficiencysometimes does not mean more power generation if the outlettemperature of the heat source is high and less heat is utilized. Toremediate this drawback, the power recovery efficiency h0 isintroduced as the ultimate evaluation index in consideration of thewaste heat recovery ratio hwh [22,25]:

h0 ¼ Wnet

Qh0¼ Wnet

Ghcphðth1 � th0Þ¼ Wnet

Ghcphðth1 � th7Þth1 � th7th1 � th0

¼ hthhwh (28)

hwh ¼ th1 � th7th1 � th0

(29)

T2T1

R

A1

P1

V3V2

V1V4

PH1

S4

4'

6 718

12

8

16'3'

173

16

c1

c2

T2T1

R

A1

P1

V3V2

V1V4

PH1

S4

4'

6 718

12

8

16'3'

173

16

c1

c2

er; E1—first evaporator; E2—second —pumps; PH1, PH2—preheaters; T2—turbines; V1~V5—valves

vaporization Kalina cycle (DPVeKC2).

Table 1Mathematic model of DPV-KC2.

Equipment Item Calculation formula No.

Key parameters basic solution p1ðor h1; s1Þ ¼ fðt1; xbÞ (1)work solution p2ðor h10; s10Þ ¼ fðt10; xwÞ (2)saturate vapor t14ðor h14; t13; h13Þ ¼ fðxw; p15Þ (3)super heating vapor h15ðor s15Þ ¼ fðt15; xw; p15Þ (4)saturate vapor t23ðor h23; t22; h22Þ ¼ fðxw; p24Þ (5)super heating vapor h24ðor s24Þ ¼ fðt24; xw; p24Þ (6)circulation multiple f f ¼ ðxw � xdÞ=ðxb � xdÞf ¼ G1=G16 ¼ G1=ðG11 þ G20Þ (7)

Evaporator E1 transferring heat QhE1 ¼ Ghcph(th1�th4) ¼ G11(h15�h13) (8)Economizer E3 transferring heat QhE3 ¼ GhE3cph(th4�th7) ¼ G11(h13�h12) (9)Evaporator E2 transferring heat QhE2 ¼ GhE2cph (th4eth7) ¼ G20 (h24eh21) (10)Turbine T isentropic T1 outlet h16s0 ¼ fðp1; xw; s15Þ (11)

isentropic T2 outlet h16s00 ¼ fðp1; xw; s24Þ (12)actual turbine outlet h16 ¼ ðG11h160 þ G20h1600 Þ=G (13)turbine work WT ¼ WT1 þWT2 ¼ G11wT1 þ G20wT2

¼ ½G11ðh15 � h160sÞ þ G20ðh24 � h1600sÞ � hT¼ G11ðh15 � h160 Þ þ G20ðh24 � h1600 Þ

(14)

Recuperator R heat transfer h16 � h17 ¼ ðh4 � h2ÞG3=G ¼ G3ðh4 � h2Þ (15)Low-p-absorber A1 mixing h18 ¼ ½h17 þ ðf � 1Þh7�=f (16)

transferring heat Gc1cpcðtc2 � tc1Þ ¼ f Gðh18 � h1Þ (17)Separator S parameters xdðor x400 ;h40 ;h400 Þ ¼ fðp2; t4Þ (18)Preheater PH1 transferring heat G40 ðh6 � h40 Þ ¼ G11ðh12 � h11Þ (19)Preheater PH2 transferring heat G400 ðh5 � h400 Þ ¼ G20ðh21 � h20Þ (20)Valve V2 enthalpy h7 ¼ h6 (21)Mid-p-absorber A2 mixing h9 ¼ G400h5 þ ðf � G3Þh2 (22)

transferring heat Gc3cpcðtc4 � tc3Þ ¼ Gðh9 � h10Þ (23)Pump load WP ¼ WP1 þWP2 þWP3

¼ ½G1ðh2s � h1Þ þ G11ðh11s � h10Þþ G20ðh20s � h10Þ� =hp

¼ G1ðh2 � h1Þ þ G11ðh11 � h10Þ þ G20ðh20 � h10Þ

(24)

Cycle net work output Wnet Wnet ¼ WT �WP (25)total absorbing heat Qh ¼ Qh1þ Qh2 ¼ QhE1 þ QhE3 þ QhE2 (26)

Z. Zhu et al. / Energy 112 (2016) 420e429424

where, th1 and th7 are inlet and outlet temperatures of the heatsource, �C; th0 is the lowest possible waste heat utilization tem-perature which is set as 90 �C in this paper, for below this tem-perature the heat transfer surface material might be corrode by thecondensed acid from flue gases. The power recovery efficiency h0 isthe product of thermal efficiency hth and waste heat recovery ratiohwh.

