Thermodynamic Analysis on Work Transfer Process of Two Gas Streams

Nov 2, 2010 - Therefore, the compression of LP gas stream will occur as a polytropic process rather than an adiabatic process. Similarly, expansion of...
0 downloads 0 Views 287KB Size
Download PDF
12496

Ind. Eng. Chem. Res. 2010, 49, 12496–12502

Thermodynamic Analysis on Work Transfer Process of Two Gas Streams Jian-Qiang Deng,*,† Ji-Quan Shi,‡ Zao-Xiao Zhang,† and Xiao Feng† School of Energy and Power Engineering, Xi’an Jiaotong UniVersity, Xi’an 710049, Shannxi, People’s Republic of China, and Imperial College London, London SW7, 2AZ, United Kingdom

A novel concept of gas-gas work exchanger (WE) is proposed for recovery of mechanical energy. Its thermodynamic process is analyzed by using the energy conservation law and the real gas’s pressure-specific enthalpy diagram. An in-depth work evaluation model of the work transfer process is carried out. A simplified equation for quick forecast work recovery efficiency of a gas-gas work exchanger is derived. The performances of a gas-gas work exchanger are analyzed by predigesting some precondition. The work recovery efficiency of a gas-gas work exchanger is found to be lower than that of a liquid-liquid work exchanger, e.g., the work recovery efficiency of a diatomic molecule gas drops from 0.75 to 0.46 as the compression ratio is increased from 1.5 to 3.0. The higher compression rate results in more work loss. In the example case of this work, supposing the same nitrogen stream supplies the power for recovery, a three-stage recovery process can recover 79% more power than a single stage process. A low-pressure stream can be compressed and rise its temperature far higher than that of two original temperatures of the streams. It is a new approach to energy transfer driven by pressure difference and it is wholly different from the heat transfer in a heat exchanger (HE). A network combining WEs with HEs is proposed for recovering energy thoroughly and flexibly. Introduction Just like a heat exchanger (HE) or a mass exchanger (ME), the latter is used to recover valuable materials, a work exchanger (WE) can be used to recover mechanic energy, or more specifically shaft work. While the state parameter in a heat exchanger (mass exchanger) is temperature (concentration), pressure is the main state variable for a work exchanger, where pressurization/depressurization of fluid streams taking place. Whenever a high-pressure fluid stream, or simply stream HP, is depressurized in such a manner that expansion occurs, a potential exists for mechanical energy recovery. However, pressurizing a low-pressure fluid stream, or simply stream LP, always requires mechanical energy. Obviously, a match of the two streams in a WE will transfer mechanical energy as shaft work from stream HP to stream LP.1 Such a work transfer unit was first conceived by Cheng in 1967.1 Lately, it has been developed into an energy recovery device (ERD), also referred to as a pressure exchanger. Nowadays, ERD plays an important role in the operation of a reverse osmosis (RO) process for desalination. Development and improvement in the performance of ERD has led to significant reduction in the power consumption of seawater reverse osmosis (SWRO). In the late 1970s, the specific energy consumption (SEC) for the SWRO system was 20 kW · h · m-3. Owing to the improvement in the achievable recoveries of RO membranes and efficiencies of the pumping and the energy recovery system, the SEC was reduced to 8 kW · h · m-3 by the mid 1980s. Despite this reduction in power consumption, the energy consumption still accounted for 75% of the total operating cost of the SWRO system. By the turn of the 21st century, the energy recovery device could achieve 93%-97% net energy transfer efficiency (or work recovery efficiency). With the advent of these new technologies, the SEC dropped to as low as 2.0 kW · h · m-3.2 * To whom correspondence should be addressed. Tel.: +86 29 82663413. Fax: +86 29 82668566. E-mail: [email protected]. † Xi’an Jiaotong University. ‡ Imperial College London.

