(Re fi ning Process Department, Sinopec Engineering Incorporation, Beijing 100101)

A Comparative Study on Heat Transfer Performance of Typical Petrochemical Reactors

Li Yuxin

(Re fi ning Process Department, Sinopec Engineering Incorporation, Beijing 100101)

The performance of heat transfer is a key issue for reactor design in petrochemical industry. Since the heat transfer in reactors is a complicated process and depends on multiple parameters, the evaluation of the heat transfer performance is usually challenging, and few previous studies gave an overall view of heat exchange performance of different types of reactors. In this review, heat transfer coeffcients of two types of petrochemical reactors, including the packed bed and the fuidized bed, were systematically analyzed and compared based on a number of reported correlations. The relationship between heat transfer coeffcients and fuid fow velocity in different reactors has been well established, which clearly demonstrates the varying range of their heat transfer coeffcients. Heat transfer coeffcients of gas-phase packed bed can exceed 200 W/m2·K, rather than the suggested values (17—89 W/m2·K) mentioned in the literature. The fuidized bed shows better performance for both two-phase and three-phase beds as compared to the packed bed. Systems with liquid phase also show better heat transfer performance than other phases because of the larger heat capacity of liquid. Thus the industrial three-phase fuidized beds have the best heat transfer performance with an overall heat transfer coeffcient of greater than 1 000 W/m2·K. The heat transfer results provided by this review can afford not only new insights into the heat transfer in typical reactors, but also the basis and guidelines for reactor design and selection.

heat transfer; packed bed; fuidized bed; loop reactor; transfer coeffcient

1 Introduction

The petrochemical processes are foundations of modern industry. The most important petrochemical processes include fluid catalytic cracking (FCC), continuous catalytic reforming (CCR), hydrotreating (HT), hydrocracking (HCR), alkylation, ethylene oxide (EO) synthesis, syngas-to-olefins process, polymerization, etc. Each process is unique and challenging as compared with others. However, if the aspect of their reaction heat characteristics is considered, these processes can be grouped into three types, viz.: endothermic, mild exothermal, and strong exothermic reactions. Endothermic reactions require the exterior heat supply, such as the catalytic reforming process. FCC is also an endothermic reaction[1], because the cracking process requires heat supply from the combustion in a regenerator. Mild exothermal reaction needs heat removal, e. g. by interstage cooling used in the hydrotreating process[2]. Strong exothermic reactions usually proceed in reactors characterized by high-effciency heat transfer, such as EO synthesis, polymerization[3], and syngas-to-olefns process[4].

Due to the distinguished thermic features of petrochemical processes, the heat transfer performance of reactors is one of the most important factors for reactor design. Various types of reactors have been employed for the abovementioned processes according to different heat removal capabilities[5]. The main types include the packed bed and the fuidized bed. Packed beds are most widely used in gas-solid and gas-liquid-solid systems. For example, multitubular reactors comprising a fixed bed with large heat exchange area per unit of bed volume have been used to produce ethylene oxide. Fluidized beds are applied in both reaction and regeneration processes in FCC plants. Three-phase fluidized beds, such as slurry beds and ebullated beds, are usually used to upgrade heavy oilsor syngas-to-olefins process because of their good heat transfer performance. And the loop reactor, a special form of liquid-solid fuidized bed, is usually used in polymerization processes.

The exothermal reactions dominate most of the reactions in petrochemical industry. In these cases, the heat should be removed without delay to avoid temperature runaway as well as the formation of “hot spots”. In general, indirect heat exchange through installed surfaces within the reactor is widely used because direct contact between the reactant and cooling fow is avoided[6]. Therefore, the comparison of heat transfer performance of typical reactors through exchanging heat indirectly was focused on in this study.

Aiming at choosing an “ideal” reactor with high energy effciency for a proper process, one should evaluate and try to match the reaction heat with the heat removal capability of the reactors economically. Thus, the heat transfer characteristics of reactors should be frstly well described. Although the heat transfer processes generally involve multistep in multiphase, it is generally accepted that the effective heat transfer coefficient of the reactor is one of the most important parameters that affecting the heat transfer performance. Many studies[7-14]have addressed the heat transfer mechanism and correlations of heat transfer coefficients, and some of the studies have well described the heat performance of a certain type of reactor, such as the gas-solid bubbling bed[11-12,15]. However, to the best of our knowledge, few studies have addressed the comparison of the heat transfer coeffcients of different types of reactors. Additionally, the varying ranges of heat transfer coeffcients of typical reactors in the literature are sometimes ambiguous and even misleading, and the coeffcients have not been systematically analyzed or summarized, which may bring inconvenience to the reactor selection and design in the petrochemical industry.

