Effective diffusivity of oxygen in the ash layer of Huadian oil shale semicoke

Abstract

Diffusion of oxygen in the ash layer usually dominated the combustion of oil shale semicoke particles due to the high ash content. Thus, effective diffusivity of oxygen in the ash layer was a crucial parameter worthy of careful investigation. In this paper, the effective diffusivity of oxygen in the ash layer of Huadian oil shale semicoke was measured directly using an improved Wicke-Kallenbach diffusion apparatus. The experimental results showed that higher temperature would lead to a higher effective diffusivity and a thicker ash layer had the negative effect. Especially, the effective diffusivity along the direction perpendicular to bedding planes was much lower than that along the direction parallel to bedding planes. In addition, an effective diffusivity model was developed, which could be used to describe the mass transfer of oxygen in the ash layer of oil shale semicoke.

Graphical abstract

Keywords

oil shale semicoke / diffusivity / pore structure / ash layer

1 Introduction

With global energy consumption increasing continually and conventional fossil fuel reserves decreasing, unconventional fossil fuels, such as oil shale, have attracted increasing attentions [1]. Oil shale has a high content of organic matter, such that it could be used to produce shale oil by retorting [2]. The organic matter in oil shale is called kerogen. With oil shale heated in inert atmosphere up to a certain temperature, kerogen first degrades to bitumen, and then decomposes into shale oil, gas, and water [3]. Finally, solid residues, referred to as oil shale semicoke, remain, which consist of carbonaceous matter and minerals [4]. The direct landfill of oil shale semicoke might pollute the environment due to its toxic heavy metals and organic compounds. Oil shale semicoke combustion has the potential to be a good choice, which not only avoids direct landfill, but also recovers the heat of oil shale semicoke [5,6].

There are obvious ash layers in oil shale semicoke particles after combustion. The ash layers are quite compact because the high ash content of oil shale semicoke is as high as 70% [7]. The compact ash layers results in a high diffusion resistance for oxygen, making the combustion process quite slow and under diffusion control [8]. Due to the slow combustion rate and low calorific value, it is not easy to solely combust oil shale semicoke which has to be combusted with other solid fuels such as oil shale, coal, and biomass [9–12]. It is difficult to burn out large oil shale semicoke particles with the diameter greater than 1.5 mm, shown by the unreacted core remaining in the particle center after combustion for a long time [13]. The shrinking-core model is usually used to simulate the combustion of oil shale semicoke. However, there is not a good agreement between the modeling results and the experimental results under the assumption of a constant diffusivity of oxygen in the ash layer [14].

The pores in oil shale semicoke have diameters ranging from 1 to 100 nm, and their structures are quite different [15–17]. The Knudsen number of oxygen in the oil shale semicoke particles is about 0.7 to 300 at the temperature range from 300 K to 1200 K, meaning that diffusion of oxygen in the oil shale semicoke particles is complicated and both molecular diffusion and Knudsen diffusion occurs [18]. Pore structure has a significant effect on the gas diffusion within solid particle [19,20]. Thus, the diffusivity of oxygen in the oil shale semicoke ash layer should be variable and dependent on the pore structure and temperature.

Currently, there are two kinds of diffusivity models that describe oxygen mass transfer in the solid fuel ash layer. One is the diffusivity model that assumes pore structure theoretically. Wheeler has assumed that pores are uniform cylinders that are parallel to each other and proposed a diffusivity model related to porosity and tortuosity of the porous structure [21]. The tortuosity is an empirical parameter in the range from 2 to 8 for some solid fuels [22–24]. Wakao and Smith have developed a diffusivity model that assumes the diffusion channels are macro and micro pores in series [25]. Johnson and Stewart have assumed that both molecular diffusion and Knudsen diffusion happen in a single pore channel and developed a diffusivity model by integrating single pore diffusivity along the whole pore diameter distribution [26]. The other is the empirical model that considers the properties of solid fuels or the impacts of reactions. Fu and Zhang have investigated 17 kinds of coal char with different ash contents and related the diffusivity to the ash content [27]. Yan et al. have developed a diffusivity model that takes the ash layer thickness into account based on the one dimensional model [28].

However, the assumptions on which those theoretical diffusivity models are based are not suitable for the pore structure of oil shale semicoke. Thus, theoretical diffusivity models including the parallel pore model and the random pore model do not have good agreements with the experimental results [8]. Besides, there are no appropriate empirical parameters of oil shale semicoke for the empirical diffusivity models. Liu et al. [29] and Yang et al. [30] have found that mass transfer of oxygen in the ash layer of oil shale char particles is anisotropic due to its layered structure. Thus, there lacks an appropriate diffusivity model that can describe the mass transfer of oxygen in the ash layer of oil shale semicoke particles.

