Heat Transfer Investigation and Modeling of Heat Integrated Distillation Column

Fang Jing; Wang Yijing; Su Weiyi; Xuan Bihan; Li Chunli

(School of Chemical Engineering, Hebei University of Technology, Tianjin 300130)

Abstract: The high degree of reversibility of heat integrated distillation column (HIDiC) has been thermodynamically interpreted by the entropy method. In this paper, a heat transfer model and a more universal method were proposed, through which the overall heat transfer coefficient at different height of column under different operating conditions could be obtained before the experiment. Then the separation of a binary ethanol-water system was carried out experimentally as a case study to verify the heat transfer model and the aforementioned calculation method. The close results between the calculation, the simulation,and the experiments suggested that the proposed model and the calculation method in this paper were accurate and applicable.Meanwhile, it was demonstrated that the HIDiC shows obvious effect of reducing entropy increase and improving thermodynamic efficiency as compared to conventional distillation column.

Key words: heat integrated distillation column; heat transfer model; separation process

1 Introduction

Distillation is the most mature technology for separation in the chemical engineering especially in the petrochemical industry, however, its outstanding separation performance is achieved at the sacrifice of a considerable amount of energy consumed with low thermodynamic efficiency.

For a binary separation distillation column, the rectifying section can be seen as a heat source that must release a certain amount of heat, while the stripping section is a heat sink that must take in a certain amount of heat. This inherent property makes it possible for conventional distillation column to fulfill internal heat integration. That is why the heat integrated distillation column (HIDiC) has been noticed by many researchers.

In the HIDiC, the rectifying section is placed inside the stripping section for sharing the same central axis.Based on the principle that the rectifying section and the stripping section need multiple condensation and evaporation separately, the heat released from the rectifying section can be used in the stripping section.Then energy saving can be achieved by reducing the heat loads of condenser and reboiler as shown in Figure 1. To guarantee the necessary driving force for heat transfer, the rectifying section should be operated under higher pressure than the stripping section. Therefore a compressor and a throttling valve are installed between the two sections to adjust the pressure difference as shown in Figure 1.

Figure 1 The typical configuration of HIDiC

The HIDiC was first conceptually proposed by Haselden[1]for air separation. Then Flower and Jackson[2]further systematized the concept and pointed out the advantages of this technology through simulation study based on the second law of thermodynamics. After that, the idea was evaluated by Mah and coworkers[3]under the name of Secondary Reflux and Vaporization (SRV) in 1977.It was indicated that the heat exchange between the rectifying and stripping sections must be at the same elevation. Furthermore, Fitzmorris, et al.[4]analyzed the thermodynamic availability of the C2splitter using the SRV method. In addition, Nakaiwa, et al.[5-6]performed both simulation studies and pilot-plant experiments to illustrate that the HIDiC has an excellent performance in energy saving and energy efficiency enhancement compared with the conventional counterparts.

In the study of the feasibility of design and operation,the hydraulics and other characteristics of the HIDiC were determined, and the results showed that significant energy saving can reach up to 70% in a PP-splitter, while an efficient conceptual design procedure of the HIDiC utilizing the pinch analysis has also been proposed[7]. Then Olujic and Fakhri[8]introduced two intensified HIDiCs,one of which could reduce the consumption of steam in the reboiler, while the other could avoid a trim-condenser,respectively. The application and performance of the HIDiC were also illustrated by case study referred to in the literature. Specifically, the gas-liquid distribution and the position of pinch point were analyzed in the annular structure of HIDiC by Yuan Xigang and coworkers[9-12]in the Tianjin University. They pointed out that the capacity of heat transfer in HIDiC increased with an increasing compression ratio.

In order to achieve efficient heat integration, different HIDiC designs have been reported, including the concentric HIDiC[13-16], the partitioning wall HIDiC[17-20],the shell & tube HIDiC[21-23], and the plate heat exchanger HIDiC[24-26]. Among these designs, the concentric configuration shows excellent performance in heat transfer, because the heat in the rectifying section does not leak to the environment in principle[27], and at the same time, it can reduce the volume and the manufacturing difficulty of the pressure vessel.

Keigo Matsuda and coworkers[28]simulated the HIDiC with the rate-based model, in which the correlation of the mass transfer coefficient and the Chilton-Colburn analogy were used to estimate the heat transfer coefficient of the liquid phase. The results showed that the estimated overall heat transfer coefficient, regardless of the column height and the operating conditions, was nearly the same as that measured in the experimental plant. B. Suphanit[29]investigated two different heat distribution schemes, i.e.uniform heat transfer area and uniform heat distribution,by applying a novel approach to solve the simulation problem in Aspen Plus. The comparison of the two distribution schemes was discussed via two widely-used case studies, namely the benzene-toluene separation and the propylene-propane splitter, and it was found that the most suitable heat distribution scheme was case-specific.Despite the obvious potential, the HIDiC is still hardly implemented in industrial practice due to difficulties related with equipment design and lack of experimental data obtained in a sufficiently large scale. The only HIDiC design reaching the commercialization stage was a twopressure single shell column introduced by a Japanese engineering contractor as described in a recent patent application[30].

