Improving the Heat Integration of Distillation Columns in a Cryogenic

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Improving the Heat Integration of Distillation Columns in a Cryogenic Air Separation Unit L. V. Van der Ham*,† and S. Kjelstrup†,‡ † ‡

Department of Chemistry, Norwegian University of Science and Technology, 7491 Trondheim, Norway Department of Process and Energy, Delft University of Technology, 2628CA Delft, The Netherlands. ABSTRACT: The distillation columns of a two-column cryogenic air separation unit (ASU) are responsible for a considerable part of the total ASU inefficiencies. The efficiency of a conventional distillation column can be increased by distributing the reboiler and condenser duties over a larger part of its length. In an ASU, this can be realized by moving the low-pressure column (LPC) down along the high-pressure column (HPC), thus increasing the number of heat-integrated stages (HI stages). We present an assessment of the effect that such an intensification of the heat integration has on the performance of the ASU distillation section, using the entropy production as performance criterion. When keeping the operating pressures fixed, the entropy production in the LPC is replaced by entropy production in the HI stages, without affecting the total entropy production. Reducing the pressure ratio enables a reduction in the LPC entropy production without increasing the contribution of the HI stages. For a probable value of the heattransfer capacity per stage, increasing the pressure in the LPC results in a decrease of 21% in the total entropy production, while decreasing the pressure in the HPC results in a decrease of 23%. Decreasing the pressure in the HPC when using an opportunistic heat-transfer capacity yields a decrease of 31%. The reductions in entropy production materialize eventually as changes in the required ASU compressor, pump, and expander duties. Compared to the addition of either an additional heat exchanger or an additional distillation column, the use of HI stages seems to be the most promising method for improving the thermodynamic performance of a cryogenic ASU. More-detailed experimental data are required to simulate heat-integrated distillation columns accurately.

1. INTRODUCTION The use of an Integrated Gasification Combined Cycle (IGCC) with precombustion CO2 capture is one of the main candidates for carbon capture and storage on an industrial scale. In an IGCC, purified oxygen is required in the gasification step and purified nitrogen is used as diluent in the gas turbine. In case of a coal-based IGCC, additional nitrogen is required to transport coal into the gasifier.1 The purified oxygen and nitrogen are usually obtained using cryogenic distillation of air.2,3 1.1. Cryogenic Air Separation. A cryogenic air separation unit (ASU) consists of four main process sections: a feed purification and pressurization section, a main heat exchanger (MHX), a distillation section, and a product pressurization section. Figure 1 shows the process flowsheet of a two-column ASU design, which has been described in more detail elsewhere.4 It was revealed using exergy analysis that most of the process inefficiencies are located in the feed pretreatment and the distillation sections. A large exergy loss is related to the use of cooling water during feed pressurization. The most important destruction of exergy occurs in the distillation columns.4 The current work focuses on reducing the irreversibilities in the distillation section of an ASU. The distillation section of a cryogenic ASU usually contains two distillation columns equipped with structured packing. By operating them at different pressures and by positioning the lowpressure column (LPC) on top of the high-pressure column (HPC), it is possible to use a single heat exchanger that is functioning as a reboiler for the LPC and as a condenser for the HPC. The majority of the pretreated feed air enters the HPC, r 2011 American Chemical Society

which removes some of the nitrogen as high-purity liquid (HP N2) and vapor (MP N2) streams. The remaining mixture is subcooled using the LPC top-product, depressurized using throttle valves, and fed into the LPC. The LPC produces the oxygen product (O2) and a low-purity nitrogen stream (LP N2). 1.2. Distillation Columns with Distributed Heat Duties. In a two-column ASU design, the heat integration between the distillation columns is concentrated at a single point; the reboiler condenser. However, from a thermodynamic point of view, it can be favorable to distribute the thermal energy transfer over a larger part of the column length (see, for example, the work of Nakaiwa and Ohmori5). The two most common types of distillation columns that involve thermal energy transfer along their entire lengths are diabatic distillation columns and heat-integrated distillation columns (HIDiCs). 1.2.1. Diabatic Distillation Columns. A diabatic distillation column is characterized by the presence of heat exchangers along its entire length. The heat exchangers in the rectifying section of the column are all removing thermal energy and together replace the condenser; the heat exchangers in the stripping section are all adding thermal energy and replace the reboiler. In the ideal limit, all heat exchangers operate independently, enabling full control over the temperature profile inside the column. However, it is not straightforward to implement completely independent heat Received: February 25, 2011 Accepted: June 9, 2011 Revised: June 2, 2011 Published: June 09, 2011 9324

dx.doi.org/10.1021/ie200383s | Ind. Eng. Chem. Res. 2011, 50, 9324–9338

Industrial & Engineering Chemistry Research

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Figure 2. Schematic of the original type of heat integration in a HIDiC (left) and the type suggested by Røsjorde14 (right).

Figure 1. Schematic of a two-column ASU design.

exchangers in practice, because it requires the availability of thermal energy at many different temperatures. A practical way to limit the number of required temperature levels is to connect several heat exchangers to each other and operate them in series, yielding sequential heat exchangers; but this removes some of the control over the temperature profile. By varying the heat-transfer area per heat exchanger, it is still possible to control the temperature profile to some extent. Various theoretical studies have investigated the optimal distribution of heat duties over the length of an ideal diabatic distillation column.611 It was found that the most important heat exchangers are those close to the top and the bottom of the column and, in some cases, those close to the feed location. 1.2.2. Heat-Integrated Distillation Columns. A heat-integrated distillation column (HIDiC) can be regarded as a conventional distillation column that is split into two at its feed location. Heat integration is realized by positioning the two parts next to each other and operating them at different pressures. The original top (or rectifying) section of the column is operated at a higher pressure than the original bottom (or stripping) section, since the rectifying section requires the removal of thermal energy and the stripping section requires the addition of thermal energy. Transferring thermal energy along the length of the integrated column decreases the required reboiler and condenser duties. However, to sustain a pressure difference between the two column parts, a compressor and a throttle valve are needed. It is the net effect of the added compressor duty and the decreased reboiler and condenser duties that determines the thermodynamic feasibility of a HIDiC. When the rectifying and stripping sections of a HIDiC contain equal numbers of stages, both their tops and bottoms are typically positioned next to each other. When the sections contain unequal numbers of stages, it is no longer possible to realize heat integration between all stages. Theoretical investigations by de Rijke12 assessed the performance of three different separation cases that have unequal numbers of stages in their rectifying and stripping sections. For each of the cases, he compared two possible column

configurations: one with the two columns aligned at the top and one with the two columns aligned at the bottom. The best configurations were those where the top and bottom of the original column were positioned closest to each other. De Rijke also compared the performance of HIDiCs with a uniform heat distribution with the performance of HIDiCs with a uniform distribution of the heat-transfer area. He found that the a uniform distribution of heat-transfer area yields the best HIDiC design. A similar conclusion was reached by Suphanit.13 Røsjorde14 conducted an optimization study where a total amount of heat-transfer area could be freely distributed over the entire length of a HIDiC. He found that the area should preferably be located around the top and the bottom of the integrated column. As an interesting alternative to a HIDiC with heat integration between all stages, he suggested a HIDiC with integration between the top and bottom stage of the original column only. Both the original and suggested types of heat integration are schematically shown in Figure 2. 1.2.3. Distributing Heat Duties in an ASU Distillation Section. Instead of inventing a completely new process flowsheet for the separation of air based on the use of either diabatic distillation columns or HIDiCs, it is also possible to try to incorporate some of their characteristics into an existing cryogenic ASU design. The design of a two-column ASU shows the closest resemblance with a HIDiC, especially with the alternative suggested by Røsjorde.14 Both a two-column ASU and a HIDiC consist of two heat-integrated columns that are operating at different pressure levels. The main difference between the two is that a twocolumn ASU contains two columns that operate in series, whereas a HIDiC is a single column that is split into two. A HIDiC with heat integration between all stages and the HIDiC suggested by Røsjorde can be regarded as two extremes. In the current work, we investigate the set of column configurations between those extremes. That is, we assess the effect of intensifying the heat integration between the two columns of an ASU by gradually moving down the LPC along the HPC. The current work is a combination and extension of two preliminary studies that have been submitted as conference contributions.15,16 1.3. Evaluating ASU distillation section efficiency. As explained elsewhere,4 the thermodynamic efficiency of an ASU distillation section must be evaluated based on the second law of thermodynamics. This means that a quantity such as the amount of exergy destruction or the amount of entropy production should 9325