3. Results and discussion

The calculation conditions and constraints are set as following:the inlet temperatures of both heat source and cooling water arerespectively 400 �C and 25 �C; the pinch temperature difference inevaporators is 20 K in consideration of poor heat transfer coefficientof flue gas side, while that in other heat exchangers is 5 K; themaximum evaporation pressure is not exceed 20 MPa, the quality(dryness) of vapor at outlet of turbine is higher than 85% and theexhaust temperature of heat source is not lower than 90 �C. Thecirculation multiple f which is defined as the flow rate ratio of thebasic solution over work solution is set as 5 in this paper.

3.1. Concentrations

The relationship between the basic concentration and the workconcentration is tied in heating the basic solution for desorptionprocess by work solution from the turbine exhaust in the recu-perator to ensure a greater pressure drop in turbine while the heattransfer pinch point difference is still greater than the requiredvalue. The concentrations of work solution xw were taken values of0.4, 0.45 and 0.5.

Fig. 3 shows the influences of the basic and work concentrationsof solution on the performances of the DPVeKC2. Fig. 3a shows thatthe temperature differences at inlet and outlet of the recuperator

and the bubble point of basic solution in the recuperator increasewith the increase of basic concentration at work concentration of0.4, 0.45 or 0.5. Fig. 3b shows that the lowepressure pL of the cycleincreases while the midepressure pM is not affected by the increaseof the basic concentration with fixed work concentration, since thelowepressure and the midepressure are determined by the bubbletemperature saturation pressures of basic and work concentrationsrespectively. Fig. 3c shows that the thermal efficiency and the po-wer recovery efficiency decrease with the increase of the basicconcentration at fixed work concentration, even though the wasteheat recovery ratio increases. Therefore, the optimum value of thebasic concentration with a given work concentration is at theintersect point with the dash line corresponding to the lowestpinch temperature difference in recuperator as shown in Fig. 3a,which might not be the one at bubble point of basic solution in therecuperator.When the concentration of work solution is 0.4, 0.45 or0.5, the corresponding optimum concentration of basic solution is0.245, 0.2755 or 0.3138 respectively.

3.2. Vaporization parameters

For power recovery from a sensible waste heat source withcertain inlet temperature, the evaporation pressure has greatimpact on the heat transfer curves and consequently on the effi-ciency of the cycle. For feasibility, the dew point temperature t14 istaken as the variable to demonstrate such impact.

Fig. 4a shows the evaporation pressure pH and the exhausttemperature of the heat source th7 versus the dew point tempera-ture t14 at different work concentration xw and basic concentrationxb pairs. It can be seen that the evaporation pressure increases withthe increase of either the dew point temperature or work con-centration. The restriction line of high pressure 20 MPa is plottedon the figure. The figure shows also that the exhaust temperature of

Fig. 3. Influences of basic solution xb on performances of the DPVeKC2 (th1 ¼ 400 �C,tc1 ¼ 25 �C). (a) Pinch temperature differences of recuperator Dt, (b) low pressure pLand mid pressure pM, and (c) efficiencies hth, h0 and hwh.

Fig. 4. Evaporation pressure, exhaust temperature of the heat source and efficienciesversus evaporation dew point t14 and work concentration xw (th1 ¼ 400 �C, tc1 ¼ 25 �C).(a) Evaporation pressure pH and exhaust temperature of the heat source th7, and (b)efficiencies hth, h0 and hwh.

Z. Zhu et al. / Energy 112 (2016) 420e429 425

the heat source increases with the increase of the dew point tem-perature or decrease of the work concentration. The restriction lineof the lowest exhaust temperature 90 �C of heat source is alsoplotted on the figure.

