How to approach Carnot cycle via zeotropic working fluid: Research methodology and case study

Accepted Manuscript How to approach Carnot cycle via zeotropic working fluid: Research methodology and case study

Weicong Xu, Shuai Deng, Wen Su, Ying Zhang, Li Zhao, Zhixin Yu PII:

S0360-5442(17)32061-3

DOI:

10.1016/j.energy.2017.12.041

Reference:

EGY 11990

To appear in:

Energy

Received Date:

03 July 2017

Revised Date:

10 November 2017

Accepted Date:

10 December 2017

Please cite this article as: Weicong Xu, Shuai Deng, Wen Su, Ying Zhang, Li Zhao, Zhixin Yu, How to approach Carnot cycle via zeotropic working fluid: Research methodology and case study, Energy (2017), doi: 10.1016/j.energy.2017.12.041

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT 1

How to approach Carnot cycle via zeotropic working fluid：

2

Research methodology and case study

3

The authors: Weicong Xu a, Shuai Deng a, Wen Su a, Ying Zhang a, Li Zhao a,*,

4

Zhixin Yu b

5

a

6

University), Ministry of Education of China, Tianjin, 300072, China

7

b

8

Norway.

9

* Corresponding author. Tel: 86-22-27890051; Fax: 86-22-27404188;

Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin

Department of Petroleum Engineering, University of Stavanger, N-4036 Stavanger,

10

E-mail: [email protected]

11

Highlights

12

A 3D construction method of thermodynamic cycles is presented by adding the

13

thermodynamic coordinate of the working fluid.

14

Based on construction method, the basic system composed by ORC sub-system and

15

compositions regulating system is put forward.

16

The representative case is presented to demonstrate the feasibility of the 3D

17

construction method.

18

Abstract

19

A great amount of researches on thermodynamic cycles have been active in

20

recent years, such as ORC (organic Rankine cycle), Kalina cycle, et al. However, the

21

ultimate aim of such researches, which could even be traced back to more than one

22

century ago, has not changed with a tireless pursuing to Carnot cycle. In exiting

ACCEPTED MANUSCRIPT 23

researches, the working fluid, as a medium for energy conversion, is commonly

24

considered to play an important role in the thermodynamic cycle: (1) relative to ideal

25

cycle, most of actual power cycles in the engineering field cannot operate without

26

working fluid; (2) energy efficiency, considering the analysis of second-law

27

efficiency, of actual cycle has a significant decrease due to the introduction of

28

working fluid. Thus, working fluid is a hot spot in the research of thermodynamic

29

cycle in recent years.

30

Zeotropic mixture, which commonly consists of two or more pure working fluids,

31

has flexibility in thermos-physical properties with a possible potential to enhance the

32

cycle performance. The effects of thermos-physical properties of zeotropic mixture

33

should be considered when determining the cycle structure and the design of

34

components. This paper presents a novel construction method of thermodynamic

35

cycle based on the zeotropic mixture. By adding the thermodynamic coordinate of

36

working fluid, a 3D cycle diagram based on the traditional temperature and entropy

37

cycle diagram is applied for performance analysis of cycle. According the proposed

38

construction method, a baseline cycle, composed by ORC sub-system and

39

compositions regulating sub-system, is put forward and available compositions

40

regulating techniques for such cycle are discussed as well. Finally, a representative

41

case is described briefly and the features are summarized. This work provides a new

42

methodology view to guide researchers in energy-efficient design of thermodynamic

43

cycles.

44

ACCEPTED MANUSCRIPT 45

Key words

46

Organic Rankine cycle; ORC; construction method; zeotropic mixture; compositions

47

adjustable

48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

Nomenclature Symbols c p Q U W s S T V v

μ n αV f

specific heat capacity (kJ·kg-1·K-1) pressure (MPa) heat transferred (J) internal energy (J) work (J) specific entropy (J·kg-1·K-1) entropy (J·K-1) temperature (K) volume (m3) specific volume (m3·kg-1) chemical potential (J·mol-1) amount of substance (mol) volume expansion coefficient (K-1) objective function



66

m

mass flow rate (kg/s)

67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82

x

degree of dryness

Subscripts and superscripts c critical state D dew point B boiling point i number of variables L low temperature H high temperature Carnot Carnot cycle eva evaporator con condenser exp expender pump working fluid pump wf working fluid hse heat source

ACCEPTED MANUSCRIPT 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103

hsk in out Ⅰ Ⅱ Ⅲ

heat sink inlet point outlet point compositionsⅠ compositionsⅡ compositionsⅢ

Greek symbols η ρ

efficiency density (kg/m3)

Abbreviations ORC PTORC STORC HC HFC CHP CAORC CHP GWP

organic Rankine cycle parallel two-stage organic Rankine cycle series two-stage organic Rankine cycle hydro carbon hydro fluorine carbon combined heat and power compositions adjustable organic Rankine cycle combined heat and power global warming potential

104 105

1

Introduction

106

With the development of economy, energy consumption is increasing

107

significantly, and also causes serious environmental pollution [1]. On the challenges

108

of collaborative development between environmental and energy, it is meaningful to

109

adjust the energy structure and strategy from two aspects: promoting the development

110

of renewable energy utilization technologies and improving the utilization efficiency

111

of existing technologies. Thermodynamic cycles are the fundamental theories of the

112

energy conversion technologies. Most widely used thermodynamic cycles originate

113

from the Carnot cycle, which can be divided into positive and negative cycle [2]. The

114

positive cycle converts heat into mechanical or electrical power, such as Rankine

ACCEPTED MANUSCRIPT 115

cycle. The negative cycle transfers heat from low temperature sink to high

116

temperature source by consuming mechanical or electrical power, such as heat pump.

117

Various actual cycles have been evolved from Carnot cycle, but the Rankine

118

cycle has been most widely used and has a maximum capacity on thermal energy

119

conversion. As an efficient way to convert thermal energy into power or mechanical

120

work, organic Rankine cycle (ORC), which has the same structure as steam Rankine

121

cycle but using organic fluid as working fluid, has been favored by scholars in recent

122

years. Due to the advantages of simple structure, less maintenance and possibility of

123

small scales, ORC has been widely applied for various types of source, such as solar

124

energy [3, 4], biomass energy [5, 6], geothermal energy [7, 8], ocean energy [9] and

125

waste heat [10] etc.

126

Taking ORC as an example, the conventional methods on cycle construction

127

could be divided into three steps. (1) Selection of cycle structure. According to the

128

heat source and demand side requirements, a simple ORC, regenerative ORC, multi

129

cogeneration cycle or others should be selected as circulation structure. (2)

130

Determination of working fluid. The working fluid which is suitable for heat source

131

temperature and shows best thermal performance, economical and environment

132

friendly should be chosen as cyclic working fluid. Subsequently, the thermodynamic

133

parameters of the key points in the cycle should be calculated. (3) Design of key

134

components. According the thermodynamic parameters and thermos-physical

135

properties of working fluid that determined previously, the key components should be

136

designed. The performance could be tested after the system established. In the last

ACCEPTED MANUSCRIPT 137

twenty years, a large number of researchers focused on the study of ORC system

138

according the steps mentioned above, but the statistical results based on data collected

139

from 175 published papers on experimental study prove that the second law efficiency

140

of ORC is still generally lower than 50% [11].

