Characteristic Analysis and Optimal Design on Heat-Transfer Capacity

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Separations

Characteristic Analysis and Optimal Design on Heat-Transfer Capacity for Energy Saving of Heat-Integrated Air Separation Columns Zhiyu Wang, Xinggao Liu, Shenghu Xu, Daoxiong Xie, Qiquan Chen, Jianbin Zhong, and Jinghe Zheng Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.8b00735 • Publication Date (Web): 04 May 2018 Downloaded from http://pubs.acs.org on May 6, 2018

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Industrial & Engineering Chemistry Research

Characteristic Analysis and Optimal Design on Heat-Transfer Capacity for Energy Saving of Heat-Integrated Air Separation Columns Zhiyu Wang1, Xinggao Liu*,1, Shenghu Xu2, Daoxiong Xie2, Qiquan Chen2, Jianbin Zhong2, Jinghe Zheng2 1

National Engineering Research Center of Industrial Automation, Control Department, Zhejiang

University, Hangzhou 310027, P. R. China 2

China Petroleum Chemical Co Jiujiang branch, Jiujiang 332004, P. R. China

ABSTRACT: Researches on characterizing and optimizing heat-transfer capacity (UA), an important design parameter determining separation efficiency and energy consumption in heat-integrated air separation columns (HIASC), are presented. The mathematical mechanism model of HIASC is built firstly, then characteristics of UA is explored. It is discovered that on one hand increasing of UA will lead to higher compressor load and thus brings higher energy consumption, however on the other hand increasing of UA will benefit mass transfer and conversely reduces energy consumption. For this reason, the optimal design on UA makes available the maximum energy efficiency together with the considerable saving of the equipment investment, which provides guidelines for further designing of HIASC. Furthermore, an optimal partially coupled structure of HIASC is developed to exploit energy saving potential by lowering minimum temperature difference. The obtained optimization results show that the optimal design of UA for a fully coupled HIASC has achieved a 41.5% reduction in energy consumption compared to conventional air separation columns (CASC), and up to 46.9% energy reduction is achieved by applying the optimal partially coupled design. Keywords cryogenic air separation, heat-integrated distillation columns, energy-saving characteristics, optimal thermal coupling distribution

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

1.

INTRODUCTION

Air separation is a common process to produce industrial gases including oxygen and nitrogen, and has wide application in chemical industries, integrated gasification combined cycle, oxy-combustion power plant, etc..1–3 At present, air separation can be achieved by a variety of technologies, for example, distillation, membranes and adsorption. Cryogenic distillation is capable of simultaneously producing a large amount of high-purity gas products from atmospheric air and is most widely used among the above-mentioned methods.4 In spite of its wide application, cryogenic distillation is also an energy-intensive process which is operated at a rather low thermodynamic efficiency, thus energy-saving optimization is currently in urgent need.5 In the purpose of energy-saving and cost reduction, many new energy-saving cryogenic air separation technologies have been proposed and studied in the last two decades, for example, the elevated-pressure cryogenic air separation unit,6 the recuperative vapor recompression air separation process,7 and the air separation process based on cold energy recovery of liquefied natural gas,8 et al. The heat-integrated air separation column (HIASC) has approximately 40% energy-saving potential compared to the conventional air separation column (CASC), and could be the most promising air separation technology according to our previous work.9 Heat-integrated distillation columns (HIDiC) used in HIASC was firstly proposed by Mah et al.10 as secondary reflux and vaporization (SRV). In the HIDiC, the temperature difference between the stages is utilized to improve energy efficiency.11 Modeling and optimization of heat integrated distillation systems have received intensive research attention. Olujic et al.12 presented a study on the conceptual design of an economically attractive HIDiC in a propylene-propane splitter. Suphanit13 studied the optimal heat distribution in an HIDiC for propylene/propane separation. Chen et al.14 proposed a method for configuring a simplified ideal HIDiC in terms of the separations of ethylene-ethane and benzene/toluene binary mixture. Wakabayashi et al.15 used H-xy and T-xy diagrams to design HIDiC for benzene/toluene separation. The above-mentioned work plays an important role in applying heat integration technology to distillation columns for the binary mixture. Typical two-column cryogenic distillation process consists of two distillation columns operating at a different pressure.16 This native structure of cryogenic distillation columns precisely meet the basis 2


