- Email: [email protected]
Fractal heat conduction model of semi-coke bed in waste heat recovery heat exchanger
Journal of Cleaner Production 258 (2020) 120663
Contents lists available at ScienceDirect
Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro
Fractal heat conduction model of semi-coke bed in waste heat recovery heat exchanger Haibo Gao a, Yongqi Liu a, *, Bin Zheng a, Peng Sun a, Min Lu a, Guangdong Tian b, c a
School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, Shandong, 255049, PR China Transportation College, Jilin University, Changchun, 130022, PR China c School of Mechanical Engineering, Shandong University, Jinan, 250061, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 October 2019 Received in revised form 14 January 2020 Accepted 18 February 2020 Available online 19 February 2020
In order to realize the waste heat recovery of the high-temperature semi-cokes, the heat exchanger with one time heat transfer was put forward and the fractal heat conduction model was established for the first time. The internal structure of semi-cokes with different diameters in the heat exchanger was analyzed, and the internal structure was taken into account in the fractal heat conduction model. Furthermore, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. The results showed that, the internal structure of semi-cokes in the heat exchanger determines the fractal heat conduction characteristics, and the influence of porosity on the equivalent thermal conductivity calculated by the fractal heat conduction model is less than the fractal dimension and the contact resistance number. The equivalent thermal conductivity calculated by the fractal heat conduction model is closer to experimental values than that calculated by the traditional volume average model, and the error of the equivalent thermal conductivity between the experimental values and the fractal heat conduction model is less than 6%, thus the fractal heat conduction model is valid and feasible. © 2020 Elsevier Ltd. All rights reserved.
Handling editor: Panos Seferlis Keywords: Semi-coke Internal structure Fractal heat conduction Heat transfer Model Waste heat recovery
1. Introduction With the development of economy, the energy and environment problems become more and more serious, so energy conservation and environmental protection are imminent (Cheng et al., 2019; Li et al., 2018a,b; Norambuena-Contreras et al., 2017; Tian et al., 2019, 2017). The method of industrial waste heat recovery is a powerful way to realize the recycling of energy (Feng et al., 2016; Qin and Chang, 2017; Vance et al., 2019). Semi-coke can be obtained by the low temperature distillation of coal, whose temperature is up to 600 C, and the high temperature semi-cokes carry a lot of sensible energy. However, the sensible energy of semi-cokes with high temperature has not been recovered, resulting in energy waste and environmental pollution (Zheng et al., 2016). Therefore, the waste heat recovery of high temperature semi-cokes is of great significance. At present, there are two main cooling methods for the high temperature semi-cokes. The heat exchanger with one time heat
* Corresponding author. E-mail address: [email protected] (Y. Liu). https://doi.org/10.1016/j.jclepro.2020.120663 0959-6526/© 2020 Elsevier Ltd. All rights reserved.
transfer was proposed by our research group and it was used as the third method. (1) Coke wet quenching: high temperature semi-coke is immersed directly in water for cooling, and this causes environmental and water pollution (Gao et al., 2009; Zhang et al., 2009). The coke wet quenching is shown in Fig. 1. At the same time, the semi-coke has a high moisture content and the semi-coke needs to be dried again by consuming a lot of energy (Huang, 2014). (2) Coke dry quenching (two time heat transfer): the sensible energy of high temperature semi-cokes is recovered through two heat transfer processes in the coke dry quenching. Firstly, the sensible energy of semi-cokes is transferred to cold gas, then the sensible energy of hot gas will be absorbed by the boiler, as shown in Fig. 2. That is to say, the sensible energy of high temperature semi-cokes is recovered through two heat transfer processes in the coke dry quenching, thus the heat transfer efficiency of the dry coke quenching for the waste heat recovery is still very low. Although many scholars show that the dry coke quenching is superior to the wet coke
2
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
Fig. 1. Coke wet quenching. Fig. 3. Heat exchanger with one time heat transfer (one time heat transfer).
Fig. 2. Coke dry quenching (two time heat transfer).
quenching, the heat transfer efficiency of the dry coke quenching in the waste heat recovery process is still very low (Feng et al., 2008; Sun et al., 2015). (3) Heat exchanger with one time heat transfer (one time heat transfer): in order to overcome the disadvantages of the above two methods, the heat exchanger with one time heat transfer was proposed by our research group for the first time, and it has been applied in the industrial production. The heat exchanger with one time heat transfer is shown in Fig. 3. The sensible energy of high temperature semi-cokes is recovered only through one heat transfer process, unlike the coke dry quenching, which requires two heat transfer processes for waste heat recovery. When the semi-cokes pass through the heat exchanger by the force of gravity, the sensible energy of high temperature semi-cokes is absorbed directly by the cooling water in the heat exchanger to produce steam only through one time heat transfer process. The heat exchanger with one time heat transfer has the following advantages: the investment of heat exchanger with one time heat transfer is only one tenth of the investment of coke dry quenching. The heat exchanger with one time heat transfer not only can realize the efficient utilization of sensible energy of semi-coke (h 70%) but also can reduce environmental and water pollution. Meanwhile, the moisture content of semi-coke is only 15% of wet
coke quenching, saving the fuel for drying, so the semi-coke is easier to meet quality requirements. The semi-cokes only rely on the force of gravity to flow through the heat exchanger, and extra power is not needed to transport the semi-cokes. It can be seen from the above analysis, the heat exchanger with one time heat transfer has many advantages. However, there is no suitable heat transfer model to describe the heat transfer between the slow-flowing semi-cokes and the heat exchanger. Therefore, the establishment of the fractal heat conduction model is urgently needed to describe the heat conduction problem of semi-cokes in the new heat exchanger with one time heat transfer, where this work focuses on. Based on literature reviews and the present situation of the waste heat recovery of the high-temperature semicokes, our research group proposed the heat exchanger with one time heat transfer. Besides, the internal structure of semi-cokes with different diameters in the heat exchanger with one time heat transfer was obtained and analyzed. Furthermore, the internal structure of semi-cokes in the heat exchanger was taken into account in the fractal heat conduction model, and the effect of fractal dimension, contact resistance number and porosity on the fractal heat conduction model was discussed. Finally, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. At the same time, the discussion on the results and applications of fractal heat conduction model are carried out. The contributions of this work are as follows: (i) the heat exchanger with one time heat transfer is put forward for the first time; (ii) the internal structure of semi-coke bed with different diameters in the heat exchanger is obtained and analyzed, and the internal structure of semi-cokes in the heat exchanger is taken into account in the fractal heat conduction model; (iii) the fractal heat conduction model is established for the first time, and it is demonstrated through the experiment; and (iv) the fractal heat conduction model is more accurate than the traditional volume average model, and the application of the fractal heat conduction model can demonstrate the rationality of the fractal heat conduction model. The structure of the paper is shown as follows. Section 2 reports the current research status and the research gap. Section 3 describes the physical problem. Section 4 establishes the fractal heat conduction model of semi-cokes in the heat exchanger with one time heat transfer. Section 5 verifies the fractal heat conduction model, and discusses the effects of the internal structure of semi-
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
coke bed on the fractal heat conduction model. In the last section, conclusions are obtained. 2. Literature review This section is divided into two parts. The first subsection introduces the research status of the waste heat recovery technology for high temperature particles and the second subsection finds out the research gap. 2.1. Current research status Over the past few decades, numerous researches on the waste heat recovery technology of high temperature particles have been carried out. According to the published references, this section reviews progress on the available waste heat recovery techniques (i.e. fluidized bed, moving bed and packed bed) depending on the solid particle size. 2.1.1. Fluidized bed Recently, extensive studies about the heat transfer characteristics of particles in the fluidized bed have been explored. Lechner et al. (2014) experimentally investigated the heat transfer mechanism in fluidized beds equipped with horizontal heat exchanger surfaces of tube bundles. The heat exchanger with a shallow gassolid fluidized bed was experimentally researched in order to analyze energy recovery from solid particles leaving a combustion process (Rodriguez et al., 2002). Singh and Ghule (2016) designed a novel stripper ash cooler for circulating fluidized bed boiler, and the influence of particle size and the fluidization velocity of ash on the heat transfer performance has been investigated. Zeng et al. (2011) proposed a novel compound fluidized bed ash cooler, and it had a well separation effect and a good cooling effect. Kamble et al. (2014) developed the neural network model to predict the average heat transfer coefficient for horizontal tube immersed in gas-solid fluidized bed of large particles. An experimental study is carried out in order to introduce a volumetric heat transfer coefficient for fluidized bed drying to eliminate the uncertainties of the determination of the heat transfer surface between the gas and the particles (Tibor and Viktor, 2018). The above analysis shows that, fluidized bed is mainly used for waste heat recovery from high temperature particles with small particle and large resistance coefficient. Although the fluidized bed has a much higher heat transfer coefficient, the operating and maintenance costs are higher. 2.1.2. Moving bed The research of moving bed mainly focuses on the establishment of heat transfer model and the analysis of heat transfer process. Zheng et al. (2019)a,b established the unsteady heat transfer model to study the influence of particle diameter on particle temperature distribution. Cui et al. (2017) proposed the mathematical model for a moving cooling packed clinker bed, and the theoretical study was performed into the coupled gas-solid heat transfer process. Zhou et al. (2018) established the physical and chemical model for the indirectly heated moving bed, and a new oil shale refinery process with the indirectly heated moving bed is proposed. Gao et al. (2019)a,b established the 1-D fractional equation to study the heat transfer of particles. Isaza et al. (2017) obtained the analytical solution for the energy model of a moving bed heat exchanger that includes axial heat conduction. Liang et al. (2019) established the Lagrangian descriptions of particle and gas energy equation in a countercurrent moving bed, and two typical scenarios of waste heat recovery for high-temperature particles were researched. Herz et al. (2012) experimentally researched the influence mechanism of operational parameters on the heat transfer
3
between the cylinder and the particles. Zheng et al. (2019)a,b experimentally investigated the volumetric exergy transfer coefficient in vertical moving bed for sinter waste heat recovery. Zhang et al. (2013) investigated the fractal heat conduction problems of slag by using fractal properties, and the fractal properties of materials determine the heat transfer properties. Wang et al. (2014) investigated the waste heat recovery methods of blast furnace slag and analyzed the cooling process of steel slag particles in the moving bed. According to the published references, extensive studies about the waste heat recovery of moving bed are mainly focus on the high temperature particles of medium size. Although the moving bed has the characteristics of low cost and stable operation, the heat transfer coefficient of moving bed is lower than that of fluidized bed. Basically, the waste heat recovery of moving bed is still at early stage, and the future work should be focused on the enhanced heat transfer technology of moving bed. 2.1.3. Packed bed Packed beds of particles are widely used in industries such as chemical catalytic reactors (Partopour and Dixon, 2016), high temperature gas-cooled nuclear reactors (Abdulmohsin and AlDahhan, 2015), thermal energy storage systems (Lu et al., 2016), solar receivers (Zhu and Xuan, 2017) and so on. Li et al., 2018a,b studied the heat transfer of smooth or dimpled spheres in the structured packed beds by numerical simulation. Bu et al. (2014) researched the thermal contact resistance modification between particles in the heat transfer process. Naghash et al. (2016) estimated the convective heat transfer coefficient for airflow passing through randomly packed beds of silica gel by using the inverse simulation. Singhal et al. (2017) proposed a new methodology for deriving heat transfer correlations from PR-DNS of very dense particle packings relevant for packed bed applications. Esence et al. (2019) developed a versatile one-dimensional numerical model able to describe many packed-bed configurations, and this model is able to treat liquid and gaseous heat transfer fluids. Halkarni et al. (2017) investigated the behavior of wall heat transfer coefficient in randomly packed beds of uniform sized spheres using infrared thermography. Hou et al. (2018) established the CFD model for predicting the heat transfer in the packed bed, in which the heterogeneous fluid flow was resolved by considering the oscillatory behavior of voidage and the effective fluid viscosity. It can be known from the above references, the packed bed technology for high temperature particles is mainly used for large particles, and it can only satisfy the hot particles with an uniform size or narrow range. The heat transfer coefficients between air and high temperature particles in the packed bed are relatively lower than those in fluidized bed and moving bed. Further emphasis should be given on the efficient organization of cascade waste heat recovery and optimization of operating parameters. 2.2. Research gap By summarizing and analyzing the previous research results, the previous researches mainly focus on the available waste heat recovery techniques (i.e. fluidized bed, moving bed and packed bed) depending on the high temperature particle size, and the current technologies can only satisfy the hot particles with an uniform size or narrow range. For the high temperature semi-cokes with wide particle size distribution range, a new waste heat recovery equipment is urgently needed, and there is no waste heat recovery equipment for semi-cokes at present. In fact, the internal structure of semi-cokes in the heat exchanger has a great effect on the heat conduction of high temperature semi-cokes. However there is a lack of investigations on the internal structure and fractal heat conduction model for the semi-cokes in the heat exchanger. To fill
4
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
Fig. 4. The structure of the heat exchanger.
this gap, the heat exchanger with one time heat transfer was put forward and the fractal heat conduction model was established for the first time. Meanwhile, the internal structure of semi-coke bed with different diameters is obtained, and the effect of the internal structure is considered by the fractal heat conduction model. Furthermore, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. Finally, the results and discussions on the fractal heat conduction model are carried out.