In this article, a novel calculation method was applied to the heat transfer model of HIDiC, through which the overall heat transfer coefficient of different elevation of column under different operating conditions was obtained before the experiment. It could provide an efficient way to predict the energy consumption.

2 Mathematical Model

2.1 Thermodynamic analysis

The thermodynamic efficiency of a separation process can be defined as:

where Wminis the minimum amount of work required by each mole of feed to make a complete separation, which can be calculated as follows:

where R is the ideal gas constant, T is the absolute temperature of the mixture and xiis the mole fraction of component i in the feed.

Wlin equation (1) is the energy loss caused by process irreversibility in the mass and heat transfer, pressure distribution, and remixing within a distillation column. It can be expressed as:

where ΔS is the entropy change, and T0is the absolute temperature of the environment.

Equations (1)―(3) show that the thermodynamic efficiency of a process is closely related to its irreversibility which can be reflected by the entropy production. Consequently,it is of great significance to use the entropy method to evaluate the process. Meanwhile, based on the first and second laws of thermodynamics, the amount of energy loss caused by irreversibility can be expressed accurately. For the conventional distillation process in Figure 2 (a), the following equations are tenable:

where SF, SD, SWare the entropy of the feed, the distillate flow, and the bottoms, respectively. Specifically, QRebis the heat duty of the reboiler, Qcis the heat duty of the condenser, Tcwis the temperature of the cooling medium,Tstis the temperature of the heating medium, and T0is the temperature of the environment. Additionally, ΔSgCDiCis the entropy production and ηCDiCis the thermodynamic efficiency of conventional distillation column.

Generally, the thermodynamic efficiency of conventional distillation column is quite low, roughly about 10%[8].

The effect of heat integration on distillation process can be conveniently estimated by using the McCabe-Thiele diagram, as shown in Figure 3.

As shown in Figure 3, the operating lines of conventional column (CDiC) are straight. Therefore the mass transfer driving force of CDiC is nonuniformly distributed along the length of the column,and the smallest value appears at the feed position,which tends to increase towards both ends of the column. That is one of the main reasons leading to the high degree of irreversibility in distillation process.

Figure 2 Conventional distillation column and heat integrated distillation column

Figure 3 McCabe-Thiele diagram of CDiC and HIDiC

However, the operating line of HIDiC is a continuous curve that is parallel to the equilibrium curve, and then the mass transfer driving force is uniformly distributed along the length of the column. If these two curves overlap, the entropy production and the energy loss is zero, and thus the distillation process is perfectly reversible.

Figure 4 Diagram of concentric HIDiC

For a diabatic distillation process as shown in Figure 2(b), or a more specific configuration, e. g. the concentric HIDiC as shown in Figure 4, the entropy change can be calculated through the entropy balance function based on the heat transfer model mentioned above. The equation for the rectifying section is expressed as equation 8, where VRB, LRB, LSD and VSD represent the corresponding streams in Figure 4.

In Equation 8, V is the vapor flow rate, L is the liquid flow rate, and D is the distillate flow rate. Specifically, ΔSfRcan be calculated by the following equation:

Similarly, the entropy balance function for the stripping section can be written as:

To solve the functions, the following equation can be used:

For the adiabatic compressor, the following equation is tenable:

where the subscript comp represents the compressor.

By integrating the entropy balance equations (8)―(13),the entropy change of the heat integrated distillation process can be obtained:

where ΔSgis the entropy change, ΔSfis the entropy flow,Tsiis the temperature of tray i in the stripping section, and TRiis the temperature of tray i in the rectifying section.

It should be emphasized here that although the HIDiC and distillation columns with intermediate heat exchangers seem rather different in process configurations, it is similar in terms of the relationship between the reboiler heat duty and the integration heat duty[31-32]:

Thus the degree of irreversibility can be calculated by the entropy change:

Upon considering the general characteristics of HIDiC,the following inequalities are satisfied:

where the subscript cw represents the cooling water, and st stands for the heating steam.

Thus,

It is clear that the degree of irreversibility of HIDiC is less than that of the CDiC due to the internal heat integration.That is why HIDiC can outperform its counterparts in energy saving.

