Modeling and Flow Sheet Simulation of Selected Mechanical Recycling Processes for Li-Ion Batteries 

3.1 Cutting Mill

Cutting mills are often used for the second comminution step in the battery recycling process chain or, in case of small cells, are also able to break up and comminute entire cells as usually fulfilled by a shredder. Therefore, two different model approaches are developed due to the different requirements when modeling entire battery cells or individual electrode pieces as mill feed. To keep the cutting mill model (using entire cells) simple, the particle sizes of the different materials inside the battery are not considered. Thus, the model should just depend on the battery cell.

3.1.1 Cutting Mill Model for Battery Cells

The cutting mill model for fragmentation of entire battery cells is based on experimental data achieved for cylindrical cells. The experiments were carried out with different grid sizes of the bottom screen inside the mill. For the model development, the main components of the battery like the anode (coated copper foils), cathode (coated aluminum foils), and separator as well as the casing material of the battery were considered. The black mass was not investigated at this stage due to the concentration on the larger particles. The mass distributions of the particle sizes of the different materials were used to calculate the cumulative PSDs. Comparing the different screen sizes, the product sizes resulting from the cutting process are coarser for the larger grid sizes. The larger the grid sizes, the faster the particles leave the mill through the screen. The shorter residence time leads to larger particle sizes and broader distributions.

This model should calculate the product particle sizes independently of the specific material sizes within the cell, since these are not known. The model considers the entire battery cell as feed material. To calculate this, the product distributions are described by a Weibull distribution (Eq. 1). The parameters k and λ vary for each material and grid size. Consequently, they are determined by fitting Eq. 1 to the experimental data. To simplify this, the Weibull distribution (Eq. 1) is modified to contain also the grid size d_m as a parameter normalizing the particle size x.

(1)

where d_m is the grid size and x the particle size. The results are exemplarily shown for the coated aluminum foils (from the cathode) in Fig. 2 for a normalized particle size. The normalized graphs have a similar course for each grid size, so average values for k and λ can be calculated for each material (Fig. 2a, black line). The result is an equation to calculate the cumulative PSD depending on the particle size and the grid size inside the mill. By that, the number of individual equations is significantly reduced to the number of battery materials. For each material inside the battery mix, the PSD can be calculated according to these results for the Al foils. However, the main advantage is the creation of a predictive formula which calculates the PSD for every grid size, without the need of further experiments. In Fig. 2b, this is shown for a grid size of 15 mm. However, this equation is only proved valid for the experimentally investigated range of grid sizes yet.

3.1.2 Cutting Mill Model for the Secondary Comminution of Battery Materials

This model can be used for individual recyclates achieved from a preceding shredder and separation process, e.g., electrode foils alone. In this case, the model is based on the breakage behavior of the feed particles, e.g., foil pieces, fed to the mill. No further materials like harder casing materials have to be considered which are protecting the materials inside the battery cells from fragmentation. The model describes the changes in the PSD depending on the feed material sizes and the comminution time.

The experimental data of crushed copper foil particles are shown in Fig. 3. Through these resulting particle size distributions, the ratio in which the different feed particle sizes are crushed into the smaller particle sizes can be determined. These values can be used to create a comminution matrix. In this case the comminution matrix describes the changes in the PSD for a time step of 10 s according to the experimental data generation.

In the next step, the grid size should be integrated into this model approach. The probability of a particle to leave the mill though the screen is depending on different aspects. One aspect considered here, is the ratio between the open screen area and the total screen area φ ¹⁴. The number of revolutions influences the number of contacts of the particles on the screen. This is considered here in the parameter n. For an initial approach, it was assumed that each particle moves in the mill with the same number of revolutions. The number of contacts on the screen is also influenced by the filling degree. A higher amount of particles decreases the particles' possibility to stay on the screen area. This is considered in the parameter a. For an initial approach, a linear decrease of the number of contacts by rising filling degree was assumed. This influence will be investigated in more detail in further investigations. The last influence considered here is the probability of a particle to pass through the screen W. This is calculated with the screen grid size d_m, the wall thickness of the screen grid d_G, and the size of the particle x ¹⁵.

(2)

These three aspects are included in the following Eq. 3.

(3)

This results in the same dependencies and similar formula as for a vibration screen ¹⁶. Eq. 3 can be combined with the comminution matrix. Due to the matrix time step of 10 s, the probability to leave the mill through the screen has also to be calculated for the same time step. These two approaches are combined in Eq. 4.