To fill these gaps, herein a comprehensive review has been provided on the heat transfer coefficients of typical reactors. Some reported heat transfer coeffcients and correlations for the packed beds[14,16-17]and the fuidized beds[18-19]were reviewed and compared. In these correlations, the fuid velocity is one of the most important parameters, since it can be used to conveniently calculate and compare the heat transfer coefficients of different types of reactors. Based on these summarized results, we successfully established the relationship between heat transfer coeffcients and the operating fuid velocity. The reasonable variation range of heat transfer coeffcients for different types of reactors is demonstrated. The systematic comparison and summary provided in this review would likely lead to an intuitive understanding of heat transfer performance of typical petrochemical reactors, which could help engineers to select or design more effcient reactors in the future.

2 Heat Transfer in Typical Reactors

2.1 Packed bed

2.1.1 Trickle bed

Trickle bed is one of important members of packed beds and has been widely used in HT process[17,20]. The heat transfer in a packed bed is complicated[18]. The complexities mainly include conducting the heat transfer among particles in both radial and axial directions, realizing the convective heat transfer between the bed particles and the gas fow, and implementing the heat transfer between the bed wall and bed particles.

The solid particles together with fuid fow are usually treated hypothetically as one bed to simplify calculations. Then the radial heat transfer process can be described by heat conduction. The whole heat transfer process is composed of axial heat transfer and radial heat conduction. The radial and axial effective heat transfer coeffcients are defned asΛerandΛea, respectively. For a cylindrical differential element from a trickle bed, the heat balance equation is:

and in case of boundary conditions:

The axial heat transfer can be ignored because the bed heat transfer mainly occurs in the radial direction. Most previous studies[21-26]focused on developing correlations to calculate the effective radial thermal conductivity and heat transfer coeffcient as functions of dimensionless parameters such as the Reynolds number.

The bed conductivity is correlated to the conductivity ofparticles/fuid, liquid hold-up, the Reynolds number and the liquid Peclet number. Table 1 presents the different correlations developed previously for bed conductivity in the case of two-phase fow in packed bed reactors. Most correlations include two terms: conductive and convective contribution. As a case study, the bed conductivity of some industrial residue hydrotreater reactor was calculated using the same operating conditions as listed in the last row of Table 1. The results indicate that the values from the equations of Lamine[27]and Taulamet[14]are similar for the trickling fow, ～14 W/m·K. However, the values from equations of Weekman[28]and Specchia[13]are very different. Especially for the equation of Specchia[13], the calculated conductivity was 8.5×105W/m·K. The unexpected values can be attributed to the particle to reactor diameter ratio (dp/D) derived from laboratory scale reactor, not from industrial scale reactor. The diameter ratio of the laboratory scale reactor differs from the industrial scale reactors in hundreds or even thousands of times. Therefore, the equation cannot be directly used in the industrial scale.

Table 1 Correlations for bed effective thermal conductivity

Table 2 Correlations for wall heat transfer coefficient

The wall heat transfer coefficients (hw) of trickle beds were also investigated by a few studies[13,27,29-31]. Specchia and Baldi[32]distinguished two flow regimes in trickle bed, viz.: the low interaction regime (LIR) and the high interaction regime (HIR), in presenting results on pressure drop and liquid holdup for two-phase concurrent downfow in packed beds. The frst three equations in Table 2 are correlations ofhwfor LIR, which are correlated to the number groups such as the Reynolds number, the Prandtl number and the Nusselt number[13,29-30]. The calculated heat transfer coefficients in LIR using different correlations are presented in Figure 1. Because the infuence of superficial gas velocity on the heat transfer coefficient is much smaller as compared to the liquid flow[27], the gas velocity is fxed at 0.05 m/s while the liquid velocity varies from 0.003 to 0.013 m/s. The heat transfer coeffcients obtained from both types of correlations gradually increase with the increment of liquid velocity. The difference in heat transfer coefficients calculated by correlations for LIR is relatively small, andhwincreases along with the superfcial liquid velocity.

