Modeling, Characteristic Analysis, and Optimization of Ideal Internal

Article pubs.acs.org/IECR

Modeling, Characteristic Analysis, and Optimization of Ideal Internal Thermally Coupled Air Separation Columns Liang Chang, Xinggao Liu,* Liankui Dai, and Youxian Sun State Key Laboratory of Industry Control Technology, Control Department, Zhejiang University, Hangzhou 310027, P.R. China ABSTRACT: Cryogenic air separation is currently the most widely used but energy-intensive technology for producing large quantities of oxygen and nitrogen, where cryogenic distillation consumes about 75% of the whole air separation field; however, its thermodynamic efficiency is very low. A novel structure of a full tower ideal internal thermally coupled air separation column (ITCASC) is therefore first proposed in this paper. A rigorous mathematic model and parameter analysis are then presented. Research results show that the proposed ITCASC process can yield high-purity products of both oxygen and nitrogen simultaneously and especially has a strong driving force of heat transfer, which reveals the larger energy-saving potential in the ITCASC process. Furthermore, an optimization model of the operation parameters is presented, where both the actual energysaving potential and the ideal energy-saving potential of ITCASC are investigated. Comparative studies against the conventional cryogenic air separation column (CASC) are carried out in detail. Research results show that the proposed ITCASC process has a larger extraction rate and better energy efficiency, where the nitrogen extraction rate increases 177.94% and the unit energy consumption decreases 40% compared to the CASC process with the same product purity requirements, revealing the advantages and promising application prospect of the proposed ITCASC process.

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INTRODUCTION An air separation plant separates atmospheric air into its primary components, typically nitrogen and oxygen and sometimes also argon and other rare inert gases for the steel, chemical, semiconductor, aeronautical, food processing, and health care industries. There are various technologies that are used for the separation process. The pressure swing absorption (PSA) method has become a unit operation widely used for gas separation or purification. PSA is attractive because it does not require separate adsorption steps that need heat input. Membrane technology for gas separation has developed rapidly in recent years, and organic polymeric membranes have been used commercially for oxygen separation. However, the former units are typically used to separate only a single component from ordinary air, and the product purity is not very high.1−3 Production of high-purity oxygen, nitrogen, and argon requires cryogenic distillation. The cryogenic separation process requires a very tight integration of heat exchangers and separation columns to obtain a good efficiency, and all energy for refrigeration is provided by compression of the air at the inlet of the unit. Cryogenic distillation consumes a large amount of energy and takes up about 75% of the whole air separation field. Much research about modeling, optimal design, and a control algorithm has been carried out to raise the product purity of cryogenic distillation and reduce its energy consumption.4−10 The internal thermally coupled distillation column (ITCDIC) has been regarded as a promising heat-integrated distillation column due to its large energy-saving potential.11,12 The early concept of the ITCDIC was proposed by Mah13 et al. It has received increasing attention in recent years.14−20 The main characteristic of ITCDIC is that the rectifying section is operated at a higher pressure than the stripping column, which can be easily applied to the air separation. Many countries such as Japan, Holland, and the United States have conducted © 2012 American Chemical Society

national projects for development of internal thermally coupled air separation column (ITCASC).21−25 L. V.Van der Ham23 improved the structure of the CASC by moving the lowpressure column (LPC) down along the high-pressure column (HPC), thus increasing the number of heat-integrated stages (HI stages). Reducing the pressure ratio enabled a reduction in the LPC entropy production without increasing the contribution of the HI stages. However, the structure was an improvement of the CASC process, without eliminating the condensing reboiler, the main heat transfer still produced by the condensing reboiler, its thermal coupling was still in part, so that the energy-saving effects were not obvious. Moreover, it was difficult to yield high-purity oxygen and nitrogen simultaneously, which is usually required by the practical product process of cryogenic separation. Previous work by our group investigated the modeling and steady behavior analysis of the ITCASC process proposed by Yan.25 The related solution procedures were given. Detailed behavior analysis was carried out. The research results revealed that the separation effect of the ITCASC process was better and exhibited different behaviors compared to the CASC process. However, the structure was also an improvement of the CASC process: its main heat transfer was still produced by a condensing reboiler, and the extraction rate is low. On the basis of previous work, a novel structure of ITCASC is derived in this paper, which abandons the structure of CASC and applies full tower internal thermally coupled. Withdrawing a side stream at the argon-rich stage, the structure can obtain high-purity products simultaneously and a better separation Received: Revised: Accepted: Published: 14517

