A Targeting Methodology for Multistage Gas-Phase Auto Refrigeration

May 23, 2007 - Gas-phase refrigeration systems can provide cooling down to cryogenic temperatures, using auto refrigeration to cool the refrigerant be...
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Ind. Eng. Chem. Res. 2007, 46, 4497-4505

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PROCESS DESIGN AND CONTROL A Targeting Methodology for Multistage Gas-Phase Auto Refrigeration Processes Nipen M. Shah* and Andrew F. A. Hoadley† Building 36, Department of Chemical Engineering, Monash UniVersity, Clayton, VIC 3800 Australia

Many chemical processes require refrigeration over a broad range of low temperatures. Gas-phase refrigeration systems can provide cooling down to cryogenic temperatures, using auto refrigeration to cool the refrigerant before it is expanded. The economics of these systems are dominated by the shaftwork supplied to the compressors and the capital cost of the rotating equipment, both the compressors and the turboexpanders. A shaftwork targeting method has been developed for gas-phase refrigeration systems that require a continuous cooling load from ambient to some minimum temperature. The method involves the use of a number of gas-phase refrigeration loops which are matched against the grand composite curve. The targeting method is used to demonstrate the relationship between the expansion/compression pressure ratio and the heat-exchange design parameter ∆Tmin. The potential for shaftwork recovery from surplus cold streams is also explored. Some interesting insights from the targeting are the relative insensitivity of the pressure ratio and the importance of the isentropic efficiency especially for energy recovery from cold streams. 1. Introduction Refrigeration is a process that is extensively used in the chemical industries. One of the most common examples of a low-temperature refrigeration process is the liquefaction of natural gas (LNG). It has been predicted that the LNG demand will grow rapidly over the next decade.1 Refrigeration and liquefaction are the key sections of the LNG plant. The liquefaction section of an LNG plant typically accounts for 3040% of the capital cost of the overall plant.2 There are several licensed processes available for LNG with different applications, for example, PRICO3 and Phillips Optimized process.4 In the last of these, refrigeration and liquefaction of the natural gas is achieved in a cascade system comprised of three different pure refrigerants: propane, ethane, and methane. Each refrigerant requires separate compression. On the other hand, in the PRICO process, a single mixed refrigerant (SMR) process is used, which is made up of nitrogen, methane, ethane, propane, and isopentane. In this process only one compressor train is used to achieve the desired refrigeration and liquefaction. The primary goal of any new developments in refrigeration is to achieve high efficiency, thus saving energy or reducing the capital cost. Gas-phase refrigeration can provide nearisentropic expansion and auto refrigeration. Moreover, it has the ability to provide very close heat transfer and can, if required, recover the shaftwork from any surplus cold stream. The gasphase refrigeration system uses turboexpanders to recover shaftwork. New turboexpander technology has the potential to significantly change refrigeration technology.2 It is already used extensively in natural gas treatment plants to maximize ethane recovery and minimize energy consumption.5 The major function of turboexpanders is to provide cooling through the * To whom correspondence should be addressed. E-mail: Nipen. [email protected]. Fax: +61 3 9905 5686. † E-mail: [email protected].

expansion of a gas while simultaneously recovering shaftwork. However, they can also handle significant amounts of condensing liquid as well as flashing liquid without much loss in efficiency. To facilitate the selection and design of gas refrigeration systems, it is necessary to determine the shaftwork targets for the refrigeration systems using pinch analysis. The overall design of a process consists of two stages: targeting and design. Targeting is basically an analysis tool that provides the initial screening of the process to identify the most promising design options, and in the design stage the options selected from targeting are further developed for detailed design. Linnhoff and Dhole6 provided a graphical method for minimizing the shaftwork associated with the Heat Exchange Network (HEN) of a subambient process based on the exergy grand composite curves (EGCC). In this method shaftwork can be estimated by calculating the area between the EGCC and the utility levels. Generally, this analysis is used to minimize the shaftwork required by a refrigeration system. However, auto refrigeration systems introduce the complication that the warm refrigerant must also be included in the hot composite curve, which in turn is incorporated in the EGCC. In addition to the heat-transfer requirements, shaftwork targets must also include the actual efficiencies of the mechanical components. Feng and Zhu7 extended this concept and proposed a new diagram, called the Ω-H diagram that can represent all kinds of systems, where Ω is the ratio of exergy to energy. This hybrid of pinch and exergy analysis helps identify the sources of inefficiencies within a given process. The alternative approach to targeting has been to employ optimization methods to reduce a superstructure-based model.8-10 These methods, although being very flexible, do not provide the same insights into the system design which can be gained from using targeting based on the refrigeration thermodynamics. In addition to these approaches, there are some that combine the benefits of thermodynamic analysis and optimization