In this paper, the diffusivity of oxygen in the ash layer of Huadian oil shale semicoke particles was determined by conducting diffusion experiments in different conditions. An effective diffusivity model considering temperature, ash layer thickness, and diffusion direction was developed, which have a good agreement with the experiment results. This diffusivity model could be used to describe the oil shale semicoke combustion.

2 Experiment

2.1 Apparatus

One dimensional combustion under ash layer diffusion control isusually used to estimate the diffusivity of oxygen in the ash layer of oil shale semicoke or other solid fuels by indirectly relating the diffusivity to the burnout time [27]. This approach might not be very precise due to its hypothesis of simple combustion mechanism and far lower reaction resistance than diffusion resistance [29]. However, few research has been conducted to directly measure the diffusivity of oxygen in the ash layer of oil shale semicoke.

The ash residue of oil shale semicoke particles can be polished as porous pellet intact due to its high ash content and good mechanical strength. Thus, a steady-state and high temperature diffusion method, improved from the diffusion method developed by Wicke and Kallenbach [31], was used in this paper to measure the diffusivity of oxygen in the ash layer of oil shale semicoke under different conditions, as shown in Fig. 1. Cylindrical ash samples were installed in the diffusion cell, and the opposite faces of the diffusion cell were exposed to streams with different gas composition. The diffusion cell was made of quartz which could be heated electrically. The compositions of streams were controlled by a mass flowmeter and a gas mixing chamber. The mass transfer was guaranteed to be a strict diffusion process by the imposed concentration gradient across the sample pellet, which was realized by keeping the pressures in the up and down part of quartz chamber equalized. The compositions of streams leaving the diffusion cell was measured by an in-process instrument GAM 200 mass spectrometer. At steady-state, the diffusivity of oxygen in the pellet is assumed to obey Fick’s law and is calculated by

(1)De={\displaystyle \frac{NL}{\mathrm{\Delta }c}},

where N is the diffusion rate, mol/(m²·s); L is the thickness of the pellet, m; and Δc is the difference between the molar concentration of oxygen at the opposite faces of the pellet, mol/m³. N and Δc are calculated from the flow rate and compositions of streams leaving the diffusion cell and the pellet cross-sectional area.

In the experiments, stream A was the mixture of O₂ and CO₂ and stream B was pure CO₂. The fraction of O₂ in stream A varied from 25% to 100%. Four gas admission rates (80, 100, 125, and 150 mL/min) were compared in the experiments, as depicted in Fig. 2. The experimental results were almost the same. Thus, the volume flow rate of the stream was set to be 100 mL/min, which was high enough to avoid the errors from the gas concentration gradient above the pellet faces and low enough to yield available data on the mass spectrometer. The diffusion temperature varied from 293 K to 1073 K, which covered the combustion temperature in most industrial applications. Gas mixtures were introduced into the diffusion cell after the diffusion temperature had been kept around the preset value. The measurements were conducted after the gas concentrations of the exit were stable. Thus, the experiments were conducted at a quite stable state and repeated twice to ensure the reliability of the data.

Before the experiments, the gas tightness of the diffusion cell were examined. The upper surface and the lower surface of the sample were taped by the sealing adhesive tape. Then the steams were introduced into the diffusion cell and measured. The results demonstrated that the gas composition of the steam did not change, proving that the gas tightness was appropriate and the gas would not diffuse through the gap between the sample and the quartz cell.

2.2 Samples

The ash samples of oil shale semicoke were prepared by using Huadian oil shale, a Chinese oil shale whose physical properties were listed in Table 1. The oil shale particles were combusted in a muffle furnace at 1073 K for 2 h. With a long combustion time of 2 h, the oil shale particles can be burnt out and only a little volatile and fixed carbon remained. Not much mineral would decompose at 1073 K, ensuring that the ash sample had a similar porous structure with the real ash layer of oil shale semicoke particles. Especially, the mass loss of ash sample after each diffusion experiment was measured to ensure the consistency of the porous structure. Meanwhile, a combustion temperature of 1073 K provided a large enough temperature range for investigating the effects of temperature on the mass transfer of oxygen in the ash layer of oil shale semicoke.

The ash of oil shale semicoke particles was polished as cylindrical pellets. Several cylindrical pellets were mounted parallelly in the diffusion cell with high temperature resisting sealant. The cross-sectional area of the cylindrical pellets in the diffusion cell was 0.0002 m². The thicknesses of the cylindrical pellets used in the experiments were 0.003, 0.005, 0.008, and 0.010 m. Besides, the ash of oil shale semicoke particles was polished along the direction parallel and perpendicular to bedding planes respectively to investigate the mass transfer in different directions. The schematic of samples in the direction parallel and perpendicular to bedding planes is illustrated in Fig. 3.