June 13, 2012 September 18, 2012 October 11, 2012 October 11, 2012 dx.doi.org/10.1021/ie3015582 | Ind. Eng. Chem. Res. 2012, 51, 14517−14524

Industrial & Engineering Chemistry Research

Article

heat exchange between the two columns. A certain amount of heat is therefore transferred from the HPC to the LPC because of the internal thermal coupling, which leads to downward reflux flow for the HPC and upward vapor flow for the LPC. As a result, the structure can operate without a condensing reboiler and energy savings are realized. Mathematical Model. The mathematical model based on the schematic diagram of the ITCASC is derived by applying energy, component, and overall material balances and vapor− liquid equilibrium under the following conventional assumptions: (1) complete mixing on each tray, (2) negligible heat losses in the tray, (3) constant pressure drop on each tray, and (4) uniform pressure and temperature on each tray.26 The basic equations of the ITCASC are derived as follows. Material balance for each component

effect than the CASC. A rigorous mathematic model and related simulation algorithm are proposed, which provides an efficient tool for further parameter and optimization analysis. Research results show the feasibility and advantage of the proposed ITCASC process. An optimization model of the operation parameters is further proposed, and the energy-saving potential with actual industrial constrains and ideal constrains is investigated, thus, obtaining the optimal operation pressures. Driving force and separation effect analysis between the optimization results and the nonoptimization results are carried out in detail. The energy consumption, extraction rate, economic benefits, and more detailed comparative studies against the CASC are also carried out, and the research results show the advantages of the proposed ITCASC process.

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MODELING Schematic Diagram of the Novel ITCASC. Figure 1 shows the schematic diagram of an internal thermally coupled

Lj − 1xi , j − 1 − (Vj + Gj)yi, j − (Lj + Sj)xi , j + Vj + 1yi , j + 1 = −Fjzi , j

(1)

where L is the liquid flow rate, V is the vapor flow rate, G is the gas side stream, S is the liquid side stream, x is the liquid mole fraction, y is the vapor mole fraction, z is the feed mole fraction, and F is the feed flow rate. Subscript i represents a particular species or component, and j represents the stage number. Energy balance Lj − 1HjL− 1 − (Vj + Gj)HjV − (Lj + Sj)HjL + Vj + 1HjV+ 1 = −FjHjF + Q j

(2)

The variable H represents the mole enthalpy and Q the rate of heat transfer. The superscript L represents liquid flow, V represents vapor flow, and F represents feed flow. Thermal coupling Q j = UAj × ΔTj

(3)

where UA is the heat transfer coefficient and ΔT is the temperature difference of each coupled stage. Mole fraction summations C

∑ xi ,j = 1 i=1

(4)

Figure 1. Schematic diagram of ITCASC. C

∑ yi ,j = 1

distillation air separation plant. The compressed air for liquefaction is cooled and the gaseous products of air separation are rewarmed both in the main heat exchanger (E1). Compressed air (F) feeds at the bottom stage of the highpressure column (HPC). The oxygen-rich liquid air (LAIR) flows through the heat exchanger (E2) and throttling valve (V1) into the low-pressure column (LPC), providing downward liquid flow. The oxygen-rich vapor air (GAIR) at the top stage of the LPC along the reverse path flows into the HPC, providing upward vapor flow. Low-purity liquid nitrogen product (WLN) is withdrawn from the stage at the highest argon concentration. A compressor (C2) and a throttling valve (V1) are installed between the rectifying section and the stripping section so that the rectifying section is operated at a higher pressure and higher temperature than those of the stripping section, the LAIR of the HPC can flow to the LPC, and the GAIR of the LPC can flow to the HPC. Internal thermal coupling is accomplished through

i=1

(5)