10.1021/ie060868j CCC: $37.00 © 2007 American Chemical Society Published on Web 05/23/2007

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temperature on the cold side is a shifted temperature represented by the asterisk which is defined as

T/n ) Tn - ∆Tmin

(1)

In other words, T/n represents the temperature ∆Tmin colder than Tn. Generally, the value of ∆Tmin for cryogenic processes ranges from 1 to 4 °C. An energy balance across the expander and process heat exchanger, Xn, in Figure 3 gives Figure 1. Simple refrigeration cycle.

methods. Li et al.11 suggested an approach for overall energy integration and optimal synthesis of subambient systems based on the EGCC and superstructure optimization. Lee et al.12 proposed a methodology for the synthesis of mixed refrigerant systems that identifies a set of refrigerant compositions that can provide the best match of composite curves and minimizes the temperature cross within a heat exchanger. Outside gas plant optimization,5,13 there has been very little research on multistage gas-phase refrigeration processes. In this paper, a systematic shaftwork targeting methodology for gas-phase refrigeration systems is outlined. A number of example problems are used to demonstrate the relationship between the most important parameters in the synthesis of gasphase refrigeration cycles. Furthermore, the potential for shaftwork recovery from surplus cold streams is explored. 2. Multistage Gas-Phase Auto Refrigeration Figure 1 shows a simple refrigeration cycle that involves an evaporator, a compressor, a condenser, and an expansion valve. The saturated refrigerant is compressed to a higher pressure in the compressor. The superheated fluid is then condensed in the condenser to saturated liquid before being expanded across the valve. The refrigerant vaporizes partially across the valve and passes through the evaporator where it exchanges heat with the process and leaves as a saturated vapor. In this cycle, the shaftwork is supplied in the compressor. The expansion is isenthalpic and no work is recovered. The gas-phase refrigeration system works on the concept of the Reverse-Brayton cycle, shown in Figure 2. Here, the refrigerant at a high pressure is expanded to a lower pressure across an expander where some work, Wout, is extracted. The refrigerant then exchanges heat with the hot process, after which it passes through a heat exchanger where it exchanges heat with the warm refrigerant before being compressed back to the higher pressure. This process is called auto refrigeration as there is no external utility used for the precooling of the warm refrigerant, except for removal of the heat of compression above ambient temperature. A multistage refrigeration cycle can be formed based on the concept of auto refrigeration.14 The nth stage of a multistage refrigeration process is shown in Figure 3 where the hot process is cooled from Tn-1 to Tn. This represents the coldest stage of the process. The hot gas exiting the compressor is cooled down to ambient using the discharge cooler, Cn. It is then precooled to Tn-1 by exchanging heat with the low-pressure refrigerant in the auto refrigeration exchanger. The gas stream is then expanded through En, after which the cold gas is exchanged against the / . The temperature hot process where it is heated from T/n to Tn-1 of the hot stream represents its actual temperature while the

/ Qn + mnh(Tn-1, P0) ) WEn + mnh(Tn-1 , P1)

(2)

Here, WEn is the work recovered in the expander En and Qn is the heat duty associated with the nth stage. To avoid pinching within the heat exchanger, ∆Tmin is maintained across both ends of the heat exchanger. This can only be achieved if the product of the mass flow rate m and the specific heat CP, i.e., mCP is constant for both hot and cold streams. However, the value of CP changes with temperature and pressure. If the temperature change is the same for both streams, the temperature effect can be neglected. However, the cold stream enters the auto refrigeration exchanger at a lower pressure, and for nonideal gases, the heat capacity changes significantly with pressure, especially when the temperature is close to the vapor dew point. Therefore, to compensate for the effect of pressure on CP, a supplementary flow must be added to the low-pressure side. The amount of the supplementary flow for the nth stage can be calculated from the following equation:

