2.1. Materials

The nuclear graphite samples include IG-110 (Toyo Tanso Co. Ltd., Janp), NBG-18 (SGL Carbon Group, Germany) and NG-CT-10 (FangDa Carbon New Material Co.,Ltd, China). NBG-18 was chosen due to the interest of the Next Generation Nuclear Plant program for high irradiation dose regions of the Very High Temperature Reactor (VHTR). IG-110 is a fine grained historical reference grade and is being used in VHTR. NG-CT-10 is under development in China in many ways similar to IG-110. Table 1 lists properties of the three types of nuclear graphite. Samples prepared for μ-CT pore analysis were machined into cylinders of Φ 1.5 mm × 10 mm. To prevent oxidation of the graphite, the samples were vacuum dried for 2 h at 150°C.

2.2.μ-CT and image analysis

The nuclear graphite samples were imaged on a μ-CT at Sanying Precision Engineering Research Center (nanoVoxel-2100, Sanying, China). The system is shown in Fig. 1. An X-rays were generated from a tungsten target bombarded by 60 kV 120 μA electrons and were focused to spot size of 1.5 μm. The sample-to-detector distance was 10 cm and source-sample distance was 20 cm. The exposure time was 85 s with pixel size of about 0.91 μm. Since the resolution determines the slice thickness, so the minimum voxel size was 0.91 μm× 0.91 μm× 0.91 μm, with voxel values ranging from 0 to 255 corresponding to the attenuation coefficient. A CCD camera was used to obtain two-dimensional X-ray images for 1000 layers. During the CT scan the sample was rotated at different projection angles between 0°and 180°, in 0.5° steps. The absorption radiographs for different viewing angles were projected onto a CdWO4 fluorescent screen and recorded by the CCD camera of 1024×1024 pixel. To correct for electronic noise and variations in the X-ray brightness in the experiment, light-field images (i.e. X-ray illumination on, and the specimen out of the beam) and dark-field images (i.e. X-ray illumination off) were recorded. Projection images were reconstructed using the FDK algorithm developed by Feldkamp^[18].

Fig.1.Full-screen View

The μ-CT system. (a) X-ray sources system, (b) Sample stage, (c) Flat panel detector, (d) Optocoupler detector system.

Image segmentation and pore morphology analysis were completed with the Avizo Fire 8.0 ^[19]. Sub-volumes of 450×450×450 voxels (i.e. 410 μm × 410 μm × 410 μm) were extracted from the samples. Before analysis, the IG-110, NGB-18 and NG-CT-10 data were smoothed with Non-Local Means filtering ^[20] and bilateral filtering, respectively. Then, a locally adaptive segmentation method, such as the indicator kriging method ^[21], was used to separate pores from the solid phase. Briefly, a lower (T₀) and an upper (T₁) limit were selected by visual inspection of the image histograms. Voxel values below T₀ and above T₁ were identified as the pore and solid phases, respectively. Voxels with grayscale values between T₀ and T₁ were classified as pores or solids depending on the local covariance determination. Details of the indicator kriging method are given in Refs. [21,22].

2.3. Quantification of 3D microstructures

The workflow to analyze the pore space geometry using Avizo PNM is outlined in Fig. 2. Detailed theories of the processes employed are described in Ref.[23]. The medial axis of pore space was extracted from the segmented images and computed using morphological erosion based on the LKC algorithm ^[24]. The distance between the skeleton and the nearest solid phase was recorded as the burn number. Meanwhile, the medial axis trimming must be performed to remove dead end and isolated paths for the computation of skeletons. Next, pore throats, defined as the minimum cross-sectional area of each channel, should be found out by Dijkstra shortest paths algorithm ^[25]. Subsequently, pore and throat structure parameters, such as pore and throat size, surface area, and geometrical tortuosity were analyzed based on pore-throat network and the medial axis.

Fig.2.Full-screen View

Schematic sequential diagram of the pore-throat network construction.