(4)

The mass of particles m_y,i in size class y at time point i is calculated with the mass at the previous time step in the size classes above m_x,i–1, the probability to leave the mill within 10 s P₁₀ and the matrix value C_xy. The resulting PSD for screen sizes of 6 and 8 mm are shown in Fig. 4. At this stage, the model has the limitation of the 10 s time step. This leads to the case that only processes with residence times above 10 s can be calculated. Consequently, screen sizes of more than 8 mm cannot be described due to residence times below 10 s determined experimentally.

3.2 Zig-Zag-Sifter

For the zig-zag-sifter, several model approaches exist ¹⁷, e.g., Tomas and Gröger ¹⁸ or Lukas et al. ¹⁹ whose model has also been implemented to Dyssol. In this case, the model approach of Tomas and Gröger ¹⁸ was used to calculate the separation function of the material.

(5)

with the volume flow in the heavy and light fraction, and , the cut size x_T, exponent α, which can be set as 0.5 ¹⁸, and the number of separation stages z. For the ratio of the volume flow rates, the following approximation can be made ¹⁸:

(6)

with the particle mass load of the air μ_s,g and the densities of the particles ρ_s and air ρ_g. The particle mass load is calculated by the ratio of feed mass flow to air flow.

This model does not consider the influence of the particle shape. In case of battery recycling, this is an important aspect. The battery materials have different shapes after shredding and secondary comminution, especially when looking at the current collector foils ²⁰. They have a rather flake shape. This leads to a different buoyancy behavior which has to be considered in the model. Due to this broad range of particle shapes, the experimental data show broader separation functions than calculated with this model.

Therefore, a calibration parameter β is added to this model to consider the complex particle shape and adapt it to the experimental data. The results are shown in Fig. 5. An approximate value of 0.067 m³s⁻¹ was used for the air flow rate and the material-specific parameters in Tab. 1. Approximations had to be made for the density of the particles. The particles are not compact particles but compacted and compressed pieces of foil with corresponding air inclusions inside the particles. Therefore, the weight of a certain amount of particles with the same particle size class was determined and an average density for the particles was calculated (compared to a spherical particle). The feeding rate to the sifter varies for the different experimental data points. For the calculation of the separation function and a first implementation of this model to the flow sheet simulation software, a mean value for the feeding rate is used. This mean value shows a good approximation of most data points.

For the separator foils, no separation curve was determined experientially. The foils end up completely in the light fraction due to the considered process parameters. For the simulation model (Sect. 4.2), assumptions have been made with the use of literature data. These values are not validated and are only used for demonstration purposes in the simulation.

(7)

As such separation functions can directly be used in the dynamic flow sheet simulation, they are determined for each material. Based on this, for a certain material, the mass flow of the heavy and light fraction can be calculated based on the input feed size of the materials.

4.1 Simulation Results for the Cutting Mill

The cutting mill model was implemented with linear approximations of the throughput. These were derived from experimental data of the residence time of model materials in the mill depending on the bottom screen size. The results in Fig. 6a show the time course of the holdup mass inside the mill. The mill is fed with 200 g s⁻¹ of the considered cylindrical battery cells for 2 s at the beginning and again after 10 s. The mass inside the mill is rising due to the feed material. At the time point when the material supply stops, the holdup mass is getting lower until the next battery cells are added to the process. With the smallest screen considered, the mill needs the longest time to empty. Compared to the holdup mass, the mass flow in Fig. 6b shows the highest flow rate for the screen size of 10 mm. The mass flow for the screen size of 6 mm is approximately half of this value.

The particle sizes for the different materials were calculated using Eq. 1. Due to the independence of the feed particle sizes of the certain materials, the PSDs are calculated only based on the fed cylindrical cells. Thus, the PSD of the feed does not change during the process. The mass flow adjusts directly with these PSDs (Fig. 6c). The time dependence of the PSD is to be specified in further investigations.

4.2 Simulation Results for the Zig-Zag-Sifter

The zig-zag-sifter is simulated for the three different battery materials Cu, Al, and separator foils. The separation function is calculated for an air flow of 0.04 m³s⁻¹. The particles are fed to the sifter in a continuous mode (0.5 g s⁻¹) with consistent mass fractions of the three materials. The cut size of the Cu and Al foils was investigated experientially and approximated for different volume flows. For the separator foils, the cut size could not be determined with the settings examined so far as they end up almost completely in the light fraction due to the low density. Therefore, assumptions have been made that the separation function can only be calculated for low air flows. For the simulation, the assumption has been made that only a small amount will end in the heavy fraction, so the separation function does not reach the value of 1 at the considered particle size range.