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of HIDiC, so it is natural to apply HIDiC technology to the cryogenic distillation process.17 However, the structure of HIASC is different from those common HIDiCs in the open literature. In the HIASC, the air needs to be compressed before fed into the columns, which is a major energy consumer in the whole process; besides, a side stream of low-purity liquid nitrogen product needs to be withdrawn at the argon-rich stage, which is not involved in other HIDiC applications. In terms of modeling and simulation, the cryogenic operating conditions and the non-ideal three-component system involved in the air separation process can cause strong nonlinearity and complexity in the system,18 and specialized methodologies are needed for modeling and analysis for such nonlinear systems.19–23 Heat-transfer capacity (UA) is a fundamental design parameter in the HIASC to determine the heat-integrated configuration.24 UA is a physical quantity used to describe thermal power per unit temperature difference in a heat exchanger. It is the product of the overall heat-transfer coefficient (U) and the effective heat-transfer area (A) of a heat exchanger, and is usually considered in conjunction during the conceptual design stage. Only a few studies on heat integration configuration of HIASC have been carried out. Fu25 analyzed the characteristic of HIASC based on the nonlinear wave model, pointing out the nonlinearity and asymmetry of the HIASC. Van der Ham and Kjelstrup26 studied the influence of heat integration has on the performance of the air separation process by the means of entropy analysis, providing an overall method for evaluating the performance of the distillation section. In our previous work,27 characteristic analysis and optimization of UA is carried out to obtain the minimum operating pressure, which is not sufficiently rigorous for optimization of energy consumption.28–30 Configuration design of UA is an indispensable but relatively unexplored research content of the HIASC. This paper, therefore, presents a study on characterization and optimization of UA in the HIASC. The research of this paper shows that increase of UA under specific circumstances will lead to the increased electrical power of compressor and thus higher energy consumption, and an optimal value of UA can be found to achieve maximum energy efficiency, which can also save equipment investment at the same time. The structure of this paper is as follows: a simulation model of HIASC is firstly built, then 3



characteristics of UA is studied to specify optimization strategy. The factors that decide energy consumption of HIASC are then reassessed, and a more accurate objective function in the optimization problem is presented at last, leading to solid optimization results. 41.5% power consumption is reduced compared to the conventional air separation columns (CASC) by optimally designing UA, and up to 46.9% reduction can be achieved by taking a partially coupled column structure which allows applying a higher value of UA.

2.

CHARACTERISTIC ANALYSIS

Figure 1. Schematic Diagram of HIASC (GAIR, gas air; LO, liquid oxygen; GN, gas nitrogen; WLN, low-purity liquid nitrogen; E1, E2, heat exchanger; V1, throttling valve; C1, C2, air compressor). 2.1.

Structure Description. Figure 1 illustrates the schematic diagrams of HIASC. HIASC

mainly consists of a high-pressure column (HPC) and a low-pressure column (LPC). These two columns are connected by a compressor (C2) and a throttling valve (V1). Atmospheric air is compressed in a compressor (C1) and cooled in the main heat exchanger (E1), then is fed into the bottom of HPC after being. High-purity oxygen and nitrogen are maintained from the bottom of LPC and top of HPC, respectively. HIASC is distinguished from CASC by the plate-fin heat exchangers installed between the HPC and the LPC, which provide sufficient heat transfer capability even if the 4


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tray spacing is small. The heat transfer contributes to the increase of both the downward reflux flow rate in the rectifying section and the upward vapor flow rate in the stripping section. The heat duty of the condenser and the reboiler is therefore significantly reduced, thus energy-saving is achieved. For an ideal HIDiC, it is possible to completely eliminate the condenser or the reboiler.31 2.2.