2.4. Permeability simulation and estimation

The absolute permeability was simulated using Avizo Xlab-Hydro (Fig.3) with input of the modified binary images. Stokes equation ^[26] was solve based on a finite-volume method which builds the volume mesh

Fig.3.Full-screen View

Typical computational geometries used for Avizo simulations.

where u is the fluid velocity vector, P is the pressure, and μ is the dynamic viscosity. The absolute permeability ^[27] was evaluated by Darcy’s law. And the Avizo Xlab-Hydro solver was validated by comparing with theoretical models and standard glass bead packaging models^[28].

where O/S is Darcy’s velocity, k is the absolute permeability, μ is the dynamic viscosity of the flowing fluid, ▽P is the pressure difference applied around the sample, and L is the length of the sample in the flow direction.

3.1. Slice analysis for the nuclear graphite samples

The μ-CT is an effective tool for visualization of an arbitrary cross section (slice) in the samples. It is possible to analyze the morphological characteristics on any slice without damaging the nuclear graphite samples. The SEM images and the tomographic images after μ-CT recovery data are shown in Fig. 4. The shrinkage cracks formed during calcinations, and pore structure, can be seen in the images. However, they are of different types. In Figs. 4(a)and 4(b), the shrinkage cracks run parallel to the major axis of the particle in IG-110. Figs. 4(d) and 4(e) show that NG-CT-10 has similar microstructure to IG-110, but the pores in NG-CT-10 are more elliptical, and shrinkage cracks are more numerous and of greater thickness, than those observed in IG-110.The filler material in NBG-18, pitch-based graphite, appears to be spherical in nature, but the shrinkage cracks in NBG-18 vary greatly in size. Many larger shrinkage cracks, as shown in Fig 4(g) and 4(h), are oriented with their long axis approximately tangential to the particle’s radial direction. While the IG-110 and NG-CT-10 samples have small pores, the NBG-18 has much bigger pore inside. This is consistent with the SEM results in Ref.[9].

Fig.4.Full-screen View

SEM images and CT images of IG-110, NG-CT-10 and NBG-18. P, pore; B, binder; F, filler; C, shrinkage crack.

Fig.4 shows that NBG-18 has more big pores than IG-110 and NG-CT-10. This may lead to greater molten salt infiltrate. The 3D pore structures for IG-110 and NG-CT-10 exhibit similar honeycomb patterns, while continuous longer and bigger channels were found in the NBG-18 only. It is good for gas diffusion and molten salt flowing.

3.2. Quantification of pore and throat networks

The reconstructed 3D model of pore structure and the pore-throat network for the three types of nuclear graphite are shown in Fig. 5. Their general pore and throat structure information are given in Table 2.

Fig.5.Full-screen View

3D structure (a) and pore-throat networks (b) of IG-110, NG-CT-10 and NBG-18 nuclear graphite samples (410 μm × 410 μm ×410 μm)The rainbow colors represent distance of the path to the closest grain voxels, with blue color being very narrow channels, and red color being wider channels.

The rainbow colors nodal in Fig.5(b) represent the pore diameter, and the distance of two pores represents the throat structure. The porosity is 27.1% for IG-110 and 28.9% for NG-CT-10, being slightly higher than the data in Ref.[12]. The μ-CT can detect the close pore in nuclear graphite, which may cause slightly increase in porosity. The porosity of NBG-18 is as big as 50.1%, because of much bigger pores in this type of graphite. Therefore, it would provide much more spaces for molten salts. As known, more pathways can lead to a more connected pore network and less tortuous pathway through the volume. The pore connectivity rates are 97.6%, 99.8% and 98.6% for IG-110, NG-CT-10 and NBG-18, respectively. This is much convenient for gas diffusion and molten salt flowing.

From Table 2, NBG-18 has the highest porosity and the most pores and throats, and the biggest mean area of throats and average coordination number. The bigger pores formed by vibration can have a major effect on water or molten salt flow.

Pore-size distribution is expressed as the frequency distribution of logarithmic effective radii. As shown in Fig.6, pore sizes of the three types of nuclear graphite are in unimodal structure peaked at around 7 μm of equivalent diameter. The pore-size volumes are peaked at 14 and 12 μm for IG-110 and NBG-18, respectively, but the pore-size volume of NG-CT-10 is almost the same at equivalent diameters of 4-20 μm.