∆mn )

[ ] CPh,n CPc,n

- 1 ‚mn

(3)

where CPh,n and CPc,n are the specific heats of hot and cold streams passing through the auto refrigeration exchanger Hn-1 in the nth stage, respectively. Here, mn is the refrigerant flow rate in the process heat exchanger, Xn. Although the supplementary flows ensure the ∆Tmin across the ends of each auto refrigeration exchanger, the potential still exists for the heat exchanger to be pinched internally, as presented schematically in Figure 4. This is most likely to occur in the colder stages or in the liquefaction temperature region, where the CP of either the hot or cold stream is changing significantly with temperature. To overcome this problem, McCarthy and Hoadley15 proposed the idea of decomposing the auto refrigeration heat exchangers. For example, the auto refrigeration exchanger in the nth stage can be decomposed into n - 1 exchangers as shown in Figure 5. Here, supplementary flows can be added or removed from the cold refrigerant stream depending upon the requirement. The supplementary flows are taken from the previous loops. As the change in the heat capacities is more significant at lower temperatures, the last or the coldest auto refrigeration exchanger, Hn,n-1 in Figure 5, requires greater flow than any other exchangers in that stage. Hence, the excess flow is withdrawn from the low-pressure refrigerant stream before it enters the next auto refrigeration exchanger. This flow can be utilized in the previous stages. The multistage auto refrigeration process discussed so far is shown in Figure 6 with n refrigeration stages. Each multistream heat exchanger, Hi, along with a compressor, Ki, and an expander, Ei, represents one refrigeration stage. The process hot stream, which requires cooling, enters from the left and exits from the last exchanger, after passing through n heat exchangers.

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Figure 2. Reverse-Brayton refrigeration cycle.

Figure 3. nth refrigeration stage of a multistage refrigeration cycle.

Figure 4. Composite curves showing the possibility of pinching within the heat exchanger.

Figure 6. Theoretical multistage refrigeration process.

Figure 5. nth refrigeration stage with decomposed auto refrigeration exchangers.

The warm refrigerant also enters from the left, exchanges heat with the cold refrigerant, expands in the expander, and then cools the hot process stream. To avoid exergy losses associated with mixing streams of different temperatures, the temperatures of all streams entering and exiting any exchanger are matched. For example, all hot streams enter the exchanger Hi at temperature Ti-1 and exit at Ti. Another important assumption made is that the pressure ratio in each refrigeration stage is the same. All streams exiting the expanders are at pressure P1, and they are compressed back to P0 before entering the auto refrigeration exchangers. This assumption strongly relies on the fact that the friction losses are neglected. 3. Shaftwork Recovery Loop There are many processes that often involve a cold separation unit, where one or more cold streams reject heat. An example of this is the nitrogen rejection unit in many LNG processes. These cold sinks could be used in process-to-process heat transfer depending upon the shape of the grand composite curve (GCC). However, this may result in some exergy losses. With condensation refrigeration systems, shaftwork can be

reduced by using these cold sinks to subcool the refrigerant which reduces the overall refrigerant flow rate. Alternatively, with gas-phase systems, it is also possible to recover power from these cold sinks. The shaftwork recovery loop is shown in Figure 7. / In the ith temperature interval, Ti-1 to T/i , there is an energy deficit. The power recovery loop is typically a heat engine cycle, the reverse of Figure 3. Taking the gas stream leaving the process exchanger at Ti, it is compressed so that the exit / . This gas is then temperature from the compressor is Ti-1 reheated by exchange with the gas going to the process exchanger in the auto refrigeration exchanger, Yi. Heat is then added, possibly using the waste heat from a cooler in Figure 3, followed by an expansion where net shaftwork is recovered. The pressure on the hot refrigerant side is lower; hence, a small side stream is removed, analogous to the side streamadded in Figures 3 and 5. The pressure ratio in the shaftwork recovery loop need not be the same as that in the refrigeration loops. 4. Thermodynamic Analysis Exergy analysis is widely used to determine the thermal inefficiencies associated with the chemical processes. Moreover, it helps the designer to better understand the process behavior. The term exergy is defined as the maximum amount of work that can be extracted from a process when brought into

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Figure 7. Shaftwork recovery loop.