Model description. The majority of the energy is consumed by the compressor in a HIASC.

The compressor brake power (W, expressed in units of W) is calculated by32 µ −1   µ   P   −1 out W= Vin RTin   − 1 ⋅η  µ −1  Pin   

µ

(1)

where V is the mole flow rate (expressed in units of mol/s), T is the temperature (Kelvin), P is the pressure (Pa), R is the universal gas constant (R = 8.314 J/mol/K), the subscript “out” represents outflow, and the subscript “in” represents inflow. The value of the polytropic index ( µ ) is taken to be 1.4, and the value of thermal efficiency ( η ) is taken to be 0.68. To estimate the annual energy consumption and the operation cost, it is assumed that the HIASC is operated at an uptime of 300 days per year, 24 hours per day, and the unit price of electricity is 0.2 $/kWh. The steady-state model of the HIASC is derived from the equation sets as follows. In this model, it is assumed that no pressure drop occurs across stages and all stages are ideally mixed. The subscript j denotes the stage number counting from the top of HPC to the bottom of LPC. The subscript i denotes one of the three main components, which are nitrogen, oxygen and argon, respectively. The heat-transfer rate between thermally coupled stages:

Q j = UA j × ∆T j

(2)

where Q is the heat transfer rate, UA is the heat transfer capacity, and ∆T is the temperature difference. Heat balance equations:

L j −1H Lj −1 + V j +1H Vj +1 − ( L j + S j )H Lj − (V j + G j ) H Vj + Fj H Fj − Q j = 0

(3)

where L is the liquid flow rate, V is the vapor flow rate, F is the feed flow rate, S is the liquid 5



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withdraw flow rate, G is the vapor withdraw flow rate, and H is the mole enthalpy. The superscript L denotes liquid, V denotes vapor, and F denotes feed. Material balance equations:

L j −1 xi , j −1 + V j +1 yi , j +1 − ( L j + S j ) xi , j − (V j + G j ) yi , j + Fj zi , j = 0

(4)

where x denotes liquid mole fraction, y denotes vapor-liquid mole fraction and z denotes feed mole fraction, respectively. Summary equations: 3

∑x

i, j

=1

(5)

=1

(6)

i =1 3

∑y

i, j

i =1

Vapor-liquid equilibrium equations:

yi , j = ki , j xi , j

(7)

where k is the vapor-liquid equilibrium coefficient. The value of k is a complex function of temperature, pressure and mole fraction of both liquid and vapor flow:

ki , j = f (T j , p j , xi , j , yi , j )

(8)

The function is solved with Peng-Robinson state equation,33 and Harmens rule is employed as the mixing rule.34 An 80-stage HIASC model is built with parameters similar to a typical CASC, as stated in Table 1. Table 1. Design and Operation Conditions of HIASC Model number of stages

HPC 40, LPC 40

pressure of HPC, Pa

579573

feed flow rate, mol/s

128.1

feed thermal condition

0.26

feed stage

40 of HPC

withdraw stage of WLN

5 of LPC

withdraw rate of WLN, mol/s

18 6


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In the characteristic analysis, the number of stages for HPC and LPC are equal. The feed stage is the bottom stage of HPC. WLN is withdrawn to improve the purity of oxygen and nitrogen products. UA is initially set as 4000 W/K, then is increased by 20% to 4800 W/K. The same value of UA is used for all stages in the columns. The profile of the two conditions is compared to study the influence of UA on the operation of HIASC. 2.3.

Thermal Coupling Contribution Analysis. One of the distinguishing characteristics of

HIASC is the thermal coupling contribution between each pair of stages, as is shown in Figure 2. When UA is increased by 20%, the value of thermal coupling over the whole HIASC also increases by around 20%, which is roughly equal to the increase rate of UA. According to Eq. (2), the thermal coupling between two specific stages is the product of UA and temperature difference ∆T of the corresponding stages.