There are principally two kinds of ERDs in SWRO, the centrifugal type and the positive displacement (PD) type. In a Pelton turbine, which utilizes the centrifugal principle, transference of hydraulic energy is accomplished through two stepsshydraulic energy to mechanical power then back to hydraulic energy. In PD-type devices (original work exchanger), however, hydraulic energy in the high pressure brine can be transferred directly to feed seawater. Therefore, the work exchanger has higher energy transfer efficiency than centrifugal types of ERDs. Work exchangers have been mainly used in seawater reverse osmosis desalination systems, where both feedwater and brine are almost incompressible. In principle, they may be applied to any high-pressure processing systems where it is also desirable to recover mechanical energy to offset the energy requirement for pressurization of low pressure streams. Some recent work has begun to address various gas or steam pressure energy related networks in process industries. Manninen and Zhu presented a systematic methodology for gas turbine integration to an existing site.3 Han et al. described an online optimization system developed and applied to the condensing steam turbine network of a chemical plant.4 Aspelund et al. studied the integration of pressure and heat energy in the context of subambient cooling process using exergy calculations.5 Razib et al. employed the concept of superstructure and formulate the energy saving on compressor network synthesis as a mixedinteger nonlinear program (MINLP).6 Del Nogal et al. studied the synthesis of mechanical driver and power generation to find a feasible network to meet the demand of different compressor stages.7 A potential application field of pure gas-gas work exchanger may be refinery hydrogen management in the oil refining industry. The refinery contains some processes that are hydrogen sources and others that are hydrogen sinks. All gas sources are managed to match with the demands of the gas sinks’ pressures, concentrations, and temperatures, etc. A gas-gas work exchange network maybe go into effect as an existed mass exchange networks in the refining industry.

10.1021/ie1011323  2010 American Chemical Society Published on Web 11/02/2010

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

12497

Figure 1. Work exchanger in a shaft work transfer process.

Figure 3. p-V diagram for a work exchanger in SWRO.

Figure 2. Pressure change and valve position in each operational mode of a work exchanger: (a) nonflow depressurization; (b) low-pressure displacement; (c) nonflow pressurization; and (d) high-pressure displacement.

This work presents a thermodynamic analysis of the performance of a work exchanger where energy is transferred between two gas streams, or a gas-gas work exchanger. In the displacement vessel of the work exchanger, a piston moving and compressing gas stream LP like a split piston in a reciprocating compressor.8 According to this similarity, the theory and experiences on the reciprocating compressor are referred in this work. General Concepts of a Work Exchanger. Figure 1 shows a sketch of a WE containing two displacement vessels, whereby an LP stream is pressurized from source pressure pLP,s to target pressure pLP,t, and a HP stream is depressurized from source pressure pHP,s to target pressure pHP,t. The work-exchange process involves the following four consecutive steps (Figure 2):9 (a) Nonflow Depressurization. The displacement vessel 1 is initially filled with the HP stream through valve V3, with the other three valves (V1, V2, and V4) closed. By closing valve V3 and opening valve V4, the content in the vessel is depressurized, until the vessel pressure is lower than the LP stream pLP,s. Valves V1 and V2 are in the closed position during this operation. (b) Low-Pressure Displacement. When the pressure on the right-hand side of the piston drops below pLP,s, valve V1 opens to let in the low-pressure feed into the left-hand side of the piston. The piston moves from the left to the right, pushing out the depressurized product through valve V4. At the end of this operation, the vessel is filled with the low-pressure feed on the left-hand side of the piston. (c) Nonflow Pressurization. With valve V4 closed and valve V3 open, some high-pressure product at pHP,s flows into the righthand side of the piston of the vessel to pressurize the content to the target pressure pLP,t. During this operation, valves V1 and V2 are in the closed position. (d) High-Pressure Displacement. By simultaneously opening valves V2 and V3, the pressurized LP stream is displaced out of

the vessel to join the high-pressure processing system by the incoming HP feed. The piston in vessel 1 moves from the righthand end to the left-hand end. At the end of this operation the vessel is filled with high-pressure feed at pHP,s. Then, the cycle (or operation) returns to step (a) and starts over again. The two vessels 1 and 2 take turns to work. Assuming no other energy loss, such as due to friction between the vessel and wall, the reversible indicated work of each stream only for pressurization/depressurization can be expressed as follows:9 -WLP )