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coefficient, the vapor density, and the maximum vapor flow rate. More details can be found in sectionA.3 in the Appendix. The heat exchanger that is functioning as a reboilercondenser is modeled as an additional equilibrium stage, present in both the HPC and the LPC. When moving down the LPC along the HPC, the heat exchanger functions as a condenser for the HPC and as an intermediate heat exchanger for the LPC. This ensures the availability of a liquid nitrogen product. It is assumed that the distillation columns and heat exchangers operate at constant pressures, and that there is no loss of lowtemperature thermal energy to the surroundings.

Figure 3. Schematic of the ASU distillation section. The vertical positions of the two columns are inverted compared to reality.

be used as basis. Because there is no energy input or output within the distillation section of an ASU (except for thermal losses), using amounts of energy is meaningless. Therefore, an evaluation criterion based on the first law of thermodynamics is not suitable. 1.4. Aim of the Work. The aim of this study is to assess how intensification of the heat integration between distillation columns of a two-column ASU affects its distillation section performance, using the total entropy production as performance criterion. A possible performance improvement will materialize as a quality decrease of the feed streams, and/or a quality increase of the product streams. For a cryogenic ASU, a higher quality corresponds to a lower temperature, a higher pressure, more liquid phase, and higher purities; a lower quality corresponds to a higher temperature, a lower pressure, more vapor phase, and purities close to the air composition. The lowest-possible quality corresponds to atmospheric conditions.

2. MODEL DESCRIPTION A detailed description of the model is given in Appendix A; the main properties are repeated here for the sake of convenience. The thermodynamic properties required to model the distillation section are calculated using a reference equation of state by Lemmon et al.,17 assuming a binary mixture of nitrogen and oxygen. The feed air has a nitrogen mole fraction of 0.79. Figure 3 shows a schematic representation of the distillation section of a cryogenic ASU, with numbered process streams. The vertical positions of the two distillation columns are inverted in the schematic. The distillation columns are modeled using theoretical equilibrium stages. Moving down the LPC along the HPC is modeled by increasing the number of heat-integrated stages (HI stages) that is used. The heat duty of an HI stage is calculated using the temperature difference between the stages in the two columns and using the heat-transfer capacity per stage. Two values for the heat-transfer capacity will be used in this work; a probable value and a opportunistic value. They are based on assumptions concerning the column diameter, the type of structured packing that is used, the overall heat-transfer

3. CALCULATIONS The calculations have been performed using Matlab. A detailed solution procedures for the flowsheet and the process units can be found in Appendix B; the main aspects are repeated here for the sake of convenience. The flowsheet shown in Figure 3 is solved by iteration over the heat duties of the reboiler condenser and the HI stages, and over the low-purity nitrogen product (stream 17). The liquid air feed into the HPC (stream 2) is used to control the oxygen recovery rate, and the total air flow rate is fixed at 1.0 mol/s. Streams 7 and 8 are used to minimize the entropy production in the distillation section. For the base case design described in section 4.1, both the flow rates are optimized. The found optimal value for stream 8 is used for all other cases that are studied in this work. The flow rate of stream 7 is reoptimized for all combinations of operating pressures, based on a configuration with the reboilercondenser as only HI-stage. The performance of all column configurations is evaluated using the total entropy production (dS/dt). This quantity can be calculated using the entropy balance over the system. Using the stream numbering in Figure 3, this results into dS ¼ F5 S5 + F6 S6 + F16 S16 + F19 S19 F2 S2 F3 S3 F4 S4 dt ð1Þ The total entropy production is directly proportional to the total exergy destruction, with the ambient temperature of T0 = 298.15 K being the proportionality factor.

4. CASE DESCRIPTIONS 4.1. Base Case Design. The base case design that is used in the current work is derived from the state-of-the-art two-column ASU design shown in Figure 1 and described in more detail by Van der Ham and Kjelstrup.4 Most design characteristics are directly copied from this original design to the base case design that is used in this work. A few simplifications have been made in order to facilitate the calculations. 4.1.1. Distillation Columns. The HPC is operating at 4.8 bar and contains 51 stages, including a condenser. A 0.5 K subcooled liquid feed enters the HPC at stage 42, counting from top to bottom. The bottom stage is fed with a 27.0 K superheated vapor feed. A high-purity gaseous nitrogen product is withdrawn from the vapor that is entering the condenser. A part of the condensate is withdrawn as high-purity liquid nitrogen product. Both product streams have exactly the same composition. In addition to the liquid bottom stream, liquid is withdrawn from the column at stages 11 and 42. These three streams are fed to the LPC. 9326



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Table 1. Overview of the Studied Cases case 1

case 2

case 3

case 4

case 5

HI stages

no

yes

yes

yes

yes

fixed low pressure

yes

yes

no

yes

yes

fixed high pressure

yes

yes

yes

no

no

17

17

17

44

UAa a

See section A.3 in Appendix A for more details on the values of UA.

The LPC is operating at 1.3 bar and contains 56 stages, including the reboiler. An 11.7 K superheated vapor feed enters the column at stage 25, again counting from top to bottom. The three streams originating from the HPC are partially vaporized upon passing the throttle valves. Their liquid parts enter the column at stages 1, 16, and 28; their vapor parts enter the column at stages 1, 15, and 27. A low-purity gaseous nitrogen product is withdrawn from the top of the column, and a liquid oxygen product is withdrawn from the reboiler. 4.1.2. Subcoolers. The minimum temperature difference in both subcoolers amounts to 2.5 K. 4.1.3. Product and Process Specifications. The original design is defined by two product specifications: an oxygen mole fraction of 0.95 in the oxygen product, and a ratio of 3.20 between the molar flow rates of the oxygen and the high-purity liquid nitrogen products. In addition, the nitrogen fraction of the high-purity nitrogen products is required to be at least 0.999; however, this was never a limiting specification. The molar flow rate of the vapor feed to the LPC always amounts to 1.5% of the total feed flow rate. The oxygen recovery was found to amount to 96% in the original design; this value is used as specification for the base case design used in this work, as well as for all other configuration variations. 4.1.4. Model Simplifications. Compared to the original design used in Van der Ham and Kjelstrup,4 three simplifications have been made. First, it is assumed that the process streams contain two components only: nitrogen and oxygen. In the original design, argon was also included as a mixture component. The second simplification used in this work is the assumption that the distillation columns and heat exchangers operate at constant pressures. In the original design, the pressure drop in the distillation columns amounts to ∼1 mbar per theoretical equilibrium stage. In the subcoolers, it is ∼50 mbar for the vapor stream and ∼100 mbar for the liquid streams. The third simplification is the assumption that no low-temperature thermal energy is lost to the surroundings. The original design included energy losses from the distillation columns and the heat exchangers. The effect of these simplifications is the same for all process configurations studied in this work. Therefore, they do not have any influence on a comparison between the different configurations. 4.2. Adjusting Operating Pressures. While moving down the LPC along the HPC, the condenser of the HPC is moving up along the LPC. This causes the temperature difference in this heat exchanger to increase, resulting in a lower amount of required heattransfer area. Instead of increasing the temperature difference and reducing the amount of heat-transfer area, it is also possible to keep the temperature difference at its base case value by decreasing the ratio of the column operating pressures. This can be done by either lowering the pressure in the HPC, or by increasing the pressure in the LPC. The effect of both strategies on the distillation section performance is investigated in the current study.