3 Results and discussion

3.1 Validation of Fick’s law

As introduced above, the mass transfer of oxygen in the ash layer of oil shale semicoke was assumed to obey Fick’s law to calculate the effective diffusivity. However, the gas diffusion in solid fuel pores might not follow Fick’s law [32]. Thus, it is necessary to validate whether it obeys Fick’s law or not.

The effective diffusivities in the direction parallel to bedding planes at different gradients of oxygen concentration were displayed in Fig. 4. There was no consistency between the effective diffusivity and the gradient of oxygen concentration. Although a little variation existed, it could be supposed that the effective diffusivity did not vary with the gradient of oxygen concentration in principle. Thus, it is reasonable to assume that the mass transfer of oxygen in the ash layer of oil shale semicoke obeys Fick’s law.

3.2 Effects of diffusion temperature

The effective diffusivities in the direction parallel to bedding planes at different diffusion temperatures and ash layer thicknesses were exhibited in Fig. 5. For different pellet thicknesses, the effective diffusivity in the direction parallel to bedding planes increased significantly with the diffusion temperature in the range from 297 K to 1073 K. By fitting the data, it was found that the effective diffusivity in the direction parallel to bedding planes were proportional to 1.39, 1.52, 1.47, and 1.44 power of the diffusion temperature, respectively. As is known, for molecular diffusion, the diffusivity is proportional to 1.75 power of the temperature. For Knudsen diffusion, the diffusivity is proportional to 0.5 power of the temperature. Thus, it could be supposed that both molecular and Knudsen diffusion played important roles in the mass transfer of oxygen in the ash layer of oil shale semicoke.

3.3 Effects of ash layer thickness

The effective diffusivities in the direction parallel to bedding planes at different ash layer thicknesses were plotted in Fig. 6. For different diffusion temperatures, the effective diffusivities decreased significantly with the ash layer thickness. At the ash layer thickness of 0.003 and 0.005 m, the effective diffusivities measured in the experiments were in the range from 5.0 × 10⁻⁸ to 1.6 × 10⁻⁶ m²/s, which was consistent with the results in Refs. [8,29]. However, at the ash layer thickness of 0.008 and 0.01 m, the measured effective diffusivities were in the range from 8.0 × 10⁻¹⁰ to 3.2 × 10⁻⁸ m²/s, which was much lower than those in existing researches. It is, therefore, worth mentioning that such large ash layer of oil shale semicoke has never been investigated before.

In the experiments, the thinner ash layer samples were polished from the thicker ones. The ash layer samples with different thicknesses had similar pore structures which were measured by N₂ adsorption, as shown in Fig. 7. Thus, it was the ash layer thickness but not the pore structure difference that decreased the effective diffusivity. As the ash layer became thicker, less pores in the ash layer worked for gas diffusion. Theoretically, only the effective pore channel that connected the two surfaces of the ash layer sample help gas diffusion. If the ash layer was thicker, more pore channels were blocked before they connected the two surfaces. This hypothesis is illustrated in Fig. 8. Besides, this might explain why oil shale semicoke particles were quite difficult to burn out. The thicker ash layer in the combustion increased the diffusion resistance significantly, preventing oxygen from diffusing into the unreacted core.

3.4 Comparison of diffusion direction

As mentioned above, the layered structure in oil shale particles might lead to the anisotropy of the effective diffusivity. Figure 9 is a comparison of the effective diffusivity in the direction parallel and perpendicular to bedding planes, at the same the diffusion temperature of 293 K and the ash layer thickness of 0.005 m. The effective diffusivity in the direction perpendicular to bedding planes was approximately 1/3 of that in the direction parallel to bedding planes. From SEM photographs shown in Fig. 10, it was seen that the pores in the planes parallel to bedding planes were smaller and less than those in the planes perpendicular to bedding planes. When diffusing in the direction perpendicular to bedding planes, oxygen diffused through the planes parallel to bedding planes. Thus, it was more difficult for oxygen to diffuse in the direction perpendicular to bedding planes.

The large difference between the effective diffusivities in the direction parallel and perpendicular to bedding planes indicated that the mass transfer of oxygen and the combustion of the oil shale semicoke might be anisotropic. The mass transfer of oxygen and the combustion in the direction parallel to bedding planes might be faster than those in the direction perpendicular to bedding planes.

3.5 Effective diffusivity model

3.5.1 Theory

As discussed above, the ash layer thickness has important effects on the oxygen diffusion by changing the number of effective pore channels that connects diffusion surfaces. Thus, the diffusivity of oxygen at each infinitesimal element in the diffusion direction might be different. The effective diffusivity of oxygen in the whole ash layer should be related to that at each infinitesimal element in the diffusion direction.