∫

+WHP )

∫

PLP,t

PLP,s pHP,t

pHP,s

|pp p Vdp ) pV | p Vdp ) pV

LP,t,VLP,t

LP,s,VLP,s

HP,t,VHP,t

HP,s,VHP,s

-

∫

VLP,t

VLP,s

-

∫

VHP,t

VHP,s

pdV

(1)

pdV

(2)

Each expression contains two terms: one being the difference in the flow work under the high and low pressures and the other being the indicated work for a corresponding nonflow process. The difference of these two terms gives the indicated work for a flow process. In a SWOR system, dealing with seawater and brine streams, for reason of liquid’s incompressible character, the indicated ˙ can be simplified from eqs 1 and 2 to power W ˙ LP ) -V˙LP∆pLP ) -V˙LP(pLP,t - pLP,s) W

(3)

˙ HP ) V˙HP∆pHP ) V˙HP(pHP,t - pHP,s) W

(4)

When analyzing the process of work exchange, the indicated works of the two streams recover and supply may be assumed to be equal, if energy loss due to frictional resistance and throttling can be ignored. Thus, V˙HP(pHP,t - pHP,s) ) -V˙LP(pLP,t - pLP,s)

(5)

The p-V diagram of a liquid-liquid work exchanger used in SWRO is given in Figure 3.9 Thermodynamic Process of a Gas-Gas WE. Due to the much higher compressibility of gases compared with liquids, the transfer of mechanical energy between a high-pressure gas stream and a low-pressure gas stream is considerably different from that between a high-pressure liquid stream and a low-

12498

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

Figure 5. p-h diagram for a gas-gas work exchanger. Figure 4. p-V diagram for a gas-gas Work exchanger.

pressure liquid stream. First, there will be a clearance volume for the LP stream in the vessel, which includes the clearance between the piston and the left-hand end of vessel and the channel of vessel to the valve. The compressed LP gas at pressure pLP,t in the clearance volume will expand when the high-pressure gas stream in the opposite side of piston flows out from the vessel. The clearance volume will decrease the gas displacement of low-pressure stream. The relative clearance volume is defined as follows: R ) V0 /Vh

(6)

where V0 is the clearance volume and Vh is the stroke volume of the piston. Second, the temperature of the LP gas stream, which is often lower than the inner surface of vessel initially, will increase as it is being compressed, and eventually becomes higher than the vessel temperature. Therefore, the compression of LP gas stream will occur as a polytropic process rather than an adiabatic process. Similarly, expansion of gas in the clearance volume of vessel and depressurization of HP gas in the whole vessel are also polytropic process. Figure 4 shows the p-V diagram for both the LP stream (1A-B-2) and the HP stream (3-C-D-4) of a gas-gas work exchanger. For the LP (HP) stream: A-B (3-C′′) corresponds to nonflow pressurization (step c in Figure 2); B-2 (C′′-C) corresponds to high-pressure displacement (step d in Figure 2); 2-1 (C-D-D′′) corresponds to nonflow depressurization (step a in Figure 2) and first part of low-pressure displacement (step b in Figure 2), during which the gas at pLP,t in clearance volume expands with the depressurization of the HP stream; and finally 1-A (D′′-4) corresponds to the second part of step b. The thermodynamic analysis is based on the following assumptions: (1) Kinetic energies of the gas streams at the work exchanger inlets and outlets are negligible. (2) Pressure losses in the pipes and valves are negligible. (3) The fictional losses of the piston moving in the vessel, and the impact energy losses about the piston hitting the two vessel’s heads are both negligible. (4) There is no heat transfer between gas and vessel wall/ vessel heads, and between the gas streams at different temperatures. (5) The work exchanger is well insulated with heat-protection materials, i.e., the heat loss to surrounding environment is negligible. (6) The whole system is in thermodynamic equilibrium. All flow, compression, and expansion processes are analyzed based on their average pressures, temperatures, and other physical parameters. The fluctuation of pressure in the vessel is ignored.

