Mapping Metals Incorporation of a Whole Single Catalyst Particle Using Element Specific X-ray Nanotomography

Full-field transmission X-ray microscopy has been used to determine the 3D structure of a whole individual fluid catalytic cracking (FCC) particle at high spatial resolution and in a fast, noninvasive manner, maintaining the full integrity of the particle. Using X-ray absorption mosaic imaging to combine multiple fields of view, computed tomography was performed to visualize the macropore structure of the catalyst and its availability for mass transport. We mapped the relative spatial distributions of Ni and Fe using multiple-energy tomography at the respective X-ray absorption K-edges and correlated these distributions with porosity and permeability of an equilibrated catalyst (E-cat) particle. Both metals were found to accumulate in outer layers of the particle, effectively decreasing porosity by clogging of pores and eventually restricting access into the FCC particle.


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for motor jitter, and 3D tomographic slices were reconstructed using an iterative algebraic reconstruction technique. 1,8 Visualization and analysis of the 3D tomographic data set was performed with Avizo™ Fire software.

Fe and Ni distribution maps
Collecting data above and below the elemental K-edge of Fe and Ni establishes a means of visualization by absorption contrast of the respective elements. For all other species the contrast is negligible. Thus, by taking the difference from each pair of tomography sets, the Fe or Ni distribution within the FCC catalyst can be visualized. The 3D elemental distribution volumes were calculated by subtracting the 3D dataset below the edge (7060 eV for Fe and 8300 eV for Ni) from the above the edge (7180 eV for Fe and 8400 eV for Ni) datasets

Radial Calculations
The radial evaluation was performed using in-house developed code using MATLAB® by MathWorks Inc. Radial "slices" were determined by calculating a distance map on the full 3D volume with respect to the surface, 9 then each voxel with the same distance from the surface were grouped. This method was used to determine the radial elemental concentration of Fe and Ni (Fig. 4a) using the Fe and Ni distribution maps. Furthermore, in conjunction with these elemental distribution maps, we used the dataset at 7060 eV as the 3D dataset to represent the particle without the presence of any metals, to determine how the porosity changes with the insertion of metals in to the pore. This was established by thresholding and binarizing each elemental map as well as the particle volume (7060 eV). By adding the binary maps for each metal in to the pore space ("0 value") of the binary volume, one can determine the amount of porosity change with the presence of each metal.

Permeability
We investigated the spatial dependence of permeability based on the macro-pores of the FCC particle.
Using the tomography data collected at 7060eV, permeability measurements were carried out on 31 uniform sub-volumes (each 3.2 x 3.2 x 3.2 µm 3 ): one in the center of the FCC particle, and five subvolumes each in the positive and negative x, y, and z directions. To account for the fairly spherical shape S4 of the whole particle we performed a permeability calculation for each of the 31 sub-volumes along the direction leading to the center of the particle: the 5 sub-volumes along the positive x-axis were evaluated using a flow direction pointing in the negative x direction, while the 5 sub-volumes along the negative xaxis were evaluated for flow in the positive x direction. Simulations for the sub-volumes along the y and z-axis were performed in a similar manner.
Permeability measurements were carried out on the segmented sub-regions (shown in Figure S1) using Avizo XLabHydro software (results in Table S1). The XLabHydro software estimates the magnitude and direction of the velocity field of an incompressible steady-state fluid by numerically solving the Stokes equations of fluid motion: where is the viscosity, and સ ሬ ሬറ is the pressure gradient of the fluid that gives rise to flow at a velocity, . In FCC particles, diffusion of hydrocarbons across a concentration gradient facilitates flow within the FCC particle. However, permeability can also be used to demonstrate the size and accessibility of macropore channels within the FCC particle. 10 Absolute permeability is determined using Darcy's Law, where Q is the global volume flow rate of the fluid, k is permeability, A is the cross-sectional area, and L is the length of the sample volume. Permeability is a material property and thus the measured absolute permeability for the FCC particle is not affected by changing the fluid that moves through it. Thus, by changing the fluid viscosity from the more viscous vacuum gas oil (VGO) vapor to a more fluid hydrocarbon gas, e.g. as resulting from cracking of the VGO, only the mass flow velocity of the fluid is changed according to Darcy's Law, while permeability remains constant.
These simulations provide information about the connected macro-pore space within each sub-volume, but can also be used to estimate the permeability of the sub-volume for a specific transport direction. The central sub-volume was evaluated in the positive x, y, and z-directions. The results of these simulations S5 are reported in Figure S2. As expected, permeability in each of the sub-regions depends significantly on their porosity, as shown by the logarithmic relationship 11 plotted in Figure S2, a. The spread in the data points further confirms that determined porosity and permeability values are within the same range for all six flow directions, confirming that there is no preferential direction within the spherical particle. We then considered the spatial position of each sub-volume within the particle (Figure S2 b). The plot shows that sub-volumes closer to the surface (at larger distances from the central sub-volume) tend to have smaller porosities and therefore smaller permeability (see also Table S1). This is in agreement with the previously observed ( Figure 2) denser surface regions.
In the second step we inspected two representative, larger sub-volumes in the particle (Figure 4 and S3) comparing elemental distributions and results from the permeability measurement. Here, velocity streamlines were generated based on the magnitude and direction of the velocity tensors, generated from the Stokes equations of fluid motion. The direction and magnitude of these streamlines were then compared to the spatial heterogeneities found for the Fe and Ni distributions.

b) a)
S6 Figure S1. The FCC particle was separated into 31 subregions (1 in the center, and 5 in the positive and negative x, y, and z directions) for permeability measurements. a) Subregion volumes for the x, y and z directions. b) Subregions overlaid onto the respective portion of the FCC catalyst particle showing that the subvolumes are sampling the particle radially along the x, y and z directions. Figure S2. (a) Permeability versus porosity as determined in 31 separate sub-volumes within the FCC particle (1 center (black), 5 in the positive and negative x (red), y (blue) and z (green) directions). One outlier was removed from both graphs for better readability, namely the sub-volume in the z-direction (+6.4 µm) with values of 0.098 and 2.1E-10 for porosity and permeability, respectively. This outlier indicates a sub-volume with extremely small permeability, i.e. a part of the FCC particle that is almost completely blocked for mass transport in the z-direction. (b) As in a), but with markers grouped according S7 to the spatial position of the sub-volumes with respect to the central sub-volume. The distances indicate the distance of the center of the respective sub-volume to the center of the central sub-volume. See supporting information (Table S1) Table S1. Radius, solid fraction, pore fraction, and permeability k within the 33 regions illustrated in Figure S4.