# How Insoluble Inclusions and Intersecting Layers Affect the Leaching Process within Potash Seams
## 4 Discussion  
The results show that the influence of insoluble inclusions and intersecting layers strongly depends on the dissolution rate of the soluble minerals. In cases of low dissolution rates (\(k_{max}\) = 5 \(\times\) 10\({}^{-6}\) cm/s), the evolution of the leaching zone is only slightly affected (Figure 7a,b and Figure 10), although local and average flow velocities are significantly changed (Figure 8a,b). In contrast, heterogeneities lead to a reduction in penetration depth (Figure 12) and higher permeation ratios (Figure 7c,d) if dissolution rates are high (\(k_{max}\) = 5 \(\times\) 10\({}^{-4}\) cm/s). These differences can be explained by a distinction between reaction-dominated and transport-dominated systems. A fully reaction-dominated system (Da \(<<\) 1) is given if the effective dissolution rates of sylvite and carnallite according to Equation (1) correspond to the maximum dissolution rate, i.e., if their saturation only shows a very slight increase along the dissolution front. In this case, the dissolution front is planar and neither local nor overall changes in flow velocity affect the growth rate of the leaching zone: it is entirely controlled by the reaction speed. This case is given for \(k_{max}\) = 5 \(\times\) 10\({}^{-6}\) cm/s at the start of the simulation. However, after some years, the saturations along the dissolution front become high enough to significantly reduce the dissolution rate of sylvie and carnallite, making the system only partly reaction-dominated (Da \(\approx\) 1). The reason for that can be a decrease in flow velocity or an increase in the length of the dissolution front. As a result, the dissolution front becomes inclined and a sylvinitic zone as well as a barrier are formed (Figure 9). If the entire dissolution front is inclined and covered by a sylvinitic zone, the system is fully transport-dominated (Da \(>>\) 1), as given for \(k_{max}\) = 5 \(\times\) 10\({}^{-4}\) cm/s. These systems are much more sensitive to changes in flow velocity. Therefore, they are much more affected by heterogeneities influencing both the local distribution and the average flow velocity (Figures 8, 10 and 12). The Damkohler number is a useful indicator to determine if a system is dominated by reaction or transport [6; 34; 35]. Generally, the simulation results show that an overall Da calculated from the average flow velocity and the saturation-dependent dissolution rate of the inflowing solution corresponds to the observed leaching zone shapes. In cases of \(k_{max}\) = 5\(\times\)10\({}^{-4}\) cm/s, Da \(>>\) 1 is given and a funnel shape can be observed, including a barrier at the left and a sylvinitic zone along the entire dissolution front (Figure 11). These are typical indicators for a transport-dominated system [6]. In cases of \(k_{max}\) = 5 \(\times\) 10\({}^{-6}\) cm/s, the dissolution front is planar in the beginning when Da \(<\) 1, whereas it becomes inclined as Da rises above one, with a sylvinitic zone and barrier rising from the bottom (Figure 8a,b and Figure 9a-c). However, insoluble inclusions make it more difficult to identify this point in time, because the average flow velocity evolves less regularly (Figure 8b) and strong local deviations occur, resulting in small sylvinitic zones near the inclusions and a more irregular dissolution front (Figure 10a-c). In cases of intersecting layers, Da has to be determined for each sub-system or convection cell, and if the layer is inclined, the time period in which Da rises above one does no longer correlate with the formation of sylvinitic zones and barriers (Figures 8a and 10d-f). From our point of view, the reason for this is a change in the length of the dissolution front: if it increases, higher saturations can be reached at the bottom without a change in flow velocity, and vice versa. All in all, the larger the heterogeneities are in size, the less appropriate an overall Damkohler number is to determine if the system is dominated by reactions or transport.