Figure 4. Overview of the change in entropy production and its distribution over the process units for an increasing number of HI stages and fixed operating pressures.

4.3. Case Overview. Five different cases are studied in this work. The first case is the base case, described in section 4.1; it does not involve any HI stages. The other four cases are all based on the base case, but they do include HI stages. They differ from each other in the operating pressures and the heat-transfer capacity that are used. The second case uses the same operating pressure as the base case. In the third, the pressure in the LPC is allowed to increase, while in the fourth and fifth cases, the pressure in the HPC is allowed to decrease. Cases 2, 3, and 4 all use the probable heat-transfer capacity described in section A.3 in Appendix A. The fifth case uses the opportunistic heat-transfer capacity. The case details are summarized in Table 1.

5. RESULTS 5.1. Base Case Characteristics. The base case design is defined by the process characteristics described in section 4.1. The resulting properties of all process streams are listed in Table C1 in Appendix C. The total entropy production in the distillation section amounts to 3.94 J/(K s) per mole feed. In Appendix C, it is shown how the total entropy production of the base case is distributed over the main components of the distillation section, along with a comparison with the values calculated for the original process design used in Van der Ham and Kjelstrup.4 5.2. Fixed Pressures. Figure 4 shows how the entropy production in the distillation section changes when the number of HI stages is increased, while keeping the operating pressures fixed. The most important changes in the entropy production are a large decrease in the LPC contribution and a large increase in the contribution of the heat integration between the two columns. The entropy production in the HPC decreases slightly, while the contributions of the subcoolers and the throttle valves remain unchanged. It is interesting to notice that there is practically no change in the total entropy production. The entropy production due to the heat integration is related to thermal energy transfer only, whereas in the distillation columns, it is caused by both mass and energy transfer. By increasing the number of HI stages, it is possible to shift the entropy production from the distillation columns to the HI stages. Or, in 9327



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Figure 5. Temperature profile change in the stripping section of the low-pressure column, for an increasing number of HI stages and fixed operating pressures.

Figure 6. Overview of the change in heat duties for the reboiler condenser (QRC), the HI stages (QHI), their sum (Qtot), and the reboilercondenser temperature difference (ΔTRC) for an increasing number of HI stages and fixed operating pressures.

other words, it is possible to replace the entropy production due to mass transfer by entropy production due to thermal energy transfer. Sections 5.2.1 and 5.2.2 explain in more detail why the entropy production in the LPC and due to heat integration are changing. Similar to the total entropy production, there is practically no change in the properties of the process streams; they are the same as the stream properties listed in Table C1 in Appendix C for the base case. The only exception is the distribution of the total heat duty over the reboilercondenser and the other HI stages, which is treated in more detail in section 5.2.2. 5.2.1. LPC Stripping Section. The maximum decrease in entropy production in the LPC amounts to 1.61 J/(K s), which is 41% of the total entropy production. To understand better why the entropy production in the LPC decreases, we must look in more detail at its stripping section, which is the heat-integrated part of the column. Figure 5 shows how the temperature profile in this part of the column changes when the number of HI stages increases. The right-most profile belongs to the configuration with a single HI stage (being the reboilercondenser), this is the base case design. Going from the right to the left, more and more HI stages are added. All profiles have the same top and bottom temperatures. In the base case, the major part of the total temperature change is located in a few bottom stages. The other stages in the stripping section are relatively ineffective. When increasing the number of HI stages, the reboilercondenser moves up along the LPC. This causes the large temperature change to shift up along the column as well. Contrary to the stages at the top of the stripping section, the HI stages below the reboilercondenser do contribute to the total temperature change. This causes the temperature change above the reboiler condenser to become smaller. For the leftmost profile, the temperature change above the reboilercondenser has almost completely disappeared; the HI stages account for almost the entire temperature change. The temperature profiles shown correspond to the composition profiles, because an equilibrium stage model is used to simulate the distillation columns. Therefore, a large change in

temperature corresponds to a large change in composition, which means that a relatively large amount of mass has been transferred. When we compare the profiles of the configurations with 1 and with 24 HI stages, we see that adding HI stages causes the total temperature and composition changes to be distributed much more evenly over the entire stripping section. The entropy production is a function of the mass and thermal energy fluxes. Therefore, a more-even distribution of the mass and energy transfer corresponds to a more-even distribution of the entropy production. Studies on the state of minimal entropy production in a process unit have shown that an optimal process unit design is related to an even distribution of the entropy production, which is also known as equipartition of entropy production.18,19 Van der Ham et al.20 have suggested that the coefficient of variation of an entropy production profile be used as criterion for the degree of equipartition. A high coefficient of variation is related to a low degree of equipartition and perfect equipartition corresponds to a coefficient of variation equal to zero. Using this criterion, it can be calculated that the degree of equipartition decreasses from a value of 2.48 for the base case to a value of 0.74 for the configuration with 24 HI stages. This indicates a substantial increase in the degree of equipartition. 5.2.2. Heat Integration. The increase in entropy production due to heat integration can be understood better by looking at changes in the heat duties and the temperature difference in the reboilercondenser; they are shown in Figure 6. Figure 6 shows that, by increasing the number of HI stages, the heat duty of the reboilercondenser is replaced by the heat duty of the HI stages. However, the total heat duty remains constant. An increase in the number of HI stages also causes an increase of the temperature difference in the reboilercondenser. Thus, overall, the same amount of thermal energy is being transferred, but over a larger temperature difference. This explains the increase in entropy production, since it is given by the product of the heat flux and the difference in the inverse temperature. The heat duty of the reboilercondenser has almost reached a value of zero for the column configuration with 24 HI stages. This is the reason why no more additional HI stages can be added. For configurations with 25 or more HI stages, the reboilercondenser 9328



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Figure 7. Overview of the change in entropy production and its distribution over the process units for an increasing number of HI stages and an increasing low-pressure level (see Figure 8).

Figure 9. Overview of the change in entropy production and its distribution over the process units for an increasing number of HI stages and a decreasing high-pressure level (see Figure 10).

Figure 8. Overview of the change in heat duties for the reboiler condenser (QRC), the HI stages (QHI), their sum (Qtot) for an increasing number of HI stages and an increasing low pressure level (PLPC).

Figure 10. Overview of the change in heat duties for the reboiler condenser (QRC), the HI stages (QHI), and their sum (Qtot) for an increasing number of HI stages and a decreasing high-pressure level (PHPC).

duty would become too low to enable the production of a liquid product from the top of the HPC. The required heat-transfer area in the reboilercondenser is a function of the ratio between its heat duty and temperature difference. Because its heat duty is decreasing and its temperature difference is increasing, the amount of required heat-transfer area decreases rapidly. The configuration with 24 HI stages requires only 2% of the heat-transfer area that is required in the base case. Therefore, the addition of HI stages is accompanied by a substantial decrease in size of the reboiler condenser. 5.3. Increasing the Low Pressure. Figure 7 shows how the entropy production in the distillation section changes when the number of HI stages is increased, while increasing the pressure in the LPC and keeping the temperature difference in the reboiler condenser constant.