equilibrium with the ambient. When a process experiences any change, the maximum amount of work that can be extracted or the minimum amount of work that is needed can be calculated by the following equation:

∆Ex ) ∆h - T0∆S

(4)

Here, ∆h, ∆S, and T0 represent the change in enthalpy, the change in entropy, and the ambient temperature, respectively. Nonideal mixing, finite driving force, mechanical friction, etc. are the main causes of exergy loss. If zero ∆Tmin across the heat exchanger, 100% isentropic efficiency (reversible process), and isothermal compression in the compressor are assumed, the theoretical amount of shaftwork required for the given duty can be calculated. The isothermal work, per kmol of refrigerant, required for compression can be calculated using the following equation which has been derived from the Virial equation of state:

W ) Z1RT ln

[ ] [

]

P1Z2 P 1 P2 +B P2Z1 Z1 Z2

Figure 8. Algorithm for the targeting method for a multistage refrigeration process.

(5)

where B is the Virial coefficient and can be calculated using the following equation:

B)

Z1 - Z2 1 1 V1 V2

(

)

(6)

Here, Z is the compressibility factor, V is the molar volume, and T is the temperature in Kelvin. The theoretical net shaftwork is the shaftwork for isothermal compression minus the shaftwork calculated from the equation of state enthalpies for isentropic expansion. If the thermodynamic efficiency is less than 100%, then there are exergy losses associated with the flow sheet such as non-isothermal and non-isobaric mixing operations. 5. Targeting Methodology for the Multistage Refrigeration Processes As already mentioned, in the initial configuration of refrigeration loops there was a possibility of pinching in the auto refrigeration heat exchangers, especially in the coldest stage. Therefore, McCarthy and Hoadley15 presented a more refined method that incorporated the solution to the problem of pinching by introducing the concept of decomposed heat exchangers. The step-by-step method is presented using an algorithm shown in Figure 8. In the initial steps, the compressor/expander efficiency and the number of refrigeration stages are selected. The procedure for selecting the number of refrigeration stages is shown separately in Figure 9. At the beginning, the GCC is plotted to identify the cooling duty requirements and the initial and the final temperatures. Then the compressor/expander efficiency is selected. The next step is the selection of the total number of refrigeration stages. The pressure ratio is then determined using the algorithm shown in Figure 9. The values of φ and the temperatures on

Figure 9. Algorithm to calculate the number of refrigeration stages (cooling only).

the refrigerant side (Tout and Tin) are then supplied to the algorithm shown in Figure 8. With use of these temperatures, a set of the intermediate cooling temperatures is generated which is used to calculate the cooling duty associated with each stage. The final or the coldest stage calculations are performed first as there is no supplementary flow going to the next stages. After calculation of the supplementary flow requirements for the auto refrigeration exchangers associated with this final stage, the calculations for the preceding or hotter stages are performed. As discussed earlier, the coldest auto refrigeration exchanger requires a greater supplementary flow than any other exchangers; therefore, the excess flow is withdrawn from the cold refrigerant stream before it enters the next exchanger. These flows are then used in the previous stages. Hence, these excess flows should