(7) There are sufficient vessels in the WE system to enable it work in a seemingly continuous manner in terms of charging and discharging of gases. And the pressures in inlet and outlet pipes are stable. (8) Unless stated otherwise, the pressure differences across the piston during the low-pressure and high-pressure displacement steps are neglected. In practice, the pressure difference across the piston must be greater than the minimum pressure difference required, i.e., pHP,s - pLP,t g ∆pmin

(7)

pLP,s - pHP,t g ∆pmin

(8)

The pressure difference is approximately 0.035-0.070 MPa in SWRO systems.1 Although specific enthalpy of a stream commonly makes sense only when the stream flows continuously, and obviously the fluids flow inside a WE intermittently, we still use Figure 5, a pressure-specific enthalpy (p-h) diagram describing the different thermodynamic states of the LP and HP streams in one stroke. Actually, it is a conventional method that analyzing performance of a refrigeration cycle and its reciprocating compressor with p-h diagram. LP Stream. From the inlet (state 1) to the outlet (state 2), the LP stream goes through three stages: 1-A, A-B, and B-2, and two intermediate states A and B (Figures 4 and 5). The latter are considered to mark the transition between (A) a flowing gas to being stationary and (B) from being stationary to a flowing gas. In the analysis of a thermal cycle containing a compressor, it is commonly considered that the compressing process is an adiabatic, isentropic one. The enthalpy difference between the state of the inlet and the outlet of the compressor is equal to the indicated work done by the compressor. Similarly in the analysis of a gas-gas WE, the specific work done to the LP stream is considered to be equal to the enthalpy difference between the inlet and the outlet of the LP stream: wLP ) h2 - h1

(9)

Since the heat conduction in the WE actually exists, the real end state of LP is corrected to state 2′ (see Figure 5). There is an adiabatic coefficient of compression amending the ideal process 1-2 by eq 10. The coefficient is seriously influenced by the heat transfer inside the WE. Once more heat conducts to LP, smaller coefficient is achieved. η ) (h2 - h1)/(h2′ - h1) The temperature of corrected state 2′ is as follows:

(10)

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

t2′ ) f(pLP,t, h2′)

(11)

The corresponding expansion indicated power of HP gas stream during depressurization is as follows:

HP Stream. From the inlet (state 3) to the outlet (state 4), the stream HP can be determined by energy conservation eq 12. wLP ) h2′ - h1 ) χmass · (h3 - h4) ) χmass · wHP

(12)

where χmass is the mass flow ratio of stream HP vs LP. Since the volume flow of HP stream shall be equal to that of LP stream, the mass flow ratio of stream HP vs LP is as follows: χmass ) V1 /V3

(13)

The molar flow ratio of stream HP vs LP is: χmole ) (V1 · MLP)/(V3 · MHP)

(14)

where M is mole mass of a certain gas sort. The temperature of state 4 is as follows: t4 ) f(pHP,t, h4)

WLP ) pLP,sλvVh

[( )

pLP,t n n - 1 pLP,s

(n-1)/n

-1

]

[( )

pLP,t n n - 1 pLP,s

(n-1)/n

-1

]

[( ) pLP,t pLP,s

1/m

-1

]

(17)

(18)

If the HP stream feed pressure pHP,s is significantly higher than pLP,t, compression of the LP stream maybe achieved by a volume of HP stream, termed equivalent volume Veq (Figure 4), which is less than the vessel volume Vh. The equivalent volume is given by the following:

(

Veq ) Vh

pLP,t + ∆pmin pHP,s

)

1/m

(19)

Assuming potential expansion work of HP gas can be utilized in an expansion machine. Equaling to the area of 3-C-D-4 in Figure 4, the maximum expansion indicated work done by the HP gas stream in one stroke is given by the following: WE ) pHP,tVHP,t