141

There naturally emerges a question: how to further approach Carnot cycle. A

142

great amount of researches has been conducted strictly around the aforementioned

143

three steps in the traditional research method. And the distribution diagram of exiting

144

researches in recent years is shown in Fig. 1.

145 146

Fig. 1 Distribution diagram of exiting researches

147

(1) Cycle structure. The most fundamental structure of ORC includes four

148

processes as evaporation, expansion, condensation and compression which are

149

performed by evaporator, expander or turbine, condenser and pump respectively.

150

Many researchers studied the new cycle structure originated from the fundamental

151

structure of ORC in recent years. Li et al. [12] put forward parallel two-stage organic

152

Rankine cycle (PTORC) and series two-stage organic Rankine cycle (STORC) both

153

with two evaporators. Cycle configuration was evaluated and the optimal system

154

parameters, system irreversible loss were obtained by numerical analysis. The results

155

shown that STORC could reduce more irreversible loss than PTORC at the same

156

operating conditions. Li et al. [13] evaluated different types of power cycles (Rankine

157

cycle, transcritical cycle and combined cycle) and different cycle configurations

158

(saturated or superheating, with or without regenerator) under different heat source

ACCEPTED MANUSCRIPT 159

temperatures. An optimal cycle configuration was proposed for each temperature

160

range. Lecompte et al. [14] presented an overview of ORC architectures for waste

161

heat recovery applications. Based on the available literatures, ten different ORC

162

structures were discussed critically and the development trend, potential knowledge

163

gaps were identified.

164

(2) Selection of working fluid. Working fluid is the carrier of energy transfer and

165

conversion in ORC, and its thermos-physical properties could affect the performance

166

of the system directly. Yang et al. [15] introduced a model based on Claussius-

167

Claperyron equation to compare and explain the effects of the critical temperature (Tc)

168

and boiling temperature (Tb) of working fluid on the performance of ORC system. A

169

composite indicator of Tc and Tb was proposed for selection of working fluid. Zhai et

170

al. [16] analyzed the influence of thermos-physical properties of HC (hydro carbon)

171

and HFC (hydro fluorine carbon) working fluid on the system performance and

172

introduced screen evaluation indicators related to the molecular structures by using a

173

theoretical ORC model. Two main conclusions were drawn: (1) working fluid with

174

double bonds or cyclic structure showed better performance; (2) working fluid with

175

higher ratio of the specific heat capacity to the latent heat and positive mass variation

176

with the system evaporating temperature provide more work output. Bao et al. [17]

177

reviewed the researches on the selection of working fluid for ORC system detailed.

178

The thermos-physical properties of pure working fluid and zeotropic mixture were

179

compared and discussed. The selection principle was presented by authors.

180

(3) Components and experiment. After determining the cycle structure and the

ACCEPTED MANUSCRIPT 181

optimal working fluid, the design of components (such as evaporator, turbine or

182

expander, condenser, pump etc.) is another vital process. Sauret et al. [18] presented

183

the basic criteria for the application of radial-inflow turbines for ORC system and

184

designed a series of radial-inflow turbines, based on one-dimensional models, for

185

cycles operating in different conditions. They found that the generation of turbines

186

had relationships with dimensions. Kang et al. [19] experimentally studied the

187

performance of a radial turbine applied in ORC system and analyzed the factors

188

which may influence the performance of turbine and ORC system. Zhou et al. [20]

189

reformed a scroll compressor into expander, tested the expander performance using

190

R123 as working fluid and analyzed the effect of operating conditions on work output.

191

Qiu et al. [21] systematically summarized the working principles, characteristics,

192

market research of several kinds of expanders or turbines and discussed the selection

193

of expanders or turbines for ORC-based CHP system. As the component that

194

consumes main electric energy in ORC system, the efficiency of the working fluid

195

pump will significantly affect the performance of the system. But only few

196

researchers focused on the performance of pump. Lei et al. [22] experimentally

197

studied the electrical efficiency of a Roto-Jet pump under a simulative organic

198

Rankine cycle condition by using R123 as working fluid and the results showed that

199

the efficiency of the pump ranged from 11% to 23%. In [23], they also researched the

200

electrical efficiency of a multistage centrifugal pump in the same test rig and using

201

same working fluid. The results shown that the efficiency was from 15% to 65.7%.

202

Landelle et al. [24] investigated the performance of reciprocating pump for ORC from

ACCEPTED MANUSCRIPT 203

three aspects: energetic performance, volumetric efficiency and cavitation limits. The

204

results shown that the organic fluid results in a lower volumetric efficiency compared

205

to water. By analyzing the pumping work using 18 different organic working fluids,

206

Borsukiewicz-Gozdur [25] tried to find out correlations between the thermos-physical

207

properties of working fluid and performance of cycle. The power decreased factor K

208

was introduced to analyzed the working fluid suitability.

209

After a detailed literature research on exiting publications, we found that in

210

addition to three specific research fields related to cycle design, a reasonable

211

methodology on how to link such three fields efficiently step by step is also lack

212

which directly leads to a chaos on design methodology. Although the theory of ideal

213

cycle (such as Carnot cycle) and real cycle (such as Stirling cycle, Brayton cycle) is

214

comparatively complete, it is not very instructive to the construction of actual cycle.

215

The diagram of development bottleneck to approach ideal cycle is shown in Fig. 2.

216

The main obstacles could be summarized as two parts. The first is that the actual cycle

217

is carried out under the conditions of finite time, finite temperature difference and

218

finite heat transfer area. Curzon and Ahlborn studied the thermodynamic cycle under

219

finite conditions earlier [26]. On this basis, extended research is carried out by

220

Esposito [27] and Sheng [28] etc. Second is that the using of working fluid introduces

221

some constraints which increase the irreversible losses in the system, such as non-

222

isentropic expansion process and non-isentropic compression process. Therefore, the

223

effects of thermos-physical properties of working fluid on the performance of system

224

should be considered when determining the cycle structure and design of main

ACCEPTED MANUSCRIPT 225

components rather than a passive choice and mechanized screening. Moreover, the

226

application of pure working fluid reduces the flexibility of thermodynamic cycles. In

227

summary, the rare work on how to functionalized working fluid in cycle design is one

228

of the main “development bottleneck” that restricts the actual cycle approach to the

229

ideal cycle. Therefore, a novel construction method of thermodynamic cycle base on

230

zeotropic mixture is required, considering a great amount researches has already been

231

conducted around zeotropic mixture.

232 233

Fig. 2 Diagram of development bottleneck to approach ideal cycle

234

This paper presents a novel construction method of thermodynamic cycle using

235

zeotropic mixture. Based on the traditional temperature and entropy cycle diagram, a

236

novel construction method forms a three-dimensional cycle diagram by adding the

237

dimension of the properties of working fluid. With a full consideration on the effects

238

of thermos-physical properties of working fluid on each thermodynamic process, it

239

would push the actual cycle closer to the ideal cycle. This method will guide

240

researchers in designing new cycle structure to achieve the efficient utilization of

241

medium and low temperature heat. The content of each part of the article is arranged

242

as follows. Section 2 presents the principle of 3D construction. Section 3 presents a

243

basic cycle based on the construction method and introduces the key components in

244

the cycle. Section 4 presents a specific case that using this construction method and

245

compares the thermal efficiency and thermodynamic perfection with traditional ORC

246

using pure working fluid. Section 5 summarizes the main conclusions.