The entropy production in all process units decreases as the number of HI stages increases. The maximum total decrease in entropy production occurs for the maximum number of HI stages and amounts to 0.83 J/(K s). This equals a reduction of 21%, compared to the base case. The most important decrease is located in the LPC, which accounts for 77% of the total reduction. The reduction in the LPC is again caused by the fact that relatively ineffective stages in the stripping section are replaced by the more-effective HI stages. The case is the same in the HPC, but to a lower extent. The reduction in entropy production in the subcoolers and throttle valves is related to the decreased pressure ratio. A lower pressure ratio directly affects the entropy production in the throttle valves. It affects the subcoolers by reducing the temperature difference between the inlet streams, which lowers the heat duties. The contribution of the reboilercondenser is decreasing, because the average 9329



Figure 11. Overview of the change in entropy production and its distribution over the process units for an increasing number of HI stages, using an opportunistic heat-transfer capacity, and a decreasing highpressure level (see Figure 12).

temperature difference of the HI stages is below the temperature difference in the reboilercondenser. Figure 8 shows how the heat duties change when the number of HI stages is increased, while increasing the pressure in the LPC and keeping the temperature difference in the reboilercondenser constant. It can be seen that by increasing the number of HI stages, a part of the reboilercondenser heat duty is replaced by the duty of the other HI stages. However, the total duty does not remain constant; it has increased by 3.5% for the configuration with 26 HI stages, relative to the base case. This increase is caused by the fact that operating a distillation column at a higher pressure decreases the composition change per theoretical equilibrium stage. Therefore, more reboiler duty is required in the LPC in order to achieve the same degree of separation, using the same number of theoretical stages. For this case, the maximum number of HI stages is limited by the product specifications. Increasing the number of HI stages above 26 results in a configuration that can no longer satisfy the required specifications; the part of the LPC between its lowest feed stage and the reboilercondenser can no longer perform the required separation task. For the maximum number of HI stages, the low-pressure level increases up to a value of 1.62 bar, resulting in a decrease in the pressure ratio of 20%. The heattransfer area required in the reboilercondenser has decreased by 19%, compared to the base case. 5.4. Decreasing the High Pressure. Figure 9 shows how the entropy production in the distillation section changes when the number of HI stages is increased, while decreasing the pressure in the HPC and keeping the temperature difference in the reboiler condenser constant. The entropy production in all process units decreases as the number of HI stages increases. The maximum total decrease in entropy production occurs again for the maximum number of HI stages. It amounts to 0.93 J/(K s), which equals a reduction of 23%, compared to the base case. The LPC accounts again for 77% of the total reduction. The explanations for the reductions in the various process units are similar to those given in section 5.3.

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Figure 12. Overview of the change in heat duties for the reboiler condenser (QRC), the HI stages (QHI), their sum (Qtot) for an increasing number of HI stages using an opportunistic heat-transfer capacity and a decreasing high-pressure level (PHPC).

Figure 13. HI-stage temperature difference profile for different numbers of HI stages, using an opportunistic heat-transfer capacity and a decreasing high-pressure level.

Figure 10 shows how the heat duties change when the number of HI stages is increased, while decreasing the pressure in the HPC and keeping the temperature difference in the reboiler condenser constant. Increasing the number of HI stages again replaces some of the reboilercondenser heat duty with the duty of the other HI stages. For the current case, the total duty decreases by 2.0% for the configuration with 26 HI stages, relative to the base case. This decrease is caused by the fact that operating a distillation column at a lower pressure increases the composition change per theoretical equilibrium stage. Therefore, less condenser duty is required in the HPC in order to achieve the same degree of separation, using the same number of theoretical stages. The maximum number of HI stages is again limited by product specifications. The high-pressure level decreases to a value of 3.95 bar, resulting in a decrease of 18% in the pressure ratio. The 9330



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Table 2. Comparison between the Five Studied Casesa

NHI

case 1

case 2

case 3

case 4

case 5

1

24

26

26

26

17

17

17

44

UAHI (W/K) PLPC (bar)

1.30

1.30

1.62

1.30

1.30

PHPC (bar)

4.80

4.80

4.80

3.95

3.70

ΔTRC (K)

2.23

10.23

2.23

2.23

2.23

QRC (kW)

a

2.65

0.25

2.14

2.01

1.81

QHI (kW) Qtot (kW)

2.65

2.40 2.65

0.60 2.74

0.59 2.60

0.77 2.57

F2 (mol/s)

0.421

0.421

0.417

0.416

0.415

F6 (mol/s)

0.162

0.162

0.147

0.167

0.164

F7 (mol/s)

0.179

0.179

0.192

0.186

0.195

F19 (mol/s)

0.559

0.560

0.574

0.535

0.527

T19 (K)

95.1

95.1

95.1

92.7

92.0

The case details are explained in more detail in section 4.

heat-transfer area required in the reboilercondenser has decreased by 24%, compared to the base case. 5.5. Opportunistic Heat-Transfer Capacity. Figure 11 shows how the entropy production in the distillation section changes when the number of HI stages is increased, while decreasing the pressure in the HPC and using an opportunistic value for the heat-transfer capacity. The entropy production in all process units decreases as the number of HI stages increases. The maximum total decrease in entropy production occurs again for the maximum number of HI stages. It amounts to 1.23 J/(K s), which equals a reduction of 31%, compared to the base case. The LPC accounts for 75% of the total reduction. The explanations for the reductions in the various process units are similar to those given in section 5.3. Figure 12 shows how the heat duties change when the number of HI stages is increased, while decreasing the pressure in the HPC and using an opportunistic value for the heat-transfer capacity. Increasing the number of HI stages again replaces some of the reboilercondenser heat duty with the duty of the other HI stages. For the current case, the total duty decreases by 2.9% for the configuration with 26 HI stages, relative to the base case. This decrease is again caused by the lower pressure in the HPC. The maximum number of HI stages is again limited by product specifications. The high-pressure level decreases to a value of 3.70 bar, resulting in a decrease in the pressure ratio of 23%. The heat-transfer area required in the reboilercondenser has decreased by 32%, compared to the base case. 5.5.1. HI-Stage Temperature Differences. Figure 13 shows how the temperature difference profile of the HI stages changes when their number is increased, while decreasing the pressure in the HPC and using an opportunistic value for the heat-transfer capacity. The maximum temperature difference always occurs in the reboilercondenser. When using 5 or 10 HI stages, the minimum temperature difference occurs at the bottom of the LPC; however, when adding more HI stages, the minimum is located within the heat-integrated part of the column. The minimum is the lowest for the maximum number of HI stages. Its position is located around the 10th and 11th HI stages. The temperature difference is