3. Description of physical problem The high temperature semi-cokes are cooled directly by the heat exchanger with one time heat transfer, the internal and external heat exchangers are composed of heat exchange pipes and membrane walls, as shown in Fig. 4. As the cooling water flows through the heat exchanger, the sensible energy of semi-cokes is recycled by the cooling water. At the same time, the water pipe is arranged in the middle of the heat exchanger to spray cooling water into the heat exchanger, and the high temperature semi-cokes vaporize cooling water to form steam. As the steam moves upward, steam and semi-cokes will form convection heat transfer in the upper part of the heat exchanger. Our research group has investigated the convection heat transfer of steam and semi-cokes in the upper half of the heat exchanger in Ref. (Gao et al., 2019a,b). However, the heat transfer problem of semi-cokes in the lower half of the heat exchanger with one time heat transfer has not been studied, so the heat transfer problem of semi-cokes in the lower half of the heat exchanger was selected for study in this work. In the lower half of the heat exchanger with one time heat transfer, there are three types of heat transfer (heat conduction, radiation heat transfer and convection heat transfer) between semi-coke and wall, as shown in Fig. 5. The heat conduction mainly includes the following three heat transfer pathways: (1) heat conduction in direct contact between semi-coke and wall, as shown in heat transfer mode A; (2) heat conduction of gap gas film between semi-coke and wall, as shown in heat transfer mode B; (3) heat conduction of gas film near the contact surface between semicoke and wall, as shown in heat transfer mode C. The radiation heat transfer mainly refers to radiation heat transfer of semi-coke to the wall, as shown in heat transfer mode D. The convection heat transfer mainly refers to convection heat transfer between gas and wall, as shown in heat transfer mode E. It can be seen from Fig. 5 that the heat transfer mode between semi-cokes is the same as the heat transfer between semi-coke and wall. Due to the semi-cokes flow down very slowly (4 105 m/s), there is little change in the position of semi-cokes, therefore, the static semi-cokes were used for research. Due to the symmetrical structure of heat exchanger, one fourth width of semi-coke bed was taken as the research object, as shown in Fig. 6. Since there is no
Fig. 5. Three types of heat transfer.
steam flowing through the lower part of the heat exchanger and the velocity of semi-cokes is slow, convection heat transfer is ignored (Leng, 2008). Under the water pipe, the temperature of semi-cokes
Fig. 6. Research object.
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
is below 200 C, thus the radiation heat transfer was neglected in this study. Zheng et al. (2018) showed that the heat transfer mode of particles at any given moment is mainly heat conduction. The heat conduction is the main mode of heat transfer for semi-cokes in the lower half of the heat exchanger. However, the heat conduction problem of semi-cokes has not been studied, so the heat conduction problem of semi-cokes was selected for study in this work. 4. Establishment of fractal heat conduction model for semicoke bed Due to the internal structure of semi-cokes in the heat exchanger has an important influence on the fractal heat conduction model, this section is divided into two parts. The first subsection introduces the calculation methods of internal structure for the semi-coke bed, and the second subsection describes the establishment of the fractal heat conduction model for semi-coke bed. 4.1. Calculation methods of internal structure for the semi-coke bed 4.1.1. Computer tomography (CT) experiments and images processing Six different diameters of semi-coke were obtained by the sieve method, and they are 3mm/9mm/19mm/37mm/55mm/65 mm, respectively. X-ray CT is the efficient tool to observe the internal structures of the object in industry and medicine (Peng et al., 2011; Tian et al., 2012; Zhao and Peng, 2017; Zhang et al., 2015). The internal structure of semi-coke bed was obtained by the spiral CT machine for the first time, and the CT images were segmented by image binarization method to obtain the bit binary images. Due to an appropriate threshold has direct impact on the success of image binarization, the porosity of semi-coke bed calculated by drainage method was used to compare with the porosity of semi-coke bed calculated by image binarization processing method. When the error of porosity calculated by the two methods is less than 5%, the selected threshold of image binarization processing method is considered reasonable. The comparison between CT image and bit binary image of semi-coke bed is shown in Fig. 7. As can be seen from Fig. 7, the bit binary image can well describe the internal structure of semi-coke bed, thus the bit binary image can be used for subsequent research.
5
to the mathematic expression of box-counting method by using the MATLAB program. The mathematic expression of fractal dimension (Grossu and El-Shamali, 2013) is written:
D ¼ lim
log NðrÞ
(1)
r/0 logð1=rÞ
where D denotes fractal dimension, r denotes length, N(r) denotes the box number. The contact number of the single semi-coke particle was calculated by a lot of CT images, and the average value of twenty particles was used to replace the contact number. The porosity can be calculated according to the void area of bit binary image, and the average value of all bit binary images was used to replace the porosity.
4.2. Establishment of fractal heat conduction model 4.2.1. Fractal heat conduction path The semi-cokes in the heat exchanger is discontinuous media and the internal structure of semi-cokes in the heat exchanger has fractal properties. The heat transfer path of semi-cokes in the heat exchanger is a fractal curve, not a straight line. For example, like the 3rd random Koch curve, the fractal heat conduction path is presented in Fig. 8. As shown in Fig. 8, the path of heat conduction is a fractal curve, not a straight line, which means the length of the heat transfer path and the contact resistance number are actually increasing.
4.2.2. Calculation of fractal curve length This work assumes that the sensible energy is transmitted through parallel multi-strand identical fractal curves in semi-coke bed. The empirical formula for calculating the length of coastline proposed by L. f. Richardso in 1961 was used to calculate the fractal curve length (Zhang, 1995). The empirical formula is written:
4.1.2. Calculation methods of internal structure The fractal dimension can describe the complexity of the internal structure for semi-cokes in the heat exchanger. The power spectral method, the structure function method and the boxcounting method can be employed to calculate the fractal dimension (Wang et al., 2015). The box-counting method has a good calculation effect, so the fractal dimension was calculated according
Fig. 7. The CT images and bit binary images.
Fig. 8. The fractal heat conduction path.
6
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
5. Results and discussions
LðaÞ ¼ L0 a1D
(2)
where L(a) denotes the fractal curve length, a denotes the ratio scale, L0 is the distance of a straight line between two ends of a fractal curve, D is the fractal dimension of the fractal curve. 4.2.3. Establishment of the fractal heat conduction model The fractal heat conduction path can be simplified into the parallel gas phase and solid phase paths. The diagram of the fractal heat conduction model is shown in Fig. 9. L0 is the distance of a straight line between two ends of a fractal curve, and L(a) denotes the fractal curve length. The S denotes the macroscopic cross section area of semi-coke bed, 4 denotes the porosity, Rc denotes the contact resistance between semi-cokes. The geometric structure, the contact resistance and the semicoke diameter are considered into the equivalent thermal resistance in the fractal heat conduction model. According to the fractal heat conduction model in Fig. 9, the equivalent thermal resistance R of semi-coke bed can be expressed as follows:
(3)
where Rs denotes the thermal resistance of solid, Rg denotes the thermal resistance of gas, ls denotes the thermal conductivity of semi-coke, lg denotes the thermal conductivity of gas, d denotes the semi-coke diameter. The formula (2) is taken into the formula (3), and the formula (3) is then deformed to obtain the fractal expression of the equivalent thermal conductivity le as follows: R 4ð14Þlg ls
4lg þ ð1 4Þls þ c d ls a1D 1 þ Rc ð14ÞS d
(4)
The formula (4) is derived from fractal theory, and it contains the influence of fractal dimension on the equivalent thermal conductivity, so the application of formula (4) has certain limitation. The application limitation of formula (4) is that, the fractal dimension can be obtained only if the research object has two basic characteristics of fractal (self-similarity and scale invariance). At the same time, the fractal heat conduction model is verified under certain experimental conditions, so the fractal expression of the equivalent thermal conductivity in the formula (4) has the limitation for particle size (3 mme65mm) and particle temperature (T 100 C).
5.2. Model verification and discussion To further investigate the fractal heat conduction problem of semicokes in the heat exchanger with one time heat transfer, the verification of the fractal heat conduction model was carried out by experiment. The equivalent thermal conductivity of semi-cokes was measured by the DRS-III thermal conductivity tester. The experimental system includes the heating surface, the cooling surface, the
2.00
Fractal dimension Contact number Porosity
1.95 1.90
12
50
8
1.80
6
1.75
4
1.70
Fig. 9. The diagram of fractal heat conduction model.
60
10
1.85
1.65
14
0
10
20
30 40 50 Diameter (mm)
60
2 70
40 30 20
Porosity(%)
le ¼
The effects of the diameter on the internal structure of semicokes in the heat exchanger is depicted in Fig. 10. Since the internal structure of semi-cokes in the heat exchanger is calculated by averaging multiple experiments, the error bars are included in Fig. 10. It can be seen from Fig. 10 that the errors of the internal structure of semi-cokes in the heat exchanger are within an acceptable range. As is shown in Fig. 10, when the diameter increases from 3 mm to 65 mm, the fractal dimension decreases from 1.95 to 1.73, the contact number decreases from 13 to 4, and the porosity increases from 5.4% to 52.1%. The reason for this is that, with the increase of the diameter, the arrangement of semi-cokes becomes simpler and the complexity of internal structure decreases gradually, so the fractal dimension gradually decreases. The number of semi-coke in the same space gradually decreases and the less chance of contact between semi-cokes, so the contact number decreases as the semi-coke diameter increases. The voids between semi-cokes gradually become larger with the increase of diameter, so the porosity gradually increases with diameter. This means that, as the semi-coke diameter increases, the distance of heat transfer and the contact resistance number decrease, and the share of gas heat transfer is gradually increasing. The study of internal structure lays a foundation for the explanation of heat conduction mechanism.
Contact number
Rs Rg LðaÞ ¼ Sle Rs þ Rg LðaÞ LðaÞRc LðaÞ ¼ þ ð1 4ÞSls 4Slg d LðaÞ LðaÞRc LðaÞ þ þ ð1 4ÞSls 4Slg d
5.1. Effects of diameter on the internal structure of semi-coke bed
Fractal dimension
R¼
Due to the internal structure of semi-cokes in the heat exchanger has an important effect on the fractal heat conduction model and the semi-coke diameter directly determines the internal structure of semi-cokes in the heat exchanger, this section is divided into two parts. The first subsection introduces the effects of the semi-coke diameter on the internal structure of semi-cokes in the heat exchanger. The second subsection verifies and discusses the fractal heat conduction model.