Phase equilibrium relation for each component, k is the vapor−liquid equilibrium coefficient yi , j = ki , jxi , j

(6)

In general, K values and molar enthalpies in these equations are complex implicit functions of stage temperature, stage pressure, and equilibrium mole fractions ki , j = ki , j(xi , j , yi , j , Pj , Tj)

(7)

HjL = HL(xj , Pj , Tj)

(8)

HjV = HV (yj , Pj , Tj)

(9)

The tridiagonal matrix method and bubble point method are used to solve the model. Physical properties of oxygen, 14518

dx.doi.org/10.1021/ie3015582 | Ind. Eng. Chem. Res. 2012, 51, 14517−14524


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nitrogen, and argon are computed from the Peng−Robinson state equation.27 The energy required for the separation process of CASC and ITCASC is the energy consumption of the compressor. For the adiabatic compression process, theoretical compression work is ε − 1/ ε ⎛⎛ ⎞ Pout ⎞ ε ⎜ − 1⎟⎟ W= PinVin⎜⎜ ⎟ ε−1 ⎝⎝ Pin ⎠ ⎠

(10)

where ε is the adiabatic compression index, the subscript in represents inflow of the compressor, and the subscript out represents outflow of the compressor. The revenue R of the nitrogen and oxygen products is calculated by multiplying the production flow rate and unit price. The energy consumption for unity unit products of ITCASC and CASC is represented by W/R, which can be used in comparing the unit energy consumption of ITCASC and CASC process.

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Figure 2. Liquid Composition distribution.

CHARACTERISTIC ANALYSIS Table 1 shows the operation conditions of an ITCASC similar to the CASC. Containing 35 stages, the high-pressure column

Table 2. Comparison of the Products Purity nitrogen product purity, % oxygen product purity, %

Table 1. Operating Conditions feed flow rate, mol/s feed temperature, K feed pressure, Pa flow rate of WLN, mol/s withdraw stage of WLN stage number feed composition (N2, Ar, O2) UA, W/K

128.1 99.54 579573 18 stage 45 HPC:35 LPC:35 0.78118, 0.00932, 0.2095 2380

ITCASC

L. V. Van der Ham23

99.9 99.7

100.0 95.0

distribution of argon composition also helps us to choose the side stream stage number of argon if we further consider the argon column. Figure 3 shows the temperature profile of the entire column. The solid curve is the temperature distribution of the HPC, and

(HPC) is operating at about 5.8 MPa and numbered from 1 to 35 from the top to the bottom. The bottom stage is fed with a 99.54 K mixed vapor−liquid feed. A high-purity gaseous nitrogen product is withdrawn from the top stage of the HPC. The low-pressure column (LPC) is operating at 1.1 MPa and numbered from 36 to 70. A low-purity liquid nitrogen product (WLN) is withdrawn from stage 45, and a liquid oxygen product is withdrawn from the bottom stage of the HPC. More operation conditions are shown in Table 1. Figure 2 shows the distribution of the liquid composition for each stage. In the HPC the purity of the nitrogen increases from the stage 35 to 1 and it reaches 99.9% at the top stage as a product. While the purities decreases for the oxygen and argon. In the LPC the purities of oxygen increases from the stage 36 to 70, and at 70th stage, it reaches 99.7% as a product. Nitrogen and oxygen products satisfy the purity requirements. Table 2 shows the product purity comparison of the ITCASC process proposed in this papar and the structure proposed by L. V. van der Ham.23 Nitrogen product purity in the two structures can both achieve high-purity requirements. Oxygen product purity is only 95% in L. V. van der Ham’s structure, and it is difficult to yield high-purity oxygen and nitrogen simultaneously, while in our structure the oxygen product purity is 99.7% and both the nitrogen and the oxygen products satisfy the high-purity requirements. The highest purity of the argon appears at the 46th stage, which reveals that we can remove most of the argon by withdrawing WLN around the 46th stage and obtain highpurity nitrogen and oxygen products at the same time, while the