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also be considered when calculating the total refrigerant requirements for the later stages. The shaftwork targeting method presented in Figures 8 and 9 applies to processes that require only cooling. However, as discussed in section 3, there are many processes that often involve a cold separation unit, where one or more cold streams may require reheating, and in these cases there is an opportunity to recover the shaftwork from the cold sinks. In these circumstances, the targeting method needs to be changed so that it can incorporate shaftwork recovery from these cold sinks between T0 and Tn. The procedure to calculate the number of stages changes slightly from that given in Figure 9. The targeting method will calculate the number of shaftwork recovery stages rather than the refrigeration stages. The pressure ratio is calculated by putting a number of compression loops in series rather than expansion loops as in the case of refrigeration. The temperature at the inlet of the compressor Ki+1 (Tin) is set to be ∆Tmin colder than Tout for Ki. The procedure continues with new loops added, until the value of Tout is achieved which is ∆Tmin hotter than Tn. 6. Results and Discussion In this section, the targeting methodologies discussed in the previous section are demonstrated with some example problems. All these results have been generated with a commercial simulation package, HYSYS (HYSYS is a registered trademark of Aspen Technology Inc.), for solving mass and the energy balances. The Peng-Robinson equation of state is used for the calculations.16 6.1. Nitrogen Cooling. It is required to cool a 1000 kmol/h nitrogen gas stream at 2850 kPa from 30 to -145 °C with nitrogen gas as the refrigerant using the multistage refrigeration process shown in Figure 10. The shaftwork targets for three different cases are shown in Figure 11. The cumulative shaftwork is plotted as a function of heat load along with the GCC. The intermediate cooling temperatures are plotted on the secondary axis. The y-axis shows the total amount of shaftwork required to achieve the desired cooling, which can be seen using either the heat load or the cooling temperatures. In the first case, the curve with the dotted line at the bottom of the figure shows the results for the reversible conditions, i.e., 100% isentropic efficiency, zero ∆Tmin, and isothermal compression. The simulation results based on the isothermal compression and isentropic expansion are shown by the dashed line whereas the exergy change for the process stream calculated by eq 4 is shown by the crosses. There is a very good agreement between both data sets which signifies that there are no significant exergy losses associated with the flow sheet. In the last two cases, the isentropic efficiency of the compressor and expanders is reduced to 80% and the ∆Tmin is increased to 4 °C. The results are plotted for two different values

Figure 10. Flow diagram for the nitrogen cooling process.

of pressure ratio φ: 2.53 (four stages) and 1.75 (seven stages). Apparently, there is an increase in shaftwork with the pressure ratio; however, the increase is marginal, i.e., 5%. The insensitivity of the shaftwork targets to the pressure ratio is explained in the next section. 6.2. Effect of ∆ Tmin and O on Shaftwork Targets. The pressure ratio, φ, is a very important parameter in the synthesis and optimization of gas-phase refrigeration systems. Shaftwork targets are sensitive to the pressure ratio; the larger the pressure ratio, the higher the heat of compression, the higher the exergy losses, and hence the higher the shaftwork requirements. On the other hand, a higher pressure ratio results in a lower number of refrigeration stages. Therefore, the pressure ratio governs the shaftwork targets (operating cost) as well as the capital cost. It also affects the match between the cold composite curve and the hot composite, depending upon the shape of the process hot composite curve. When the pressure ratio required from the compressor is higher than what a single stage can produce, multistage compression is used. Moreover, in practice the pressure ratio is also limited by the temperature of the outgoing gas, which is generally kept below 150 °C. In the case of temperatures higher than this limit, multistage compression with interstage cooling is employed. In Figure 12 three cases with different overall pressure ratios have been considered. In each case multistage compression is used while maintaining nearly the same pressure ratio across each compressor stage. In the first case four compression stages are used, in the second case three stages, and in the third case two compression stages. After each compression stage, the refrigerant gas is cooled to 30 °C. The results are plotted for zero ∆Tmin, which eliminates the exergy losses associated with the heat transfer. It can be seen that the shaftwork requirements for all three cases do not differ significantly despite having a different number of refrigeration stages. This is a very useful result as the flow sheet could be designed for a higher pressure ratio and with fewer refrigeration stages. This will lead to the reduction in the capital cost while keeping the operating cost almost the same. However, there lies a disadvantage of carrying out refrigeration with fewer stages, as sometimes a small temperature difference across a single stage is desirable for matching the composite curves in the liquefaction region. This will be explained in more detail in the LNG case. When the above results are reproduced without using the interstage cooling, the shaftwork targets changes significantly with the pressure ratio as shown in Figure 13. Here, nitrogen at 2850 kPa is cooled from ambient to below -140 °C, using nitrogen gas also as the refrigerant. In this case, perfect heat exchange is assumed, i.e., ∆Tmin ) 0 °C. Since different pressure ratios have been used for a fixed value of ∆Tmin, the final cooling temperatures are different. Therefore, for a certain value of heat

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Figure 11. Shaftwork targets for nitrogen cooling from 30 to -145 °C. Case 1: φ ) 1.75, ∆Tmin ) 0 °C, ηisen ) 1.0. Case 2: φ ) 2.53, ∆Tmin ) 4 °C, ηisen ) 0.8. Case 3: φ ) 1.75, ∆Tmin ) 4 °C, ηisen ) 0.8.