10 0
Fig. 10. Effect of diameter on the internal structure of semi-cokes in the heat exchanger.
heat insulating material and measurement system, as depicted in Fig. 11. The experiment process is as follows: turn on the power when the experimental system is connected. Turn on the DRS-III thermal conductivity tester and adjust the heating surface temperature to 100 C. Adjust the constant temperature water bath to keep the cooling surface temperature at 25 C. Open the computer and data acquisition software to record the experimental temperature. When the temperature is stable, the semi-coke temperature is collected. The equivalent thermal conductivity in the experiment can be calculated by formula (5):
le ¼
ql Th Tc
(5)
where le denotes the equivalent thermal conductivity, q denotes the heat flux, l denotes the height of semi-coke bed, Th denotes the heating surface temperature, Tc denotes the cooling surface temperature. As with a report of every experimental research, the analysis of the experimental uncertainties in calculating the results must be given proper attention. The analysis of experimental uncertainties was carried out to improve the experimental reliability. The experimental uncertainty in the heat transfer was mainly caused by temperature measurement errors and heat balance errors, the equivalent thermal conductivity was calculated by taking the average value of several experiments. The temperature measurement errors mainly comes from the measurement error of thermocouple, and the measurement error of thermocouple is ±1 C. The experimental uncertainty of heat balance was ±3%. Detailed error analyses showed that the experimental uncertainties in the equivalent thermal conductivity were estimated to be ±4%. At the same time, the error analysis of the equivalent thermal conductivity in the experiment was carried out in Fig. 12, and the error bars showed that the error of the equivalent thermal conductivity was within the allowable range. In formula (4), if Rc ¼ 0 and D ¼ 1, the formula (4) becomes the traditional volume average formula in Ref. (Zou et al., 2015), and the traditional volume average formula is as follows:
Fig. 11. The experimental schematic diagram.
e(W/(m·K))
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25
7
Experiment Formula 4 Formula 6
0
10
20
30 40 50 Diameter (mm)
60
70
Fig. 12. The comparison of the equivalent thermal conductivity calculated by different methods.
le ¼ 4lg þ ð1 4Þls
(6)
The equivalent thermal conductivity was obtained by the formula (4), the formula (5) in the experiment and formula (6). The comparison of the equivalent thermal conductivity calculated by the three methods is shown in Fig. 12. In Fig. 12, comparing to the equivalent thermal conductivity obtained by the formula (6), the equivalent thermal conductivity calculated by the formula (4) is closer to the formula (5) in the experiment, and the error between the formula (4) and formula (5) in the experiment is less than 6%. Therefore, the fractal expression of the equivalent thermal conductivity in the formula (4) can describe the heat conduction problem of semi-coke bed more accurately than formula (6). The internal structure of semi-cokes in the heat exchanger has great effect on the heat conduction characteristics, and the internal structure was taken into account in the fractal heat conduction model, thus the fractal heat conduction model considering the internal structure of semi-cokes in the heat exchanger is closer to the real heat conduction of semi-cokes in the heat exchanger than other models. At the same time, the heat conduction path of semicokes in the heat exchanger is a fractal heat conduction path, not a straight line, which means the length of the heat conduction path and the contact resistance number are actually increasing, thus the fractal heat conduction path of the fractal heat conduction model is closer to the real heat conduction path of semi-cokes in the heat exchanger than other models. According to the above analysis, it is reasonable and feasible to choose the fractal heat conduction model to study the heat conduction of semi-cokes in heat exchanger. As can be seen from Fig. 12, the equivalent thermal conductivity increases gradually with increasing the semi-coke diameter. It can be seen from the information of the internal structure obtained in Fig. 10, with the increase of diameter, the fractal dimension and contact number decrease gradually, and the porosity increases. This means that the heat conduction path and the contact resistance number decrease gradually, and this is favorable for heat conduction. The heat flux is mainly transported along the semi-cokes rather than through the gas, so the increase of porosity is not conducive to heat conduction. However, the equivalent thermal conductivity increases with the semi-coke diameter in Fig. 12, so the influence of porosity on the equivalent thermal conductivity calculated by the fractal heat conduction model is less than the
8
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
110 Formula (6) Experiment Formula (4)
100
Temperature (
)
90 80 70 60 50 40 30 20 -40
0
40
80 120 160 Height (mm)
200
240
Fig. 13. Temperature comparison of the three methods.
fractal dimension and contact resistance number. The above analysis shows that the internal structure has an important effect on the fractal heat conduction model. In order to further clarify the rationality of choosing fractal heat conduction model, the temperature comparison of the three methods was carried out. The temperature was obtained by the formula (4), the formula (5) in the experiment and formula (6), and the temperature comparison of the three methods is shown in Fig. 13. In Fig. 13, the height refers to the distance between the semi-cokes and the heating surface, and the temperature of semicokes decreases with increasing the height. As can be seen from Fig. 13, the average error of temperature between the formula (4) and the experiment is 4.7%, and the average error of temperature between the formula (6) and the experiment is 9.2%, thus the temperature calculated by the formula (4) is closer to the experimental temperature than formula (6). It can be seen from the
temperature analysis in Fig. 13, the fractal heat conduction model can accurately predict the temperature distribution of semi-cokes in the exchanger with one time heat transfer, so it is advisable to establish the fractal heat conduction model to research the heat conduction of semi-cokes in heat exchanger. The fractal dimension can describe the complexity of the internal structure of semi-cokes in the heat exchanger. The larger the fractal dimension, the more complex the internal structure of semicokes in the heat exchanger. The effect of fractal dimension on the heat flux is depicted in Fig. 14. As can be seen from Fig. 14, when the fractal dimension of semi-coke bed increases from 1.732 to 1.952, the heat flux decreases from 501 W/m2 to 249 W/m2. The reason for this is that, the internal structure complexity of semi-cokes in the heat exchanger increases gradually with the increase of the fractal dimension, thus the heat conduction path length and complexity increase gradually. The increase of the heat conduction path length and complexity leads to the decrease of heat transfer efficiency, thus the heat is more difficult to flow through the semi-coke bed. To sum up, the heat transfer resistance increases with the increase of fractal dimension, so the heat flux decreases gradually with the increase of fractal dimension. Through the verification and discussion of the fractal heat conduction model, it can be seen that the internal structure of the semi-cokes in the heat exchanger has great effect on the heat conduction characteristics, and the fractal heat conduction model considering the internal structure of semi-cokes in the heat exchanger can well describe the heat conduction problem. About the application of the fractal heat conduction model, the fractal heat conduction model can accurately predict the temperature distribution of semi-cokes in the exchanger with one time heat transfer. 6. Conclusions In order to realize the waste heat recovery of the high temperature semi-cokes, the heat exchanger with one time heat transfer was put forward and the fractal heat conduction model was
550
Heat flux (W/m2)
500 450 400 350 300 250 200 1.70
1.75
1.80 1.85 1.90 Fractal dimension
Fig. 14. The effect of fractal dimension on the heat flux.
1.95
2.00
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
established for the first time. The internal structure of semi-coke bed with different diameters is obtained, and the effect of the internal structure is considered by the fractal heat conduction model. Furthermore, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. Finally, the results and discussions on the fractal heat conduction model are carried out. Major conclusions are as follows: (1) The internal structure of semi-cokes in the heat exchanger with one time heat transfer has an important effect on fractal heat conduction model. With increasing the diameter from 3 mm to 65 mm, the fractal dimension decreases from 1.95 to 1.73, the contact number decreases from 13 to 4, and the porosity increases from 5.4% to 52.1%. This means that the heat conduction path and the contact resistance number decrease gradually, and this is favorable for heat conduction. The heat flux is mainly transported along the semi-cokes rather than through the gas, so the increase of porosity is not conducive to heat conduction. (2) The geometric structure, the contact resistance and the semicoke diameter are considered into the equivalent thermal resistance in the fractal heat conduction model. Comparing to the equivalent thermal conductivity obtained by the traditional volume average model, the equivalent thermal conductivity obtained by the fractal heat conduction model is closer to experimental values, meaning the fractal heat conduction model can describe the heat conduction problem of semi-cokes in the heat exchanger with one time heat transfer more accurately than other models. (3) The equivalent thermal conductivity increases with diameter, and the influence of porosity on the equivalent thermal conductivity calculated by the fractal heat conduction model is less than the fractal dimension and contact resistance number.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Haibo Gao: Conceptualization, Investigation, Writing - original draft, Writing - review & editing. Yongqi Liu: Methodology, Resources, Project administration, Funding acquisition. Bin Zheng: Supervision, Software. Peng Sun: Formal analysis, Writing - review & editing. Min Lu: Validation, Data curation. Guangdong Tian: Formal analysis, Visualization. Acknowledgments These works were supported by National Key R&D Program of China (2017YFB0603504-2) and Shandong Provincial Natural Science Foundation, China (ZR2018MEE006 and ZR2017LEE019). References Abdulmohsin, R.S., Al-Dahhan, M.H., 2015. Characteristics of convective heat transport in a packed pebble-bed reactor. Nucl. Eng. Des. 284, 143e152. https:// doi.org/10.1016/j.nucengdes.2014.11.041. Bu, S.S., Yang, J., Zhou, M., Li, S.Y., Wang, Q.W., Guo, Z.X., 2014. On contact point modification for forced convective heat transfer analysis in a structured packed bed of spheres. Nucl. Eng. Des. 270, 21e33. https://doi.org/10.1016/ j.nucengdes.2014.01.001.