The resulting separation function can be seen in Fig. 7. The separation function of the Cu foils has the steepest slope due to the higher particle densities. With these separation functions and the feed particle sizes the mass output of the material in the heavy and light fraction is calculated in the simulation (Tab. 2). Due to the steep separation function of the Cu foils, the highest amount of the Cu ends up in the heavy fraction. The aluminum foils end up in the light fraction with a higher amount under the considered process parameters.

The shown values are based on various assumptions which had to be made to create this model approach for this difficult material system. The results based on the data in Fig. 5. The data were extrapolated for the simulation. These values are not validated. The extrapolation above particle sizes of 10 mm determined experientially must be considered critical in this case, since a possible change in buoyancy behavior of larger particles is not taken into account. In further investigations, this knowledge gap is to be closed and the model should be able to reproduce the material behavior inside the sifter more accurate to depict the important influences in case of battery recycling.

4.3 Simulation Results of Interconnected Processes

Through the interconnection of these two processes, the dynamic behavior and the influence of a preceding process on a subsequent process can be demonstrated. The shown simulation results are based on a shortened process chain, only considering the first and last process step. The intermediate processes would additionally influence the result but are neglected for this example to show the interaction of these processes in a simplified way. In this case, the mill as first stage is operated with entire cylindrical cells in a continuous mode with an inlet material mass flow of 0.5 g s⁻¹. The grid size of the mill is 10 mm. Among the set process parameters, the holdup mass inside the mill achieves a steady state after 60 s (Fig. 8). The mass flow out of the mill depends on the holdup material composition and the grid size and is adjusted according to the calculated holdup. The mass flow out of the mill is used as input mass flow for the zig-zag-sifter. Therefore, the holdup mass of the sifter is changing until the cutting mill mass flow reaches a steady state.

Due to the changes in the input flow of the sifter, the separation functions change, too. In Fig. 9, these changes can be seen for the Cu, Al, and separator foils. Due to the small material flow rate at the beginning of the process, the separation functions are relatively sharp according to the material properties and process parameters. The more material enters the sifter and the higher the mass load is, the broader are the separation functions. Broader separation functions mean a less efficient separation. Accordingly, a lower throughput results in a more efficient separation and a higher mass recovery and purity of the battery materials. As soon as the steady state is reached, the separation functions remain constant. If the input mass flow would fluctuate, the separation function would always adapt to the current conditions, so the influences of the recovery rate of the materials can be investigated by these simulations.

The adjusting separation function also influences the mass flows in the heavy and light fraction (Fig. 10a). These mass flows are calculated for every time step depending on the results for the input mass flow, its particle sizes, and the separation function. The mass flow of the heavy and light fraction also reaches the steady state due to the steady state of the feed mass flow, as does the separation curve. Since the other process parameters are kept constant, the ratio of heavy and light mass flow does not change any further. Due to the considered material composition, the small particle sizes after this cutting mill process, and the set air flow, the mass flows mainly into the light fraction.

The separator foils end up in the light fraction with an amount of more than 90 % (Fig. 10b, Tab. 3). This high number was predicted due to the low density of the material. In the literature, the amount of separator foils which end up in the heavy fraction was found to be higher as well as the amount of aluminum in the light fraction was found to be lower ⁵. This can be explained due to lower volume flows and accordingly lower air velocities (4.16 m s⁻¹ compared to 1.08–1.32 m s^{−1 5}). Also, during the battery recycling, there are often inclusions of different materials. When separator foils are connected with some heavier particles, the amount which ends up in the heavy fraction is higher. The consideration of these mixed materials was not included in the development of these initial models and simulations but will be a part of future investigations.

The Cu particles are the only material in this simulation which ends up in the heavy fraction with a higher amount, although still a significant proportion of these particles ends up in the light material (Tab. 3).

Comparison with the particle sizes (Fig. 10c) shows that the separator foils end up in the light fraction even if the particle sizes are larger than the sizes of the other materials. Between the input particle size and the size of the light fraction is just a slight difference for the separator foils. For the Cu and Al particles which have a similar feed particle size, the particle sizes in the heavy and light fraction differ more from each other. The amount of particles which end up in the heavy fraction is higher for the Cu particles due to its higher density. Therefore, the particle sizes in the heavy fraction are smaller than the Al particle sizes.