Figure 14. Effect of φ on shaftwork targets for nitrogen cooling with ∆Tmin ) 4 °C, ηisen ) 0.8, and no interstage cooling.

Figure 15. Effect of ∆Tmin on shaftwork targets. Figure 12. Effect of interstage cooling on shaftwork targets with ∆Tmin ) 0 °C and ηisen ) 0.8. Case 1: φ ) 3.33 (overall), φ ) 1.35 (compression stages). Case 2: φ ) 2.35 (overall), φ ) 1.329 (compression stages). Case 3: φ ) 1.744 (overall), φ ) 1.321 (compression stages).

Figure 13. Effect of φ on shaftwork targets for nitrogen cooling with ∆Tmin ) 0 °C, ηisen ) 0.8, and no interstage cooling.

load, for example, 1600 kW, shaftwork requirements can be considered. It can be observed that the shaftwork requirement increases by 10.71% and 23.5% when the pressure ratio is increased from 1.744 to 2.35 and 3.33, respectively. This is expected and is due to the increased conversion of shaftwork to heat during the recompression of refrigerant in each loop at the higher pressure ratio. The results shown in Figure 13 are reproduced for ∆Tmin ) 4 °C, as shown in Figure 14. To compare these results with the previous case, the coldest loop for φ ) 2.35 has been neglected. Again, observing the shaftwork targets for Q ) 1600 kW, it can be seen that the shaftwork targets are not very sensitive to the pressure ratio as the change in the shaftwork is only 3.7% and 12.9%. This is because as ∆Tmin increases, the overlap of the temperatures between the stages increases and with more stages (low φ case) the total overlap is greater. Hence, the

shaftwork becomes relatively insensitive to the pressure ratio. If the ∆Tmin is decreased to 1 °C for φ ) 2.35, the shaftwork requirement curve would be almost identical to the curve for φ ) 1.744 and ∆Tmin ) 4 °C in Figure 14. This can be better explained with Figure 15. Here, the y-axis refers to the increase in the shaftwork requirements with the increase in the ∆Tmin from 0 to 5 °C with reference to the targets based on the zero ∆Tmin, W0. As the pressure ratio decreases or the number of refrigeration stages increases, the shaftwork requirement increases with the ∆Tmin. This fact reinforces the argument made earlier that as the number of stages increases, the overlap of the temperatures increases due to the imposed ∆Tmin. In other words, the loss in the shaftwork is greater for φ ) 1.744 (7 stages) compared to φ ) 3.33 (3 stages). This insensitivity to pressure ratio is very interesting as it allows the capital cost of the two most important parts of the system, the number of expanders and the heat exchange network, to be optimized. The cost of the heat exchangers will be directly related to 1/∆Tmin, while the number of expanders is related to 1/(φ -1). 6.3. Natural Gas Liquefaction. A 1000 kmol/h natural gas stream at 5500 kPa consisting of 96.929 mol % methane, 2.938 mol % ethane, 0.059 mol % propane, 0.01 mol % n-butane, and 0.064 mol % nitrogen is to be liquefied by cooling it from ambient temperature to -145 °C. Foglietta1 proposed a dual independent expander refrigeration system to liquefy natural gas using the feed gas to provide cooling to an intermediate temperature level and then nitrogen refrigerant to subcool the liquefied gas. The flow diagram for this process is shown in Figure 16. The partition temperature between these two independent cycles provides an extra degree of freedom. The shaftwork targets for two different cases are shown in Figure 17. In the

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Figure 16. Flow diagram for the dual expander refrigeration process for LNG.

Figure 17. Grand composite curve and shaftwork targets for LNG. 3-3 system: φ ) 2.198 (NG cycles), φ ) 1.721 (N2 cycles). 4-3 system: φ ) 1.829 (NG cycles), φ ) 1.74 (N2 cycles).