9
Cheng, Z.L., Guo, Z.G., Tan, Z.T., Yang, J., Wang, Q.W., 2019. Waste heat recovery from high-temperature solid granular materials: energy challenges and opportunities. Renew. Sustain. Energy Rev. 116, 109428 https://doi.org/10.1016/ j.rser.2019.109428. Cui, Z., Shao, W., Chen, Z.Y., Cheng, L., 2017. Mathematical model and numerical solutions for the coupled gas-solid heat transfer process in moving packed beds. Appl. Energy 206, 1297e1308. https://doi.org/10.1016/ j.apenergy.2017.10.011. , J.F., Stutz, B., 2019. A versatile one-dimensional Esence, T., Bruch, A., Fourmigue numerical model for packed-bed heat storage systems. Renew. Energy 133, 190e204. https://doi.org/10.1016/j.renene.2018.10.012. Feng, J.S., Dong, H., Gao, J.Y., Li, H.Z., Liu, J.Y., 2016. Numerical investigation of gassolid heat transfer process in vertical tank for sinter waste heat recovery. Appl. Therm. Eng. 107, 135e143. https://doi.org/10.1016/ j.applthermaleng.2016.06.175. Feng, Y.H., Zhang, X.X., Yu, Q., Shi, Z.Y., Liu, Z.C., Zhang, H., Liu, H.F., 2008. Experimental and numerical investigations of coke descending behavior in a coke dry quenching cooling shaft. Appl. Therm. Eng. 28 (11e12), 1485e1490. https:// doi.org/10.1016/j.applthermaleng.2007.09.001. Gao, H.B., Liu, Y.Q., Song, X.Y., Zheng, B., Sun, P., Lu, M., Ma, Y.X., Gao, Z.Q., 2019a. Numerical study of heat transfer characteristics of semi-coke and steam in waste heat recovery steam generator for hydrogen production. Int. J. Hydrogen Energy 44 (46), 25160e25168. https://doi.org/10.1016/j.ijhydene.2019.05.155. Gao, H.B., Liu, Y.Q., Zheng, B., Sun, P., Lu, M., Yin, Q., 2019b. Modeling of fractal heat conduction of semi-coke bed in waste heat recovery steam generator for hydrogen production. Int. J. Hydrogen Energy 44 (46), 25240e25247. https:// doi.org/10.1016/j.ijhydene.2019.05.098. Gao, J.J., Zhao, S.F., Zheng, Y.T., Guo, J.W., 2009. Comparative analysis between wet coke quenching and dry coke quenching. Sci-tech Information Development & Economy 19 (23), 199e201. Grossu, I.V., EI-Shamali, S.A., 2013. Hyper-Fractal Analysis v04: implementation of a fuzzy box-counting algorithm for image analysis of artistic works. Comput. Phys. Commun. 184, 1812e1813. https://doi.org/10.1016/j.cpc.2013.02.026. Halkarni, S.S., Sridharan, A., Prabhu, S.V., 2017. Measurement of local wall heat transfer coefficient in randomly packed beds of uniform sized spheres using infrared thermography (IR) and water as working medium. Appl. Therm. Eng. 126, 358e378. https://doi.org/10.1016/j.applthermaleng.2017.07.174. Herz, F., Mitov, I., Specht, E., Stanev, R., 2012. Experimental study of the contact heat transfer coefficient between the covered wall and solid bed in rotary drums. Chem. Eng. Sci. 82, 312e318. https://doi.org/10.1016/j.ces.2012.07.042. Hou, B.L., Ye, R.M., Huang, Y.Q., Wang, X.D., Zhang, T., 2018. A CFD model for predicting the heat transfer in the industrial scale packed bed. Chin. J. Chem. Eng. 26 (2), 228e237. https://doi.org/10.1016/j.cjche.2017.07.008. Huang, X.C., 2014. Technical features of the water-seal coke quenching technology of the vertical internal-heating semicoke oven. Coal. Chem. Ind. 42 (4), 30e32. Isaza, P.A., O’Brien, A., Warnica, W.D., Bussmann, M., 2017. Assessing axial heat conduction in moving bed heat exchangers. Int. J. Therm. Sci. 120, 303e313. https://doi.org/10.1016/j.ijthermalsci.2017.06.004. Kamble, L.V., Pangavhane, D.R., Singh, T.P., 2014. Experimental investigation of horizontal tube immersed in gas-solid fluidized bed of large particles using artificial neural network. Int. J. Heat Mass Tran. 70, 719e724. https://doi.org/ 10.1016/j.ijheatmasstransfer.2013.11.073. Lechner, S., Merzsch, M., Krautz, H.J., 2014. Heat-transfer from horizontal tube bundles into fluidized beds with Geldart A lignite particles. Powder Technol. 253, 14e21. https://doi.org/10.1016/j.powtec.2013.10.041. Leng, T.T., 2008. Simulation Study of Discrete Element Method on Granular Flow and Heat Transfer. Dalian University of Technology. Li, L., Lei, Y.L., Wu, S.M., Huang, Z.Y., Luo, J.Y., Wang, Y.F., Chen, J.B., Yan, D., 2018a. Evaluation of future energy consumption on PM2.5 emissions and public health economic loss in Beijing. J. Clean. Prod. 187, 1115e1128. https://doi.org/10.1016/ j.jclepro.2018.03.229. Li, S.Y., Zhou, L., Yang, J., Wang, Q.W., 2018b. Numerical simulation of flow and heat transfer in structured packed beds with smooth or dimpled spheres at low channel to particle diameter ratio. Energies 11 (4), 937. https://doi.org/10.3390/ en11040937. Liang, X., Liu, X.J., Xia, D.H., 2019. Lagrangian simulation and exergy analysis for waste heat recovery from high-temperature particles using countercurrent moving beds. Appl. Therm. Eng. 160, 114115 https://doi.org/10.1016/ j.applthermaleng.2019.114115. Lu, J.F., Chen, Y., Ding, J., Wang, W.L., 2016. High temperature energy storage performances of methane reforming with carbon dioxide in a tubular packed reactor. Appl. Energy 162, 1473e1482. https://doi.org/10.1016/ j.apenergy.2015.03.140. Naghash, M., Fathieh, F., Besant, R.W., Evitts, R.W., Simonson, C.J., 2016. Measurement of convective heat transfer coefficients in a randomly packed bed of silica gel particles using IHTP analysis. Appl. Therm. Eng. 106, 361e370. https:// doi.org/10.1016/j.applthermaleng.2016.06.027. Norambuena-Contreras, J., Silva-Robles, E., Gonzalez-Torre, I., Saravia-Montero, Y., 2017. Experimental evaluation of mechanical and thermal properties of recycled rubber membranes reinforced with crushed polyethylene particles. J. Clean. Prod. 145, 85e97. https://doi.org/10.1016/j.jclepro.2017.01.040. Partopour, B., Dixon, A.G., 2016. Reduced microkinetics model for computational fluid dynamics (CFD) simulation of the fixed-bed partial oxidation of ethylene. Ind. Eng. Chem. Res. 55, 7296e7306. https://doi.org/10.1021/acs.iecr.6b00526. Peng, R.D., Yang, Y.C., Ju, Y., Mao, L.T., Yang, Y.M., 2011. Computation of fractal
10
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
dimension of rock pores based on gray CT images. Chin. Sci. Bull. 56 (31), 3346e3357. https://doi.org/10.1007/s11434-011-4683-9. Qin, S.Y., Chang, S.Y., 2017. Modeling, thermodynamic and techno-economic analysis of coke production process with waste heat recovery. Energy 141, 435e450. https://doi.org/10.1016/j.energy.2017.09.105. cora, A.A.B., Bizzo, W.A., 2002. Heat recovery from hot solid Rodriguez, O.M.H., Pe particles in a shallow fluidized bed. Appl. Therm. Eng. 22 (2), 145e160. https:// doi.org/10.1016/S1359-4311(01)00076-X. Singh, R.I., Ghule, K., 2016. Design, development, experimental and CFD analysis of a prototype fluidized bed stripper ash cooler. Appl. Therm. Eng. 107, 1077e1090. https://doi.org/10.1016/j.applthermaleng.2016.07.044. Singhal, A., Cloete, S., Radl, S., Quinta-Ferreira, R., Amini, S., 2017. Heat transfer to a gas from densely packed beds of monodisperse spherical particles. Chem. Eng. J. 314, 27e37. https://doi.org/10.1016/j.cej.2016.12.124. Sun, K., Tseng, C.T., Wong, D.S.H., Shieh, S.S., Jang, S.S., Kang, J.L., Hsieh, W.D., 2015. Model predictive control for improving waste heat recovery in coke dry quenching processes. Energy 80, 275e283. https://doi.org/10.1016/ j.energy.2014.11.070. Tian, G.D., Zhang, H.H., Feng, Y.X., Jia, H.F., Zhang, C.Y., Jiang, Z.G., Li, Z.W., Li, P.G., 2017. Operation patterns analysis of automotive components remanufacturing industry development in China. J. Clean. Prod. 164, 1363e1375. https://doi.org/ 10.1016/j.jclepro.2017.07.028. Tian, G.D., Liu, X., Zhang, M.H., Yang, Y.S., Zhang, H.H., Lin, Y., Ma, F.W., Wang, X.Y., Qu, T., Li, Z.W., 2019. Selection of take-back pattern of vehicle reverse logistics in China via Grey-DEMATEL and Fuzzy-VIKOR combined method. J. Clean. Prod. 220, 1088e1100. https://doi.org/10.1016/j.jclepro.2019.01.086. Tian, W., Dang, F.N., Chen, H.Q., 2012. Fractal analysis on meso-fracture of concrete based on the technique of CT image processing. J. Basic Sci. Eng. 20 (3), 424e431. https://doi.org/10.3969/j.issn.1005-0930.2012.03.009. Tibor, P.D., Viktor, S., 2018. Volumetric heat transfer coefficient in fluidized bed dryers. Chem. Eng. Technol. 41 (3), 628e636. https://doi.org/10.1002/ ceat.201700038. Vance, D., Nimbalkar, S., Thekdi, A., Armstrong, K., Wenning, T., Cresko, J., Jin, M.Z., 2019. Estimation of and barriers to waste heat recovery from harsh environments in industrial processes. J. Clean. Prod. 222, 539e549. https://doi.org/ 10.1016/j.jclepro.2019.03.011. Wang, B., Wang, X.C., Yuan, Y.C., Zhou, Q.P., 2014. Advances in the study of the blast furnace slag waste heat recovery technologies. J. Eng. Therm. Eng. 29 (2), 113e120. https://doi.org/10.16146/j.cnki.rndlgc.2014.02.001. Wang, Q.Y., Liang, Z.Q., Wang, X.B., Zhao, W.X., Wu, Y.B., Zhou, T.F., 2015. Fractal analysis of surface topography in ground monocrystal sapphire. Appl. Surf. Sci. 327, 182e189. https://doi.org/10.1016/j.apsusc.2014.11.093.
Zeng, B., Lu, X.F., Gan, L., Shu, M.L., 2011. Development of a novel fluidized bed ash cooler for circulating fluidized bed boilers: experimental study and application. Powder Technol. 212 (1), 151e160. https://doi.org/10.1016/j.powtec.2011.05.005. Zhang, H., Ma, J.H., Wang, J., Liu, Y., Han, H., Lu, H.B., Moore, W., Liang, Z.R., 2015. Statistical image reconstruction for low-dose CT using nonlocal means-based regularization. Part II: an adaptive approach. Comput. Med. Imag. Graph. 43 (6), 26e35. https://doi.org/10.1016/j.compmedimag.2015.02.008. Zhang, J., Shi, Z.G., Xue, L.S., 2009. Technical revamping of low moisture coke quenching for conventional coke wet quenching technology. Coal. Chem. Ind. 37 (2), 56e58. Zhang, J.Z., 1995. Fractal. Tsinghua University Press, Beijing. Zhang, Y.Z., Yang, A.M., Yang, X.J., 2013. 1-D heat conduction in a fractal medium: a solution by the local fractional fourier series method. Therm. Sci. 17 (3), 953e956. https://doi.org/10.2298/TSCI130303041Z. Zhao, Y.X., Peng, L., 2017. Investigation on the size and fractal dimension of nanopore in coals by synchrotron small angle X-ray scattering. Chin. Sci. Bull. 62 (21), 2416e2427. https://doi.org/10.1360/N972016-00970. Zheng, B., Liu, Y.Q., Zou, L.C., Li, R.Y., 2016. Heat transfer characteristics of calcined petroleum coke in waste heat recovery process. Math. Probl Eng. 2016, 2649383 https://doi.org/10.1155/2016/2649383. Zheng, B., Sun, P., Liu, Y.Q., Zhao, Q., 2018. Heat transfer of calcined petroleum coke and heat exchange tube for calcined petroleum coke waste heat recovery. Energy 155, 56e65. https://doi.org/10.1016/j.energy.2018.05.013. Zheng, B., Sun, P., Zhao, Q., Liu, Y.Q., Zhang, Z.L., 2019a. Effects of particle sizes on methanol steam reforming for hydrogen production in a reactor heated by waste heat. Int. J. Hydrogen Energy 44 (11), 5615e5622. https://doi.org/10.1016/ j.ijhydene.2018.07.163. Zheng, Y., Cai, J.J., Dong, H., Feng, J.S., Liu, J.Y., 2019b. Experimental investigation of volumetric exergy transfer coefficient in vertical moving bed for sinter waste heat recovery. Energy 167, 428e439. https://doi.org/10.1016/ j.energy.2018.10.110. Zhou, H.R., Zeng, S., Yang, S.Y., Xu, G.W., Qian, Y., 2018. Modeling and analysis of oil shale refinery process with the indirectly heated moving bed. Carbon. Resour. Convers. 1 (3), 260e265. https://doi.org/10.1016/j.crcon.2018.08.001. Zhu, Q.B., Xuan, Y.M., 2017. Pore scale numerical simulation of heat transfer and flow in porous volumetric solar receivers. Appl. Therm. Eng. 120, 150e159. https://doi.org/10.1016/j.applthermaleng.2017.03.141. Zou, L.C., Liu, Y.Q., Zheng, B., Liu, R.X., Qi, X.N., 2015. The effects of physical parameter variation on heat transfer characteristics of calcined petroleum coke waste heat utilization exchanger. Carbon Tech. 34 (3), 59e64. https://doi.org/ 10.14078/j.cnki.1001-3741.2015.03.014.