ACCEPTED MANUSCRIPT 247

2

The principle of 3D construction method

248

2.1

Ideological sources

249

In 1909, Constantin Carathéodory presented a work on an axiomatic approach to

250

thermodynamics [29]. The equations of thermodynamics originate from Pfaff

251

expression, which is linear differential form, as follows:

df   X i dxi

252

(1)

253

where i ranged from 1 to n. If i is supposed to 2, the equation (1) could be derived into

254

equation (2). The most common thermodynamic relation between U, Q and W could

255

be derived from equation (2). Meanwhile, the axiomatic thermodynamic also solved

256

equation (1) for every case, such as i >2.

df 

257

f f dx  dy x y

(2)

258

In the field of chemical thermodynamics [30], Gibbs equation is expressed as

259

equation (3). In addition to the work and heat, the chemical potential is introduced.

260

This shows that thermodynamic equations are not closed by internal energy, heat and

261

work. More thermodynamic parameters could be introduced reasonably, and of

262

course, a strict follow on axiomatic approach [29] and existing successful application

263

[30] is required.

dU  TdS - pdV   i dni

264

(3)

i

265

2.2

3D conception

266

According to Carnot principle, the highest efficiency of a heat engine operating

267

between the two thermal energy reservoirs at low temperatures TL and high

268

temperatures TH is:

ACCEPTED MANUSCRIPT

Carnot  1 

269

TL TH

(4)

270

The thermal efficiency of the Carnot cycle is only related to the heat source

271

temperature and the heat sink temperature, but has nothing to do with the thermos-

272

physical properties of working fluid and the type of reversible engine used [31].

273

However, the realization of the actual cycle, in most traditional industrial applications,

274

has to rely on working fluid. Different from the traditional steam Rankine cycle,

275

organic Rankine cycle has many candidates for working fluid. And the thermos-

276

physical properties of working fluid would affect the performance of ORC system

277

significantly. Therefore, the working fluid selection is a key process in the research of

278

ORC system.

279

As described in section 1, the methods of working fluid selection commonly used

280

in the existing studies are based on the overall thermal efficiency of ORC system. The

281

basic steps are as follows. First, a dynamic or steady-state mathematical model of the

282

ORC system is established. Second, the thermos-physical properties of candidate

283

working fluids are brought into the mathematical model and the thermal efficiency is

284

calculated. Last, the optimal working fluid is selected according the value of thermal

285

efficiency. Although these methods are simple and widely applicable, the mechanism

286

of the influence of the working fluid thermos-physical properties on the performance

287

of ORC system would not been explained. More important, the efficiencies of

288

expander and pump are commonly assumed to be fixed for different working fluids.

289

This assumption seems irrational for analyzing the effects of the working fluid on

290

ORC system performance. Some researchers explored a parameter to characterize the

ACCEPTED MANUSCRIPT 291

effects of working fluid thermos-physical properties on ORC system performance.

292

But no unified conclusions have been drawn until now.

293

In order to understand the effect mechanism of working fluid thermos-physical

294

properties on performance of ORC system, it is necessary to research every process

295

(compression process, evaporation process, expansion process and condensation

296

process) in ORC system. Manente et al. [32] presented an accurate prediction of

297

turbine efficiency taking into account the influence of the working fluid thermos-

298

physical properties. The results showed that the working fluid with high critical

299

temperature would provide high turbine efficiency. Lio et al. [33] considered that the

300

influence of the working fluid should not be neglected when design the expander.

301

They explored the effects of working fluid thermos-physical properties on the turbine

302

efficiency and provided a design criterion. By a comprehensive review of volumetric

303

expanders applied in ORC system for low grade heat and waste heat recovery, Imran

304

M et al. [34] pointed out that the choice of expander is significantly correlated with

305

working fluid. In addition to the effects on the expansion machine, Xu et al. [35]

306

experimentally researched the effects of working fluid in compression process and

307

proposed a novel parameter αV/ρcp to indicate the influence of working fluid thermos-

308

physical properties on the isentropic efficiency of pump applied in ORC system.

309

There are also optimum working fluids in evaporation and condensation process to

310

make the thermal matching between the working fluids and the heat source or heat

311

sink best. The actual cycle is commonly accomplished by only one pure working fluid

312

or single compositions of zeotropic mixture. The selected working fluid can’t meet

ACCEPTED MANUSCRIPT 313

the requirements of all thermodynamic processes in ORC at the same time. Even the

314

working fluid with best performance of whole ORC system may not optimize the

315

performance of each thermodynamic process. This is the main reason that leads to a

316

great gap between the actual thermodynamic cycle and the ideal cycle.

317

A novel construction method of thermodynamic cycle based on the zeotropic

318

mixture is proposed in this paper to solve the problems mentioned above. The core

319

concept of this method is to achieve the best performance of each thermodynamic

320

process by switching the working fluid between each thermodynamic process, so that

321

the performance of whole system would close to the ideal cycle. The ORC is

322

commonly analyzed in a 2D temperature versus entropy diagram. By introducing the

323

compositions of zeotropic mixture as the third thermodynamic coordinate, that is

324

using various compositions of zeotropic mixture in different process, the novel

325

construction method could achieve the best performance of each process, so as to

326

realize the 3D thermodynamic construction of actual cycle.

327

The principle of the construction method is shown in Fig. 3. For a clear

328

description of the principle, the following assumptions are made: (a) the working fluid

329

X shows better performance in isothermal process (evaporation process and

330

condensation process); (b) the working fluid Y shows better performance in isentropic

331

process (compression process and expansion process). The actual cycle process is A1

332

→B1→B2→C2→C1→D1→D2→A2→A1, as follows:

333

A1→B1：The working fluid that implements this process is X, which could

334

achieve good thermal matching with the heat source to reduce the irreversible loss in

ACCEPTED MANUSCRIPT 335

evaporation process;

336

B1→B2：The working fluid is switched from X to Y;

337

B2→C2：The working fluid that implements this process is Y, which shows

338

better isentropic efficiency in expansion process to increase energy output;

339

C2→C1：The working fluid is switched from Y to X;

340

C1→D1：The working fluid that implements this process is X, which could

341

achieve good thermal matching with the heat sink to reduce the irreversible loss in

342

condensation process;

343

D1→D2：The working fluid is switched from X to Y;

344

D2→A2：The working fluid that implements this process is Y, which shows

345

better isentropic efficiency in compression process to decrease energy input;

346

A2→A1：The working fluid is switched from Y to X;

347

The projection of this 3D thermodynamic cycle on the T-S diagram is ideal

348

Carnot cycle:A0→B0→C0→D0→A0. The principle above mentioned is aimed at the

349

cycle, which is accomplished by two different working fluids. According to the core

350

concept of this principle, the cycle could also be completed by three or four different

351

working fluids.

352

Fig. 3 The principle diagram of the 3D construction method

353 354

3

The basic cycle

355

3.1

Cycle structure

356

The principle of 3D construction method of thermodynamic cycle is introduced in

ACCEPTED MANUSCRIPT 357

the second section. Theoretically, the thermodynamic cycle requires completely

358

switching between different working fluids to optimize the performance of each

359

thermodynamic process. However, it is difficult to switch the pure working fluid

360

completely in the current cycle using the existing technology. The zeotropic mixture

361

is suitable for this cycle due to the different thermos-physical properties for different

362

compositions. The switching between different compositions could meet the

363

requirements of different processes to the thermos-properties of the working fluid.