first case, a 3-3 system, three natural gas cycles and three nitrogen cycles are used, whereas in the second case, a 4-3 system, four natural gas cycles and three nitrogen cycles are used. The cumulative shaftwork target for the dual gas-phase refrigeration system is 6.1 kW‚h/kmol LNG, which is about 7% greater than a single mixed refrigerant process which requires 5.7 kW‚h/kmol for the same feed and equipment constraints.17 As found in the nitrogen case study, the targets are quite insensitive to pressure ratio, with a decrease in the number of stages from 7 (4-3 system) to 6 (3-3 system), resulting in an increase in the net shaftwork target of just 1.2%. In the natural gas case, the coldest stage with the feed gas refrigerant provides most of the condensation of the process stream. This stage is the most difficult for matching the ∆Tmin in the refrigerant/process heat exchanger. In the 3-3 system, the condensation occurs in the third refrigeration stage. The composite curves for this stage are shown in Figure 18. There is some degree of pinching near the colder end of the system. The variations in specific heat are significant as the gas approaches its dew point, so much so that although there were flow corrections to account for this, pinching is still occurring between these points, internal to the heat exchangers. This can be improved if a lower pressure ratio is used, as shown in Figure 19. In the case of the 4-3 system, the liquefaction occurs in the fourth stage as shown in Figure 19. Here there is no possibility of pinching within the exchanger. So in this case a higher

Figure 18. Composite curves for the third stage of the 3-3 system.

Figure 19. Composite curves for the fourth stage of the 4-3 system.

number of refrigeration stages are preferred to improve the thermal efficiency of the system. 6.4. Subambient Heating of N2 Gas Stream. Shaftwork can be recovered from a cold process which requires subambient heating using the shaftwork recovery loop discussed in section 3. The power recovery process is demonstrated for a single cold nitrogen stream with a flow rate of 1000 kmol/h which is to be reheated from -115 to 30 °C using three power recovery loops. Figure 20 shows the GCC for this single-stream problem. In the first case perfect equipment, i.e., 100% isentropic compression and expansion, is used. The compression is performed isothermally at 30 °C and the ∆Tmin is set to 0 °C, i.e., infinite heat exchange area. The simulation results based on the isothermal compression are shown by solid triangular

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Figure 20. GCC and incremental shaftwork recovery curves for N2 heating from -115 to 30 °C using three shaftwork recovery loops.

points whereas the exergy change for the process stream is shown by the dashed line. The agreement between the two is very good. In other words, the flow sheet configuration is near optimal. In the second case the equipment efficiencies are reduced to 80%, the compression is adiabatic, and the ∆Tmin is 4 °C. The incremental shaftwork curve (T0 ) 30 °C) is shown in Figure 20. Compared with the theoretical curve, only a small fraction of the shaftwork is recovered, with no net benefit in the second loop and losses due to reduced equipment efficiencies in the warmest loop. If waste heat is available to boost the gas temperature prior to expansion, leading to a temperature of 130 °C on the exit of the expander, significantly greater shaftwork can be recovered. 7. Conclusions and Future Work Gas-phase refrigeration is a very flexible form of refrigeration, which can achieve a wide range of cooling using a single working fluid. In the case of the liquefaction of LNG, a dual gas-phase system can achieve net shaftwork requirements which are only slightly higher than single mixed refrigerant (SMR) systems, but without the complications of careful matching of refrigerant against the feed composition. They also exhibit an interesting insensitivity to the compression ratio, which can be exploited in the economic optimization of the process. This issue will be addressed in the future. Gas-phase systems can also be used in a heat engine process to exploit any surplus cold streams. However, this study has shown that unless equipment efficiencies are very high (greater than 90%), these cold sinks should be first employed to reduce the refrigeration requirement by direct heat exchange, rather than the recovery of shaftwork. However, if there is no net refrigeration requirement, energy from cold sinks can be recovered using gas-phase systems, but the amount of shaftwork recovered is also dependent on the temperature of the waste heat available to boost the temperature prior to expansion.

Nomenclature Roman Symbols B ) virial coefficient C ) cooler CP ) molar specific heat [kJ kmol-1 °C-1] E ) expander H ) heater H ) auto refrigeration heat exchanger h ) molar enthalpy [kJ kmol-1] K ) compressor P ) pressure [Pa] P0 ) initial pressure at the expander inlet [Pa] P1 ) pressure at the expander outlet [Pa] Q ) heat exchanger duty [kJ h-1] R ) gas constant [m3 Pa mol-1 K-1] S ) molar entropy [kJ kmol-1 °C-1] T ) temperature [°C] T0 ) ambient temperature [°C] V ) molar volume [m3 kmol-1] Win ) work supplied to compressor [kW] Wout ) work recovered from expander [kW] X ) process heat exchanger Y ) auto refrigeration heat exchanger in the shaftwork recovery loop Z ) compressibility factor Greek Symbols ∆Ex ) molar exergy change [kJ kmol-1] ∆h ) molar enthalpy change [kJ kmol-1] ∆m ) supplementary refrigerant flow rate [kmol h-1] ∆S ) molar entropy change [kJ kmol-1 °C -1] φ ) pressure ratio () P0/P1) ηc ) Carnot factor ηisen ) isentropic efficiency Ω ) energy level or ratio of exergy to energy