Fig. 4b shows the curves of thermal efficiency hth, power re-covery efficiency h0 and waste heat recovery ratio hwh versus thedew point temperature at different work concentrations. Thethermal efficiency hth increases with the increase of the dew pointtemperature. Nevertheless, the power recovery efficiency h0 levelsat first and then drops with the increase of dew point temperatureat fixed work solution, and its curve is much flatter indicating thatthe impact of the dew point temperature on the power recoveryefficiency is not remarkable. The waste heat recovery ratio de-creases with the increase of the dew point temperature or thedecrease of the work concentration. The power recovery efficiencyincreases with the increase of work concentration at fixed dewpoint temperature, which is mainly due to the higher waste heatrecovery ratio at richer work concentration. Obviously, the schemewith work concentration 0.5 and the dew point temperaturearound 280e290 �C possesses better power recovery efficiencythan other schemes. The work concentration higher than 0.5 is notdiscussed because it might result in excessive high pressure.

For the modified dual-pressure vaporization Kalina cycle(DPVeKC2) the split point between E1 and E3 and the superheatdegree of the second evaporation pressure vapor need be opti-mized. Fig. 5a shows the second evaporation pressure pH2 and theexhaust temperature of the heat source th7 versus the supercooldegree Dt130e13 at outlet of the economizer under different work

Z. Zhu et al. / Energy 112 (2016) 420e429426

concentrations xw and the evaporation dew point in E1 t14 andsuperheat degree of vapor at outlet of E2 Dt24e23 are 290 �C and60 K respectively. It can be seen that the second evaporationpressure decreases with the increase of the supercool degreeDt130e13 or the decrease of the work concentration. The figureshows also that the exhaust temperature of the heat source de-creases with the increase of either the supercool degree Dt130e13 orthe decrease of the work concentration. The restriction line of thelowest exhaust temperature of 90 �C of heat source is also plottedon the figure.

Fig. 5b shows the curves of thermal efficiency hth, power re-covery efficiency h0 and waste heat recovery ratio hwh versus thesupercool degreeDt130e13 at different work concentrations andwitht14 and Dt24e23 are 290 �C and 60 K respectively. The thermal effi-ciency hth decreases with the increase of either supercool degreeDt130e13 or work solution. The waste heat recovery ratio increaseswith the increase of either the supercool degree Dt130e13 or thework concentration. Nevertheless, the power recovery efficiency h0levels with the increase of dew point temperature at fixed worksolution, indicating that the impact of the supercool degree Dt130e13on the power recovery efficiency is not significant. Obviously, thescheme with work concentration of 0.5 and the supercool degree

Fig. 5. Second evaporation pressure, exhaust temperature of heat source and effi-ciencies versus supercool degree Dt130e13 and work concentration xw (th1 ¼ 400 �C,tc1 ¼ 25 �C, t14 ¼ 290 �C, Dt24e23 ¼ 60 K). (a) Second evaporation pressure pH2 andexhaust temperatures of heat source th7, and (b) efficiencies hth, h0 and hwh.

Dt130e13 around 5e20 K possesses better power recovery efficiencythan other schemes.

Fig. 6a shows the curves of the second evaporation pressure pH2and the exhaust temperature of the heat source th7 versus the su-perheat degree of vapor at outlet of the second evaporator Dt24e23under different work concentrations xw and with t14 and Dt130e13are 290 �C and 15 K respectively. It can be seen that the secondevaporation pressure decreases with the increase of the superheatdegree Dt24e23 or the decrease of the work concentration. Thefigure shows also that the exhaust temperature of the heat sourcedecreases with the increase of either the superheat degree Dt24e23or the work concentration. The restriction line of the lowestexhaust temperature of 90 �C of heat source is also plotted on thefigure.

Fig. 6b shows the curves of thermal efficiency hth, power re-covery efficiency h0 and waste heat recovery ratio hwh versus thesuperheat degreeDt24e23 at different work concentrations andwitht14 and Dt130e13 are 290 �C and 15 K respectively. The thermal effi-ciency hth decreases with the increase of either the superheat de-gree Dt24e23 or the work concentration. The waste heat recoveryratio increases with the increase of either the superheat degreeDt24e23 or the work concentration. Nevertheless, the power re-covery efficiency h0 increases first and then levels with the increase

Fig. 6. Second evaporation pressure, exhaust temperature of heat source and effi-ciencies versus superheat degree Dt24e23 and work concentration (th1 ¼ 400 �C,tc1 ¼ 25 �C, t14 ¼ 290 �C, Dt130e13 ¼ 15 K). (a) Second evaporation pressure pH2 andexhaust temperature of heat source th7, and (b) efficiencies hth, h0 and hwh.