364

Some researchers studied the compositions regulation of zeotropic mixture in recent

365

years. Collings et al. [36] proposed a novel ORC system using zeotropic mixture, with

366

compositions tuning system to adjust the compositions of mixture during different

367

heat sink temperature. Yang et al. [37] presented a combined power and ejector-

368

refrigeration cycle, in which the zeotropic mixture was divided into two different

369

compositions entering the power cycle and refrigeration cycle respectively.

370

Zeotropic mixture is considered as potential working fluid that could improve

371

cycle performance significantly, which show the main characteristics of temperature

372

glide and compositions shift. Zeotropic mixture is made up of two or more pure

373

working fluids with different boiling temperature under same pressure. During

374

evaporation process at constant pressure, the working fluid with lower boiling

375

temperature would evaporate first. This causes that the compositions in the liquid

376

phase and vapor phase are always different and changing continuously. The change of

377

compositions results in the change of evaporation temperature until the evaporation

378

process finished. The same phenomenon exists in the condensation process at constant

ACCEPTED MANUSCRIPT 379

pressure because the component with high boiling temperature would condensate

380

firstly. Fig. 4. shows the temperature versus compositions diagram for zeotropic

381

mixture of R245fa/R134a under the pressure of 1000 kPa. TD and TB represent the

382

dew point temperature and bubble point temperature of zeotropic mixture with

383

constant compositions respectively. The temperature difference between TD and TB is

384

the gliding temperature, ΔT. Point A and B represent the compositions of vapor phase

385

and liquid phase at equilibrium state under constant temperature and pressure.

386 387

Fig. 4 Phase equilibrium diagram of R245fa/R134a

388

The characteristic of temperature glide optimizes the thermal matching between

389

zeotropic mixture and heat sources or heat sink. Thus, the irreversible loss in

390

evaporation process and condensation process decrease. As shown in fig. 4, the

391

gliding temperature is different for different component proportion. Therefore,

392

different heat source and heat sink correspond to different optimum compositions.

393

Through the literature review in section 1, we found that the selection parameters of

394

the optimal working fluid in compression process and expansion process are different.

395

The thermos-physical properties of zeotropic mixture are different among different

396

compositions, which would satisfy the standard in compression process and expansion

397

process respectively. If the compositions of zeotropic mixture could be adjusted

398

actively in the cycle, the ORC system would be more flexible and efficient.

399

According the contents mentioned above and the principle of 3D construction, a

400

basic cycle based on zeotropic mixture is put forward. The diagram of basic system is

ACCEPTED MANUSCRIPT 401

shown in fig. 5, which is coupled by ORC sub-system and compositions regulating

402

sub-system. The main components of compositions regulating sub-system are four

403

compositions regulators which will adjust the compositions of zeotropic mixture

404

between main components of ORC sub-system to satisfy the requirements for

405

thermos-physical properties of working fluid in each process. It should be explained

406

that the regulator in this system is indefinite, because the study of this component is

407

still in its infancy. Therefore, a special description is presented in section 3.2.

408

Fig. 5 Diagram of basic cycle based on zeotropic cycle

409 410

3.2

Key component-compositions regulator

411

This section presents several existing separation and mixing techniques: T-

412

junction, gas-liquid separator, distillation tower, absorption and adsorption, as shown

413

in fig. 6. These techniques are divided into three classes according to the separation

414

principle: separation by phase, by chemical action and by intermolecular forces. The

415

working fluid need to keep two-phase during the separation if it is separated by phase.

416

The main objective is to describe techniques that could be used for compositions

417

regulating in the system described above.

418

Fig. 6 Diagram of compositions regulator

419 420

3.2.1 Separation by phase

421

a. T-junction

422

T-junction is widespread in factories and life, which has the advantages of simple

ACCEPTED MANUSCRIPT 423

structure and low cost. The working medium at the two-phase state enters the T-

424

junction from the inlet, as shown in Fig. 6(a), and then the liquid phase flows out from

425

the lower exit and gas phase out from the upper outlet due to the action of gravity. As

426

the difference compositions of zeotropic mixture between gas phase and liquid phase,

427

the phase separation could separate the compositions. Since 1986, some scholars have

428

studied the phase separation in T-junction, but most of them focused on the separation

429

of air and water [38, 39]. Different from organic working fluid, there is no difference

430

in compositions between the two phases of water and air. In recent years, T-junction

431

is introduced into some novel thermodynamic cycles. Tuo et al. [40] applied the T-

432

junction into a novel vapor compression A/C system with flash gas bypass method to

433

separate the gas and liquid of R134a and R410A before the evaporator. After a series

434

of detailed experimental study, they found that the separation efficiency depends on

435

the inlet conditions, diameter of pipe and the angle between the entrance and the exit

436

pipe [41]. Zheng and Zhao [42] presented a two-stage heat pump combined with

437

vapor expander and compressor using zeotropic mixture R152a/R227ea as working

438

fluid. The T-junction is used to separate the phase and compositions of zeotropic

439

mixture. After that, they experimentally research the separation of phase and

440

compositions of pure working fluid and zeotropic mixture respectively. For the

441

separation of pure working fluid, the vapor phase Froude number effects the

442

separation efficiency significantly [43]. And the inlet conditions, outlet conditions,

443

mass fraction of components and inlet quality all affect the efficiency of compositions

444

separation [44].

ACCEPTED MANUSCRIPT 445

b. Gas-liquid separator

446

The gas-liquid separator has similar structure with T-junction but with larger

447

cavity, as shown in Fig. 6(b). The larger space allows the gas and liquid to be

448

separated completely. Therefore, the efficiency of phase separation in gas-liquid

449

separators is commonly assumed to be 100% [45, 46]. Tan et al. [45] presented an

450

auto-cascade ejector refrigeration cycle with zeotropic mixture R32/R236fa. The

451

working fluid is divided into the gas phase with low boiling point R32-rich at the top

452

of separator and liquid phase with high boiling point R236fa-rich at the bottom of

453

separator. The gas-liquid separator is also used in trigeneration system combined the

454

ORC and heat pump [46]. The separator is applied in the condensation process to

455

regulate the compositions of working fluid in the following high temperature

456

evaporation process and low temperature process. After the separator, the working

457

fluid could satisfy the demand of thermos-physical properties in two different

458

circulations respectively to improve overall system efficiency.

459

c. Distillation tower

460

The distillation tower has similar working principles with T-junction and gas-

461

liquid separator, as shown in Fig 6(c). Although the structure is more complex and

462

more expensive, the distillation tower has the advantage of active regulation.

463

Distillation towers, however, are also energy intensive and are not widely used in

464

energy systems. Collings et al. [36] presented a dynamic ORC based on the zeotropic

465

mixture R134a/R245fa with the compositions tuning system to improve thermal

466

matching degree between working fluid and ambient conditions. The distillation

ACCEPTED MANUSCRIPT 467

tower was applied in the compositions tuning system. The temperature at the bottom

468

of distillation tower is high and the temperature at the top of tower is relatively low.