The last two correlations in Table 2 are suitable for HIR, and a notable different dependence on liquid mass flow rate (Gl) arises. Specchia[13]reported thathwis slightly dependent onGlin high interaction region (pulsed fow), and is equal to 2 100 W/(m2·K) on an average. Buthwis positively related toGlin Lamine’s correlation.

Figure 1 Calculated heat transfer coef fi cients in LIR by different correlations

The estimation ofhwis challenging because it involves a number of effects including changes in particle packing and fluid flow in the near-wall region[33]. So the consistency of the correlations mentioned above is unsatisfactory, and the deviation possibly derives from the differences in experimental heat transfer data. Therefore, comparison of these different correlations is challenging, and more systematic experimental work is needed for this purpose.

2.1.2 Gas-solid fi xed bed

Heat transfer in gas–solid packed bed systems has been critically reviewed by Balakrishnan and Pei[16]. The heat transfer coeffcient of a packed bed is much greater than that of an empty tube at the same superficial velocity owing to the increased turbulence in the presence of particles. For convenience, many correlations for the effective heat transfer rate of the whole bed have been obtained from experimental data in the fxed bed. Many factors can affect wall heat transfer coeffcient, and the factors include the superfcial fuid velocity, the heat capacity, the particle diameter, the porosity, etc[34-38]. When the bed height is unknown, the following correlation suggested by Li, et al.[39-40]is more convenient for calculation.

In case of multitubular reactors used in the EO synthesis process, ifug= 0.4 m/s, the heat transfer coefficient obtained from Eq. (2) is 295 W/m2·K. The value is comparable to the value used in industrial reactors, but exceeds the common range of 17—89 W/m2·K[41-45]. This value is also greater than the results reported by Froment[46]under similar value of the Reynolds number. It can be seen that the tested heat transfer coeffcients given in the literature are unduly “conservative” for industrial applications.

2.2 Fluidized bed

2.2.1 Gas-solid bubbling fl uidized bed

The heat transfer performance between bubbling fuidized beds and submerged surfaces is usually described by heat transfer coeffcients. Assignation of a thermal resistance to a gaseous boundary layer at the heat transfer surface is the most general approach[47-50]. The correlation for vertical tubes (SI units) from Wender and Cooper[15]is

which is suitable for 0.01≤Rep≤100.

Another approach presented by Martin[11-12]utilized the analogy between the particle motion in fuidized beds and the kinetic motion of molecules in gases. The equation is:

where,

As mentioned earlier, the fluidized beds are typically applied in FCC unit, in which a catalyst cooler is generally needed to remove the excess heat in the regenerator. The catalyst cooler of regenerator operates in bubbling regimes, and the heat transfer coefficients calculated by the above two correlations are 933 W/(m2·K) and 583 W/(m2·K), respectively, while taking the superfcial velocity of fuidization air as 0.10 m/s. The mean value of heat transfer coefficients calculated from the two mechanisms is 758 W/(m2·K). But in engineering calculation, a safety factor should be also included for ensuring safe operation.

2.2.2 Gas-solid fast fl uidized bed

Similar to the case of bubbling beds, attention should be paid to the heat transfer between the fast fuidized bed and the heat transfer surfaces. Parameters that affecthwinclude the bed density, the superfcial gas velocity, the sizeof solid particle, the bed temperature and the geometry of heat transfer surface[51-56].

Because the heat capacity of the particles is much larger than that of the gas, the convective particles primarily contribute to the heat transfer in circulating fluidized beds. Therefore, the bed density is one of the most important factors of heat transfer. The convective heat transfer coeffcients depend on the solid particle concentration and the renewal frequency on the heat transfer surfaces.

Divilio and Boyd[57]reported the following relationship between the heat transfer coeffcient and the bed density by ftting experimental data:

whereρmspis the cross-sectional-averaged bed density.

2.2.3 Gas–liquid–solid three-phase fl uidized bed

The bubbling slurry bed and the ebullated bed are studied in this section, but the three-phase fluidized beds with mechanical stirring are not included. The slurry bed reactors exhibit obvious advantages of good heat transfer effect and homogeneous temperature distribution, and lots of studies have been focusing on this topic[58-67].