Figure 2. Thermal coupling distribution comparison before and after UA+20%. From the research above, the conclusions can be made: (a) the heat-transfer capacity UA is the most important design parameter to affect thermal coupling in HIASC; (b) although UA is widely increased by 20%, temperature difference ∆T is barely affected. Furthermore, UA is the product of U and A of the heat exchangers. Although stronger thermal coupling can be achieved by increasing UA, either U or A has to be increased, correspondingly. In the conceptual design stage, it is generally sufficient to 7



take U as a constant13 and adjust UA by merely varying A, which is usually limited due to the usually small tray spacing used for air separation, though. The price of heat exchangers could increase sharply if A is enlarged beyond a certain extent because of the difficulty of structure design. If it is necessary to adjust UA by varying U, a novel material for heat exchangers may be introduced, which will lead to an even more dramatic rise in the price. In order to reduce the equipment cost of HIASC, it is important to choose an optimal value of UA, which provides an approach for the design of heat exchangers in the HIASC.

Figure 3. Temperature distribution comparison before and after UA+20%. To further study the specific effect of UA on ∆T, the temperature contribution in HIASC with the two different values of UA is obtained and shown in Figure 3. The curve with higher temperature is the profile of HPC, while the curve with lower temperature is the profile of LPC. After UA is increased by 20%, the temperature of stages in HPC and the top four stages of LPC both decreases, while the temperature of other parts in LPC increases, but the change is very slight, where the largest changing ratio is only about 0.2%. The temperature of the compressed fluid in Eq. (1) is located at 1st stage of LPC and is only slightly decreased from 79.75 to 79.58K. Generally, the temperature distribution in HIASC is mainly influenced by PH , and is almost unaffected by overall heat-transfer

8


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coefficient determined by the material or effective area of heat exchangers. This conclusion proves the validity of the results drawn from Figure 2, and also lays a theoretical foundation for actual operation about the temperature and design optimization of the HIASC. 2.4.

Vapor Flow Rate Distribution Analysis. The Figure 4 shows the vapor flow rate

distribution. The vapor flow rate is much higher in the middle part of the HIASC. Thermal coupling is improved along with the increase of UA, which contributes to liquefaction in HPC and vaporization in LPC on each stage, so the slope of the curve will increase sharply. Additionally, at the bottom of LPC, the vapor flow rate is restricted to be fixed by mass balance equation over the whole columns. Consequently, the vapor flow rate at top of LPC increases from 203.47 mol/s to 243.37 mol/s, and the increasing ratio is 17.3%, which is slightly smaller than the increasing ratio of UA. According to Eq. (1), energy consumption of the compressor is proportional to the molar flow rate of the compressed fluid. As a consequence, increasing of UA alone will typically result in the growth of energy consumption. As a conclusion, minimum of energy consumption cannot be achieved by increasing UA as large as possible, which will also result in a higher capital cost. An optimal value or range of UA may exist to minimize energy consumption of HIASC. This provides a theoretical background for further studies on optimization of UA in HIASC.

Figure 4. Vapor flow rate distribution comparison before and after UA+20%. 9



Meanwhile, strengthening liquefaction and vaporization is equivalent to increasing the reflux and boil-up ratio of HIASC, so the separation capacity of HIASC is improved.35 Correspondingly, it is possible to lower PH , which will conversely reduce the load of the compressor according to Eq. (1). Besides, the decrease of pressure will also have a direct influence on the temperature of HPC and narrows the temperature difference between thermal coupled stages, which consequently cut down the inflow rate of the compressor. As a summary, although increasing of UA alone will result in higher energy consumption of compressor, the pressure required to get products of equal purity can be lowered, and conversely lower energy consumption. Consequently, the function of energy consumption and UA will be non-monotonic, and further studies are needed.

Figure 5. Vapor flow rate distribution comparison with optimized pressure before and after UA+20%. 2.5.