469

The gas phase of zeotropic mixture produced at the bottom flows to the top due to

470

buoyancy. As the temperature decreases in ascending process, R245fa condenses into

471

liquid and flows back to the bottom. Eventually, almost pure R245fa leaves from the

472

bottom of distillation tower and almost pure R134a at the top of distillation tower.

473

3.2.2 Separation by chemical action

474

Absorption is widely used in carbon dioxide capture and absorption heat pumps

475

[47, 48]. The working principle is that the target components in a mixture are

476

absorbed into the absorbent by chemical action, and the remaining components leave

477

freely, as shown in Fig. 6(d). Introducing absorption into the ORC system could

478

regulate the compositions of zeotropic mixture to meet the requirements in each

479

process. However, there are still many difficulties and challenges: (1) The selection or

480

design of working pairs. The commonly used absorbent in the absorption heat pumps

481

are H2O–LiBr and NH3–H2O pairs, which are rarely used in power cycles. (2) The

482

construction of actual cycle. In the process of carbon dioxide capture, the remaining

483

gas could release into the atmosphere after the absorption of carbon dioxide. But the

484

absorption and desorption processes need to form a cycle in the power system.

485

Therefore, it is key issue to construct a continuous and efficient power cycle.

486

3.2.3 Separation by intermolecular forces

487

Adsorption is the result of interaction between adsorbate molecules and

488

molecular adsorbent, as shown in Fig. 6(e)., it is the behavior of gas adsorbate in solid

ACCEPTED MANUSCRIPT 489

adsorbent surface [49]. Adsorption is divided into physical adsorption and chemical

490

adsorption according to the different binding forces in the adsorption process.

491

Physical adsorption relies on the van der Waals force which is ubiquitous among

492

molecules. It has been commonly used in adsorption cooling system since 1848 [50].

493

Commonly used physical adsorbents are activated carbon, silica gel and zeolite. The

494

activated carbon could form adsorbent pairs with methanol and ammonia. Silica gel

495

and zeolite correspond to water generally. In recent years, some researchers have

496

studied the adsorption characteristics of organic working fluid onto activated carbon,

497

which could apply in ORC system [51]. Same as absorption, the selection or design of

498

working pairs which suitable for the ORC system is one of the key issue.

499

4

Case study

500

In this section, a compositions adjustable organic Rankine cycle (CAORC) is

501

introduced carefully, which is a specific system based on the principle of 3D

502

construction and basic cycle mentioned in section 2 and section 3 respectively. In the

503

actual cycle, the heat source cannot be infinitely large, and the temperature will

504

change in the endothermic and exothermic process. The ideal cycle consisting of

505

variable temperature heat sources and heat sink is the Lorenz cycle. Thus, the goal of

506

CAORC is to approach Lorenz cycle.

507

4.1 The introduction of CAORC

508

Zeotropic mixture is used in CAORC, but different compositions circulated in

509

different sub-systems. The diagram of CAORC is presented in Fig. 7. The main

510

components of the system include: working fluid pump, evaporator, gas-liquid

ACCEPTED MANUSCRIPT 511

separator, expanderⅠ, generatorⅠ, throttle valve, internal heat exchanger, expander

512

Ⅱ, generatorⅡ, condenser and mixer. There are three different compositions of

513

zeotropic mixture in the whole cycle: (1) CompositionsⅠ circulates in working fluid

514

pump and evaporator; (2) CompositionsⅡ

515

CompositionsⅢ circulates in throttle valve, expanderⅡ and condenser. The

516

adjustment between different compositions of zeotropic mixture is realized in gas-

517

liquid separator and mixer. The heat transfer between compositionsⅡ

518

compositionsⅢ is realized in internal heat exchanger.

circulates in expanderⅠ. (3)

and

519

The circulation process is as follows: The working fluid out of the mixer with

520

compositionsⅠ is pressurized by the working fluid pump to the evaporation pressure

521

(A→B). The high pressure working fluid from the pump enters the evaporator to

522

absorb heat and changes into a gas-liquid two-phase state (B→C→D). The working

523

fluid in two-phase state is separated into a saturated gaseous working fluid with

524

compositionsⅡ (D→E) and a saturated liquid working fluid with compositionsⅢ (D

525

→H) in the gas-liquid separator, which is also called as compositions regulator in

526

section 3. After that, the gaseous working fluid passes through the expanderⅠ and

527

outputs work (E→F). The expanderⅠ drives the generatorⅠ to generate electricity.

528

The saturated liquid working fluid from the bottom of the gas-liquid separator

529

changes into gas-liquid two-phase state through throttle valve (H→I). After that, the

530

working fluid in the two-phase state is heated to a saturated gaseous by the exhausted

531

steam from expanderⅠ in the internal heat exchanger (I→J). In this process, the

532

exhaust steam from expanderⅠ is condensed into saturated liquid (F→G). The

ACCEPTED MANUSCRIPT 533

saturated gaseous working fluid passes through the expanderⅡ (J→K), which drives

534

the generatorⅡ to generate electricity. Subsequently, the exhaust steam from the

535

expanderⅡ is condensed to saturated liquid state (K→L). The saturated liquid

536

working fluid with compositionsⅡ from the internal heat exchanger and the working

537

fluid with compositionsⅢ from the condenser are mixed into the initial compositions

538

Ⅰ in the mixer (L&G→A). At this point, the cycle is finished. Fig. 8 shows the

539

corresponding temperature-entropy-compositions diagram of CAORC. Circulation

540

→E→F→G process of working fluid is: A→B→C→D →H→I→J→K→L →A.

{

}

541

Fig. 7 Diagram of CAORC

542 543

Fig. 8 T-s-θ diagram of the CAORC

544 545

4.2 Features

546

In order to further illustrate the advantages of the CAORC, some features are

547 548

summarized as follows: 

Using zeotropic mixture.

549

Due to the characteristic of variable temperature phase change at constant

550

pressure, the zeotropic mixture shows better thermal matching with the heat

551

source and heat sink. That is, the average temperature difference in the heat

552

transfer process decreases. Therefore, the application of zeotropic mixture

553

reduces the irreversible losses during evaporation and condensation process

554

compared with the organic Rankine cycle using pure working fluid. In

ACCEPTED MANUSCRIPT 555

addition, the system would operate at a relatively low pressure when using

556

zeotropic mixture [52].

557



Compositions adjustable.

558

One of the major differences in the system is the introduction of a

559

compositions regulator. The adjustment of compositions of zeotropic mixture

560

is achieved by using gas-liquid separator in this system, which separates the

561

compositions mainly by phase separation. In evaporation process, the

562

component with lower boiling temperature would evaporate firstly. In

563

condensation process, the component with a higher boiling temperature

564

would condensate firstly. Therefore, the more volatile component shows

565

higher proportion in gas phase. The proportion in liquid phase is opposite.

566

The working fluid after separation have different thermos-physical properties

567

due to the difference of compositions. In CAORC, the initial working fluid

568

with compositionsⅠshows a favourable thermal matching with heat source

569

and heat sink, which could reduce exergy losses. In order to ensure that the

570

exhaust steam from expanderⅠ has enough thermal energy to heat the

571

working fluid at the outlet of throttle valve, the working fluid with

572

compositionsⅡ should close to dry working fluid during expansion process.

573

At the same time, in order to reduce the condenser area, the working fluid

574

with compositionsⅢ

575

expansion process.