Before developing the effective diffusivity model, a simple diffusion example was analyzed as shown in Fig. 11. For a kind of material that consists two sections with different diffusivities at a steady-state, the molar flux of gas should obey

(2)N=D{e}_{\mathrm{effective}}{\displaystyle \frac{c_{\mathrm{0}}-c_{\mathrm{2}}}{x_{\mathrm{1}}+x_{\mathrm{2}}}}=D{e}_{\mathrm{1}}{\displaystyle \frac{c_{\mathrm{0}}-c_{\mathrm{1}}}{x_{\mathrm{1}}}}=D{e}_{\mathrm{2}}{\displaystyle \frac{c_{\mathrm{1}}-c_{\mathrm{2}}}{x_{\mathrm{2}}}},

where N is the molar flux of gas, mol/(m³·s); De_effective, the effective diffusivity of this material, m²/s; De₁ and De₂ are the diffusivity of the two sections, m²/s; x₁ and x₂, the thickness of the two sections, m; and c₀, c₁, and c₂, the gas concentration at different planes, mol/m³. From Eq. (2), De_effective could be calculated from

(3)D{e}_{\mathrm{effective}}={\displaystyle \frac{x_{\mathrm{1}}+x_{\mathrm{2}}}{{\displaystyle \frac{x_{\mathrm{1}}}{D{e}_{\mathrm{1}}}}+{\displaystyle \frac{x_{\mathrm{2}}}{D{e}_{\mathrm{2}}}}}}.

If the diffusivity at each infinitesimal element of the material is only related to the thickness δ, meaning that De=De\left(\delta \right), De_effective could be calculated from

(4)D{e}_{\mathrm{effective}}={\displaystyle \frac{\delta }{{\displaystyle {\int }_{\mathrm{0}}^{\delta }{\displaystyle \frac{\mathrm{1}}{De\left(\delta \right)}}\mathrm{d}\delta }}}.

Considering the effects of diffusion temperature and ash layer thickness discussed above, it is assumed that De\left(\delta \right)=D{e}_{\mathrm{0}}(T/\mathrm{293}{)}^n\exp (-a\delta ), where n represents the positive effects of diffusion temperature, and a is an attenuation factor of effective pore channels that represents the negative effects of ash layer thickness. Thus, De_effective of the oxygen in the ash layer of oil shale semicoke could be calculated from

(5)D{e}_{\mathrm{effective}}={\displaystyle \frac{D{e}_{\mathrm{0}}(T/\mathrm{293}{)}^{n}a\delta }{\exp \left(a\delta \right)-\mathrm{1}}}.

3.5.2 Validation of the effective diffusivity model

The experimental data in the direction parallel to bedding planes were regression-fitted using the least square method to yield the parameters in the effective diffusivity model. The results are shown in Fig. 12, where n = 1.42, a = 998.5 (m⁻¹), and De₀ = 1.6 × 10⁻⁶ m²/s. It can be seen that the effective diffusivity model has a good agreement with the experimental data in the direction parallel to bedding planes. The maximum relative error is 15% at all temperatures and ash layer thicknesses, which is quite acceptable.

A comparison between the effective diffusivity of the whole ash layer and the diffusivity at the infinitesimal element at 1073 K is shown in Fig. 13. It can be seen that the diffusivity at the infinitesimal element decreases more significantly than the effective diffusivity of the whole ash layer. For an ash layer with a thickness of 0.006 m, the effective diffusivity of the whole ash layer might be as high as 1.7 × 10⁻⁷ m²/s, while the diffusivity at the location δ = 0.006 m might be as low as 2.7 × 10⁻⁸ m²/s. This significant discrepancy might explain why the core of large oil shale semicoke particles is difficult to burn out.

4 Conclusions

In this paper, Wicke-Kallenbach diffusion apparatus was improved to measure the effective diffusivity of oxygen in the ash layer of Huadian oil shale semicoke. Besides, an effective diffusivity model was developed, which could be used to describe the mass transfer of oxygen in the ash layer of Hudian oil shale semicoke. Several conclusions were drawn.

The mass transfer of the oxygen in the ash layer of oil shale semicoke obeys Fick’s law in principle, although there exists a little variation.

The effective diffusivity in the direction parallel to bedding planes increase significantly with the diffusion temperature, being proportional to 1.39–1.52 power of the diffusion temperature.

The increase of ash layer thickness has negative effects on the oxygen diffusion, probably related to decreasing the number of effective pore channels that connects the diffusion surfaces.

The effective diffusivity in the direction perpendicular to bedding planes is approximately 1/3 of that in the direction parallel to bedding planes, due to the tighter pore structure.

The results obtained by using the effective diffusivity model developed in this paper agrees well with the experimental data.

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