Table 3. Comparison between the Total Entropy Production and Its Distribution over the Different Process Units for Five Studied Cases Total Entropy Production (J/(K s)) case 1

case 2

case 3

case 4

case 5

HPC

0.846

0.759

0.802

0.827

0.834

LPC

1.906

0.296

1.269

1.190

0.991

HI stages

0.692

2.400

0.659

0.653

0.588

subcoolers

0.147

0.148

0.118

0.114

0.103

valves total

0.353 3.944

0.353 3.944

0.264 3.112

0.236 3.019

0.204 2.719

0.0%

21.1%

23.5%

31.1%

reduction

always positive, so the temperatures of the two columns are not crossing. Compared to the other cases, the current case has the lowest minimum temperature difference. This is related to the use of the opportunistic heat-transfer capacity. 5.6. Comparison. Table 2 shows a comparison between the most important results of the five cases that have been studied. For the cases that involve HI stages, the results for the maximum number of HI stages are used. When comparing cases 1 and 2, it shows that the addition of HI stages without changing any pressure does not affect any of the feed or product streams. It only affects the properties that are related to heat; the majority of the heat duty is moved from the condenser to the HI stages, the temperature difference in the condenser increases, and the resulting heat-transfer capacity in the condenser is reduced to almost zero. Fixing the temperature difference in the condenser in cases 3, 4, and 5 causes the shift of heat duty to the HI stages to be less profound than that for case 2. The change in the resulting condenser heat-transfer capacity also is much less. However, the changes in pressure that are required to keep the temperature difference constant do cause changes in the feed and product streams. Comparing cases 3 and 4 illustrates the difference between either increasing the pressure in the LPC or decreasing the pressure in the HPC. The heat duty of the HI stages are similar, but the total duty increases for case 3 and decreases for case 4. Both strategies reduce the amount of required liquid feed. In case 3, the amount of low-pressure nitrogen product (F19) increases at the expense of the amount of high-pressure nitrogen product (F6); in case 4, the opposite situation is true. Since the quality of stream F6 is higher, case 4 is more favorable in this respect. Overall, reducing the pressure in the HPC seems to be a better option than increasing the pressure in the LPC. A comparison between cases 4 and 5 shows the effect of an increased HI-stage heat-transfer capacity. Case 5 can be regarded as a more extreme version of case 4; all changes with respect to case 1 are magnified. However, the increase in the changes is smaller than the increase in the heat-transfer capacity. Table 3 shows a comparison between the total entropy production and its distribution over the different process units for the five studied cases. Comparing cases 1 and 2 shows again that the entropy production in the HPC and especially the LPC are substituted with entropy production in the HI stages. Cases 3, 4, and 5 show that fixing the temperature difference in the condenser can 9331



Figure 14. Overview of the configurational change for a case where the number of HI stages is equal to half the total number of stages. The arrows in the right figure represent the thermal energy transfer in the HI stages.

prevent the HI contribution from increasing, while still decreasing the LPC contribution. The reductions in the contributions of the LPC, HI stages, subcoolers, and valves all increase as the total reduction increases. But the reduction in the HPC contribution becomes smaller when the total reduction increases.

6. DISCUSSION 6.1. Model Improvements. The model that is used to simulate the distillation columns and their heat integration is based on several assumptions. Although these assumptions do not affect the comparison between the different cases studied in this work, it is still good to mention the ones that are expected to have the largest influence on the results of a single case. Possible future model improvements should focus on removing those assumptions. 6.1.1. Variable Heat-Transfer Coefficient. The current heatintegration model uses a single constant value for the overall heat-transfer coefficient. This value is used for all HI stages. In reality, the overall heat-transfer coefficient can be expected to depend on various factors, such as the liquid flow rate, the vapor flow rate, and the types of evaporation and condensation processes. The comparison between cases 4 and 5 shows that the value of the overall heat-transfer coefficient does have a considerable influence on the potential performance improvement when using HI stages. Therefore, more-detailed knowledge on the behavior of the overall heat-transfer coefficient is required, both theoretical and experimental. 6.1.2. Rate-Based Distillation Model. The distillation columns are simulated using the assumption that the vapor and liquid streams leaving a theoretical stage are at equilibrium with each other. This equilibrium, in reality, does not occur in a distillation column, especially not when it is equipped with structured packing. Rate-based models are often used to provide for a more accurate representation of distillation columns. (See, for example, the work of Seader and Henly21 for more details on rate-based distillation models.) The current heat-integration model uses the difference between the outlet temperatures of two heat-integrated theoretical stages. Because the temperature difference varies along the length of the heat-integrated columns, the use of theoretical stages

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involves an additional simplification. It forces the continuous temperature difference profile to be represented by a limited number of temperature differences only. Therefore, the accuracy of the heat-integration model would benefit from the use of a rate-based distillation model instead of an equilibrium stage distillation model. 6.1.3. Coupling between Mass and Thermal Energy Fluxes. In the current model, it assumed that the heat integration between the two columns does not affect their separation efficiencies (or, in other words, it is assumed that there is no coupling between mass and thermal energy fluxes). Theoretical studies have shown that the coupling between mass and thermal energy fluxes can have considerable influence on their magnitudes.22,23 Even their directions may change in some cases. The presence of HI stages can be expected to make this coupling effect more profound than in conventional distillation columns, because an additional thermal flux is present in the system. The effect of coupling between mass and thermal energy fluxes should be verified experimentally and included in the model. This will enable more-accurate predictions of the separation efficiency per column height. 6.2. Further Optimization of the Heat-Transfer Capacity. An increase in the heat-transfer capacity has a positive effect on the performance improvement that HI stages have. The opportunistic heat-transfer capacity calculated in section A.3 in Appendix A can be regarded as a simple first attempt to increase the heat-transfer capacity. There are various options that, in theory, can increase the heat-transfer capacity even further. The first two options are related to the type of structured packing that is used and the operating flow rate. The use of structured packing with a lower efficiency results in an increased theoretical stage height, and, thus, a higher heat-transfer capacity per theoretical stage. Another possibility is to operate the distillation column further below its maximum vapor flow rate. This results into a larger required column cross-section, and thus increases the number of parallel columns that is required for a given feed flow rate. Three more options involve changes to the heat-transfer area. First, the heat-transfer area can be increased by applying surface enhancements. The design described by Horiuchi et al.24 uses, for example, a wire that is wound around the inner column wall. This both increases the heat-transfer area and improves the heattransfer coefficient of the liquid film flowing down along the column wall. Other types of surface enhancements are also possible, such as small fins or engravings. A second way of increasing the effective heat-transfer area is to improve the thermal contact between the structured packing and the column wall and, thus, use the structured packing as a heat-transfer area. Normally, the packing and the wall are in contact via liquid wallwipers. Their number can be increased, or their design can be optimized for heat conduction. The third option to increase the heat-transfer area is to use smaller column diameters. Using smaller column diameters will also allow for thinner column walls, further improving the heat-transfer capacity. Distillation columns are often constructed from steel. For example, replacing steel with aluminum or copper, which have higher thermal conductivities, will also help to increase the heat-transfer capacity. Several of the suggested improvements change the character of the process unit from a heat exchanging distillation column in the direction of a distilling heat exchanger. For example, the use of a fractionating heat exchanger has been investigated by Tung et al.25 9332


Industrial & Engineering Chemistry Research One must keep in mind that this assessment of improvement possibilities focuses on the thermodynamic performance only; the effect that the changes have on the economics is not taken into account. 6.3. Other Configuration Improvement Possibilities. The current work focuses on the possible performance improvements related to the use of HI stages, in combination with adjusted operating pressures. In addition to these changes, adjustments in several other design parameters might further improve the performance of the distillation section. In the current study, the number of theoretical distillation stages remains fixed in each column. This also holds for the feed and the draw locations. Redistributing the total number of stages over the two columns, and adjusting the feed and draw locations, could further increase the distillation section efficiency. Especially interesting is the option to move the feed location of stream 15 up toward the top of the LPC, since this feed location is limiting the maximum possible number of HI stages for cases 3, 4, and 5 studied in this work. Another degree of freedom that can be introduced is the use of different types of structured packing in the two columns. Using the same type of packing in both columns, the heat-transfer capacity per column height is always the same in the two columns. By allowing different types of packing, these quantities can be decoupled, adding more optimization possibilities. In order to model heat-integrated columns that are equipped with different types of packing, a rate-based distillation model is required, as described in section 6.1.2. It should be kept in mind that choosing a different type of packing might result in higher investment costs. 6.4. Materialization of the Performance Improvement. The addition of HI stages affects both the size of the distillation section and the overall ASU performance. 6.4.1. Effect on Distillation Section Size. Figure 14 shows a conceptual drawing of how the distillation column configuration changes when using the maximum number of 26 HI stages, which is about half of the total number of stages in both columns. Moving the LPC down along, or into, the HPC results in a lower total column height. The use of HI stages also decreases the size of the reboilercondenser. This causes the total size of the cold-box in which they are located to decrease. A smaller cold-box results into lower capital costs and the costs of the reboilercondenser itself will also decrease. However, the use of HI stages also increases the capital costs, since the use of multiple parallel columns with a small diameter requires more column wall per cross-section in the heat-integrated part of the configuration. The structured packing that is used also becomes more expensive, because more-complicated shapes are involved. 6.4.2. Effect on ASU Performance. The performance improvements realized in cases 3, 4, and 5 materialize in changed inlet and outlet stream conditions of the distillation section. The compositions of the streams hardly change, but their flow rates, pressures (and, therefore, temperatures) do. Detailed simulations that accurately quantify the effects of these changes on the overall ASU performance are outside the scope of the current work. Therefore, the current assessment has a more qualitative character. The performance improvements translate in the end in decreased pump and compressor duties. In the original design described in the work of Van der Ham and Kjelstrup,4 the main air compressor, which is located upstream of stream 2, accounts