576



should show isentropic characteristics during

Self-recovery of exhaust steam of expander.

ACCEPTED MANUSCRIPT 577

In the traditional organic Rankine cycle, the regenerator is commonly used to

578

recovery the exhaust energy from expansion machine. In CAORC, the

579

exhaust energy from the compositionsⅡ is recovered by compositionsⅢ.

580

By separating the components, a part of original exhaust energy is converted

581

into work again.

582

4.3 Comparative analysis

583

In order to research the advantages of CAORC, the system based on geothermal

584

energy is analyzed in this section. A detailed mathematical model is established to

585

evaluate the effect of key parameters on the whole system performance, as shown in

586

Table 1. The net power, thermal efficiency and thermodynamic perfection were

587

selected as evaluation criteria. The net power is the difference between output power

588

of expander and power consumption of pump. The thermal efficiency, which is based

589

on the first law of thermodynamic, is the ratio of net power and heat absorbed from

590

heat source. The thermodynamic perfection, which is based on the second law of

591

thermodynamic, is the ratio of thermal efficiency and Carnot efficiency under the

592

same heat source and heat sink temperature [2]. The zeotropic mixtures of three most

593

commonly used pure working fluid (R123, R134a and R245fa) are selected as

594

candidate working fluid. Based on the mathematical model mentioned above, the

595

selection of initial working fluid and compositions was carried out. Finally, the

596

zeotropic mixture of R245fa/R123 (0.6/0.4) was selected as the working fluid of the

597

CAORC system. The thermos-physical properties of R123, R245fa and their mixtures

598

are listed in Table 2.

ACCEPTED MANUSCRIPT 599 600

Table 1. Mathematical model of CAORC

601 602

Table 2. Thermos-physical properties of working fluid

603

With the initial parameters and working conditions, the performance of CAORC

604

was compared with the ORC using pure R245fa and R123. The initial determined

605

conditions are the inlet temperature and mass flow of geothermal water, inlet

606

temperature and mass flow of cooling water. The pinch point temperature in

607

evaporation and condensation process are set to 5K. In order to ensure the heat

608

transfer in the internal heat exchanger, the pinch point temperature in the internal heat

609

exchanger is set to no less than 5K. The dryness of working fluid at outlet of

610

evaporator, the pressure ratio of expanderⅠand the pressure ratio of throttle valve are

611

three key parameters affecting the performance of CAORC system. Through

612

optimization, the operating parameters of the system in the optimal performance are

613

determined, as shown in Table 3.

614 615

Table 3. Operation parameters of CAORC system

616

The comparison results of CAORC and ORC using pure working fluid are

617

presented in Table 4. For the simple ORC system, the thermal efficiency of the system

618

increases with the increase of evaporation temperature. However, in the case of fixed

619

heat source, the increase of evaporation temperature reduces the mass flow of

620

working fluid, thereby reducing the output power. Therefore, the comparison is

ACCEPTED MANUSCRIPT 621

carried out under the condition of maximum output power both for ORC and

622

CAORC. As shown in Table 4, CAORC absorbs the least thermal energy and

623

produces the most net output power, 822.31kW. The net output power of simple ORC

624

using R245fa and R123 are 736.65kW and 717.22kW, respectively. The thermal

625

efficiency of CAORC, ORC-R245fa and ORC-R123 are 12.05%, 9.53% and 9.66%,

626

respectively. From the second law of thermodynamic point of view, the CAORC

627

shows the highest thermodynamic perfection, 43.07%. For simple ORC using R245fa

628

and R123, the thermodynamic perfections are 34.06% and 34.52%, respectively. The

629

comparative results show that CAORC has better thermodynamic performance than

630

simple ORC.

631

Table 4. Comparison of CAORC with ORC using pure working fluid

632 633

5

Conclusions

634

According to the gap that the thermodynamic perfection of exiting ORC system is

635

generally low, this paper presents a novel construction method of thermodynamic

636

cycle based on zeotropic mixture. The main conclusions are as follows.

637

(1) By adding the thermodynamic coordinate of the working fluid, a temperature,

638

entropy and compositions 3D cycle diagram is formed based on the traditional

639

temperature and entropy cycle diagram. The core concept of this method is to

640

achieve the best performance of each thermodynamic process by switching

641

the working fluid between each thermodynamic process, so that the

642

performance of whole system would close to the ideal cycle.

ACCEPTED MANUSCRIPT 643

(2) According to the construction method, a basic system composed by a ORC

644

sub-system and compositions regulating system is put forward. Many

645

researchers studied the key component compositions regulator, such as T-

646

junction, gas-liquid separator, distillation tower, absorption and adsorption. T-

647

junction, gas-liquid separator and distillation have been used to separate the

648

phase and compositions of zeotropic mixture. Absorption and adsorption are

649

widely used in cooling system, but has the potential for compositions

650

regulation although there are still some challenges.

651

(3) The representative case demonstrates the feasibility of the 3D construction

652

method. Compared to ORC using pure working fluid, the compositions

653

adjustable organic Rankine cycle shows better performance in terms of

654

thermal efficiency, thermodynamic perfection and net power.

655

Acknowledgement

656

This work is sponsored by the National Nature Science Foundation of China

657

under Grant No.51476110 and the National 863 Program of China under Grant

658

No.2015AA050403.

659 660 661 662 663 664 665 666 667 668 669 670

References [1] Group B. BP statistical review of world energy June 2014. BP World Energy Review. 2014. [2] Cengel YA. Thermodynamics: an engineering approach; 8th ed. McGraw-Hill series in mechanical engineering. 1989;33(4):1297–305. [3] Wang XD, Zhao L. Analysis of zeotropic mixtures used in low-temperature solar Rankine cycles for power generation. Solar Energy. 2009;83(5):605-13. [4] Yari M, Mehr AS, Mahmoudi SMS. Thermodynamic analysis and optimization of a novel dual-evaporator system powered by electrical and solar energy sources. Energy. 2013;61(4):646-56. [5] Qiu G, Shao Y, Li J, Liu H, Riffat SB. Experimental investigation of a biomassfired ORC-based micro-CHP for domestic applications. Fuel. 2012;96(7):374-82.