Furthermore, the thermodynamic efficiency of HIDiC can be calculated by Equation (18).

2.2 Heat transfer model

Even though the heat exchange between the rectifying section and the stripping section should reduce the heat duty of reboiler and condenser, it is quite controversial about the distribution of the internal heat exchange.Generally, the model of average heat duty (AH) as well as the temperature and the heat duty matching (THM) are usually used to describe the heat exchange distribution within HIDiC, but they are both too ideal in the aspect of energy utilization.

Figure 5 Heat transfer model of concentric HIDiC

Take a concentric HIDiC shown in Figure 5 for an example, the column is divided into several equal parts vertically, and each part represents one pairing stage. A new method was proposed to calculate the value of heat exchange at different pairing stage i:

where Qiis the heat exchange within a proper pairing stage i, Uiis the overall heat transfer coefficient of different pairing stages, A is the heat transfer area determined by the size of the column, and ΔTiis the temperature difference within the pairing stage i.

The internal heat transfer of the whole column can be expressed as:

Instead of taking Uias a constant, we strive to obtain its value and profiles through calculation. The calculated Uiare then applied to analyze the energy saving performance.

Since the gas and liquid in the distillation column are saturated, the condensation and evaporation due to the internal heat exchange occur at the same time. According to the empirical formula of Chiriac[24,32],

when (Ga ·Pr ·K″) ＜1015, the heat transfer coefficient of the rectifying section (α0) is:

When (Ga ·Pr ·K″) ＞1015, the corresponding value is:

where r is the latent heat of condensation,is the density of liquid phase, g is the gravitational constant,is the coefficient of thermal conductivity,is the viscosity of condensate liquid, Δt is the thermal driving force, Lˉis the height of the heat transfer surface, Ga and K″ are dimensionless quantity, Pr is the Prandtl number, cpis the specific heat at constant pressure, andis the heat capacity at constant pressure of the condensate liquid.

According to the empirical formula of Rohsenow[33], the heat transfer coefficient of the stripping section (αi) can be expressed as follows:

where Csfis an empirical constant depending on the heating surface and liquid combination, ρVmis the density of vapor phase, and σ is the surface tension of liquidvapor interface. These properties of vapor and liquid phases at the temperature of measuring points are reckoned by Aspen plus 7.2. On this basis, the overall heat transfer coefficient can be calculated:

where λ is the coefficient of thermal conductivity of the column wall, and b is the thickness of the wall.

2.3 Compression ratio

The compression ratio can be calculated through the following equation:

where Poutis the exhaust pressure, and Pinis the suction pressure of compressor. Generally, the smaller the compression ratio is, the higher the thermodynamic efficiency. There is a maximum thermodynamic efficiency identified at a specific compression ratio. When the thermodynamic efficiency exceeds the maximum value,it would decrease gradually with a further increase of compression ratio. Therefore, there is a most suitable compression ratio to achieve the highest thermodynamic efficiency of HIDiC. This part will be discussed in Section 3.3.

3 Experimental Results and Discussion

3.1 Experimental process and parameters

Figure 6 The configuration of pilot-plant concentric HIDiC

Figure 6 shows the configuration of a self-made pilotplant concentric HIDiC. Eight temperature measuring points were installed in the rectifying and stripping sections at regular intervals. In other words, a―h were eight measuring points in the rectifying section, while a′―h′ were eight measuring points in the stripping section. Point a and a′ were called the first pair of temperature points. The number of stages of both sections has been calibrated by the ethanol-water system at total reflux operation. The main parameters of the devices are summarized in Table 1.

Table 1 Main parameters of the experimental devices

A series of experiments were carried out under different compression ratios varying from 1.4 to 2.6. The operating parameters are shown in Table 2.

Table 2 Operating parameters

3.2 Temperature difference investigation

The temperature difference of each pair of temperature measuring points under different compression ratios is shown in Figure 7. It can be seen from Figure 7 that the temperature difference gradually increases with an increasing compression ratio. In addition, it is clear that the compression ratio must be higher than a certain value (1.7 in this case) to ensure efficient heat transfer,otherwise a reverse heat transfer may happen.