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for 68% of the total work input. The nitrogen compressor downstream of stream 6 uses 22%, and the one that is upgrading about one-fifth of stream 19 to the high-pressure level uses 8%. The remaining part of the total work input is used in the booster air compressor upstream of stream 4, and in the two pumps. The expander duties are comparable to the pump duties. A decrease in the flow rate or stream 2 directly reduces the duty of the main air compressor, which has a considerable effect on the total work input. For a fixed expander duty, a decrease in the pressure of stream 2 also reduces the duty of the main air compressor. An increase in the pressure of stream 4 has a very limited effect on the total work input, since the contribution of the booster air compressor to the total work input is very small. An increase in the flow rate of stream 6 requires a smaller part of stream 19 to be upgraded, reducing the duty for compressing this part of stream 19. But a reduced pressure of stream 6 requires more duty in the nitrogen compressor. Changes in the pressures of the streams 5 and 16 affect the pump duties. However, this hardly influences the total work input, since the pumps account for only a small part of the total work input. An increase in the pressure of stream 19 reduces the required duty in the compressor that is upgrading a part of this stream. Decreases in the compressor duties also decreases the duties of the aftercoolers. Also the MHX is affected by the changes in the process streams. A decrease in pressure ratio between the two distillation columns results in a smaller temperature difference at the cold side of the MHX, requiring more heat-transfer area. Changes in the flow rates alter the heat duty of the MHX, and therefore also affect the required heat-transfer area. The decreasing size of the cold-box will also affect the ASU performance, because it results in smaller losses of low-temperature energy to the surroundings. 6.5. Comparison with Other Structural Changes. In the work of Van der Ham and Kjelstrup,4 two other changes in the ASU flowsheet are discussed that can improve the ASU efficiency. The first one is the addition of a third distillation column, and the second one is the addition of one or two intermediate heat exchangers in the bottom section of the LPC. Addition of a third column reduced the entropy production in the distillation section by 30%, while adding intermediate heat exchangers managed to reduce it by ∼15%. From a thermodynamic performance perspective, adding an intermediate heat exchanger is thus the least promising, although it is probably less expensive than adding a distillation column or using HI stages. As discussed in sections 6.2 and 6.3, the performance improvement of using HI stages can expected to be increased even further, yielding a reduction in entropy production that is comparable or larger than when adding a third distillation column. Comparing the three alternatives based on these considerations, the use of HI stages seems to be the most promising. However, this does not necessarily mean that it also is the leastexpensive alternative.

7. CONCLUSIONS The performance improvement that can be realized by the use of heat-integrated stages (HI stages) in a two-column air spearation unit (ASU) has been assessed. Increasing the number of HI stages without adjusting the operating pressures causes the heat duty of the condenser to be taken over by the HI stages. This results in a relocalization of entropy production from the HPC and especially the LPC to the HI stages, while keeping the total 9333


Industrial & Engineering Chemistry Research entropy production unchanged. The reduction in the LPC entropy production is partly caused by a more even distribution of the entropy production in its stripping section. The increased amount of entropy production in the HI stages is mainly caused by an increasing temperature difference. At the maximum number of HI stages, the condenser requires only 2% of its base case heat-transfer area. A reduction in the ratio between the operating pressures can be used to keep the temperature difference in the condenser at its base case value. This enables a reduction in the LPC entropy production without increasing the entropy production in the HI stages, resulting in an overall decrease. For a probable value of the heat-transfer capacity, increasing the pressure in the LPC results in a maximum decrease of 21%, while decreasing the pressure in the HPC results in a maximum decrease of 23%. Decreasing the pressure in the HPC when using a opportunistic heat-transfer capacity yields a maximum decrease of 31%. All these maxima occur at 26 HI stages; this number is limited by the product specifications and the fixed feed stages. About three-quarters of the reductions are caused by the LPC, but the contributions of the other process units also decrease. The reductions in entropy production materialize as changes in the feed and product stream properties; the overall quality of the feeds is reduced and the overall quality of the products is increased. These changes eventually affect the required compressor, pump, and expander duties of the ASU. The use of HI stages also affects the size of the cold-box in which the distillation columns are located. Compared to the addition of either an additional heat exchanger or an additional distillation column, the use of HI stages seems to be the most promising method for improving the thermodynamic performance of a cryogenic ASU. In order to improve the model that is used to simulate heatintegrated distillation columns (HiDiCs), more detailed experimental data are required. The achievable heat-transfer capacity should be determined, along with its dependency on various operating conditions. In order to ensure the accuracy of ratebased distillation models when applied to heat-integrated columns, the coupling between the thermal and mass fluxes should be assessed.

APPENDIX A. DETAILED MODEL DESCRIPTION A.1. Thermodynamic Model. A reference equation-of-state by Lemmon17 is used to calculate all thermodynamic properties that are required in this work. This empirical thermodynamic model is developed to predict the properties of air-like mixtures with an accuracy that is as high as possible. It describes the Helmholtz energy of any mixture of nitrogen, oxygen, and argon as a function of temperature and density. Other thermodynamic quantities of the mixture can be calculated by combining derivatives of the Helmholtz energy, with respect to the temperature and density. A.1.1. Partial Molar Quantities. The partial molar quantities of a component are given by the derivatives of these quantities, with respect to the number of moles of this component, at constant temperature, pressure, and the number of moles of the other component(s). In the current study, the partial molar quantities are obtained by numerical evaluation of these derivatives. A.1.2. Mixture Composition. In the current work, it is assumed that air consists of a binary mixture of nitrogen and oxygen only. The biggest advantage of this assumption is that the composition of a single phase is defined by the temperature and

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Figure A1. Schematic of the four possible column configurations. From left to right: no reboiler or condenser, condenser only, reboiler only, or both a reboiler and a condenser.