Figure 3. Coupled temperature distribution.

the dotted curve is the LPC profile. The temperature in the HPC is higher than that in the LPC at each coupled stage. Owing to internal thermal coupling, a certain amount of heat is transferred from the HPC to the LPC. The heat duty generates the vapor flow for the stripping section and liquid flow for the rectifying section which reveals that the distillation process can operate without the condensing reboiler. Another important phenomenon we can find directly from Figure 3 is that the coupled temperature difference is 5−16 K. In the conventional cryogenic air separation distillation the temperature difference of the heat exchanger is 1.8 K. Thus, there is a strong driving 14519



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OPTIMIZATION In order to explore the energy-saving potential of the model, a rigorous optimization model of internal thermally coupled air separation column is further carried out. With different constrains, we investigate both the actual energy-saving potential and the ideal energy-saving potential. Furthermore, driving force, separation effect, and energy-saving analysis are studied in detail. Optimization Model. The energy required for the cryogenic separation process is mainly the energy consumption of the compressor. It has been proved that reducing the pressure of the HPC can decrease the energy consumed of the cryogenic separation process.25 According to eq 10, theoretical compression work is related to Pin, Pout, and Vin. The energy consumption of the ITCASC is

force to transfer heat from the HPC to the LPC and also a large optimization space of the rectifying section pressure. Figures 4 and 5 show the flow rate distribution of the entire column. Different from the constant molar flow character of

W = W C1 + W C2 C1 C2 = W {PinC1 , Pout , V C1} + W {PinC2 , Pout , V C2}

(11)

C1 C2 Assume that PC1 in , V , and Pin are kept the same, the flow rate C2 C2 V flowing through C2 changes slightly. PC1 out and Pout are the pressure of HPC. Therefore, the energy consumption of the ITCASC is influenced by the pressure of the HPC. As mentioned above, the pressure of the HPC can be reduced. The optimization target is the pressure minimum of the HPC. The equality constraint is the mathematical model described in the previous section. In order to guarantee the quality of the products, the purities are constrained as follow

Figure 4. Liquid flow rate distribution.

yO ≥ 99.7%

(12)

yN ≥ 99.9%

(13)

2

2

In the conventional cryogenic air separation distillation the temperature difference of the heat exchanger is 1.8 K. In order to guarantee the driving force of each coupled stage, the temperature difference of the coupled stage is constrained as follows according to the operative practice of the CASC

ΔT ≥ 1.8K

(14)

Optimization model 1 of the ideal ITCASC pressure is proposed as follows

Figure 5. Vapor flow rate distribution.

conventional distillation, each stage in the HPC transfers heat to the LPC because of the internal thermal coupling, which produces more liquid stream flowing down in the HPC and more vapor steam flowing up in the LPC along the column gradually. This phenomenon is consistent with ITCDIC28,29 and reveals the validity of our modeling. The liquid and vapor flow rate increase from stage 1 to 35 and decrease from stage 36 to 70. In Figure 4 the liquid flow rate decreases significantly at the 45th stage, since there is a liquid side stream. As can be seen from the temperature curve that the temperature difference and heat transfer is larger at the top of the HPC and LPC, so the change in slope is larger at stages 1−10 and stages 36−45. The distribution curves reveal that it is required to design the ITCASC with changing the diameter along the column of both the HPC and the LPC instead of the conventional cylinder of the CASC column, because the cross-section area of the distillation column should be proportional to the vapor flow rate while the flow of vapor of the ITCASC changes along the column.