Contents lists available at ScienceDirect
Journal of Cleaner Production journal homepage: www.elsevier.com/locate/jclepro
Fractal heat conduction model of semi-coke bed in waste heat recovery heat exchanger Haibo Gao a, Yongqi Liu a, *, Bin Zheng a, Peng Sun a, Min Lu a, Guangdong Tian b, c a
School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo, Shandong, 255049, PR China Transportation College, Jilin University, Changchun, 130022, PR China c School of Mechanical Engineering, Shandong University, Jinan, 250061, PR China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 23 October 2019 Received in revised form 14 January 2020 Accepted 18 February 2020 Available online 19 February 2020
In order to realize the waste heat recovery of the high-temperature semi-cokes, the heat exchanger with one time heat transfer was put forward and the fractal heat conduction model was established for the first time. The internal structure of semi-cokes with different diameters in the heat exchanger was analyzed, and the internal structure was taken into account in the fractal heat conduction model. Furthermore, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. The results showed that, the internal structure of semi-cokes in the heat exchanger determines the fractal heat conduction characteristics, and the influence of porosity on the equivalent thermal conductivity calculated by the fractal heat conduction model is less than the fractal dimension and the contact resistance number. The equivalent thermal conductivity calculated by the fractal heat conduction model is closer to experimental values than that calculated by the traditional volume average model, and the error of the equivalent thermal conductivity between the experimental values and the fractal heat conduction model is less than 6%, thus the fractal heat conduction model is valid and feasible. © 2020 Elsevier Ltd. All rights reserved.
Handling editor: Panos Seferlis Keywords: Semi-coke Internal structure Fractal heat conduction Heat transfer Model Waste heat recovery
1. Introduction With the development of economy, the energy and environment problems become more and more serious, so energy conservation and environmental protection are imminent (Cheng et al., 2019; Li et al., 2018a,b; Norambuena-Contreras et al., 2017; Tian et al., 2019, 2017). The method of industrial waste heat recovery is a powerful way to realize the recycling of energy (Feng et al., 2016; Qin and Chang, 2017; Vance et al., 2019). Semi-coke can be obtained by the low temperature distillation of coal, whose temperature is up to 600 C, and the high temperature semi-cokes carry a lot of sensible energy. However, the sensible energy of semi-cokes with high temperature has not been recovered, resulting in energy waste and environmental pollution (Zheng et al., 2016). Therefore, the waste heat recovery of high temperature semi-cokes is of great significance. At present, there are two main cooling methods for the high temperature semi-cokes. The heat exchanger with one time heat
* Corresponding author. E-mail address: [email protected] (Y. Liu). https://doi.org/10.1016/j.jclepro.2020.120663 0959-6526/© 2020 Elsevier Ltd. All rights reserved.
transfer was proposed by our research group and it was used as the third method. (1) Coke wet quenching: high temperature semi-coke is immersed directly in water for cooling, and this causes environmental and water pollution (Gao et al., 2009; Zhang et al., 2009). The coke wet quenching is shown in Fig. 1. At the same time, the semi-coke has a high moisture content and the semi-coke needs to be dried again by consuming a lot of energy (Huang, 2014). (2) Coke dry quenching (two time heat transfer): the sensible energy of high temperature semi-cokes is recovered through two heat transfer processes in the coke dry quenching. Firstly, the sensible energy of semi-cokes is transferred to cold gas, then the sensible energy of hot gas will be absorbed by the boiler, as shown in Fig. 2. That is to say, the sensible energy of high temperature semi-cokes is recovered through two heat transfer processes in the coke dry quenching, thus the heat transfer efficiency of the dry coke quenching for the waste heat recovery is still very low. Although many scholars show that the dry coke quenching is superior to the wet coke
2
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
Fig. 1. Coke wet quenching. Fig. 3. Heat exchanger with one time heat transfer (one time heat transfer).
Fig. 2. Coke dry quenching (two time heat transfer).
quenching, the heat transfer efficiency of the dry coke quenching in the waste heat recovery process is still very low (Feng et al., 2008; Sun et al., 2015). (3) Heat exchanger with one time heat transfer (one time heat transfer): in order to overcome the disadvantages of the above two methods, the heat exchanger with one time heat transfer was proposed by our research group for the first time, and it has been applied in the industrial production. The heat exchanger with one time heat transfer is shown in Fig. 3. The sensible energy of high temperature semi-cokes is recovered only through one heat transfer process, unlike the coke dry quenching, which requires two heat transfer processes for waste heat recovery. When the semi-cokes pass through the heat exchanger by the force of gravity, the sensible energy of high temperature semi-cokes is absorbed directly by the cooling water in the heat exchanger to produce steam only through one time heat transfer process. The heat exchanger with one time heat transfer has the following advantages: the investment of heat exchanger with one time heat transfer is only one tenth of the investment of coke dry quenching. The heat exchanger with one time heat transfer not only can realize the efficient utilization of sensible energy of semi-coke (h 70%) but also can reduce environmental and water pollution. Meanwhile, the moisture content of semi-coke is only 15% of wet
coke quenching, saving the fuel for drying, so the semi-coke is easier to meet quality requirements. The semi-cokes only rely on the force of gravity to flow through the heat exchanger, and extra power is not needed to transport the semi-cokes. It can be seen from the above analysis, the heat exchanger with one time heat transfer has many advantages. However, there is no suitable heat transfer model to describe the heat transfer between the slow-flowing semi-cokes and the heat exchanger. Therefore, the establishment of the fractal heat conduction model is urgently needed to describe the heat conduction problem of semi-cokes in the new heat exchanger with one time heat transfer, where this work focuses on. Based on literature reviews and the present situation of the waste heat recovery of the high-temperature semicokes, our research group proposed the heat exchanger with one time heat transfer. Besides, the internal structure of semi-cokes with different diameters in the heat exchanger with one time heat transfer was obtained and analyzed. Furthermore, the internal structure of semi-cokes in the heat exchanger was taken into account in the fractal heat conduction model, and the effect of fractal dimension, contact resistance number and porosity on the fractal heat conduction model was discussed. Finally, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. At the same time, the discussion on the results and applications of fractal heat conduction model are carried out. The contributions of this work are as follows: (i) the heat exchanger with one time heat transfer is put forward for the first time; (ii) the internal structure of semi-coke bed with different diameters in the heat exchanger is obtained and analyzed, and the internal structure of semi-cokes in the heat exchanger is taken into account in the fractal heat conduction model; (iii) the fractal heat conduction model is established for the first time, and it is demonstrated through the experiment; and (iv) the fractal heat conduction model is more accurate than the traditional volume average model, and the application of the fractal heat conduction model can demonstrate the rationality of the fractal heat conduction model. The structure of the paper is shown as follows. Section 2 reports the current research status and the research gap. Section 3 describes the physical problem. Section 4 establishes the fractal heat conduction model of semi-cokes in the heat exchanger with one time heat transfer. Section 5 verifies the fractal heat conduction model, and discusses the effects of the internal structure of semi-
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
coke bed on the fractal heat conduction model. In the last section, conclusions are obtained. 2. Literature review This section is divided into two parts. The first subsection introduces the research status of the waste heat recovery technology for high temperature particles and the second subsection finds out the research gap. 2.1. Current research status Over the past few decades, numerous researches on the waste heat recovery technology of high temperature particles have been carried out. According to the published references, this section reviews progress on the available waste heat recovery techniques (i.e. fluidized bed, moving bed and packed bed) depending on the solid particle size. 2.1.1. Fluidized bed Recently, extensive studies about the heat transfer characteristics of particles in the fluidized bed have been explored. Lechner et al. (2014) experimentally investigated the heat transfer mechanism in fluidized beds equipped with horizontal heat exchanger surfaces of tube bundles. The heat exchanger with a shallow gassolid fluidized bed was experimentally researched in order to analyze energy recovery from solid particles leaving a combustion process (Rodriguez et al., 2002). Singh and Ghule (2016) designed a novel stripper ash cooler for circulating fluidized bed boiler, and the influence of particle size and the fluidization velocity of ash on the heat transfer performance has been investigated. Zeng et al. (2011) proposed a novel compound fluidized bed ash cooler, and it had a well separation effect and a good cooling effect. Kamble et al. (2014) developed the neural network model to predict the average heat transfer coefficient for horizontal tube immersed in gas-solid fluidized bed of large particles. An experimental study is carried out in order to introduce a volumetric heat transfer coefficient for fluidized bed drying to eliminate the uncertainties of the determination of the heat transfer surface between the gas and the particles (Tibor and Viktor, 2018). The above analysis shows that, fluidized bed is mainly used for waste heat recovery from high temperature particles with small particle and large resistance coefficient. Although the fluidized bed has a much higher heat transfer coefficient, the operating and maintenance costs are higher. 2.1.2. Moving bed The research of moving bed mainly focuses on the establishment of heat transfer model and the analysis of heat transfer process. Zheng et al. (2019)a,b established the unsteady heat transfer model to study the influence of particle diameter on particle temperature distribution. Cui et al. (2017) proposed the mathematical model for a moving cooling packed clinker bed, and the theoretical study was performed into the coupled gas-solid heat transfer process. Zhou et al. (2018) established the physical and chemical model for the indirectly heated moving bed, and a new oil shale refinery process with the indirectly heated moving bed is proposed. Gao et al. (2019)a,b established the 1-D fractional equation to study the heat transfer of particles. Isaza et al. (2017) obtained the analytical solution for the energy model of a moving bed heat exchanger that includes axial heat conduction. Liang et al. (2019) established the Lagrangian descriptions of particle and gas energy equation in a countercurrent moving bed, and two typical scenarios of waste heat recovery for high-temperature particles were researched. Herz et al. (2012) experimentally researched the influence mechanism of operational parameters on the heat transfer
3
between the cylinder and the particles. Zheng et al. (2019)a,b experimentally investigated the volumetric exergy transfer coefficient in vertical moving bed for sinter waste heat recovery. Zhang et al. (2013) investigated the fractal heat conduction problems of slag by using fractal properties, and the fractal properties of materials determine the heat transfer properties. Wang et al. (2014) investigated the waste heat recovery methods of blast furnace slag and analyzed the cooling process of steel slag particles in the moving bed. According to the published references, extensive studies about the waste heat recovery of moving bed are mainly focus on the high temperature particles of medium size. Although the moving bed has the characteristics of low cost and stable operation, the heat transfer coefficient of moving bed is lower than that of fluidized bed. Basically, the waste heat recovery of moving bed is still at early stage, and the future work should be focused on the enhanced heat transfer technology of moving bed. 2.1.3. Packed bed Packed beds of particles are widely used in industries such as chemical catalytic reactors (Partopour and Dixon, 2016), high temperature gas-cooled nuclear reactors (Abdulmohsin and AlDahhan, 2015), thermal energy storage systems (Lu et al., 2016), solar receivers (Zhu and Xuan, 2017) and so on. Li et al., 2018a,b studied the heat transfer of smooth or dimpled spheres in the structured packed beds by numerical simulation. Bu et al. (2014) researched the thermal contact resistance modification between particles in the heat transfer process. Naghash et al. (2016) estimated the convective heat transfer coefficient for airflow passing through randomly packed beds of silica gel by using the inverse simulation. Singhal et al. (2017) proposed a new methodology for deriving heat transfer correlations from PR-DNS of very dense particle packings relevant for packed bed applications. Esence et al. (2019) developed a versatile one-dimensional numerical model able to describe many packed-bed configurations, and this model is able to treat liquid and gaseous heat transfer fluids. Halkarni et al. (2017) investigated the behavior of wall heat transfer coefficient in randomly packed beds of uniform sized spheres using infrared thermography. Hou et al. (2018) established the CFD model for predicting the heat transfer in the packed bed, in which the heterogeneous fluid flow was resolved by considering the oscillatory behavior of voidage and the effective fluid viscosity. It can be known from the above references, the packed bed technology for high temperature particles is mainly used for large particles, and it can only satisfy the hot particles with an uniform size or narrow range. The heat transfer coefficients between air and high temperature particles in the packed bed are relatively lower than those in fluidized bed and moving bed. Further emphasis should be given on the efficient organization of cascade waste heat recovery and optimization of operating parameters. 2.2. Research gap By summarizing and analyzing the previous research results, the previous researches mainly focus on the available waste heat recovery techniques (i.e. fluidized bed, moving bed and packed bed) depending on the high temperature particle size, and the current technologies can only satisfy the hot particles with an uniform size or narrow range. For the high temperature semi-cokes with wide particle size distribution range, a new waste heat recovery equipment is urgently needed, and there is no waste heat recovery equipment for semi-cokes at present. In fact, the internal structure of semi-cokes in the heat exchanger has a great effect on the heat conduction of high temperature semi-cokes. However there is a lack of investigations on the internal structure and fractal heat conduction model for the semi-cokes in the heat exchanger. To fill
4
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
Fig. 4. The structure of the heat exchanger.
this gap, the heat exchanger with one time heat transfer was put forward and the fractal heat conduction model was established for the first time. Meanwhile, the internal structure of semi-coke bed with different diameters is obtained, and the effect of the internal structure is considered by the fractal heat conduction model. Furthermore, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. Finally, the results and discussions on the fractal heat conduction model are carried out.
