3.2. The Reaction and Transport Characteristics in a Random Packed Bed
In
Section 3.1, the reaction and transport characteristics of a single large OC particle are thoroughly investigated. The investigations are extended in this section to the reaction and its relevant conjugate transports in a lab-scale random packed bed reactor to understand, at a typical external convection condition, how the intraparticle diffusion interacts with the complicated interstitial flow in the packed bed and finally affects the reactor-scale CLC processes.
The heterogeneous reactions, along with the intraparticle diffusion and interstitial transports involved in the CLC process in a fixed bed randomly packed with 597 porous spheres, were numerically simulated at
Rep = 66, which is considered at or above the threshold of external convection enhancement (refer to
Figure 3a), with the CFD method described in
Section 2. The geometric dimensions, physical properties and operating conditions with modelling are shown in
Table 5.
The radial porosity distribution profile of the current packed bed is shown in
Figure 8 and compared with the available references. The profile clearly shows that the present packing model is in good agreement with the correlation proposed by de Klerk [
37] and the algorithm by Muller [
38]. In addition, the deviations of the radial porosity distribution in the current random packing model were within ±8% (except near the axis) and ±4% for the correction by de Klerk [
37] and algorithm by Mueller [
38], respectively.
As seen in
Figure 9, the profile of axial pressure drop distribution indicates that the current packing model is in good agreement with the well-known correlation proposed by Ergun [
39] in Equation (17).
The grid independence test was performed with the single OC particle configuration. The base size of the grid was set as 3 mm, 4 mm and 5 mm, respectively, and all the validation simulations were carried out at
Rep = 100. The profiles of ΔT and conversion distribution were set on the reference line at
t = 50 s, as shown in the
Figure 10a,b. Obviously, the grid independence tests worked well for all three basic sizes. Thus, all the simulations were done with a base size of 5 mm.
Figure 11 shows the distribution of velocity (left) and ∆T (right) in an axial plane at
t = 150 s. From the velocity distribution, it can be seen that there was obvious channelling flow near the wall and core region, which is typical in packed beds with a small diameter ratio (D/d = 6), corresponding to the radial porosity distribution in
Figure 8. In addition, there was a great temperature gradient in radial direction, which was caused by the constant cool wall boundary (
T = 873 K) and the enhanced convective heat transfer by the channelling flow near the wall or the so-called wall effects.
Figure 12 illustrates the distribution of O
2 volume fraction, CuO mole fraction and temperature inside particle in an axial plane at various time moments. In
Figure 12a, the O
2 volume fraction distribution is shown at several moments, which presents the evolution of the O
2 concentration field in the bed. It can be found that the O
2 concentration gradient, larger or smaller, existed inside the particles for all the time moments except
t = 300 s. The local species concentration in particles depends on both the inward diffusion flux and the consumption rate due to the local reaction. The latter is determined by both the local species concentration and the local solid OC content, according to the Arrhenius equation. Therefore, although a complicated mechanism determines the local O
2 concentration inside a particle, the influence of internal diffusion resistance is essential or even dominant to the local species concentration, which restricts oxygen access to the particle core and thereby limits the local reaction rate in the particle centre. The most obvious presentation of the internal diffusion limitation was the concentration gradient in regions close to the bed inlet and outlet in the earlier times (20 s, 50 s and 100 s), which was characterized by the “orange rings” in the upstream (lower part of the column) and the “blue spots” in the downstream (upper part). The higher concentration layers near the particle surfaces (the “orange rings”) in the inlet region were built up due to the fast depletion of Cu and easy O
2 diffusion near the particle surface, which could not easily occur further inside the particles during the earlier period. In the downstream region, O
2 was not sufficiently provided due to the consumption in the upstream. O
2 slowly diffused and reacted with Cu in the particles and was finally used up before reaching the particle cores, leaving the cores “blue”. The “orange ring” type of high gradient distribution evolved along the axial direction with time and existed even at
t = 200 s.
The distribution of the mole fraction of CuO can be regarded as the local conversion distribution, which is closely related to the oxygen concentration distribution, as shown in
Figure 12b. When compared with the O
2 distribution in
Figure 12a, the CuO distribution is quite similar but does not coincide completely with the former. In general, CuO formed gradually from upstream to downstream and from the particle surface to the interior. The low O
2 concentration in the particle cores caused by the internal diffusion limitation resulted in a small reaction rate, and thereby reduced the local conversion. As time went on, the Cu near the surface of particle was gradually consumed, and O
2 reached the particle core, where it reacted with Cu. It can be found that the complete conversion of the oxygen carrier Cu in packed bed took a long time, and even at
t = 200 s, unreacted oxygen carrier remained in the cores of the particles downstream.