pressure only. This simplifies the solution procedure for especially the distillation columns. The feed air mixture is assumed to have a nitrogen mole fraction of 0.79 and an oxygen mole fraction of 0.21. A.2. Process Units and Flowsheet. Figure 3 shows a schematic representation of the distillation section of a cryogenic ASU, with numbered process streams. The vertical positions of the two distillation columns are inverted in the schematic. A.2.1. Distillation Columns. The distillation columns are modeled using theoretical equilibrium stages (see, for example, the work of Seader and Henley21 for more details). It is assumed that the columns operate at a constant pressure and that there is no loss of low-temperature thermal energy to the surroundings. A.2.2. Heat-Integrated Stages. The main aim of the current study is to evaluate how the distillation section performance changes when the heat integration between the two columns is increased by moving down the LPC along the HPC. In terms of theoretical equilibrium stages, this corresponds to increasing the number of heat-integrated stages (HI stages). The heat duty between two HI stages (QHI) can be calculated by multiplying the temperature difference between the two stages (ΔTHI) by the overall heat-transfer coefficient (U) and the available heat-transfer area (A). In this work, the stage outlet temperatures have been used in order to calculate temperature differences between HI stages. The overall heat-transfer coefficient and the heat-transfer area available per stage are combined into a single quantity: the heat-transfer capacity per theoretical stage (UA). It is described in more detail in section A.3 in Appendix A. A.2.3. ReboilerCondenser. The heat exchanger that is functioning as a reboilercondenser is modeled as an additional equilibrium stage, present in both the HPC and the LPC. What happens with the reboilercondenser when the LPC is moved down along the HPC remains to be decided. In theory, there are four possible configurations. A first option is to remove the heat exchanger completely and rely on the heat transfer between the HI stages only. The next two options are to keep a single heat exchanger and have it either function as reboiler for the LPC and as intermediate heat exchanger for the HPC, or as condenser for the HPC and intermediate heat exchanger for the LPC. A fourth possibility is to add a second heat exchanger and have both previous functionalities. The four configurations are schematically illustrated in Figure A1. In order to keep the number of heat exchangers unchanged and to ensure the availability of a liquid nitrogen product, a decision was made to use the second configuration: a single heat exchanger that functions as a condenser for the HPC. 9334



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A.2.4. Subcoolers. The subcooling step within the distillation section is simulated using two separate subcoolers. In the first one, stream 7 is cooled using stream 17, yielding streams 10 and 18. In the second one, streams 8 and 9 are cooled using stream 18, yielding streams 11, 12, and 19. The outlet temperatures of streams 11 and 12 are assumed to be the same. It is also assumed that the subcoolers operate at a constant pressure and that there is no loss of low-temperature thermal energy to the surroundings. A.2.5. Throttle Valves. The throttle valves are modeled as adiabatic pressure decrease processes. This means that there is no loss of low-temperature thermal energy to the surroundings. A.3. Heat-Transfer Capacity per Theoretical Stage. One of the key design variables for HiDiCs is the heat-transfer capacity per theoretical equilibrium stage. In concentrically integrated columns that are equipped with structured packing, the amount of heat-transfer area can be calculated by multiplying the height of a theoretical stage with the circumference of the inner column. The diameter of a column is usually determined by its vapor flow rate; it is chosen such that the F-factor, which is given by the square root of the vapor mass density multiplied with the superficial vapor velocity, is always below a critical value. Both this critical F-factor (Fmax) and the height of a theoretical stage are performance properties of the structured packing that is used. In order to make a realistic estimate for the heat-transfer capacity per theoretical stage, we need to select the type of structured packing and values for the inner column diameter, the overall heat-transfer coefficient, and the operating conditions in the column. Using these values, it is possible to calculate the maximum molar vapor flow rate that can be allowed in a single column of the chosen diameter, based on the definition of the F-factor:

V

max

¼F

max

πD2i 4

!sffiffiffiffiffiffiffiffiffi FVmol Mmol

ð2Þ

The ratio between this maximum flow rate per column and the actual required flow rate determines the number of parallel Table A-1. Approximate Properties of Several Types of Structured Packing Montz B1-series

B1-150

B1-250

B1-500

Sulzer Mellapak

170.Y

250.Y

500.Y

NTH (stages/m)

2

3

4

Fmax (Pa1/2)

3.0

2.5

2.0

columns that is needed. The heat-transfer capacity per stage must be multiplied with the number of parallel columns. A.3.1. Structured Packing. Structured packing is commonly characterized using graphs of its separation efficiency and its pressure drop as function of the F-factor. The separation efficiency is usually given by the number of transfer units per meter of packing (NTH) or its inverse, the height equivalent to a theoretical plate (HETP). Up to the critical F-factor, the separation efficiency decreases slightly as the F-factor increases. However, above the critical F-factor, the packing starts to flood and the separation efficiency diminishes. The critical F-factor is mainly determined by the type of packing, but it also depends on the liquid flow rate in the column. In the current study, we assume that the separation efficiency has a constant value, up to the critical F-factor, above which it becomes zero. The critical F-factor is assumed to be independent of the liquid flow rate. Some approximate values for the separation efficiency and critical F-factor of some standard types of structured packing are listed in Table A-1. Using less-efficient packing increases the amount of heattransfer area per equilibrium stage and allows for either a higher throughput or a lower pressure drop. But it also requires a higher column. For a given total feed flow rate, a higher throughput would lower the amount of heat-transfer capacity, because the number of parallel columns decreases. A.3.2. Inner Column Diameter. A small column diameter results in a high heat-transfer capacity, but it also requires a high number of parallel columns for a given total feed. Two Japanese pilots of a concentric HIDiC used inner column diameters in the range of 0.140.27 m,24,26 yielding an average of value of 0.20 m. A.3.3. Overall Heat-Transfer Coefficient. It is not straightforward to obtain a reliable estimate for the overall heat-transfer coefficient; only three experimental results are available in the open literature for heat transfer between two HiDiC parts that are equipped with structured packing.24,27,28 They all report a single value that represents the entire column. Their values range between 670 W/(m2 K) and 1100 W/(m2 K) and have an average value of ∼800 W/(m2 K). A.3.4. Operating Conditions. The operating conditions in the column determine the vapor density. At the top of the HPC, the mixture will always have a very high nitrogen fraction. This leaves the operating pressure as the most important factor that influences the vapor density. The pressure affects the vapor density directly, and indirectly via the dew point temperature of the mixture. For a decreasing pressure at a constant temperature, the vapor density decreases. The dew-point temperature also decreases for a decreasing pressure, which causes a slight increase

Table A-2. Characteristics for Calculating the Amount of Heat-Transfer Capacity per Theoretical Equilibrium Stage per Mole Feed, for a Conservative, Probable, and Opportunistic Case conservative case, c

probable case, p

opportunistic case, o

0.20

0.14

0.10

3

2

2

A (m2/stage)

0.21

0.22

0.16

U (kW/(m2 K))

0.80

0.80

1.10

UA (kW/(K stage)) Fmax (Pa1/2)

0.17 2.5

0.18 3.0

0.17 2.5

FV (mol/m3)

700

700

560

Vmax (mol/s)

12

7.3

2.8

UA per mole feed (W/(K stage))

10

17

44

Di (m) NTH (stages/m)

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Table C1. Process Stream Properties of Cases 1 and 2 stream

flow rate (mol/s)

1

1.000

2

vapor fraction (mol/mol)

pressure (bar)

temperature (K)

N2 fraction (mol/mol)

enthalpy (kJ)

entropy (J/K)