Z. Zhu et al. / Energy 112 (2016) 420e429 427

of superheat degree Dt24e23 at fixed work solution, indicating thatthe impact of the superheat degree Dt24e23 on the power recoveryefficiency is not great. Obviously, the scheme with work concen-tration of 0.5 and the superheat degree Dt24e23 around 60 K pos-sesses better power recovery efficiency than other schemes.

Optimization from separate parameter discussion may notcapture the overall optimal result, so the orthogonal sensitiveoptimization approach was adopted. Fig. 7 shows the curves ofthermal efficiency hth, waste heat recovery ratio hwh and powerrecovery efficiency h0 versus the evaporation dew point tempera-ture t14 with different combinations of supercool degree Dt130e13and superheat degree Dt24e23 at work concentration 0.5.

Under conditions of th1 ¼400 �C, tc1 ¼ 25 �C and xw ¼ 0.5, Fig. 7aand b shows that the thermal efficiency hth increases with the in-crease of t14 or decrease of Dt130e13 and Dt24e23, and the waste heatrecovery ratio hwh increases with decrease of t14 or increase ofeither Dt130e13 or Dt24e23. From the Fig. 7c it could be learned thateach curve has an optimum evaporation dew point temperature t14,and both the optimal value of power recovery efficiency h0 and thecorresponding t14 increase along with the increase of supercooldegreeDt130e13 at constant superheat degree Dt24e23 or the increaseof superheat degree Dt24e23 at constant supercool degree Dt130e13 inthe range of discussed conditions. The highest value of power re-covery efficiency h0 in the whole range is around t14 ¼ 300 �C,Dt130e13 ¼ 5 K, Dt24e23 ¼ 75 K.

3.3. Status point parameters of DPVeKC2

Table 2 demonstrates the parameters of status points of theoptimum scheme of DPVeKC2 under inlet temperatures of heatsource and cooling water of 400 �C and 25 �C respectively andcirculation multiple of 5 with the dew point temperature 300 �C,work and basic concentrations of solution of 0.5 and 0.3138, su-percool degree Dt130e13 and the superheat degree Dt24e23 of 5 K and75 K respectively. The total flow rate of work solution in the turbineis set as unit value of 1 kg s�1 for convenience.

Fig. 7. Efficiencies versus evaporation dew point temperature t14 at different supercooldegree Dt130e13 and superheat degree Dt24e23 (th1 ¼ 400 �C, tc1 ¼ 25 �C, xw ¼ 0.5). (a)Thermal efficiency hth, (b) waste heat recovery ratio hwh, and (c) power recovery ef-ficiency h0.

3.4. Comparison of DPVeKC2 with DPVeKC and Kalina cycle (KC)

Table 3 shows the performance comparison of the DPVeKC2,DPVeKC and KC under the same initial condition that the tem-peratures of heat source and cooling water are 400 �C and 25 �Crespectively, the concentrations and the dew point temperature ofevaporation all take the optimized value. The DPVeKC2 scheme haspower recovery efficiency of 26.4%, which is 3.4% and 15.2% higherthan that of the DPVeKC scheme and the Kalina cycle respectively.The heat transfer curves of evaporations in DPVeKC2 are shown inFig. 8. The Qh0 in the abscissa stands for the maximum availableheat from the heat source.

From the Table 3 it could be noticed that the optimized highpressure pH of either DPVeKC2 or DPVeKC ismuch higher than thatof the KC, which will increase the initial cost of the system, there-fore, somewhat lower work concentration and/or lower evapora-tion dew point might be justified in the parameter selection.

It should be declared that the performance results in Guo et al.[25] for DPVeKC are somewhat exaggerated than it should be sincethe constraint of the pinch temperature difference of recuperatorwas violated with only one point check instead of three pointscheck as shown in Fig. 3a. Thus the comparison with DPV-KC is nottaken the data from the literature [25].