Characteristics with Optimal Pressure. In this section, for each value of UA given, values

of PH and feed temperature are adjusted so that the purity of oxygen and nitrogen products does not change. Under this condition, flow rate does not change as much with UA increasing due to the decrease in pressure. Figure 5 shows the vapor flow rate distribution at both values of UA, respectively. For each model, purity of oxygen is 99.7%, and purity of nitrogen is 99.9% to meet requirements for industrial usage. In the case where UA = 4000 W/K, the optimal PH is 4.4276 × 105Pa. In the case 10


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where UA = 4800 W/K, the optimal PH is 4.3137 × 105 Pa. Because of the decreased value of PH , vapor flow rate in the whole columns drops after UA is increased, which is different from the results in Figure 4. Figure 6 shows the optimal pressure when UA changes in HIASC with each number of stages. In all cases, the increases of UA will strengthen the capacity of separation of HIASC, so PH can be reduced, which provides evidence to support the theoretical analysis made before. For HIASC with more stages, PH can be lowered while still acquiring products with same purities. When constraints on product purities are given, a minimum PH can usually be obtained. Because PH is also a major factor contributing to energy consumption, the minimum feasible value will usually also be the optimal value considering of energy consumption. It provides a theoretical basis for further study on the optimization of energy consumption of HIASC.

Figure 6. Optimal pressure where n=20, 30 and 40. Figure 7 shows how the total flow rate of compressed fluid flowing through compressor C2 is influenced by UA in HIASC with different numbers of stages. In this study, HIASC is always operating at the optimal pressure shown in Figure 6. For HIASC with a different number of stages, the influence of UA on energy consumption is not same. At a lower value of n=20, With UA increasing, 11



the flow rate always drops. In this case, increasing of UA will reduce both outflow pressure and flow rate of C2, and thus will always reduce energy consumption. When n is raised to 30, the flow rate decreases until UA increases to 6500 W/K, and begins to increase afterward. At a higher value of n at 40, the minimum point occurs at a much smaller value of UA, and flow rate nearly always increases with UA increasing. In these two cases, the functional relationship between energy consumption and UA is not monotonic, and an optimal point of UA may exist where minimum energy consumption can be achieved.

Figure 7. The total Flow rate of the compressor with optimal pressure where n=20, 30 and 40. In our previous work,27 it is assumed that the inflow rate of compressors is fixed, and this study provides a more precise and rigorous result. Under specific circumstances, increasing of UA will not only raise the capital cost, but will also result in higher energy consumption, which may seem counter-intuitive. Optimal designs cannot be acquired by simply increasing the value of UA, and optimization need to be carried out in order to minimize energy consumption. It gives proof to the analysis before and provides a solid foundation for further optimization.

3.

OPTIMIZATION 3.1.

Objective Function. Generally speaking, the majority of energy required for the HIASC is 12


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consumed by the two compressors C1 and C2. According to Eq. (1), compression work is theoretically related to Pin , Pout and Vin . The energy consumption of the HIASC is:

W = W C1 + W C2

(9)

C1 = W C1{PinC1 , Pout , V C1 , T C1} + W C2 {PinC2 , PouC2t , V C2 , T C2 }

C1

C2

Assume that Pin , Pin

C1

C2

are equal to atmospheric pressure, Pout and Pout are the pressure of

HPC, and thus is equal to PH . The flow rate V C1 flowing through C1 is determined by the feed flow rate and is not influenced by UA. T C1 and T C2 are respectively temperature of inflow of C1 and C2, and has been proven to be slightly influenced by UA. Therefore, the energy consumption of the HIASC is mainly determined by the flow rate V C2 and the pressure of the HPC. As studied above, the pressure of the HPC can be reduced with UA increasing, but the flow rate V C2 may increase, and the functional relationship between these variables is nonlinear, so how UA will influence energy consumption of the HIASC is still unclear, so the equation is simplified to: C2 ,V C2 } W = W {Pout

3.2.