3. Description of physical problem The high temperature semi-cokes are cooled directly by the heat exchanger with one time heat transfer, the internal and external heat exchangers are composed of heat exchange pipes and membrane walls, as shown in Fig. 4. As the cooling water flows through the heat exchanger, the sensible energy of semi-cokes is recycled by the cooling water. At the same time, the water pipe is arranged in the middle of the heat exchanger to spray cooling water into the heat exchanger, and the high temperature semi-cokes vaporize cooling water to form steam. As the steam moves upward, steam and semi-cokes will form convection heat transfer in the upper part of the heat exchanger. Our research group has investigated the convection heat transfer of steam and semi-cokes in the upper half of the heat exchanger in Ref. (Gao et al., 2019a,b). However, the heat transfer problem of semi-cokes in the lower half of the heat exchanger with one time heat transfer has not been studied, so the heat transfer problem of semi-cokes in the lower half of the heat exchanger was selected for study in this work. In the lower half of the heat exchanger with one time heat transfer, there are three types of heat transfer (heat conduction, radiation heat transfer and convection heat transfer) between semi-coke and wall, as shown in Fig. 5. The heat conduction mainly includes the following three heat transfer pathways: (1) heat conduction in direct contact between semi-coke and wall, as shown in heat transfer mode A; (2) heat conduction of gap gas film between semi-coke and wall, as shown in heat transfer mode B; (3) heat conduction of gas film near the contact surface between semicoke and wall, as shown in heat transfer mode C. The radiation heat transfer mainly refers to radiation heat transfer of semi-coke to the wall, as shown in heat transfer mode D. The convection heat transfer mainly refers to convection heat transfer between gas and wall, as shown in heat transfer mode E. It can be seen from Fig. 5 that the heat transfer mode between semi-cokes is the same as the heat transfer between semi-coke and wall. Due to the semi-cokes flow down very slowly (4 105 m/s), there is little change in the position of semi-cokes, therefore, the static semi-cokes were used for research. Due to the symmetrical structure of heat exchanger, one fourth width of semi-coke bed was taken as the research object, as shown in Fig. 6. Since there is no
Fig. 5. Three types of heat transfer.
steam flowing through the lower part of the heat exchanger and the velocity of semi-cokes is slow, convection heat transfer is ignored (Leng, 2008). Under the water pipe, the temperature of semi-cokes
Fig. 6. Research object.
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
is below 200 C, thus the radiation heat transfer was neglected in this study. Zheng et al. (2018) showed that the heat transfer mode of particles at any given moment is mainly heat conduction. The heat conduction is the main mode of heat transfer for semi-cokes in the lower half of the heat exchanger. However, the heat conduction problem of semi-cokes has not been studied, so the heat conduction problem of semi-cokes was selected for study in this work. 4. Establishment of fractal heat conduction model for semicoke bed Due to the internal structure of semi-cokes in the heat exchanger has an important influence on the fractal heat conduction model, this section is divided into two parts. The first subsection introduces the calculation methods of internal structure for the semi-coke bed, and the second subsection describes the establishment of the fractal heat conduction model for semi-coke bed. 4.1. Calculation methods of internal structure for the semi-coke bed 4.1.1. Computer tomography (CT) experiments and images processing Six different diameters of semi-coke were obtained by the sieve method, and they are 3mm/9mm/19mm/37mm/55mm/65 mm, respectively. X-ray CT is the efficient tool to observe the internal structures of the object in industry and medicine (Peng et al., 2011; Tian et al., 2012; Zhao and Peng, 2017; Zhang et al., 2015). The internal structure of semi-coke bed was obtained by the spiral CT machine for the first time, and the CT images were segmented by image binarization method to obtain the bit binary images. Due to an appropriate threshold has direct impact on the success of image binarization, the porosity of semi-coke bed calculated by drainage method was used to compare with the porosity of semi-coke bed calculated by image binarization processing method. When the error of porosity calculated by the two methods is less than 5%, the selected threshold of image binarization processing method is considered reasonable. The comparison between CT image and bit binary image of semi-coke bed is shown in Fig. 7. As can be seen from Fig. 7, the bit binary image can well describe the internal structure of semi-coke bed, thus the bit binary image can be used for subsequent research.
5
to the mathematic expression of box-counting method by using the MATLAB program. The mathematic expression of fractal dimension (Grossu and El-Shamali, 2013) is written:
D ¼ lim
log NðrÞ
(1)
r/0 logð1=rÞ
where D denotes fractal dimension, r denotes length, N(r) denotes the box number. The contact number of the single semi-coke particle was calculated by a lot of CT images, and the average value of twenty particles was used to replace the contact number. The porosity can be calculated according to the void area of bit binary image, and the average value of all bit binary images was used to replace the porosity.
4.2. Establishment of fractal heat conduction model 4.2.1. Fractal heat conduction path The semi-cokes in the heat exchanger is discontinuous media and the internal structure of semi-cokes in the heat exchanger has fractal properties. The heat transfer path of semi-cokes in the heat exchanger is a fractal curve, not a straight line. For example, like the 3rd random Koch curve, the fractal heat conduction path is presented in Fig. 8. As shown in Fig. 8, the path of heat conduction is a fractal curve, not a straight line, which means the length of the heat transfer path and the contact resistance number are actually increasing.
4.2.2. Calculation of fractal curve length This work assumes that the sensible energy is transmitted through parallel multi-strand identical fractal curves in semi-coke bed. The empirical formula for calculating the length of coastline proposed by L. f. Richardso in 1961 was used to calculate the fractal curve length (Zhang, 1995). The empirical formula is written:
4.1.2. Calculation methods of internal structure The fractal dimension can describe the complexity of the internal structure for semi-cokes in the heat exchanger. The power spectral method, the structure function method and the boxcounting method can be employed to calculate the fractal dimension (Wang et al., 2015). The box-counting method has a good calculation effect, so the fractal dimension was calculated according
Fig. 7. The CT images and bit binary images.
Fig. 8. The fractal heat conduction path.
6
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
5. Results and discussions
LðaÞ ¼ L0 a1D
(2)
where L(a) denotes the fractal curve length, a denotes the ratio scale, L0 is the distance of a straight line between two ends of a fractal curve, D is the fractal dimension of the fractal curve. 4.2.3. Establishment of the fractal heat conduction model The fractal heat conduction path can be simplified into the parallel gas phase and solid phase paths. The diagram of the fractal heat conduction model is shown in Fig. 9. L0 is the distance of a straight line between two ends of a fractal curve, and L(a) denotes the fractal curve length. The S denotes the macroscopic cross section area of semi-coke bed, 4 denotes the porosity, Rc denotes the contact resistance between semi-cokes. The geometric structure, the contact resistance and the semicoke diameter are considered into the equivalent thermal resistance in the fractal heat conduction model. According to the fractal heat conduction model in Fig. 9, the equivalent thermal resistance R of semi-coke bed can be expressed as follows:
(3)
where Rs denotes the thermal resistance of solid, Rg denotes the thermal resistance of gas, ls denotes the thermal conductivity of semi-coke, lg denotes the thermal conductivity of gas, d denotes the semi-coke diameter. The formula (2) is taken into the formula (3), and the formula (3) is then deformed to obtain the fractal expression of the equivalent thermal conductivity le as follows: R 4ð14Þlg ls
4lg þ ð1 4Þls þ c d ls a1D 1 þ Rc ð14ÞS d
(4)
The formula (4) is derived from fractal theory, and it contains the influence of fractal dimension on the equivalent thermal conductivity, so the application of formula (4) has certain limitation. The application limitation of formula (4) is that, the fractal dimension can be obtained only if the research object has two basic characteristics of fractal (self-similarity and scale invariance). At the same time, the fractal heat conduction model is verified under certain experimental conditions, so the fractal expression of the equivalent thermal conductivity in the formula (4) has the limitation for particle size (3 mme65mm) and particle temperature (T 100 C).
5.2. Model verification and discussion To further investigate the fractal heat conduction problem of semicokes in the heat exchanger with one time heat transfer, the verification of the fractal heat conduction model was carried out by experiment. The equivalent thermal conductivity of semi-cokes was measured by the DRS-III thermal conductivity tester. The experimental system includes the heating surface, the cooling surface, the
2.00
Fractal dimension Contact number Porosity
1.95 1.90
12
50
8
1.80
6
1.75
4
1.70
Fig. 9. The diagram of fractal heat conduction model.
60
10
1.85
1.65
14
0
10
20
30 40 50 Diameter (mm)
60
2 70
40 30 20
Porosity(%)
le ¼
The effects of the diameter on the internal structure of semicokes in the heat exchanger is depicted in Fig. 10. Since the internal structure of semi-cokes in the heat exchanger is calculated by averaging multiple experiments, the error bars are included in Fig. 10. It can be seen from Fig. 10 that the errors of the internal structure of semi-cokes in the heat exchanger are within an acceptable range. As is shown in Fig. 10, when the diameter increases from 3 mm to 65 mm, the fractal dimension decreases from 1.95 to 1.73, the contact number decreases from 13 to 4, and the porosity increases from 5.4% to 52.1%. The reason for this is that, with the increase of the diameter, the arrangement of semi-cokes becomes simpler and the complexity of internal structure decreases gradually, so the fractal dimension gradually decreases. The number of semi-coke in the same space gradually decreases and the less chance of contact between semi-cokes, so the contact number decreases as the semi-coke diameter increases. The voids between semi-cokes gradually become larger with the increase of diameter, so the porosity gradually increases with diameter. This means that, as the semi-coke diameter increases, the distance of heat transfer and the contact resistance number decrease, and the share of gas heat transfer is gradually increasing. The study of internal structure lays a foundation for the explanation of heat conduction mechanism.
Contact number
Rs Rg LðaÞ ¼ Sle Rs þ Rg LðaÞ LðaÞRc LðaÞ ¼ þ ð1 4ÞSls 4Slg d LðaÞ LðaÞRc LðaÞ þ þ ð1 4ÞSls 4Slg d
5.1. Effects of diameter on the internal structure of semi-coke bed
Fractal dimension
R¼
Due to the internal structure of semi-cokes in the heat exchanger has an important effect on the fractal heat conduction model and the semi-coke diameter directly determines the internal structure of semi-cokes in the heat exchanger, this section is divided into two parts. The first subsection introduces the effects of the semi-coke diameter on the internal structure of semi-cokes in the heat exchanger. The second subsection verifies and discusses the fractal heat conduction model.