[( )

pHP,s m m - 1 pHP,t

(m-1)/m

-1

]

(20)

where, VHP,t ) βVh

( ) pHP,s pHP,t

(m-1)/m

-1

]

(22)

The work recovery efficiency of a gas-gas work exchanger can now be computed: ˙ LP /W ˙ HP η ) WLP /WHP ) W

(23)

For a quick evaluation of the performance of a gas-gas WE, the expression for the work recovery efficiency maybe greatly simplified under the following assumptions: • The pressure differences at both ends of the vessel are negligible, i.e.: pHP,s ) pLP,t and pLP,s ) pHP,t • The polytropic expansion index is equal to the polytropic compression index, n ) m. Equation 23 now reduces to the following: pLP,sλvVh η) pHP,tVHP,t

n n-1

m m-1

[( ) [( ) pLP,t pLP,s pHP,s pHP,t

(n-1)/n

(m-1)/m

] ]

-1

( )

≈ (λv /β)

-1

PHP,s PHP,t

-1/m

(λv /β)ε-1/m

)

(24)

ε ) pLP,t /pLP,s ) pHP,s /pHP,t The expression for the volume coefficient (eq 18) can be simplified accordingly:

where λv is the volume coefficient, which is given by the following: λv ) 1 - R

[( )

pHP,s m m - 1 pHP,t

where ε is the compression (or expansion) ratio:

(16)

Or in terms of the indicated power, ˙ LP ) pLP,sλvV˙LP W

˙ E ) pHP,tV˙HP,t W

(15)

The Model of Work Recovery Efficiency. Assuming that the expansion process index (m) is equal to the compression process index (n), the indicated work for compressing the LP stream from pLP,s to pLP,t in one stroke can expressed as:10-12

12499

1/m

(21)

and β ∈[Veq/Vh, 1]. If β ) Veq/Vh, then the area of 3-C′-D′ 4 in Figure 4 is the indicated work.

λv ) 1 - R(ε1/m - 1)

(25)

Equation 24 may be further simplified by assuming that (1) the clearance volume of the vessel is negligible, i.e., R ) 0, and thus λv ) 1 in eq 25; and (2) Veq ) Vh, and thus β ) 1. It follows that, η ≈ ε-1/mor, ε-1/n

(26)

The work recovery efficiency thus reduces to a relatively simple function of the compression ratio and the compression process index. The temperature of the compressed LP gas stream can also computed by model eq 27, which describes the relationship between gas temperature and pressure in a polytropic compression process: TLP,t ) TLP,s

( ) pLP,t pLP,s

(n-1)/n

(27)

The Performance of a Gas-Gas WE. Recovery Efficient for Different Gas Sorts. Under standard conditions (0 °C, 105 Pa), an ideal monatomic molecule gas has an adiabatic process index k ) 1.66-1.67, an ideal diatomic molecule gas has an adiabatic process index k ) 1.40-1.41, and an ideal polyatomic molecule gas has an adiabatic process index k ) 1.1-1.3. The polytropic compression index, n, for a real gas can approximated by an adiabatic process index of an ideal gas in the pressure range 1-100 MPa. Typical diatomic molecule gas includes nitrogen and oxygen. Carbon dioxide is a typical polyatomic molecule gas. Air can be considered as a gaseous mixture of mainly diatomic molecule gases. The adiabatic process index km for a gas mixture can computed by

