# How Insoluble Inclusions and Intersecting Layers Affect the Leaching Process within Potash Seams
## 3 Results
### Leaching Zone Evolution for High Dissolution Rates (Da > 1)  
For \(k_{\text{max}}\) = 5 \(\times\) 10\({}^{-4}\) cm/s, the Damkohler number is clearly above one during the entire simulation time and a funnel-shaped leaching zone is formed, showing preferential dissolution within the upper half of the potash seam (Figure 11). Its width decreases nearly linearly from the top to the bottom. The lower part of the potash seam is not dissolved, resulting in an increased flattening of the dissolution front over time. As indicated in Figure 7c,d, the expansion becomes slower over time: although the leaching zone penetrates 3 m deep into the seam in the first year, it proceeds only two more meters within the second year. The precipitation of halite next to the left model boundary leads to the formation of a flow barrier within the lower half of the potash seam. Close to the entire dissolution front, a sylvinitic zone is formed (Figure 11a, yellow). Its maximum width in the horizontal direction is reached at the height of the barrier top. Basically, two different solution compositions exist within the leaching zone. The first one contains almost no Mg\({}^{2+}\) and can be found within the halite zone (Figure 11a, blue), whereas the second one shows Mg\({}^{2+}\) concentrations of >70 g/l and is present within the sylvinitic zone (Figure 11a, yellow). The border reaches from the upper end of the dissolution front to the top of the barrier and represents an area with large concentration gradients. Thus, there is a large density gradient at the border as well, representing the driving force of the free convection. Figure 11a shows that above this border, fluid flow proceeds mainly from left to right, whereas below it, the (highly saturated) solution is moving from the dissolution front back towards the left boundary. In cases of small and medium-sized halite inclusions, the flow field becomes less regular but still shows one main convection cell with undersaturated inflowing solution, mainly present within the upper-left area of the leaching zone, and highly saturated outflowing solution along the dissolution front and within the lower area (Figure 12a,b). Accordingly, the shape of the sylvinitic zone and barrier remains basically similar to the homogeneous case. However, zones containing only halite now also occur within the lower half of the leaching zone behind the barrier. In return, wide sylvinitic zones can occur in the upper half, especially above inclusions (Figure 12b). Neither the inclination of the dissolution front nor of the border between the halite and sylvinitic zone is linear anymore, and the lower end of the dissolution front is about 1 m away from the inflow compared to 0.25 m in the homogeneous case (Figures 11a and 12a,b). For broader inclusions, the flow field shows three smaller convection cells after 10 years, with each having its own  
Figure 11: Convection cell of a fully transport-dominated system: (**a**) porosity distribution and (**b**) mineralogical composition after a simulation time of 2 years for a homogeneous potash seam and \(k_{\text{max}}\) = 5 \(\times\) 10\({}^{-4}\) cm/s. barrier at the left (Figure 12c). The same applies to the sylvinitic zone. The dissolution front is subdivided into 3-4 sections with different penetration depths. Thereby, the upper one shows lower dissolution rates than the one below, leading to a recess at 1.6 m height. However, this phenomenon quickly disappears as soon as the upper half of the dissolution front is not subdivided anymore, and the flow regime changes accordingly. Between large inclusions, the flow is not disturbed and the dissolution front as well as the borders between halite and sylvinitic zones are nearly as regular as in the homogeneous case (Figure 11a). However, the overall inclination of the dissolution front is much steeper. As a result, the same permeation speed leads to smaller penetration depths within the upper part of the potash seam after 2 years, but higher permeation ratios at the end for all cases of halite inclusions (Figure 7d).