10 0
Fig. 10. Effect of diameter on the internal structure of semi-cokes in the heat exchanger.
heat insulating material and measurement system, as depicted in Fig. 11. The experiment process is as follows: turn on the power when the experimental system is connected. Turn on the DRS-III thermal conductivity tester and adjust the heating surface temperature to 100 C. Adjust the constant temperature water bath to keep the cooling surface temperature at 25 C. Open the computer and data acquisition software to record the experimental temperature. When the temperature is stable, the semi-coke temperature is collected. The equivalent thermal conductivity in the experiment can be calculated by formula (5):
le ¼
ql Th Tc
(5)
where le denotes the equivalent thermal conductivity, q denotes the heat flux, l denotes the height of semi-coke bed, Th denotes the heating surface temperature, Tc denotes the cooling surface temperature. As with a report of every experimental research, the analysis of the experimental uncertainties in calculating the results must be given proper attention. The analysis of experimental uncertainties was carried out to improve the experimental reliability. The experimental uncertainty in the heat transfer was mainly caused by temperature measurement errors and heat balance errors, the equivalent thermal conductivity was calculated by taking the average value of several experiments. The temperature measurement errors mainly comes from the measurement error of thermocouple, and the measurement error of thermocouple is ±1 C. The experimental uncertainty of heat balance was ±3%. Detailed error analyses showed that the experimental uncertainties in the equivalent thermal conductivity were estimated to be ±4%. At the same time, the error analysis of the equivalent thermal conductivity in the experiment was carried out in Fig. 12, and the error bars showed that the error of the equivalent thermal conductivity was within the allowable range. In formula (4), if Rc ¼ 0 and D ¼ 1, the formula (4) becomes the traditional volume average formula in Ref. (Zou et al., 2015), and the traditional volume average formula is as follows:
Fig. 11. The experimental schematic diagram.
e(W/(m·K))
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
0.80 0.75 0.70 0.65 0.60 0.55 0.50 0.45 0.40 0.35 0.30 0.25
7
Experiment Formula 4 Formula 6
0
10
20
30 40 50 Diameter (mm)
60
70
Fig. 12. The comparison of the equivalent thermal conductivity calculated by different methods.
le ¼ 4lg þ ð1 4Þls
(6)
The equivalent thermal conductivity was obtained by the formula (4), the formula (5) in the experiment and formula (6). The comparison of the equivalent thermal conductivity calculated by the three methods is shown in Fig. 12. In Fig. 12, comparing to the equivalent thermal conductivity obtained by the formula (6), the equivalent thermal conductivity calculated by the formula (4) is closer to the formula (5) in the experiment, and the error between the formula (4) and formula (5) in the experiment is less than 6%. Therefore, the fractal expression of the equivalent thermal conductivity in the formula (4) can describe the heat conduction problem of semi-coke bed more accurately than formula (6). The internal structure of semi-cokes in the heat exchanger has great effect on the heat conduction characteristics, and the internal structure was taken into account in the fractal heat conduction model, thus the fractal heat conduction model considering the internal structure of semi-cokes in the heat exchanger is closer to the real heat conduction of semi-cokes in the heat exchanger than other models. At the same time, the heat conduction path of semicokes in the heat exchanger is a fractal heat conduction path, not a straight line, which means the length of the heat conduction path and the contact resistance number are actually increasing, thus the fractal heat conduction path of the fractal heat conduction model is closer to the real heat conduction path of semi-cokes in the heat exchanger than other models. According to the above analysis, it is reasonable and feasible to choose the fractal heat conduction model to study the heat conduction of semi-cokes in heat exchanger. As can be seen from Fig. 12, the equivalent thermal conductivity increases gradually with increasing the semi-coke diameter. It can be seen from the information of the internal structure obtained in Fig. 10, with the increase of diameter, the fractal dimension and contact number decrease gradually, and the porosity increases. This means that the heat conduction path and the contact resistance number decrease gradually, and this is favorable for heat conduction. The heat flux is mainly transported along the semi-cokes rather than through the gas, so the increase of porosity is not conducive to heat conduction. However, the equivalent thermal conductivity increases with the semi-coke diameter in Fig. 12, so the influence of porosity on the equivalent thermal conductivity calculated by the fractal heat conduction model is less than the
8
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
110 Formula (6) Experiment Formula (4)
100
Temperature (
)
90 80 70 60 50 40 30 20 -40
0
40
80 120 160 Height (mm)
200
240
Fig. 13. Temperature comparison of the three methods.
fractal dimension and contact resistance number. The above analysis shows that the internal structure has an important effect on the fractal heat conduction model. In order to further clarify the rationality of choosing fractal heat conduction model, the temperature comparison of the three methods was carried out. The temperature was obtained by the formula (4), the formula (5) in the experiment and formula (6), and the temperature comparison of the three methods is shown in Fig. 13. In Fig. 13, the height refers to the distance between the semi-cokes and the heating surface, and the temperature of semicokes decreases with increasing the height. As can be seen from Fig. 13, the average error of temperature between the formula (4) and the experiment is 4.7%, and the average error of temperature between the formula (6) and the experiment is 9.2%, thus the temperature calculated by the formula (4) is closer to the experimental temperature than formula (6). It can be seen from the
temperature analysis in Fig. 13, the fractal heat conduction model can accurately predict the temperature distribution of semi-cokes in the exchanger with one time heat transfer, so it is advisable to establish the fractal heat conduction model to research the heat conduction of semi-cokes in heat exchanger. The fractal dimension can describe the complexity of the internal structure of semi-cokes in the heat exchanger. The larger the fractal dimension, the more complex the internal structure of semicokes in the heat exchanger. The effect of fractal dimension on the heat flux is depicted in Fig. 14. As can be seen from Fig. 14, when the fractal dimension of semi-coke bed increases from 1.732 to 1.952, the heat flux decreases from 501 W/m2 to 249 W/m2. The reason for this is that, the internal structure complexity of semi-cokes in the heat exchanger increases gradually with the increase of the fractal dimension, thus the heat conduction path length and complexity increase gradually. The increase of the heat conduction path length and complexity leads to the decrease of heat transfer efficiency, thus the heat is more difficult to flow through the semi-coke bed. To sum up, the heat transfer resistance increases with the increase of fractal dimension, so the heat flux decreases gradually with the increase of fractal dimension. Through the verification and discussion of the fractal heat conduction model, it can be seen that the internal structure of the semi-cokes in the heat exchanger has great effect on the heat conduction characteristics, and the fractal heat conduction model considering the internal structure of semi-cokes in the heat exchanger can well describe the heat conduction problem. About the application of the fractal heat conduction model, the fractal heat conduction model can accurately predict the temperature distribution of semi-cokes in the exchanger with one time heat transfer. 6. Conclusions In order to realize the waste heat recovery of the high temperature semi-cokes, the heat exchanger with one time heat transfer was put forward and the fractal heat conduction model was
550
Heat flux (W/m2)
500 450 400 350 300 250 200 1.70
1.75
1.80 1.85 1.90 Fractal dimension
Fig. 14. The effect of fractal dimension on the heat flux.
1.95
2.00
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
established for the first time. The internal structure of semi-coke bed with different diameters is obtained, and the effect of the internal structure is considered by the fractal heat conduction model. Furthermore, the fractal heat conduction model is demonstrated through the experiment, and it is compared with the traditional volume average model. Finally, the results and discussions on the fractal heat conduction model are carried out. Major conclusions are as follows: (1) The internal structure of semi-cokes in the heat exchanger with one time heat transfer has an important effect on fractal heat conduction model. With increasing the diameter from 3 mm to 65 mm, the fractal dimension decreases from 1.95 to 1.73, the contact number decreases from 13 to 4, and the porosity increases from 5.4% to 52.1%. This means that the heat conduction path and the contact resistance number decrease gradually, and this is favorable for heat conduction. The heat flux is mainly transported along the semi-cokes rather than through the gas, so the increase of porosity is not conducive to heat conduction. (2) The geometric structure, the contact resistance and the semicoke diameter are considered into the equivalent thermal resistance in the fractal heat conduction model. Comparing to the equivalent thermal conductivity obtained by the traditional volume average model, the equivalent thermal conductivity obtained by the fractal heat conduction model is closer to experimental values, meaning the fractal heat conduction model can describe the heat conduction problem of semi-cokes in the heat exchanger with one time heat transfer more accurately than other models. (3) The equivalent thermal conductivity increases with diameter, and the influence of porosity on the equivalent thermal conductivity calculated by the fractal heat conduction model is less than the fractal dimension and contact resistance number.
Declaration of competing interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. CRediT authorship contribution statement Haibo Gao: Conceptualization, Investigation, Writing - original draft, Writing - review & editing. Yongqi Liu: Methodology, Resources, Project administration, Funding acquisition. Bin Zheng: Supervision, Software. Peng Sun: Formal analysis, Writing - review & editing. Min Lu: Validation, Data curation. Guangdong Tian: Formal analysis, Visualization. Acknowledgments These works were supported by National Key R&D Program of China (2017YFB0603504-2) and Shandong Provincial Natural Science Foundation, China (ZR2018MEE006 and ZR2017LEE019). References Abdulmohsin, R.S., Al-Dahhan, M.H., 2015. Characteristics of convective heat transport in a packed pebble-bed reactor. Nucl. Eng. Des. 284, 143e152. https:// doi.org/10.1016/j.nucengdes.2014.11.041. Bu, S.S., Yang, J., Zhou, M., Li, S.Y., Wang, Q.W., Guo, Z.X., 2014. On contact point modification for forced convective heat transfer analysis in a structured packed bed of spheres. Nucl. Eng. Des. 270, 21e33. https://doi.org/10.1016/ j.nucengdes.2014.01.001.