min P = φ(UA , T F ) s. t. equality constraints: eqs 1−9 inequality constraints: eqs 12, 13, 14

In order to investigate the ideal potential of energy savings in the ITCASC process, the temperature difference constraint is ignored and the middle stages of the ITCASC are no longer thermal coupled. Optimization model 2 is min P = φ(UA , T F ) s. t. equality constraints: eqs 1−9 inequality constraints: eqs 12, 13

These are a nonlinear programming (NP) constrained optimization problem. The reduced sequential quadratic programming (SQP) is used here to solve the optimization models.30 14520



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Optimization Result. We take the nonoptimized model as case 1, the optimization model 1 as case 2, and the optimization model 2 as case 3. The optimization results are shown in Table 3. In cases 2 and 3, the optimal pressure of the HPC decreases from the original Table 3. Optimization Results of ITCASC HPC pressure, Pa feed temperature, K UA, W/K

case 2

case 3

457 745 96.48 3686

394 296 94.70 7985

5.8 MPa of case 1 to 4.6 and 3.9 MPa while the UA increases to 3686 and 7985 W/K and the feed temperature decreases to 96.48 and 94.70 K. If the pressure is reduced, the thermal coupling temperature difference will decrease. In view of the theory, in order to achieve the required separation driving force, the total heat duty should remain constant. Then the thermal coupling distribution will change by increasing UA. The above theory analysis is consistent with the research results as shown in Figures 6 and 7. More detailed analysis will be discussed below.

Figure 7. Heat duty distribution for different cases.

order to maintain the distillation separation effect the total driving force remains the same. At stages 13−25 of the dot− dash line the heat duty is very small, corresponding to the temperature profile, and the temperature difference is almost zero. Internal thermal coupling mainly occurs at the top and bottom of the ITCASC. Separation Effect Analysis. Figures 8 and 9 show the vapor and liquid flow rate distribution of the entire column for

Figure 6. Coupled temperature distribution for different cases.

Driving Force Analysis. Figure 6 shows the temperature profile of the entire column for different cases. The top three curves are the temperature distribution of the HPC, and the bottom three curves are the LPC profile. The solid line represents case 1, dotted line represents case 2, and the dot− dash line represents case 3. In the HPC of case 1, the temperature of the top stage is 95.9 K and the feed temperature at stage 35 is 99.54 K. As the pressure decreases in cases 2 and 3, the temperature of the top stage drops to 93 and 91 K and the feed temperature drops to 96.48 and 94.70 K. The energy consumption decreases. In case 2, the minimum temperature difference is 1.8 K at the middle of the columns, which satisfies the temperature constrain and reveals the validity of the optimization model. Figure 7 shows the heat duty distributions for different cases. It can be seen that by decreasing the pressure of the HPC, a part of the heat duty in the middle section is replaced by the duty of the upper section and the total duty almost remains constant, which is consistent with the theory analysis that in

Figure 8. Vapor flow rate distribution.

different cases. The solid line represents case 1, dotted line represents case 2, and dot−dash line represents case 3. In case 3 at the middle of the coupled column the heat duty transfer from the HPC to the LPC is almost zero and the vapor and liquid flow rates of stages 10−30 and 46−60 are flat, which are very similar to the conventional distillation column without internal heat transfer. Corresponding to the heat duty distribution profiles, the heat duty increases at the top stages of ITCASC in cases 2 and 3 and will generate more liquid flow in the HPC. As can be seen in Figure 9 the liquid flow of stages 1−20 increases and will be more favorable for separation of nitrogen. The heat duty 14521