ACCEPTED MANUSCRIPT 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714

[6] Kaczmarczyk TZ, Żywica G, Ihnatowicz E. The Experimental Investigation of the Biomass-Fired ORC System with a Radial Microturbine. Applied Mechanics & Materials. 2016;831:235-44. [7] Guo T, Wang HX, Zhang SJ. Fluids and parameters optimization for a novel cogeneration system driven by low-temperature geothermal sources. Energy. 2011;36(5):2639-49. [8] Hettiarachchi HDM, Golubovic M, Worek WM, Ikegami Y. Optimum design criteria for an Organic Rankine cycle using low-temperature geothermal heat sources. Energy. 2007;32(9):1698–706. [9] Sun F, Ikegami Y, Jia B, Arima H. Optimization design and exergy analysis of organic rankine cycle in ocean thermal energy conversion. Applied Ocean Research. 2012;35:38-46. [10] Tian H, Shu G, Wei H, Liang X, Liu L. Fluids and parameters optimization for the organic Rankine cycles (ORCs) used inexhaust heat recovery of Internal Combustion Engine (ICE). Energy. 2012;47(1):125-36. [11] Landelle A, Tauveron N, Haberschill P, Revellin R, Colasson S. Organic Rankine cycle design and performance comparison based on experimental database. Applied Energy. 2017. [12] Li T, Zhang Z, Lu J, Yang J, Hu Y. Two-stage evaporation strategy to improve system performance for organic Rankine cycle. Applied Energy. 2015;150:323-34. [13] Li C, Wang H. Power cycles for waste heat recovery from medium to high temperature flue gas sources – from a view of thermodynamic optimization. Applied Energy. 2016;180:707-21. [14] Lecompte S, Huisseune H, Broek MVD, Vanslambrouck B, Paepe MD. Review of organic Rankine cycle (ORC) architectures for waste heat recovery. Renewable & Sustainable Energy Reviews. 2015;47:448-61. [15] Yang L, Gong M, Guo H, Dong X, Shen J, Wu J. Effects of critical and boiling temperatures on system performance and fluid selection indicator for low temperature organic Rankine cycles. Energy. 2016;109:830-44. [16] Zhai H, Shi L, An Q. Influence of working fluid properties on system performance and screen evaluation indicators for geothermal ORC (organic Rankine cycle) system. Energy. 2014;74(5):2-11. [17] Bao J, Zhao L. A review of working fluid and expander selections for organic Rankine cycle. Renewable & Sustainable Energy Reviews. 2013;24(10):325-42. [18] Sauret E, Rowlands AS. Candidate radial-inflow turbines and high-density working fluids for geothermal power systems. Energy. 2011;36(7):4460-7. [19] Kang SH. Design and experimental study of ORC (organic Rankine cycle) and radial turbine using R245fa working fluid. Energy. 2012;41(1):514-24. [20] Zhou N, Wang X, Chen Z, Wang Z. Experimental study on Organic Rankine Cycle for waste heat recovery from low-temperature flue gas. Energy. 2013;55(1):216-25. [21] Qiu G, Liu H, Riffat S. Expanders for micro-CHP systems with organic Rankine cycle. Applied Thermal Engineering. 2011;31(16):3301-7. [22] Lei B, Wang JF, Wu YT, Ma CF, Wang W, Zhang L, et al. Experimental study

ACCEPTED MANUSCRIPT 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758

and theoretical analysis of a Roto-Jet pump in small scale organic Rankine cycles. Energy Conversion & Management. 2016;111:198-204. [23] Meng F, Zhang H, Yang F, Hou X, Lei B, Zhang L, et al. Study of efficiency of a multistage centrifugal pump used in engine waste heat recovery application. Applied Thermal Engineering. 2017;110:779-86. [24] Landelle A, Tauveron N, Revellin R, Haberschill P, Colasson S, Roussel V. Performance investigation of reciprocating pump running with organic fluid for organic Rankine cycle. Applied Thermal Engineering. 2016;113:962-9. [25] Borsukiewicz-Gozdur A. Pumping work in the organic Rankine cycle. Applied Thermal Engineering. 2013;51(1–2):781-6. [26] Curzon FL, Ahlborn B. Efficiency of a Carnot engine at maximum power output. American Journal of Physics. 1975;43(1):22-4. [27] Esposito M, Kawai R, Lindenberg K, Van dBC. Efficiency at maximum power of low-dissipation Carnot engines. Physical Review Letters. 2010;105(15):150603. [28] Sheng S, Tu ZC. Universality of energy conversion efficiency for optimal tightcoupling heat engines and refrigerators. Journal of Physics A Mathematical & Theoretical. 2013;46(40):535-6. [29] Pogliani L, Berberan-Santos MN. Constantin Carathéodory and the axiomatic thermodynamics. Journal of Mathematical Chemistry. 2000;28(1-3):313-24. [30] Briansmith B. Basic chemical thermodynamics: Oxford Univ.Pr, 1990. [31] Cengel YA, Boles MA. Thermodynamics : an engineering approach. McGrawHill series in mechanical engineering. 1989;33(4):1297–305. [32] Manente G, Lio LD, Lazzaretto A, Lund H, Kaiser MJ. Influence of axial turbine efficiency maps on the performance of subcritical and supercritical Organic Rankine Cycle systems. Energy. 2016;107:761-72. [33] Lio LD, Manente G, Lazzaretto A. Predicting the optimum design of single stage axial expanders in ORC systems: Is there a single efficiency map for different working fluids? Applied Energy. 2016;167:44-58. [34] Imran M, Usman M, Park BS, Lee DH. Volumetric expanders for low grade heat and waste heat recovery applications. Renewable & Sustainable Energy Reviews. 2016;57:1090-109. [35] Xu W, Zhang J, Zhao L, Deng S, Zhang Y. Novel experimental research on the compression process in organic Rankine cycle (ORC). Energy Conversion and Management. 2017;137:1-11. [36] Collings P, Yu Z, Wang E. A dynamic organic Rankine cycle using a zeotropic mixture as the working fluid with composition tuning to match changing ambient conditions. Applied Energy. 2016;171:581-91. [37] Yang X, Zheng N, Zhao L, Deng S, Li H, Yu Z. Analysis of a novel combined power and ejector-refrigeration cycle. Energy Conversion & Management. 2016;108:266-74. [38] Seeger W, Reimann J, Müller U. Two-phase flow in a ja:math with a horizontal inlet. Part I: Phase separation. International Journal of Multiphase Flow. 1986;12(4):575-85. [39] Azzopardi BJ, Purvis A, Govan AH. Annular two-phase flow split at an

ACCEPTED MANUSCRIPT 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799

impacting T. International Journal of Multiphase Flow. 1987;13(5):605-14. [40] Tuo H, Hrnjak P. Enhancement of vapor–liquid separation invertical impact Tjunctions for vapor compressionsystems with flash gas bypass. International Journal of Refrigeration. 2014;40:43-50. [41] Tuo H, Hrnjak P. Vapor–liquid separation in a vertical impact T-junction for vapor compression systems withflash gas bypass. International Journal of Refrigeration. 2014;40(3):189-200. [42] Zheng N, Zhao L. The feasibility of using vapor expander to recover the expansion work in two-stage heat pumps with a large temperature lift. International Journal of Refrigeration. 2015;56:15-27. [43] Zheng N, Zhao L, Hwang Y, Zhang J, Yang X. Experimental study on two-phase separation performance of impacting T-junction. International Journal of Multiphase Flow. 2016;83:172-82. [44] Zheng N, Hwang Y, Zhao L, Deng S. Experimental study on the distribution of constituents of binary zeotropic mixtures in vertical impacting T-junction. International Journal of Heat & Mass Transfer. 2016;97:242-52. [45] Tan Y, Wang L, Liang K. Thermodynamic performance of an auto-cascade ejector refrigeration cycle with mixed refrigerant R32+R236fa. Applied Thermal Engineering. 2015;84:268-75. [46] Li Z, Li W, Xu B. Optimization of mixed working fluids for a novel trigeneration system based on organic Rankine cycle installed with heat pumps. Applied Thermal Engineering. 2016;94(2324):754-62. [47] Wu W, Wang B, Shi W, Li X. An overview of ammonia-based absorption chillers and heat pumps. Renewable & Sustainable Energy Reviews. 2014;31(2):681707. [48] Ben-Mansour R, Habib MA, Bamidele OE, Basha M, Qasem NAA, Peedikakkal A, et al. Carbon capture by physical adsorption: Materials, experimental investigations and numerical modeling and simulations – A review. Applied Energy. 2016;161(1-4):225-55. [49] Ponec V, Knor Z, Černý S, Smith D, Adams NG. Adsorption on solids: Butterworths, 1974. [50] Li TX, Wang RZ, Li H. Progress in the development of solid–gas sorption refrigeration thermodynamic cycle driven by low-grade thermal energy. Progress in Energy & Combustion Science. 2014;40(1):1-58. [51] Saha BB, El-Sharkawy II, Thorpe R, Critoph RE. Accurate adsorption isotherms of R134a onto activated carbons for cooling and freezing applications. International Journal of Refrigeration. 2012;35(3):499-505. [52] Kim SG, Kim MS. Experiment and simulation on the performance of an autocascade refrigeration system using carbon dioxide as a refrigerant. International Journal of Refrigeration. 2002;25(8):1093-101.