Table 2Parameters of status points of DPVeKC2.

Statuspoint

Temperature Pressure Enthalpy Concentration Flow rate

�C MPa kJ kg�1 kg kg�1 kg s�1

1 30 0.1142 �67.19 0.3138 52 30 0.3627 �66.81 0.3138 53 30 0.3627 �66.81 0.3138 4.330 63.2 0.3627 77.33 0.3138 4.34 73 0.3627 236.5 0.3138 4.340 73 0.3627 139.6 0.2673 4400 73 0.3627 1524 0.9308 0.35 60.3 0.3627 1375 0.9308 0.36 66.5 0.3627 111.3 0.2673 47 45.7 0.1142 111.3 0.2673 48 30 0.3627 �66.81 0.3138 0.6999 56.1 0.3627 367.3 0.5 110 30 0.3627 �106.2 0.5 111 32.6 18.46 �77.05 0.5 0.73812 68 18.46 76.61 0.5 0.73813 244.7 18.46 1060 0.5 0.738130 249.7 18.46 1096 0.5 0.73814 300 18.46 2165 0.5 0.73815 380 18.46 2487 0.5 0.73816 82.6 0.1142 1782 0.5 1160 69.1 0.1142 1098 0.5 117 39 0.1142 477.6 0.5 118 44.5 0.1142 184.5 0.5 520 30.2 1.555 �104.3 0.5 0.26221 68 1.555 66.54 0.5 0.26222 82.2 1.555 133.1 0.5 0.26223 171.3 1.555 2186 0.5 0.26224 246.3 1.555 2377 0.5 0.262

Table 3Comparison of performances of DPVeKC2, DPVeKC and Kalina cycle (KC).

Item Unit DPV-KC2 DPV-KC KC

High pressure pH MPa 18.46 18.46 9.39Second high pressure pH2 MPa 1.555 0.8864 e

Low pressure pL MPa 0.1142 0.1142 0.1152Inlet temperature of

heat source

�C 400 400 400

Exhaust temperatureof heat source

�C 97.18 90.8 147.9

Turbine (T1) enthalpydrop

kJ kg�1 666.9 629.9 732

Evaporation temperaturest13et14

�C 249.7e300 249.7e300 192.6e259.9

Evaporation temperaturest22et23

�C 82.2e171.3 59.6e154.2 e

Low-p absorptiontemperatures t18et1

�C 44.5e30 44.3e30 77.4e30

Inlet temperature ofcooling water

�C 25 25 25

Thermal efficiency hth 0.2702 0.2560 0.2817Waste heat

recovery ratio hwh

0.9768 0.9974 0.8133

Power recoveryefficiency h0

0.2640 0.2553 0.2291

Fig. 8. Heat transfer curves of evaporation in DPVeKC2.

Z. Zhu et al. / Energy 112 (2016) 420e429428

4. Conclusions

1) The DPVeKC2 is a modified dual-pressure vaporization Kalinacycle that set the second evaporator parallel to the economizerfor cascade utilization of the heat source. The DPVeKC2 systemcan significantly increase the capacity of the power output orpower recovery efficiency by absorbing more heat from the heatsource with reduced exhaust temperature.

2) The power recovery efficiency is selected as ultimate evaluationindex for power generation from waste heat recovery system,which is the product of thermal efficiency and waste heat

recovery ratio. The optimizing relationship were studied be-tween basic concentration and work concentration of solutionand the optimizing evaporation dew point temperature, super-cool degree Dt130e13 and superheat degree Dt24e23 in DPVeKC2.The orthogonal sensitive optimization approach was adopted tocapture the overall optimal result.

3) Under the conditions that the inlet temperatures of heat sourceand cooling water are 400 �C and 25 �C, the optimum parame-ters are: work and basic concentrations 0.5 and 0.3138, theoptimum dew point temperature t14 300 �C, and supercool de-gree Dt130e13 5 K and the superheat degree Dt24e23 75 Krespectively. And the optimum scheme of DPVeKC2 has powerrecovery efficiency of 26.4%, which is 15.2% higher than that ofthe Kalina cycle, and the increment is mainly due to theincreased waste heat recovery ratio.

Acknowledgements

This work is supported by the National Nature Science Foun-dation Program of China (No. 51276035).

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