The coiler, the heat transfer tubes that are arranged vertically or horizontally, and the wall jacket is employed to exchange the heat produced in bubbling slurry bed. The heat transfer coeffcient is affected by several factors, including the superfcial gas velocity, the physical property of liquid phase, the solid holdup, the operating temperature and the pressure. In general, the heat transfer coeffcient increases with the increase in superfcial gas velocity, and decreases with the increase in liquid viscosity[68].

Various correlations were developed to predict the heat transfer coeffcient in slurry bubble columns. Deckwer[10]reported the machanism of heat transfer in the gas-liquidsolid bubble column and theoretically suggested an equation for heat transfer coeffcient:

The heat transfer mechanism of ebullated bed is similar to that of slurry bed, and consequently their correlation forms are similar. The correlations for slurry bed and ebullated bed are summarized in Table 3. In particular, if the correlations include the physical properties of the slurry, the slurry properties could be calculated based on the liquid and solid properties. Taking the density as an example:

The calculated heat transfer coefficients of three phases are presented in the last column of Table 3, using the operating conditions and physical properties of industrial residue hydrotreating systems in slurry bed and ebullated bed. The calculated results of these correlations are consistent.

Table 3 Heat transfer correlations for gas-liquid-solid three-phase fluidized bed

2.2.4 Loop reactors

The loop reactor could be considered as a special form of liquid-solid fuidized bed, which shows good heat transfer performance and has been successfully applied in PP synthesis process because of its large heat transfer area and satisfactory heat transfer coefficient. In the case of propylene polymerization process, a two-phase fow with propylene liquid and polypropylene particles is adopted in the loop reactor. The heat transfer coefficient can be calculated using the relationship proposed for prediction of turbulent fow in tubes[71].

whereμwis the viscosity of wall fuid andμis the viscosity of the slurry, which can be calculated by the Thomas’correlation[72]:

Thehwcalculated by Equation (8) at the propylene polymerization conditions (70oC, 4 MPa,D=0.6 m,ωs=0.5) is as high as 2 500 W/(m2·K), assigning the superficial velocity of slurry to be 7 m/s. If the fouling resistance and wall heat conductivity are considered, the overall heat transfer coeffcient is still greater than 1 000 W/(m2·K). At such a high heat transfer rate, the temperature variation could be controlled within 5oC for the propylene polymerization process.

3 Discussion

The effective heat transfer coeffcients of different types of reactors were calculated using literature correlations at typical conditions of petrochemical processes. In this part, further calculation and analysis will be done to compare the heat transfer performance of different reactors systematically and intuitively.

The superfcial fuid velocity is a primary parameter necessary for the calculation of heat transfer coeffcient in the multiphase fow system. It is therefore selected as a variable to compare the heat transfer performance of different types of reactors. The calculated variation of overall heat transfer coefficients (U) (consideringhw, fouling resistance and wall heat conduction) versus the fow velocity is shown in Figure 2. The superficial liquid velocity is chosen as a variable for loop reactors and trickle-beds while the superfcial gas velocity for other reactors. For convenient application, typical processes in petrochemical industry have covered: the ethylene oxide synthesis in the packed bed, the FCC catalyst regeneration in the gassolid fuidization bed, the residue hydrotreating process in the three-phase bed, and PP synthesis in the loop reactor.

Figure 2 Heat transfer coef fi cients of different bed types

Figure 2 shows the range of heat transfer coefficient of typical reactors at corresponding operating fuid velocity. In particular, the dotted lines present the transition region between the bubbling fluidized bed and the fast fluidized bed. The hollow square point is the turning point, where theugis the terminal velocity. Before this point, the overall heat transfer coeffcient gradually increased with the gas velocity; and beyond this speed, the overall heat transfer coeffcient declines rapidly due to the decrease in bed density.