ACCEPTED MANUSCRIPT 800

Figure captions:

801

Fig. 1 Distribution diagram of exiting researches

802

Fig. 2 Diagram of development bottleneck to approach ideal cycle

803

Fig. 3 The principle diagram of the 3D construction method

804

Fig. 4 Phase equilibrium diagram of R245fa/R134a

805

Fig. 5 Diagram of basic cycle based on zeotropic cycle

806

Fig. 6 Diagram of composition regulator

807

Fig. 7 Diagram of CAORC

808

Fig. 8 T-s-θ diagram of the CAORC

809

ACCEPTED MANUSCRIPT

Actual cycle

Cycle structure Li et al., 2015[12] Li et al., 2016[13] Lecompte et al., 2015[14]

810 811 812 813

Working fluid Yang et al., 2016[15] Zhai et al., 2014[16] Bao et al., 2013[17]

Fig. 1

Key component Sauret et al., 2011[18] Kang et al., 2012[19] Zhou et al., 2013[20] Qiu et al., 2011[21] Lei et al., 2016[22]

Ideal cycle

ACCEPTED MANUSCRIPT

814 815 816

Fig. 2

ACCEPTED MANUSCRIPT

817 818 819

Fig. 3

ACCEPTED MANUSCRIPT

370

Vapor

Temperature (K)

360

TD 

350 340

A

Dew point line

B

T

 TB

330

Bubble point line

320 310

Liquid

P=1000kPa 300 0.0

0.2

0.4

0.6

Mole Fraction of R245fa 820 821 822

Fig. 4

0.8

1.0

ACCEPTED MANUSCRIPT

ORC system Compositions regulating system Pump Evaporator Expander Condenser Compositions regulator

823 824 825

Fig. 5

ACCEPTED MANUSCRIPT outlet

outlet

separation by phase

inlet

inlet

(a) separation by chemical action 826 827 828

(b) separation by intermolecular forces

Chemical absorbent

(d)

outlet

liquid

outlet

inlet

outlet

outlet

vapor

heat

(c)

Physical adsorption bed

(e) Fig. 6

ACCEPTED MANUSCRIPT

D

B

E

②

③

⑤

⑥

I

H ①

⑦

⑨

⑧

K ⑩

829 830 831

A

⑪

④

L Fig. 7

J

F G

① Pump ② Evaporator ③ Gas-liquid separator ④ ExpanderⅠ ⑤ GeneratorⅠ ⑥ Throttle valve ⑦ Internal heat exchanger ⑧ ExpanderⅡ ⑨ GeneratorⅡ ⑩ Condenser ⑪ Mixer CompositionsⅠ CompositionsⅡ CompositionsⅢ

ACCEPTED MANUSCRIPT

832 833 834

Fig. 8

ACCEPTED MANUSCRIPT 835

Table captions:

836

Table 1. Mathematical model of CAORC

837

Table 2. Thermos-physical properties of working fluid

838

Table 3. Operation parameters of CAORC system

839

Table 4. Comparison of CAORC with ORC using pure working fluid

840

ACCEPTED MANUSCRIPT Table 1. Mathematical model of CAORC

841

Component/Efficiency

Equation

Evaporator

Qeva  m wf_Ι (hD - hB )  C p_hse m hse (Ths_in  Ths_out ) m wf_Π  xm wf_Ι

Separator

m wf_Ш  (1  x)m wf_Ι m wf_Ι hD  m wf_Π hE  m wf_Ш hH

Throttle valve

hH  hI

Internal heat exchanger

m wf_Π (hF  hG )  m wf_Ш (hJ  hI )

ExpanderⅠ

WexpΙ  m wf_П (hE  hF )expΙ

ExpanderⅡ

WexpП  m wf_Ш (hJ  hK )expП

Condenser

Qcon  m wf_Ш (hK - hL )  Cp_hsk m hsk (Thsk_out  Thsk_in ) m wf_Ι hA  m wf_Π hG  m wf_Ш hL

Mixer

Pump Net power Thermal efficiency

Thermodynamic perfection 842

m wf_Ι  m wf_Π  m wf_Ш

Wpump 

m wf_Ι (hB  hA )

pump

Wnet =WexpІ +WexpП  Wpump

 thermal 

 therm_perf 

Wnet Qeva

 thermal 1

Thsk_in Thse_in

ACCEPTED MANUSCRIPT Table 2. Thermos-physical properties of working fluid

843

Working fluid R123 R245fa R245fa/R123 844

Tb (K) 300.97 288.29 288.91

ρ (kg·m-3) 550.00 516.08 528.8

Tcr (K) 456.83 427.16 432.89

Pcr (MPa) 3.66 3.65 3.65

GWP 77 1030 -

ODP 0.02 0 -

ACCEPTED MANUSCRIPT Table 3. Operation parameters of CAORC system

845

Point A B C D E F G H I J K L 846

Temperature (K) 283.03 283.40 373.15 373.44 373.44 338.57 328.97 373.44 323.97 324.54 283.90 283.15

Pressure (MPa) 0.079 1.174 1.174 1.174 1.174 0.391 0.391 1.174 0.328 0.328 0.079 0.079

Enthalpy (kJ·kg-1) 215.18 215.99 329.94 369.26 461.54 443.10 271.81 329.71 329.71 402.70 383.05 215.32

Entropy (kJ·kg-1·K-1) 1.086 1.086 1.437 1.539 1.786 1.789 1.269 1.433 1.449 1.675 1.678 1.086

Compositions (R245fa/R123) 0.60/0.40 0.60/0.40 0.60/0.40 0.60/0.40 0.65/0.35 0.65/0.35 0.65/0.35 0.58/0.42 0.58/0.42 0.58/0.42 0.58/0.42 0.58/0.42

ACCEPTED MANUSCRIPT 847

Table 4. Comparison of CAORC with ORC using pure working fluid Parameters Geothermal water inlet temperature (K) Geothermal water outlet temperature (K) Geothermal water mass flow (kg/s) Cooling water inlet Temperature (K) Working fluids mass flow (kg/s) Net power (kW) Thermal efficiency Thermodynamic perfection

848

CAORC

ORC-R245fa

ORC-R123

393.15

393.15

393.15

334.66

326.92

329.54

27.78

27.78

27.78

283.15

283.15

283.15

44.51

32.17

35.21

822.31 12.05%

736.65 9.53%

717.22 9.66%

43.07%

34.06%

34.52%