9
Cheng, Z.L., Guo, Z.G., Tan, Z.T., Yang, J., Wang, Q.W., 2019. Waste heat recovery from high-temperature solid granular materials: energy challenges and opportunities. Renew. Sustain. Energy Rev. 116, 109428 https://doi.org/10.1016/ j.rser.2019.109428. Cui, Z., Shao, W., Chen, Z.Y., Cheng, L., 2017. Mathematical model and numerical solutions for the coupled gas-solid heat transfer process in moving packed beds. Appl. Energy 206, 1297e1308. https://doi.org/10.1016/ j.apenergy.2017.10.011. , J.F., Stutz, B., 2019. A versatile one-dimensional Esence, T., Bruch, A., Fourmigue numerical model for packed-bed heat storage systems. Renew. Energy 133, 190e204. https://doi.org/10.1016/j.renene.2018.10.012. Feng, J.S., Dong, H., Gao, J.Y., Li, H.Z., Liu, J.Y., 2016. Numerical investigation of gassolid heat transfer process in vertical tank for sinter waste heat recovery. Appl. Therm. Eng. 107, 135e143. https://doi.org/10.1016/ j.applthermaleng.2016.06.175. Feng, Y.H., Zhang, X.X., Yu, Q., Shi, Z.Y., Liu, Z.C., Zhang, H., Liu, H.F., 2008. Experimental and numerical investigations of coke descending behavior in a coke dry quenching cooling shaft. Appl. Therm. Eng. 28 (11e12), 1485e1490. https:// doi.org/10.1016/j.applthermaleng.2007.09.001. Gao, H.B., Liu, Y.Q., Song, X.Y., Zheng, B., Sun, P., Lu, M., Ma, Y.X., Gao, Z.Q., 2019a. Numerical study of heat transfer characteristics of semi-coke and steam in waste heat recovery steam generator for hydrogen production. Int. J. Hydrogen Energy 44 (46), 25160e25168. https://doi.org/10.1016/j.ijhydene.2019.05.155. Gao, H.B., Liu, Y.Q., Zheng, B., Sun, P., Lu, M., Yin, Q., 2019b. Modeling of fractal heat conduction of semi-coke bed in waste heat recovery steam generator for hydrogen production. Int. J. Hydrogen Energy 44 (46), 25240e25247. https:// doi.org/10.1016/j.ijhydene.2019.05.098. Gao, J.J., Zhao, S.F., Zheng, Y.T., Guo, J.W., 2009. Comparative analysis between wet coke quenching and dry coke quenching. Sci-tech Information Development & Economy 19 (23), 199e201. Grossu, I.V., EI-Shamali, S.A., 2013. Hyper-Fractal Analysis v04: implementation of a fuzzy box-counting algorithm for image analysis of artistic works. Comput. Phys. Commun. 184, 1812e1813. https://doi.org/10.1016/j.cpc.2013.02.026. Halkarni, S.S., Sridharan, A., Prabhu, S.V., 2017. Measurement of local wall heat transfer coefficient in randomly packed beds of uniform sized spheres using infrared thermography (IR) and water as working medium. Appl. Therm. Eng. 126, 358e378. https://doi.org/10.1016/j.applthermaleng.2017.07.174. Herz, F., Mitov, I., Specht, E., Stanev, R., 2012. Experimental study of the contact heat transfer coefficient between the covered wall and solid bed in rotary drums. Chem. Eng. Sci. 82, 312e318. https://doi.org/10.1016/j.ces.2012.07.042. Hou, B.L., Ye, R.M., Huang, Y.Q., Wang, X.D., Zhang, T., 2018. A CFD model for predicting the heat transfer in the industrial scale packed bed. Chin. J. Chem. Eng. 26 (2), 228e237. https://doi.org/10.1016/j.cjche.2017.07.008. Huang, X.C., 2014. Technical features of the water-seal coke quenching technology of the vertical internal-heating semicoke oven. Coal. Chem. Ind. 42 (4), 30e32. Isaza, P.A., O’Brien, A., Warnica, W.D., Bussmann, M., 2017. Assessing axial heat conduction in moving bed heat exchangers. Int. J. Therm. Sci. 120, 303e313. https://doi.org/10.1016/j.ijthermalsci.2017.06.004. Kamble, L.V., Pangavhane, D.R., Singh, T.P., 2014. Experimental investigation of horizontal tube immersed in gas-solid fluidized bed of large particles using artificial neural network. Int. J. Heat Mass Tran. 70, 719e724. https://doi.org/ 10.1016/j.ijheatmasstransfer.2013.11.073. Lechner, S., Merzsch, M., Krautz, H.J., 2014. Heat-transfer from horizontal tube bundles into fluidized beds with Geldart A lignite particles. Powder Technol. 253, 14e21. https://doi.org/10.1016/j.powtec.2013.10.041. Leng, T.T., 2008. Simulation Study of Discrete Element Method on Granular Flow and Heat Transfer. Dalian University of Technology. Li, L., Lei, Y.L., Wu, S.M., Huang, Z.Y., Luo, J.Y., Wang, Y.F., Chen, J.B., Yan, D., 2018a. Evaluation of future energy consumption on PM2.5 emissions and public health economic loss in Beijing. J. Clean. Prod. 187, 1115e1128. https://doi.org/10.1016/ j.jclepro.2018.03.229. Li, S.Y., Zhou, L., Yang, J., Wang, Q.W., 2018b. Numerical simulation of flow and heat transfer in structured packed beds with smooth or dimpled spheres at low channel to particle diameter ratio. Energies 11 (4), 937. https://doi.org/10.3390/ en11040937. Liang, X., Liu, X.J., Xia, D.H., 2019. Lagrangian simulation and exergy analysis for waste heat recovery from high-temperature particles using countercurrent moving beds. Appl. Therm. Eng. 160, 114115 https://doi.org/10.1016/ j.applthermaleng.2019.114115. Lu, J.F., Chen, Y., Ding, J., Wang, W.L., 2016. High temperature energy storage performances of methane reforming with carbon dioxide in a tubular packed reactor. Appl. Energy 162, 1473e1482. https://doi.org/10.1016/ j.apenergy.2015.03.140. Naghash, M., Fathieh, F., Besant, R.W., Evitts, R.W., Simonson, C.J., 2016. Measurement of convective heat transfer coefficients in a randomly packed bed of silica gel particles using IHTP analysis. Appl. Therm. Eng. 106, 361e370. https:// doi.org/10.1016/j.applthermaleng.2016.06.027. Norambuena-Contreras, J., Silva-Robles, E., Gonzalez-Torre, I., Saravia-Montero, Y., 2017. Experimental evaluation of mechanical and thermal properties of recycled rubber membranes reinforced with crushed polyethylene particles. J. Clean. Prod. 145, 85e97. https://doi.org/10.1016/j.jclepro.2017.01.040. Partopour, B., Dixon, A.G., 2016. Reduced microkinetics model for computational fluid dynamics (CFD) simulation of the fixed-bed partial oxidation of ethylene. Ind. Eng. Chem. Res. 55, 7296e7306. https://doi.org/10.1021/acs.iecr.6b00526. Peng, R.D., Yang, Y.C., Ju, Y., Mao, L.T., Yang, Y.M., 2011. Computation of fractal
10
H. Gao et al. / Journal of Cleaner Production 258 (2020) 120663
dimension of rock pores based on gray CT images. Chin. Sci. Bull. 56 (31), 3346e3357. https://doi.org/10.1007/s11434-011-4683-9. Qin, S.Y., Chang, S.Y., 2017. Modeling, thermodynamic and techno-economic analysis of coke production process with waste heat recovery. Energy 141, 435e450. https://doi.org/10.1016/j.energy.2017.09.105. cora, A.A.B., Bizzo, W.A., 2002. Heat recovery from hot solid Rodriguez, O.M.H., Pe particles in a shallow fluidized bed. Appl. Therm. Eng. 22 (2), 145e160. https:// doi.org/10.1016/S1359-4311(01)00076-X. Singh, R.I., Ghule, K., 2016. Design, development, experimental and CFD analysis of a prototype fluidized bed stripper ash cooler. Appl. Therm. Eng. 107, 1077e1090. https://doi.org/10.1016/j.applthermaleng.2016.07.044. Singhal, A., Cloete, S., Radl, S., Quinta-Ferreira, R., Amini, S., 2017. Heat transfer to a gas from densely packed beds of monodisperse spherical particles. Chem. Eng. J. 314, 27e37. https://doi.org/10.1016/j.cej.2016.12.124. Sun, K., Tseng, C.T., Wong, D.S.H., Shieh, S.S., Jang, S.S., Kang, J.L., Hsieh, W.D., 2015. Model predictive control for improving waste heat recovery in coke dry quenching processes. Energy 80, 275e283. https://doi.org/10.1016/ j.energy.2014.11.070. Tian, G.D., Zhang, H.H., Feng, Y.X., Jia, H.F., Zhang, C.Y., Jiang, Z.G., Li, Z.W., Li, P.G., 2017. Operation patterns analysis of automotive components remanufacturing industry development in China. J. Clean. Prod. 164, 1363e1375. https://doi.org/ 10.1016/j.jclepro.2017.07.028. Tian, G.D., Liu, X., Zhang, M.H., Yang, Y.S., Zhang, H.H., Lin, Y., Ma, F.W., Wang, X.Y., Qu, T., Li, Z.W., 2019. Selection of take-back pattern of vehicle reverse logistics in China via Grey-DEMATEL and Fuzzy-VIKOR combined method. J. Clean. Prod. 220, 1088e1100. https://doi.org/10.1016/j.jclepro.2019.01.086. Tian, W., Dang, F.N., Chen, H.Q., 2012. Fractal analysis on meso-fracture of concrete based on the technique of CT image processing. J. Basic Sci. Eng. 20 (3), 424e431. https://doi.org/10.3969/j.issn.1005-0930.2012.03.009. Tibor, P.D., Viktor, S., 2018. Volumetric heat transfer coefficient in fluidized bed dryers. Chem. Eng. Technol. 41 (3), 628e636. https://doi.org/10.1002/ ceat.201700038. Vance, D., Nimbalkar, S., Thekdi, A., Armstrong, K., Wenning, T., Cresko, J., Jin, M.Z., 2019. Estimation of and barriers to waste heat recovery from harsh environments in industrial processes. J. Clean. Prod. 222, 539e549. https://doi.org/ 10.1016/j.jclepro.2019.03.011. Wang, B., Wang, X.C., Yuan, Y.C., Zhou, Q.P., 2014. Advances in the study of the blast furnace slag waste heat recovery technologies. J. Eng. Therm. Eng. 29 (2), 113e120. https://doi.org/10.16146/j.cnki.rndlgc.2014.02.001. Wang, Q.Y., Liang, Z.Q., Wang, X.B., Zhao, W.X., Wu, Y.B., Zhou, T.F., 2015. Fractal analysis of surface topography in ground monocrystal sapphire. Appl. Surf. Sci. 327, 182e189. https://doi.org/10.1016/j.apsusc.2014.11.093.
Zeng, B., Lu, X.F., Gan, L., Shu, M.L., 2011. Development of a novel fluidized bed ash cooler for circulating fluidized bed boilers: experimental study and application. Powder Technol. 212 (1), 151e160. https://doi.org/10.1016/j.powtec.2011.05.005. Zhang, H., Ma, J.H., Wang, J., Liu, Y., Han, H., Lu, H.B., Moore, W., Liang, Z.R., 2015. Statistical image reconstruction for low-dose CT using nonlocal means-based regularization. Part II: an adaptive approach. Comput. Med. Imag. Graph. 43 (6), 26e35. https://doi.org/10.1016/j.compmedimag.2015.02.008. Zhang, J., Shi, Z.G., Xue, L.S., 2009. Technical revamping of low moisture coke quenching for conventional coke wet quenching technology. Coal. Chem. Ind. 37 (2), 56e58. Zhang, J.Z., 1995. Fractal. Tsinghua University Press, Beijing. Zhang, Y.Z., Yang, A.M., Yang, X.J., 2013. 1-D heat conduction in a fractal medium: a solution by the local fractional fourier series method. Therm. Sci. 17 (3), 953e956. https://doi.org/10.2298/TSCI130303041Z. Zhao, Y.X., Peng, L., 2017. Investigation on the size and fractal dimension of nanopore in coals by synchrotron small angle X-ray scattering. Chin. Sci. Bull. 62 (21), 2416e2427. https://doi.org/10.1360/N972016-00970. Zheng, B., Liu, Y.Q., Zou, L.C., Li, R.Y., 2016. Heat transfer characteristics of calcined petroleum coke in waste heat recovery process. Math. Probl Eng. 2016, 2649383 https://doi.org/10.1155/2016/2649383. Zheng, B., Sun, P., Liu, Y.Q., Zhao, Q., 2018. Heat transfer of calcined petroleum coke and heat exchange tube for calcined petroleum coke waste heat recovery. Energy 155, 56e65. https://doi.org/10.1016/j.energy.2018.05.013. Zheng, B., Sun, P., Zhao, Q., Liu, Y.Q., Zhang, Z.L., 2019a. Effects of particle sizes on methanol steam reforming for hydrogen production in a reactor heated by waste heat. Int. J. Hydrogen Energy 44 (11), 5615e5622. https://doi.org/10.1016/ j.ijhydene.2018.07.163. Zheng, Y., Cai, J.J., Dong, H., Feng, J.S., Liu, J.Y., 2019b. Experimental investigation of volumetric exergy transfer coefficient in vertical moving bed for sinter waste heat recovery. Energy 167, 428e439. https://doi.org/10.1016/ j.energy.2018.10.110. Zhou, H.R., Zeng, S., Yang, S.Y., Xu, G.W., Qian, Y., 2018. Modeling and analysis of oil shale refinery process with the indirectly heated moving bed. Carbon. Resour. Convers. 1 (3), 260e265. https://doi.org/10.1016/j.crcon.2018.08.001. Zhu, Q.B., Xuan, Y.M., 2017. Pore scale numerical simulation of heat transfer and flow in porous volumetric solar receivers. Appl. Therm. Eng. 120, 150e159. https://doi.org/10.1016/j.applthermaleng.2017.03.141. Zou, L.C., Liu, Y.Q., Zheng, B., Liu, R.X., Qi, X.N., 2015. The effects of physical parameter variation on heat transfer characteristics of calcined petroleum coke waste heat utilization exchanger. Carbon Tech. 34 (3), 59e64. https://doi.org/ 10.14078/j.cnki.1001-3741.2015.03.014.