(10)

Fully Coupled HIASC Optimization Model. In this optimization problem, a HIASC with

40-stage HPC and LPC is studied. UA is adjusted to get the minimum energy consumption, while the feed flow rate, the side stream flow rate are fixed. The same value of UA is used for all stages in the HIASC. The equality constraints are derived from the model described as Eqs. (2) – (8). The constraints on the purities of nitrogen and oxygen are as follows to guarantee product quality:

yN2 ≥ 99.9%

(11)

yO2 ≥ 99.7%

(12)

In addition, to ensure heat-transfer driving force between each pair of stages, the minimum temperature difference is set as 1.8K according to the operational practice of the CASC:

∆Tj ≥ 1.8K, j = 1...n

(13)

Between the CASC and the HIASC, only the configuration of the heat transfer exchangers is 13



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changed, while the minimum temperature difference of the heat transfer exchangers is not influenced, so the temperature difference of CASC can be applied to the HIASC. Besides, the temperature difference of 1.8 degrees is usually sufficient for the air separation process, which can still be lowered. The minimum temperature difference can be as low as 1K in some application of HIASC.36 Consequently, optimization model 1 is described as:

Min W = ϕ (UA) s.t. equality constraints: Eqs. (2) - (8)

(14)

inequality constraints: Eqs. (11) - (13) 3.3.

Partially Coupled HIASC Optimization Model. In our previous work,37 it has been

proven that the ideal potential of energy-savings can be achieved by ignoring the constraints of minimum temperature difference and stages with lower temperature are no longer thermally coupled. The Eq. (2) is now:

UAj × ∆T j Qj =  0

, ∆T j ≥ 1.8K , ∆T j < 1.8K

(15)

Optimization model 2 is described as:

Min W = ϕ (UA) s.t. equality constraints: Eqs. (3) - (8) and (15)

(16)

inequality constraints: Eqs. (11) - (12) Considering the high computational complexity of modeling and optimizing of HIASC, the optimization procedure is separated into multiple steps and solved in a circular sequential-modular approach. The procedure of optimization is separated into three modules as illustrated in Figure 8. It consists of an optimizer, an economic analysis module, and a HIASC simulation module. In the HIASC simulation module, the initial solution is hard to find for different values of the decision variables, so a time-sequence simulation is carried out based on the dynamic mass balance equation to provide initial guess and accelerate convergence:

hdxi , j /dt = L j −1 xi . j −1 + V j +1 yi , j +1 − ( L j + S j ) xi , j − (V j + G j ) yi , j + F j zi , j

(17)

where h is the liquid holdup (mol), and t is the time variable. The economic analysis module uses Eq. 14


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(1) to calculate the energy consumption and operation cost of the HIASC. The successive quadratic programming (SQP) method, which works well for medium-sized optimization procedures including this problem, is applied in the optimizer module.38 During each iteration, the optimizer receives objective function from economic analysis module as well as constraints from the HIASC simulation module, and provides new design parameters back to the HIASC model, until final optimization results are obtained.

Figure 8. Schematic diagram of optimization procedure.

4.

RESULTS AND DISCUSSION

The HIASC model before optimization is taken as case 1, the optimal fully coupled HIASC model is taken as case 2, and the optimal partially coupled HIASC model is taken as case 3. In addition, the CASC and the internal thermally coupled air separation column (ITCASC) model27 is taken for comparison. The two models have the same feed flow rate and product purity requirements as those in this work. Table 2 shows the optimization results in case 2 and 3. Table 2. Optimization Results of Design and Operation Conditions in case 2 and 3 case

case 2

case 3

thermally coupled stages

1-40

1-9, 34-40

UA, W/K

3775

6583

pressure of HPC, 105 Pa

4.6283

4.3850

inflow thermal condition

0.2842

0.2560

inflow rate of C2, mol/s

264.61

244.05

4.1.