Figure 7 Temperature difference at different compression ratios

A series of simulation studies were carried out under different compression ratios while the rectifying section and stripping section are considered to be adiabatic. Figure 8 shows the comparison of temperature profiles between experimental results and the adiabatic simulation under a compression ratio of 1.8, 2.2, and 2.6, respectively. It seems that the two temperature profiles are similar in these figures. Therefore it is reasonable to consider that the concentration distribution along the vertical column is nearly the same between the simulation and the experimental results. In addition, the value of mass transfer rate does not deviate greatly from the value of heat transfer without heat loss[34-35]. Thus we made the assumption that the temperature distribution in HIDiC and the adiabatic columns was the same under the same pressure during the calculation.As a result, the heat transfer coefficient can be calculated by using experimental temperature, with the calculation results shown in Figure 9. It can be seen that with the increase of compression ratio, the fitting between the calculated values and the experimental results is getting better and better, however the overall heat transfer coefficients would decrease when the compression ratio increases more than 2.2. The reasons for this phenomenon will be interpreted in Section 3.3.

Figure 8 Comparison of temperature profiles between experiment and simulation at different compression ratios

Figure 9 Overall heat transfer coefficient at different compression ratios

3.3 Comparison of calculation and experimental values

The amounts of heat exchange are calculated at various compression ratios, and Figure 10 shows the computational results in comparison with the experimental values. It can be seen from Figure 10 that when the compression ratio is lower than 2.2, the experimental results are generally larger than those calculated, and the higher the compression ratio is, the smaller the difference. Moreover when the compression ratio is higher than 2.2, the heat transfer rates obtained from the experiments are smaller than those calculated.It might occur, because the temperature difference between the reboiler and the condenser is large when the compression ratio is high, which could contribute to the energy savings in distillation process. However, the intense condensation occurring in the rectifying section could make the liquid film that is attached on the inner wall continuously thicken, which has a negative effect on energy saving. Moreover, the thickened liquid film might increase the heat transfer resistance, which is ignored in the calculation of overall heat transfer. Homogeneously,the intense evaporation occurs in the stripping section could cause some dry areas on the surface of the outer wall, which could also deteriorate the heat transfer efficiency. That is why the experimental heat transfer rate would decrease, while the compression ratio is too high in Figure 9.

According to the comparisons and analysis mentioned above, it can be seen that the proposed heat transfer model is reasonable, if the compression ratio lies in a specific region. In addition, the heat transfer coefficient can be calculated in this way before the experimental study, which is of great significance on designing HIDiC.

Figure 10 Comparison between calculated and experimental values of heat transfer at different compression ratios

3.4 Thermodynamic analysis

Through equations (5), (7), (14), and (18), the entropy production and thermodynamic efficiency of CDiC (when compression ratio =1) and HIDiC can be calculated,respectively. Figure 11 shows the calculation results. It can be clearly seen that the increase in entropy values of HIDiC at different compression ratios are around 11 J/(kg·K), while the value of CDiC is 14.63 J/(kg·K).The reduction of entropy increase can contribute to the improvement in the thermodynamic efficiency.Moreover, the thermodynamic efficiency of HIDiC at different compression ratios is running at about 25.5%,and the maximum value is 26.05%, which is increased by 7.43% as compared to that of the CDiC. In general,there is a sharp decline in entropy production in HIDiC as compared with CDiC, indicating that the HIDiC can provide a much more reversible process and why the HIDiC shows obvious advantage in improving the thermodynamic efficiency.

4 Conclusions

Figure 11 Comparison of thermodynamic efficiency and entropy production between CDiC and HIDiC

This paper demonstrates that the HIDiC has advantages of reducing the irreversibility and improving the thermodynamic efficiency of distillation process as compared with the conventional distillation column.In terms of performance data, the minimum increase in entropy required by HIDiC at different compression ratios is 10.71 J/(kg·K), while the increased entropy value required by CDiC is 14.63 J/(kg·K). Therefore,the maximum thermodynamic efficiency of HIDiC at different compression ratios is 26.05%, while the maximum thermodynamic efficiency of CDiC is only 18.62%. Hence, the HIDiC shows an obvious advantage in improving the thermodynamic efficiency.

A novel heat transfer model of HIDiC was presented and demonstrated, in which the overall heat transfer coefficient varied along the column and the heat distribution was not uniform along the column. It is essential that the value of overall heat transfer coefficient could be calculated so as to be independent of experimental data, since the temperature of adiabatic simulation in thermodynamic model is similar to the temperature of the HIDiC experiment. Additionally, the presented method of overall heat transfer coefficient is more universal, which has been proved to be reasonable according to experimental results.The good agreement between the calculation, simulation,and experimental results suggests that the heat transfer model presented in this paper can be well applied to the HIDiC. In addition, the overall heat transfer coefficient can be obtained before experiments, which would highlight a viable way of HIDiC design. Meanwhile,it confirms that HIDiC outperforms its conventional counterparts in terms of entropy production and thermodynamic efficiency.

Acknowledgement:This work is supported by the National Key Research and Development Program of China(2017YFB0602500) and the Foundation for High Level Talents of Hebei (A2017002032).