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Energy-Saving Analysis. The main energy consumption of cryogenic air separation is the power consumption of the compressor. In the CASC the amount of gas compressed by the compressor includes the feed flow and flow of expansion air, while in the ITCASC it includes the feed flow and flow of G1 compressed in C2. The prices of nitrogen and oxygen products are assumed to be $0.113/L and $0.176/L.31 Table 6 shows the energy comparison of different cases and the CASC. In case 1 and the CASC the energy consumption is Table 6. Energy Comparison 5

energy consumption, 10 W revenue, $/s unit energy consumption, 106J/$ compare, %

decreases at the middle to the bottom of the ITCASC in cases 2 and 3; the vapor flow generated in these stages will reduce. In Figure 8 the vapor flow decreases in cases 2 and 3; the oxygen separation effect will decrease. Data in Table 4 also confirm this Table 4. Products Comparison between Cases 1, 2, and 3 case 1

case 2

case 3

95.02 99.90 15.07 99.87 95% 56%

96.68 99.90 13.42 99.70 97% 50%

99.57 99.90 10.52 99.70 99% 40%

HECinst =

case 3

CASC

11.43 0.4463 2.561 76.56

8.99 0.4447 2.022 60.44

7.92 0.4418 1.792 53.57

11.25 0.3663 3.345 100

⎛ M&S ⎞ 0.65 ⎜ ⎟cA ⎝ 280 ⎠

where the Marshall and Swift index, M&S, was 1115.8 and the coefficient c of the ITCASC panel was 1466.72. The installed cost of the centrifugal compressor, driven by an electromotor, was based on the brake power (bp)32

phenomenon. In Table 4, the purity of nitrogen product and liquid oxygen product, which are 99.90% and 99.7%, respectively, satisfy the given constraints. The flow rate of the nitrogen product increases from 95.02 to 96.68 mol/s and 99.57 mol/s, but the flow rate of the liquid oxygen product decreases from 15.07 to 13.42 mol/s and 10.52 mol/s in a sequence in different cases, meaning that by decreasing the pressure of HPC the separation effect of nitrogen increases while the separation effect of oxygen decreases. Table 5 shows the operation conditions of the CASC; the nitrogen extraction rate is 34.9% and oxygen extraction rate 42.1%. In practical industrial applications, case 2 is the optimal model. Compared with the CASC, the oxygen extraction ratio in case 2 rises from 42.1% to 50%, increasing 18.76%, and nitrogen extraction rate increases from 34.9% to 97%, increasing 177.94%, far superior to CASC.

CC inst =

⎛ M&S ⎞ 0.82 ⎜ ⎟ × 2047.24bp ⎝ 280 ⎠

We choose the heat transfer coefficient U = 1000 W m−2 K−1; the heat transfer area per stage is 3.69 m2. Table 7 shows the Table 7. Economic Comparison of Case 2 and CASC case 2 panels cost, 105$ compressor cost, 105$ electricity, 105$ payback time, year

CASC

1.4 2.44 2.59 6.63 8.30 (1.40 + (2.44 − 2.59))/ (8.30 − 6.63) = 0.75

economic comparison of case 2 and the CASC. The panel cost of case 2 is $1.4 × 105. The compressor cost of case2 and the ITCASC are $2.44 × 105 and $2.59 × 105. The increased capital cost of the ITCASC is $1.25 × 105. The decreased operation cost of the ITCASC compared with conventional distillation columns is $1.67 × 105. The payback time is 0.75 year, which reveals that the energy consumption and economic benefits of the ITCASC are far superior to the CASC.

Table 5. Operating Conditions of CASC CASC feed flow, mol/s feed pressure, Pa flow rate of WLN, mol/s flow rate of expansion air, mol/s flow rate of nitrogen product, mol/s flow rate of oxygen product, mol/s nitrogen extraction rate, % oxygen extraction rate, %

case 2

basically the same; the optimization models of cases 2 and 3 are far less than the CASC, while the revenue of cases 1, 2, and 3 is much more than that of the CASC. The unit energy consumption of cases 1, 2, and 3 declines 24%, 40%, and 46% compared with the CASC, respectively. Capital Cost. For heat transfer panels installed in the ITCASC, a feasible value was assumed to be 1000 W/K/m2.32 The installed cost was estimated as a function of the heat transfer area,32 A (m2), using