12500

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

1 ) km - 1

∑k

i

Vi -1

(28)

where ki and Vi are the adiabatic process index and the volume fraction for component i, respectively. Figure 6 shows the work recovery efficiency for a monatomic molecule gas, a diatomic molecule gas and a polyatomic molecule gas under different compression ratios computed using eq 26. It can be seen that the work recovery efficiency for a gas-gas WE is very sensitive to the compression ratio, especially for polyatomic gases. For example, the work recovery efficiency of a diatomic molecule gas drops from 0.75 to 0.46 as the compression ratio is increased from 1.5 to 3.0. This is considerably lower than the typical work transfer efficiency that can be attended (0.93-0.97) for liquid-liquid work exchangers used in a SWRO system. Figure 7 shows the associated temperature increase in the LP gas stream at the end of compression step, computed using eq 27. It can be seen that a monatomic molecule gas would be subject to the fastest temperature rise among the three gas types considered. The Impact of Clearance Volume on Work Recovery Efficiency. As has been stated, the presence of clearance volume in a gas-gas WE system has a detrimental impact on its work recovery efficiency. This can be clearly seen in eqs 24 and 25. The relative clearance volume R causes a reduction in the volume coefficient λv, which in turn leads to a drop in the work recovery efficiency. The reduction in λv for R up to 0.2 has been computed using eq 25 for the three types of gas and the results are summarized in Table 1. The corresponding reduction in the work recovery efficiency for a pair of diatomic gas streams (m ) n ) 1.4) is plotted in Figure 8. Relative clearance volume has a nearly linear relationship with the work recovery efficiency under the reduced condition. The Effect of Multistage WE. Ammonia synthesis has been identified as a potential application for WE.9 A simple case is given here to illustrate how the work of the HP streams might be recovered in a multistaged gas-gas WE. As a typical Shell Coal Gasification Technology in Ammonia production, the Ammonia annual production is 200 000 tons/year (gas production is nearly 55 000 N m3/h). The byproduct gases are N2 at 150 °C and 3.25 MPa with an estimated rate of near 1000 m3/h. If the discharged stream N2 at 3.25 MPa were to be used as the HP stream in a gas-gas WE with pHP,t ) 1 MPa, then it would yield an indicated power of roughly 0.90 MW. An estimated work recovery efficiency of approximately 0.431 suggests that about 0.39 MW maybe recovered to compress other gas streams, say from 1.1 MPa to 3.15 MPa with ∆pmin) 0.1 MPa. In order to improve the total work recovery efficiency, a threestage gas-gas WE is proposed, in a analogue to a multistage compressor. The pressure nodes are 1.0, 1.5, 2.2, and 3.25 MPa separately. The indicated power provided by the HP stream at the three stages is 0.28, 0.30, and 0.34 MW, respectively, from the low-pressure stage to the high-pressure stage. The corresponding work recovery efficiency for the three stages is 0.75, 0.76, and 0.76 respectively. It follows that the indicated power at each stage recover by LP streams is 0.21, 0.23, and 0.26 MW, respectively, giving rise to a total of 0.70 MW. This represents an increase of 79% in the overall recovery power (0.70MW) over the one-step WE (0.39MW). The results are summarized in Table 2. All target volume flows of HP stream are directly calculated from the N2 volume flow of source state with a polytropic process.

Figure 6. Gas-gas work exchanger work recovery efficiency as a function of compression ratio under simplified conditions (eq 26).

Figure 7. Temperature rise for various compression ratios. Table 1. Volume Coefficient λv for Different Scenarios λv n ) m ) 1.66 R 0.00 0.05 0.10 0.20

n ) m ) 1.40

n ) m ) 1.10

ε ) 1.5 ε ) 2 ε ) 3 ε ) 1.5 ε ) 2 ε ) 3 ε ) 1.5 ε ) 2 ε ) 3 1.000 0.986 0.972 0.945

1.000 0.974 0.948 0.896

1.000 0.953 0.906 0.812

1.000 0.983 0.966 0.933

1.000 0.968 0.936 0.872

1.000 0.940 0.881 0.762

1.000 0.978 0.955 0.911

1.000 0.956 0.912 0.824

1.000 0.914 0.829 0.657

Thermal Effect of a Gas-Gas Work Exchange. The factors influencing a WE’s performances are mainly including the streams’ original parameters. It is discussed that the influence of the target pressure of LP on the target temperatures and flow ratios of two streams. For the purpose of theoretically analyzing the functions and their effects of a WE basing on upper thermodynamic model, CO2 stream are designated as HP streams. And the LP streams are nitrogen streams. The physical properties of gas streams are acquired by the REFPROP 7.0.13

Figure 8. Reduction in gas-gas work exchanger work recovery efficiency as a function of the .relative clearance volume for a pair of diatomic gas streams.