As heat generation is an essential goal of CLC, the investigation of ΔT resulting from the reaction is of great significance to the design and development of packed bed reactors. In
Figure 12c, the ΔT distribution is shown at several moments. Basically, the ΔT in th packed bed reactor was affected by the rate of exothermic reaction and convective heat removal. Furthermore, the ΔT in the packed bed was also determined by the effect of temperature superposition caused by heat flow from upstream. At
t = 20 s and 50 s, the temperature increased with time, and at
t = 100 s, a hot zone began to form due to the effect of the heat flow from upstream. Over time, the hot zone moved along the flow direction, and at
t = 300 s, most parts of the hot zone moved out of the bed. After this moment, the packed bed started to substantially cool from the upstream.
To fully demonstrate the effects of the bed wall and the radial porosity distribution, the scalar distributions of O
2 volume fraction, CuO mole fraction and ΔT in a radially sliced plane (
x = 50 mm in middle of packing zone) are shown at various times in
Figure 13. As a small aspect ratio (D/d) packed bed, the current reactor showed obvious wall effects, as illustrated in
Figure 11. That means there was stronger convection near the wall than in the core region, which is proved by the higher near-surface concentration of O
2 and CuO of the outer particles radially in
Figure 13a,b. Although the condition of
Rep = 66 would imply a diffusion-controlled process if a single particle was considered (as discussed in
Section 2), it seems that the stronger convection near the wall still enhanced the across-surface species transport inward and the reaction in the layer near the particle surface. On the other hand, the local conversion in the core region of the particles was very low for both inner and outer particles due to the internal diffusion limitation. In
Figure 13c, it is clearly observed that the radial temperature gradient developed from the beginning to the end of the process, which was caused by both the cool wall and wall effects.
Figure 14 shows the overall conversion profile in the packed bed over time. Although there was an axial delay of the reaction and species transport in the packed bed, the trend of the conversion-time curve in
Figure 14 is quite similar to those of the higher Reynolds numbers in
Figure 3a. The curve was somehow linear in the first half of the whole process, but the conversion became obviously slower after 150 s. Obviously, due to the large diffusion area and short diffusion distance in the layer near the particle surface, the internal diffusion capacity was much higher than that in the particle core. Therefore, the reaction rate was obviously higher during 0–150 s than later, which explains why the conversion during the second half of the process came slower. By more careful comparison, it can be found that the full conversion for the packed bed was almost 100 s longer than that in the case of the single particle. The two cases are certainly different considering the extremely complex interstitial channels in the packed bed. Except the difference of the local flow fields between the two cases, the shortage of O
2 downstream in the bed due to the consumption of O
2 can result in a smaller diffusive and convective flux into the particle cores downstream, which can determine a slower conversion.
In order to quantitatively illustrate how the temperature field evolves along the axial direction, the curves of ∆T over time at various axial positions are shown in
Figure 15. The oxidation process in the packed bed that we simulated was an exothermic reaction, in which each axial position underwent a heating from the reaction heat and convective heat flux from its upstream, and a cooling flux contributed by the cool bed wall. The complex superposition of the heat fluxes determines different history curve of ∆T at various axial positions. Among the curves, the one at
x = 45 mm showed up the maximum peak value, which was located approximately at the middle of the bed. Although the maxima of
x = 75 and 95 mm were somewhat lower, their relevant curves also maintained higher values during the whole process. Obviously, the downstream length starting from the middle of the bed received sufficient heat flux from its upstream, so that the ∆T quickly reached and maintained a higher value. However, the reaction that occurred in that part could have been delayed and slow. By contrast, the maximum temperature close to the reactor inlet (0–25 mm) reached the peak value much faster but the maxima were substantially smaller than those at positions behind them. Obviously, at the former positions, the heat flux from their upstream was not yet sufficiently large. In fact, the value of maximum ∆T at the axial positions mainly reflects how much the convective heat flux from upstream was superposed on the local heat generation. The latter is almost the same, although there was a delay in the downstream direction.
Figure 16 illustrates the local maximum ∆T (left) and the time moment to reach the maximum (right) in the axial positions, which quantitatively help us understand the distribution of hot spots in axial positions over time. Obviously, the local maximum ∆T for almost 80% length of the bed (
x = 20–100 mm) was beyond 100 K, and this maximum was reached in around 200 s.
Similarly, a temperature gradient formed and evolved in the radial direction during the oxidation process.
Figure 17 shows that the temperature distribution at different radial coordinate points on the radial plane (
x = 45 mm) developed with time. In fact, the radial temperature gradient was built up, mainly due to the cooling flux toward the cool wall and the axial convective flux, because of the channelling flow in the high-voidage region near the bed wall. However, the local heat generation may have been higher to some extent because of the enhanced species transport due to channelling flow.
In this paper, a typical small diameter ratio (D/d = 6) was selected to randomly generate a packed bed reactor with a diameter of 30 mm and a height of about 100 mm. The numerical simulation results give us a comprehensive understanding of the temporal evolution and spatial distribution of internal scalars. In addition, changing the diameter of the reaction tube and the axial packing height in a reasonable range still conform to the axial and radial distribution of our conclusion.