### Numerical Modeling of Deposit Formation

Deposit Formation (Fouling) in polymer solutions is driven by two mechanisms. Homogeneous fouling describes the growth of deposits on surfaces due to increasing polymer chain length and solution viscosity (auto-acceleration) in near-wall regions. Figure 3 shows the local increase of viscosity in regions of large residence times (i.e., vortex structures). Eventually, the chain length is sufficiently long so that gels or solids forms at the wall, leading to the plugging of the reactor. This behavior is modeled in CFD by means of a solution-viscosity approach dependent on the polymer reaction yields. This allows for optimization of geometry and operating conditions to delay and prevent cleaning intervals.

Figure 4: Homogeneous (left) and heterogeneous (right) fouling mechanisms on walls.

As the second mechanism, heterogeneous fouling (Figure 4 right) occurs through precipitation of solid polymers from the solution. These polymers can grow in size, coalesce and accumulate at surfaces. The precipitation is modeled by an Euler-Lagrangian approach. The reaction rate of the continuous (Eulerian) phase locally creates discrete (Lagrangian) particles. Both the phases are coupled to form a model predicting heterogeneous fouling locally within the reactor, as shown in Figure 5. Due to the high computational effort, only stationary simulations are feasible, and time cannot be resolved. However, the tendency of the simulation to numerically diverge indicates that fouling is likely to occur at the respective operating conditions.

Figure 5: Euler-Lagrangian particle trajectories in the reactor domain (top), particle accretion (middle) on heated reactor walls computed with the Euler-Lagrangian model and resulting pressure drop (bottom) of the continuous phase on the reactor mid-section.

Modeling for example the particle-wall interaction, the accumulation of heterogeneous deposits is investigated locally to optimize the reactor geometry and allow for long operating times of the system.