The heat transfer coefficient of gas-solid packed-bed is usually in the range of 17—89 W/m2·K[41-45], however, it is greater than 200 W/m2·K in practical industry reactors. The overall heat transfer coeffcient of packed bed in EO synthesis process is ~230 W/m2·K, which is consistent with the result calculated byhwfrom Eq. (2). The gassolid fluidized beds show better performance than the packed bed, and the heat transfer coeffcient of gas-solid bubbling bed is in the range of 400—1 000 W/m2·K. TheUof external heat exchanger of FCC regenerator, a gassolid bubbling bed, is ~450 W/m2·K. So Martin’s correlation, Eq. (4), is more favorable for this external heat exchanger. The three-phase fuidized beds such as the slurry beds have even better heat transfer performance, with the heat transfer coeffcients exceeding 1 000 W/m2·K. This value is similar to ~1 300 W/m2·K of slurry bed adoptedin the residue hydrotreating process. And the correlations in Table 3 have remarkable consistency. The mean value of these correlations could be used to predict the heat transfer coeffcient of slurry beds. The heat transfer coeffcient of loop reactors for polypropylene synthesis is up to 1 170 W/m2·K (hwis calculated by Eq.(8)), and this value is close to that of industrial reactor (1 150 W/m2·K). This value is less than 1 600 W/m2·K for the Spheripol?process, which may be attributed to the different fouling resistance of cooling water. These coefficients can provide the reference values for reactor design.

Some generalized information could be obtained from the summarized data. Figure 2 also indicates that the heat transfer coeffcient value of gas-solid two-phase reactors is lower than that of gas-liquid-solid three-phase reactors and liquid-solid reactors. Because the heat capacity of liquid is much greater than that of gas, the reactors with liquid phase have greater heat transfer coefficients. The three-phase fuidized beds have good heat transfer property and are most suitable for strong exothermic reaction, such as the syngas-to-olefins process. The loop reactors with high heat transfer coeffcient are applied in polypropylene manufacture processes where the heat duty is large and accurate temperature control is essential.

Additionally, the reactors with packed catalyst show poorer heat transfer performance as compared to that with fuidized catalyst. This applies to the case for both twoand three-phase reactors. If the packed beds are used in strong exothermic (or endothermic) reaction, one should consider the heat removal problems seriously to avoid temperature runaway. The heat transfer performance can be enhanced by the fuidized catalyst.

4 Conclusions

The heat effect is an essential element that determines a good reactor design. By summarizing and analyzing many reported correlations, the relationship between the heat transfer coeffcients and fuid fow velocity for three types of typical petrochemical reactors, including the packed bed, the fluidized bed and the loop reactor, has been established. The varying ranges of heat transfer coeffcients of typical petrochemical reactors were then systematically summarized. The summarized results could provide references for reactor selection and design. The systems operating with liquid phase have better heat transfer performance because of the larger heat capacity of liquid. The heat transfer performance of reactors can also be improved through fuidization of solid particles. Therefore, the threephase fuidized bed and liquid-solid loop reactor have high heat transfer capacity, with the heat transfer coefficients being greater than 1 000 W/m2·K, leading to their potential applications in the process of strong thermal effects.

Notations

a—parameter in Eq.6

b—bed aspect ratio (D/dep)

Cp—heat capacity, J/kg·K

hw—effective heat-transfer coeffcient, W/(m2·K)

dp—diameter of particle, m

D—reactor diameter, m

g—acceleration due to gravity, m/s2

G—mass fow rate, kg/m2·s

l—integration variable, m

L—length of reactor, m

r—integration variable, m

r0—radius of reactor, m

u—superfcial velocity, m/s

U—overall heat-transfer coeffcient, W/(m2·K)

Re—Reynolds number (ρud/μ)

Nu—Nusselt number (hd/λ)

Pr—Prandtl number (Cpμ/λ)

Pe—Peclet number (ρudCp/λ)

St—Stanton number (h/ρCpu)

Greek symbols

λ—thermal conductivity, W/(m·K)

λso—bed conductivity without liquid fow, W/(m·K)

ε—void fraction

β—total liquid saturation

βl—liquid holdup in bed void volume

μ—viscosity, Pa·s

ρ—density, kg/m3

Λ—bed thermal conductivity, W/(m·K)

ωs—solid mass fraction

Subscripts

b—bubble

ea—axial

er—radial

g—gas

p—particle

l—liquid

s—solid

sl—slurry

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Received date: 2016-07-20; Accepted date: 2016-10-15.

Dr. Li Yuxin, E-mail: liyuxin@sei. com.cn.