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010 Table 2. Recovered Power from Stream N2 as an HP in the Case three stages items

one step

WE 1

WE 2

WE 3

pHP,s (MPa) pHP,t (MPa) ε V˙HP,t (m3 · h-1) WHP (MW) η WLP (MW)

3.25 1.0 3.25 2321 0.90 0.43 0.39

1.5 1.0 1.5 2327 0.28 0.75 0.21

2.2 1.5 1.47 1742 0.30 0.76 0.23

3.25 2.2 1.48 1323 0.34 0.76 0.26

total

0.92 0.70

Supposing the LP stream, N2, is compressed from a source pressure 1.0 MPa to a varied target pressure range from 1.5 to 3.5 MPa with a source temperature 100 °C. The CO2 HP stream depressurizes from a source pressure varied from 1.5 to 3.5 MPa, with a source temperature 200 °C. The target pressure of HP is 1.0 MPa. The pressure difference, ∆pmin, is negligible here. The assumed adiabatic coefficient of compression is 0.85. The flow ratios of two gas streams and their target temperatures for different target pressures of LP (or different source pressure of HP) are shown in Figure 9. With the target pressure changing from 1.5 to 3.5 MPa, the mole flow ratio is improved from 1.20 to 2.86. Higher pressure pressurized, more HP gas needs. Since the carbon dioxide has a bigger mole mass than nitrogen, its mass flow exhausting is increasing with more rapid speed. Accompanying work transfer, the LP stream obviously from a relatively low temperature, a source temperature 100 °C, increases to a varied target temperature 154-287 °C in this case. The enlarged temperature scopes of gas streams provide more flexible approaches of energy couple transfer in an energyexchange system. A heat exchanger combined with a work exchanger can recover energy more effectively. The actual heat transfer inside the work exchanger influences the final target temperature of two gas streams and the value of adiabatic coefficient of compression.

12501

are given to illustrate the result. Several conclusions can be summarized as follow: 1. Calculating with the work recovery efficiency equation of the gas work exchanger, we can see that the gas exchanger has more work losses compared with the work exchanger dealing with liquids, e.g., the work recovery efficiency of a diatomic molecule gas drops from 0.75 to 0.46 as the compression ratio is increased from 1.5 to 3.0. 2. Since higher compression rate results in more work loss, it is advised that instead of single stage work transfer, multistage work transfer is recommended. In this work’s case, a three stage WE, each stage has a shared compression rate, recover 79% more work than a one stage WE with total compression rate. 3. Relative clearance volume has a nearly linear relationship with the work recovery efficiency under the simplified work condition. Smaller relative clearance volume helps to improve the work recovery efficiency. 4. The monatomic molecule gas has a more rapid temperature rise than the other two kinds of gases, namely diatomic and polyatomic gases. 5. The target temperature of the LP stream can be higher than the temperature of both source streams entering a WE. The enlarged temperature scopes of gas streams provide more flexible approaches of energy couple transferring in an energy exchange system. Acknowledgment This work has been supported by the National Key Natural Science Foundation of China (No: 20936004). Note Added after ASAP Publication: Corrections have been made to ref 7 and eqs 1, 2, 16, 17, 20, 22, 24, and 27 in the version of this paper that was published ASAP on November 2, 2010. The corrected version was reposted to the Web November 18, 2010. Nomenclature

Conclusions In this work, a detailed thermodynamic process of the detached working steps of the gas-gas work exchanger was built. An in-depth research of the work transfer evaluation model is provided. A work recovery efficiency simplified equation of a gas-gas work exchanger is conducted. The phenomenon of transferring mechanical and thermal energy simultaneously in a gas-gas WE is illustrated. The performance of a gas-gas WE is discussed under the same reduced conditions. The cases