Energy Consumption Analysis. The corresponding energy consumption of the three cases

as well as the CASC model mentioned above is shown in Table 3. In case 1, the HIASC is operated 15



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with operating parameters similar to a typical CASC, but the energy consumption is reduced by 25.6% compared to the CASC. That means HIASC is an efficient and energy conservative air separation method, with a minimum energy-saving potential of more than 20%. In case 2 and 3, the energy consumption is reduced by 41.5% and 46.9%, which reveals the maximum energy-saving potential of HIASC. By upgrading CASC to HIASC, up to 7.6 million dollars in annual operating cost can be saved for a single installation. Table 3. Energy Consumption Comparison

CASC27

ITCASC27

energy consumption,105 W

11.25

annual operation cost, 106 $ compare

Current work case 1

case 2

case 3

7.92

8.367

6.582

5.973

16.20

11.40

11.76

9.478

8.600

100%

70.4%

74.4%

58.5%

53.1%

In case 2, by optimally designing UA of HIASC, the energy consumption is reduced by an additional 15.9% compared to case 1, which is a considerably high energy-saving result. The minimum temperature difference occurs at the stage no. 24, of which the value is 1.8K, which is equal to the minimum temperature difference allowed. That means the constraints of temperature difference is in effect and thus the pressure cannot be further lowered, so the potential of energy-saving cannot be completely exploited. In case 3, the energy consumption is further reduced by 5.4% compared to case 2. The results conform to the general rule that higher energy-saving can be achieved by reducing the number of thermally coupled stages. Different from the fully coupled structure studied in case 2, only a total of 16 stages is still thermally coupled in case 3, which are stage number 1-9 and 34-40, specifically. Corresponding to the decrease of the number of coupled stages, UA of the remaining stages has been raised from 3775 W/K to 6583 W/K. But since the number of heat exchangers is sharply decreased, the equipment investment cost of heat exchangers can possibly be reduced. The ITCASC model was able to reduce energy consumption to 70.4% compared to the CASC model. Among the design procedures studied in this work, the case 2 reduces energy consumption to 16


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74.4%, which is not as efficient as the ITCASC model. The case 2 and case 3 can reduce energy consumption by additional 11.9% and 17.3% compared to the ITCASC model, respectively, showing obvious advantages compared to the ITCASC model. The value of UA used here is relatively high in practice. Van der Ham et al26 introduced UA per mole feed to evaluate the heat transfer configuration of HIASC. The value in that work was 44 W /K/mol per stage, while in this work it is 6583 W/K / 128.1 mol = 51 W/K/mol per stage. The values are close, which means the relatively high value of UA in this work is mainly because of the larger flow rate and thus larger heat transfer rate needed. The UA value Nakaiwa et al.39 applied is 4804 W/K per stage, which is similar to that of current work. 4.2.

Heat Duty Distribution Analysis. Figure 9 shows the value of thermal coupling in each

case. The area under the curve in each case indicates the sum of thermal coupling over the whole columns. In case 1 the area is 5.98 × 105 W, in case 2 it is 5.66 × 105 W, and in case 3 it is 5.38 × 105 W, which gradually decreases from case 1 to case 3. Since heat-transfer is related to flow rate distribution in HIASC, and the latter is the main influence factor of compressor power, so energy consumption can be lowered by reducing the amount of thermal coupling all over the columns, which provides a method for the consideration of energy-saving from an overall perspective.