Fig.6.Full-screen View

The pore size-volume distribution forIG-110, NG-CT-10 and NBG-18.

The coordination number of nodal pore in nuclear graphite is the number of its near neighbors. The average coordination numbers are 4.07, 4.31 and 6.75 for IG-110, NG-CT-10 and NBG-18, respectively. Fig. 7(a) shows the distribution of coordination number of the nuclear graphite samples. The NBG-18 differs greatly from IG-110 and NG-CT-10 in coordination number distribution. Meanwhile, the most irregular paths, with coordination number values larger than 15, were observed in the NBG-18 sample. This might be due to the larger pore size and better connectivity. More coordination numbers can lead to more connected pore networks. The coordination number of the three types of nuclear graphite are well distributed, hence desirable interconnect pore networks for gas diffusion and molten salt flowing.

Fig.7.Full-screen View

Pore coordination number distribution (a) and channel length distribution (b) for IG-110, NG-CT-10 and NBG-18.

Throat channel length refers to the distance between the centers of two adjacent nodal pores. This distance was measured along the medial axis rather than along the straight line between the two centers. The throat channel length distributions are shown in Fig. 7(b). The channel length ranges are 3-45, 3-59 and 3-104 μm for IG-110, NG-CT-10 and NBG-18, respectively. While the NBG-18 has the widest throat channel length range, the average throat lengths of IG-110 (13.7 μm) and NG-CT-10 (13.2 μm) are slightly greater than NBG-18 (12.7 μm).

In addition to pore size, pores coordination numbers, and throat channel length, the interaction between the nuclear graphite and molten salt/oxygen was closely influenced by the pore surface area and the cross-section of throats. The pore surface areas for IG-110, NG-CT-10 and NBG-18 ranged 103-4347, 103-8270, and 103-60805 μm², respectively. Their distributions are shown in Fig.8(a), peaked at around 200 μm² for all the three types of nuclear graphite. The NBG-18 has the largest number of pores and throats. Fig.8(b) shows that throat cross sections of the three samples are of similar distribution. Of the three types of nuclear graphite, NBG-18 has the largest pore surface area and throat cross-section, i.e. the most vulnerable to damages by molten salt/oxygen. Yang et al ^[29] indicated that the C-F bond could be formed in the IG-110 samples soaking with molten fluoride salts at 650°C. So the surface area and throat cross-section may play an important role in graphite infiltration experiment, which requires further study in future.

Fig.8.Full-screen View

The pore surface area (a) and throats cross section distribution (b) for IG-110, NG-CT-10 and NBG-18.

These results, together with the 2D and 3D observation, indicate that NBG-18 differs greatly in structure from IG-110 and NG-CT-10, and the IG-110 and NG-CT-10 may be more suitable for use in molten salt reactor.

3.3. The absolute permeability in pore-throat network of three nuclear graphite samples

Numerical analysis of a single-phase flow (H₂O, CO₂, O_2, FLiNaK) through a porous medium was performed. In order to validate the mathematical model, a parametric study was performed by varying the pressure gradient across the porous structure and calculating the corresponding flow rates. The flow rate varied linearly with the applied pressure gradient, as shown in Fig.9. This indicates that the Darcy’s law for the present computational geometry can be applied to the porous structure. The absolute permeability of NBG-18 (0.106 mD) much higher than IG-110 (0.064 mD) and NG-CT-10(0.090 mD).

Fig.9.Full-screen View

Volume flow rate vs applied pressure gradient. The linear relationship validates the Darcy’s law.

For the porous material, according to the realistic porous geometry of pore structure by μ-CT to make a numerical simulation analysis is an effective method. This study indicates that the NBG-18 has a large number of pores and high connectivity, so the molten salt may easily infiltrate graphite, while the IG-110 and NG-CT-10, having uniformly distributed small pores, are more suitable for use in molten salt reactor.