1,2,3,4,5,6,6′,7,8,9,10,A,B,C,C′,C′′,D,D′,D′′ ) state point in a strock R ) relative clearance volume η ) work recovery efficiency of a work exchanger ε ) pressure ratio λv ) volume coefficient h ) specific enthalpy (kJ · kg-1) k ) adiabatic process index m ) polytric expansion process index n ) polytric compression process index p ) pressure (MPa) ∆pmin ) minimum allowable pressure difference between the two sides of the piston in a work exchanger (MPa) s ) specific entropy (kJ · kg-1 · K-1) T ) temperature (°C) V ) volume fraction of certain gas V0 ) clearance volume in low-pressure cylinder (m3) Vh ) strock volume (m3) Veq ) equivalent volume (m3) V˙ ) volume flow of stream (m3 · h-1) W ) indicated work (kJ) ˙ ) indicated power of streams (MW) W Subscripts

Figure 9. The flow ratio of stream pairs and the target temperatures for the different target pressures of LP stream.

i ) certain gas HP ) high-pressure stream m ) mixed gases LP ) low-pressure stream

12502

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

s ) source t ) target

Literature Cited (1) Cheng, C. Y.; Cheng, S. W.; Fan, L. T. Flow Work Exchanger. AIChE J. 1967, 13, 438–442. (2) Sun, J. X.; Wang, Y.; Xu, S. C.; Wang, S. C. Energy Recovery Device with a Fluid Switcher for Seawater Reverse Osmosis System. Chin. J. Chem. Eng. 2008, 16, 329–332. (3) Manninen, J.; Zhu, X. X. Optimal Gas Turbine Integration to the Process Industries. Ind. Eng. Chem. Res. 1999, 38, 4317–4329. (4) Han, I. S.; Lee, Y. H.; Han, C. Modeling and Optimization of the Condensing Steam Turbine Network of a Chemical Plant. Ind. Eng. Chem. Res. 2006, 45, 670–680. (5) Aspelund, A.; Berstad, D. O.; Gundersen, T. An extended pinch analysis and design procedure utilizing pressure based exergy for subambient cooling. Appl. Thermal Eng. 2007, 27, 2633–2649. (6) Razib M. S.; Hasan M. M. F.; Karimi I. A. Optimal Synthesis of Compressor Network. Proceeding of the 7th International Conference on the Foundations of Computer-Aided Process Design (FOCAPD 2009), Colorado, 7-12 June, 2009.

(7) Del Nogal F. L.; Kim J. K.; Perry S.; and Smith R. Synthesis of Mechanical Driver and Power Generation Configurations, Part 2: LNG Applications. AIChE J. 2010, 56 (9), 2377-2389. (8) Deng, J. Q.; Gu, Z. L.; Yu, Y. Z. Impacts of the Split Conjugated Pistons in Conjugated Cylinders of a Multiple Stage Reciprocating Compressor in Start Duration. Am. Soc. Mech. Eng. 1999, 113–118. (9) Huang, Y. L.; Fan, L. T. Analysis of a Work Exchanger Network. Ind. Eng. Chem. Res. 1996, 35, 3528–3538. (10) Frenkel, M. I. Piston Compressors; Mashinostrojenie: Leningrad, 1969, (in Russian). (11) Yu, Y. Z. Handbook of Displacement Compressor; Machinery Industry Press: Beijing , 2000, (in Chinese). (12) Dagilis, V.; Vaitkus, L. Parametric analysis of hermetic refrigeration compressors. Mechanika 2009, 80, 23–29. (13) NIST. 2002. Reference Fluid Thermodynamic and Transport Properties Database (REFPROP), Version 7.0, U.S. Department of Commerce, Maryland, 2002.

ReceiVed for reView September 30, 2009 ReVised manuscript receiVed September 5, 2010 Accepted October 15, 2010 IE1011323