Figure 9. Thermal coupling distribution in case 1, 2 and 3. 17



From case 1 to case 3, the amount of thermal coupling at both ends of columns becomes larger, while in the middle part of columns it becomes lower. The conclusion can be made that the potential of energy-savings is achieved by strengthening thermal coupling at the two ends of columns, where the temperature difference is higher, so that heat exchange efficiency can be improved. In this way, it is possible to lower both the pressure of HPC and the inflow rate of the compressor, which provides another method for the consideration of saving energy consumption. Olujic et al12 studied the conceptual design of the HIDiC in the propylene-propane splitter and compared it to a column with vapor recompression system. The result showed that the electricity consumed in the HIDiC was lowered by 25.4% than that in the vapor recompression system, which achieved significant energy savings in the process. The study also indicated that the column pressure drop could lower heat transfer area requirement for heat exchangers. In this study, the HIDiC applied in air separation achieved up to 46.9% compared to the CASC, and a similar relation between the operating pressure and the heat transfer capacity can be obtained, which indicates the validity of this work and the energy saving potential of HIDiC technology. Since the two studies differ in the object and comparison basis, the results are for reference only. From the discussion above, it can be concluded that heat-transfer distribution is closely related to energy consumption of HIASC, and greater energy-savings can be achieved by improving the efficiency of heat transfer. It is possible to individually design heat-transfer configuration for all thermally coupled stages to further improve energy-savings, which deserves further research.

5.

CONCLUSION

In this study, characteristic analysis and optimization of heat-integrated air separation columns are demonstrated for a purpose of minimizing the energy consumption. Installing heat exchangers with larger heat-transfer capacity will typically strengthen the separation capacity of the HIASC, but will also result in a larger inflow rate of the compressor and thus higher energy consumption. Usually, the pressure of HPC can be lower to counter the increased energy consumption, and there exists an optimal heat-transfer configuration where maximum energy efficiency can be achieved. 18


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With the constraints of minimum temperature difference, an optimal value of UA is found for a typical fully coupled HIASC (case 2) and a partially coupled HIASC (case 3) from the perspective of energy-saving minimization. Compared to a CASC, the HIASC model (case 1) before optimization has achieved a minimum energy-saving of 25.6%. By optimally designing UA configuration, the case 2 has achieved an energy-saving of 41.5%, and the case 3 has achieved an even higher energy-saving of 46.9%. The energy consumption of case 3 has been reduced by additional 17.3% compared to the ITCASC model in our previous work. In case 3 it is also possible to lower the investment cost of heat exchangers. The research results reveal that an optimal value of UA can be found to exploit the energy-saving potential of a HIASC under certain circumstance.

AUTHOR INFORMATION

Corresponding Author *E-mail: [email protected]. Telephone: +86-571-87988336 ORCID Zhiyu Wang: 0000-0002-1836-9514 Xinggao Liu: 0000-0002-0948-1942 Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS

This work is supported by National Natural Science Foundation of China (Grant No. 61590921, 61603336) and Natural Science Foundation of Zhejiang Province (LY18D060002, LY16B040003), and their supports are hereby acknowledged.

NOMENCLATURE

Notations A = Heat-transfer area, m2 19



F = Feed flow rate, mol/s G = Vapor withdraw flow rate, mol/s H = Mole Enthalpy, J/mol h = Liquid holdup, mol k = Vapor-liquid equilibrium coefficient L = Liquid flow rate, mol/s n = Number of stages P = Pressure, Pa Q = Heat-transfer rate, W R = Gas constant, 8.314 J/mol/K S = Liquid withdraw flow rate, mol/s T = Temperature, mol/s T = Time, s U = Overall heat-transfer coefficient, W/m2/K UA = Heat-transfer capacity, W/K V = Vapor flow rate, mol/s W = Compressor brake power, W x = Liquid mole fraction, mol/mol y = Vapor mole fraction, mol/mol z = Feed mole fraction, mol/mol Greek symbols

µ = Polytropic coefficient η = Thermal efficiency ∆T = Temperature difference, K Subscript I = Type of component j = Stage number 20


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H = High pressure columns L = Low pressure columns out = Outflow in = Inflow Superscript C1 = Compressor C1 C2 = Compressor C2 F = Feed flow L = Liquid flow V = Vapor flow Abbreviations HIASC = Heat-integrated air separation columns HIDiC = Heat-integrated distillation columns CASC = Conventional air separation columns HPC

= High-pressure columns

LPC

= Low-pressure columns

SQP

= Successive Quadratic Programming

SRV

= Secondary reflux and vaporization

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For Table of Contents Only

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Characteristic Analysis and Optimal Design on Heat-Transfer Capacity

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