Figure 9. Liquid flow rate distribution.

flow rate of nitrogen product, mol/s purity of nitrogen product, % flow rate of liquid oxygen product, mol/s purity of liquid oxygen product,% nitrogen extraction rate, % oxygen extraction rate, %

case 1

188.1 579 573 156 56 66.54 21.55 34.9% 42.1%

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CONCLUSIONS Cryogenic air separation is currently the most widely used but energy-intensive technology for producing large quantities of oxygen and nitrogen. Cryogenic distillation consumes a large amount of energy and takes up about 75% of the whole air 14522



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separation field with low thermodynamic efficiency. A novel structure of an ideal ITCASC with full internal thermally coupled is applied without a condensing reboiler, which has a better separation effect and energy efficiency. A numerical model of the ITCASC is established. Withdrawing a side stream it is beneficial to yield high-purity oxygen and nitrogen simultaneously with a high extraction rate. Research results show that the main heat transfer distributed to the whole column, the thermal coupling effect is obvious, and there is a strong driving force to transfer heat from the HPC to the LPC and a large optimization space of the rectifying section pressure. A rigorous optimization model of an internal thermally coupled air separation column is further established, and analysis is carried out in detail. For the ITCASC, in order to guarantee the driving force of each coupled stage, the temperature difference of the coupled stage is constrained. The actual pressure of the HPC can drop from 5.8 to 4.6 MPa. Without the temperature constrain, the ideal pressure can drop to 3.9 MPa. The actual unit energy consumption in case 2 decreases 40%, and the ideal unit energy consumption in case 3 decreases 46% compared to the CASC process; the energy consumption decreases significantly. Compared with the CASC, the oxygen extraction rate in case 2 increases from 42.1% to 50%, the nitrogen extraction rate increases from 34.9% to 97%, increasing 177.94%, and the normalized energy consumption per unit of output decreases by 40%. The extraction rate, energy consumption, and economic benefits of the ITCASC are far superior to the CASC, and the proposed ITCASC process thus has great promising application prospect.

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H = mole enthalpy (J/mol) ε = adiabatic compression index, ε = 1.2 M&S = Marshall and Swift index c = coefficient c of ITCASC panel HECinst = installed cost of heat exchangers (U.S. dollars, $) CCinst = installed cost of the compressor (U.S. dollars, $) bp = brake power (W) Abbreviations

ITCASC = internal thermally coupled air separation column ITCDIC = internal thermally coupled distillation column CASC = conventional air separation column HPC = high-pressure column LPC = low-pressure column LO = liquid oxygen GN = gas nitrogen WLN = low-purity liquid nitrogen GAIR = oxygen-rich vapor air LAIR = oxygen-rich liquid air E1, E2 = heat exchanger C1, C2 = compressor V1 = throttling valve Subscripts

i = particular species or component j = stage number in = inflow out = outflow Superscripts

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AUTHOR INFORMATION

F = feed flow L = liquid flow V = vapor flow

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Corresponding Author

*Corresponding Author E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by Joint Funds of NSFC−CNPC of China (Grant U1162130), National High Technology Research and Development Program (863, Grant 2006AA05Z226), and Zhejiang Provincial Natural Science Foundation for Distinguished Young Scientists (Grant R4100133), and their support is thereby acknowledged.

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NOTATION P = pressure (Pa) V = vapor flow rate (mol/s) L = liquid flow rate (mol/s) T = temperature (K) x = liquid mole fraction y = vapor mole fraction z = feed mole fraction F = feed flow rate (mol/s) G = gas side stream (mol/s) S = liquid side stream (mol/s) UA = heat transfer coefficient (W/K) U = heat transfer coefficient (W/K/m2) A = heat transfer area (m2) Q = rate of heat transfer (J/s) K = vapor−liquid equilibrium 14523



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Modeling, Characteristic Analysis, and Optimization of Ideal Internal

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