0.421

0.000

4.80

95.0

0.790

1.900

22.62

3

0.564

1.000

4.80

124.8

0.790

0.924

65.68

4

0.015

1.000

1.30

95.5

0.790

0.012

1.80

5

0.066

0.000

4.80

93.5

1.000

0.163

6.00

6

0.162

1.000

4.80

93.5

1.000

0.392

23.11

7

0.179

0.000

4.80

93.7

0.971

0.492

15.39

8 9

0.160 0.418

0.000 0.000

4.80 4.80

95.5 97.6

0.788 0.600

0.720 2.641

8.58 7.73 14.02

0.790

10

0.179

0.000

4.80

82.4

0.971

0.612

11

0.160

0.000

4.80

92.7

0.788

0.747

8.30

12

0.418

0.000

4.80

92.7

0.600

2.760

6.48 14.05

13

0.179

0.029

1.30

79.7

0.971

0.612

14

0.160

0.120

1.30

81.3

0.788

0.747

8.41

15

0.418

0.099

1.30

83.0

0.600

2.760

6.69

16 17

0.212 0.559

0.000 1.000

1.30 1.30

91.3 79.9

0.050 0.985

2.624 1.168

20.93 82.82

18

0.559

1.000

1.30

86.7

0.985

1.288

84.27

19

0.559

1.000

1.30

95.1

0.985

1.433

85.86

in the vapor density. The net effect is dominated by the direct decrease in the vapor density. A reduction in the vapor density decreases the maximum vapor flow rate per column. Therefore, a decrease in operating pressure results in an increase in the heattransfer capacity. A.3.5. Resulting Heat-Transfer Capacity. Based on the values that are presented in the previous section, we can calculate the heat-transfer capacity for some different cases: a conservative case, a probable case, and an opportunistic case. The conservative case is based on average values for all variables, without trying to maximize the heat-transfer capacity. An operating pressure of 4.8 bar is used to calculate the vapor density; this is the maximum pressure used for HPC in this work. The probable case is based on the conservative one, but a smaller diameter and less efficient packing are selected. The opportunistic case uses an ever smaller diameter. In addition, the maximum overall heat-transfer coefficient, an operating pressure that is 80% of the maximum value, and a reduced maximum F-factor are selected. All cases assume a molar mass of 0.028 kg/mol. They also use the fact that, for a process with a total feed flow rate of 1.0 mol/s, the maximum vapor flow rate in the HPC amounts to ∼0.70 mol/s. The calculation inputs and results are shown in Table A-2.

APPENDIX B. CALCULATION DETAILS All calculations have been performed using Matlab. B.1. Solving the Process Flowsheet. The process flowsheet is solved using three iteration loops: one over the reboiler condenser heat duty, one over the heat duties of the HI stages, and one over the low-purity nitrogen product stream. The following routine is used: (1) Chose values for flow rates F2, F7, and F8. (2) Guess a reboilercondenser heat duty (QRC). (3) Guess temperature differences for the HI stages (ΔTHI). (4) Solve the HPC. (5) Guess low-purity N2 properties (F17 and y17).

(6) Solve the subcoolers, throttle valves, and LPC. (7) Check F17 and y17, and return to step (5) if needed. (8) Check ΔTHI, and return to step (3) if needed. (9) Check QRC, and return to step (2) if needed. The first two loops can be combined for low numbers of HI stages; however, for higher numbers, they must be separated in order for the solution to converge. Flow rate F2 is used to obtain a desired oxygen recovery rate. Flow rates F7 and F8 are chosen such that they minimize the total entropy production of the distillation section, as explained in more detail in section B.2. The value of F3 is set such that the sum of F2, F3, and F4 is always equal to 1.0 mol/s. B.1.1. Solving the Distillation Columns. Both distillation columns are solved with Matlabs fsolve function, using the stage liquid mole fractions as variables. Solving the HPC comes down to finding F6 and F9 for fixed values of the two feeds, F5, F7, F8, QRC, and QHI, while obeying the so-called MESH equations. More details on the MESH equations can be found in the literature (for example, Seader and Henley21). Based on the liquid mole fractions selected by fsolve, first the vapor mole fractions and the liquid and vapor enthalpies are calculated. Next, the top and bottom product flow rates are calculated using overall material and component balances. Stage energy balances are subsequently used to calculate the vapor and liquid flow rates for all stages except the bottom one. Next, the disagreements in the stage component balances are calculated for these stages. For the bottom stage, the disagreement in the energy balance is used, scaled with the total energy duty. The liquid mole fractions are adjusted by fsolve until all stage disagreements are below a specified maximum value. Solving the LPC comes down to finding F17 and QRC for fixed values of the three feeds, the oxygen product purity, and QHI, while obeying the MESH equations. The first two calculation steps are the same as those for the HPC. But before calculating the vapor and liquid flow rate profiles and the disagreements in the stage component balances, first the reboiler duty is calculated using the overall energy balance. A stage disagreement calculation for the bottom 9336



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Table C2. Comparison between the Distribution of the Total Entropy Production (Given in Units of J/(K s) per Mole of Feed) over the Main Components of the Distillation Section, for the Base Case Design, and the Original Design Discussed in Van der Ham and Kjelstrup4 base case design

original design

HPC

0.846

0.895

LPC reboilercondenser

1.906 0.692

2.212 0.366

subcoolers

0.147

0.327

valves

0.353

0.345

total

3.944

4.145

stage is no longer required, since the mole fraction of the bottom product is fixed, as is explained in section 4.1. B.1.2. Solving the Subcoolers. The two subcoolers are solved in series. For both subcoolers, the first solution step is to calculate the total heat capacities of the hot and cold streams. Those heat capacities are subsequently used to determine at which side of the subcooler the minimum allowable temperature difference occurs, which fixes one of the outlet temperatures. The other outlet temperature is calculated using the energy balance. As a last step, it is verified that the temperature difference at the other side of the subcooler is larger than the minimum allowable value. B.1.3. Solving the Throttle Valves. The outlet conditions of the throttle valves are found by first assuming values for the liquid outlet compositions. The component and material balances are subsequently used to find the total vapor and liquid outlet flow rates. Next, the disagreement in the energy balance is calculated. The liquid outlet compositions are adjusted until the disagreements are below a specified maximum value. B.1.4. Solution Consistency and Accuracy. After solving all process units and the flowsheet, the consistency of the found solution is checked. The disagreements in the energy, component, and material balances for all process units, distillation stages, and the entire flowsheet are calculated. All disagreements are required to be below 106, with the energy balance disagreements being scaled with the total heat duty. B.2. Optimizing the Intercolumn Flows. The intercolumn flow rates F7 and F8 are free variables; they can be used to optimize the flowsheet. In this work, they are used to minimize the entropy production in the distillation section. For the base case design described in section 4.1, both flow rates are optimized. The found optimal value for F8 is used for all other cases that are studied in this work. F7 is re-optimized for all combinations of operating pressures, based on a configuration with the reboilercondenser as only HI-stage. By choosing not to optimize F7 and F8 for each column configuration, some performance gain might be lost. This potential loss is expected to be minor, compared to other contributions to the performance gain. In case its importance is not negligible, the reported performance gains will be underestimated, compared to reality.

APPENDIX C. BASE CASE CHARACTERISTICS Table C1 lists some characteristic stream properties of the base case. (The stream numbering refers to Figure 3.) Table C2 shows how the total entropy production in the base case is distributed over the main components of the distillation section, along with a

comparison with the values calculated for the original process design used in Van der Ham and Kjelstrup.4 Overall, there is a difference of 5% between the amounts of produced entropy. This difference is mainly the result of the model simplifications described in section 4.1.4. In addition, the different thermodynamic models used for simulating the base case and the original design might have a minor contribution. Neglecting the pressure drop and the thermal energy loss in the distillation columns and in the subcoolers excludes these two types of irreversibilities from the base case. Therefore, these simplifications cause the entropy production to be lower in the base case than in the original design. The difference in the value for the reboilercondenser is related to the use of a binary mixture instead of a ternary mixture; it also is related to the neglect of the pressure drop in the distillation columns. Those two simplifications result in different temperatures at the top and the bottom of the columns. The resulting temperature difference in the reboilercondenser is ∼2.2 K in the base case design, while it is

Improving the Heat Integration of Distillation Columns in a Cryogenic

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