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Superscripts / ) shifted temperature Subscripts i ) signifies refrigeration stages j ) signifies the number for decomposed auto refrigeration exchanger AbbreViations CC ) composite curve ECC ) exergy composite curve EGCC ) exergy grand composite curve GCC ) grand composite curve HEN ) heat exchanger network LNG ) liquefied natural gas Literature Cited (1) Foglietta, J. H. Consider Dual Independent Expander Refrigeration for LNG Production. Hydrocarbon Process. 2004, 83, 39. (2) Shukri, T. LNG Technology Selection. Hydrocarbon Eng. 2004, 9 (2), 71-76. (3) Swenson, L. K. Single Mixed Refrigerant, Closed Loop Process for Liquefying Natural Gas. U.S. Patent, 4,033,735, 1997. (4) Houser, C.; Krusen, L. The Phillips Optimized Cascade Process. Presented at GASTECH 1996, Vienna, Austria, December 3-6, 1996. (5) Diaz, M. S.; Serrani, A.; Bandoni, J. A.; Brignole, E. A. Automatic Design and Optimization of Natural Gas Plants. Ind. Eng. Chem. Res. 1997, 36, 2715. (6) Linnhoff, B.; Dhole, V. R. Shaftwork Targets for Low-Temperature Process Design. Chem. Eng. Sci. 1992, 47, 2081. (7) Feng, X.; Zhu, X. X. Combining Pinch and Exergy Analysis for Process Modifications. Appl. Therm. Eng. 1997, 17, 249.

(8) Shelton, M. R.; Grossmann, I. E. Optimal Synthesis of Integrated Refrigeration Systems. I: Mixed-integer Programming Model. Comput. Chem. Eng. 1986, 10, 445. (9) Colmenares, T. R.; Seider, W. D. Synthesis of Cascade Refrigeration Systems Integrated with Chemical Process. Comput. Chem. Eng. 1989, 13, 247. (10) Vaidyaraman, S.; Maranas, C. D. Optimal Synthesis of Refrigeration Cycles and Selection of Refrigerants. AIChE J. 1999, 45, 997. (11) Li, H. Q.; Chen, Z. H.; Li, B. H.; Yao, P. J. A Combined Approach for the Overall Energy Integration and Optimal Synthesis of LowTemperature Process Systems. Proc. ESCAPE-11 2001, 1035. (12) Lee, G. C.; Smith, R.; Zhu, X. X. Optimal Synthesis of MixedRefrigerant Systems for Low-Temperature Processes. Ind. Eng. Chem. Res. 2002, 41, 5016. (13) Konukman, A. E. S.; Akman, U. Flexibility and Operability Analysis of a HEN-integrated Natural Gas Expander Plant. Chem. Eng. Sci. 2005, 60, 7057. (14) Hoadley, A. F. A.; Remeljej, C. W. Energy Targeting of AutoRefrigeration Processes with Reference to LNG Production. Chem. Eng. Trans. 2005, 7, 79. (15) McCarthy, A.; Hoadley, A. F. A. A Shaftwork Targeting Method for Gas Phase Refrigeration. Presented at Chemeca 2005, Brisbane, Australia, September 25-28, 2005. (16) Peng, D. Y.; Robinson, D. B. A New Two-Constant Equation of State. Ind. Eng. Chem. Res. 1976, 15, 59. (17) Remeljej, C. W.; Hoadley, A. F. A. An Exergy Analysis of SmallScale Liquefied Natural Gas (LNG) Liquefaction Processes. Energy 2006, 31 (12), 2005.

ReceiVed for reView July 5, 2006 ReVised manuscript receiVed March 5, 2007 Accepted March 23, 2007 IE060868J