# How Insoluble Inclusions and Intersecting Layers Affect the Leaching Process within Potash Seams
## 2 Materials and Methods
### Scenario Analysis  
In order to study the influence of heterogeneities, leaching processes in a carmallite-bearing potash seam containing insoluble layers or inclusions were simulated. Carmallitite is a very common, globally occurring potash salt whose leaching behavior was studied for homogeneous rock compositions by [PERSON] et al. [6]. It was found that transport- and advection-dominated systems (Da > 1 and Pe > 2) are most common and also most critical in the short term with regard to hazard potentials, whereas reaction- and advection-dominated systems (Da < 1 and Pe > 2) become more critical in the long term. Both cases were investigated in this study to identify possible differences in the effect of heterogeneities. According to [PERSON] et al. [6], 25 wt.% carmallite is a sufficiently high ratio to produce Pe > 2 and low enough to ensure that Darcy flow is still maintained. Therefore, a carmallite-bearing potash seam composition of 25 wt.% carmallite (KMgCl3-6H2O), 72 wt.% halite (NaCl) and 3 wt.% sylvite (KCl) was applied in all scenarios, corresponding to the volume fractions shown in Figure 5. Mineral densities and dissolution properties are  
Figure 4: Fully permeated cells can still contain non-equilibrated minerals due to their lower dissolution rates. Internal dissolution (2) within a cell reduces the amount of non-equilibrated minerals; additionally, they are considered for Interchange (1). The average porosity of the permeated part \(\Phi_{per}\) corresponds to the average porosity of the cell and is used for interchange as well as for flow and transport calculations. provided in Table 1. The dissolution rate \(k_{max}\) strongly depends on the hydrodynamic boundary conditions: it increases with flow velocity [21] and reaches values under turbulent flow conditions that are at least one order of magnitude higher than that for laminar flow [16; 19]. This is due to most salt minerals showing transport-controlled dissolution behavior, i.e., \(k_{max}\) is controlled by the thickness of the diffusive boundary layer at the mineral surface [19; 22; 23]. The boundary layer thickness, and consequently \(k_{max}\), depend on the flow velocity, diffusion coefficients and surface roughness [24; 25; 26; 27]. Based on the values of Rohr [17], an average \(k_{max}\) of \(5\times 10^{-4}\) cm/s was applied to all three minerals in Table 1. However, this is an upper value because it refers to convection in open cavities. It can be expected that convection within a porous leaching zone results in smaller flow velocities, and therefore in smaller dissolution rates. Accordingly, a second \(k_{max}\) of \(5\times 10^{-6}\) cm/s was taken into account to ensure that both transport- (Da \(>\) 1) and reaction-dominated (Da \(<\) 1) systems are investigated [6]. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Mineral** & **Density (kg/m\({}^{3}\))** & **Reaction Equation (Dissolution)** & **Log K** \\ \hline Carnallite & 1600 & KMgCl\({}_{3}\)\(\cdot\)6H\({}_{2}\)O \(\rightarrow\) SCI\({}^{-}\) + 6 H\({}_{2}\)O + K\({}^{+}\) + Mg\({}^{2+}\) & 4.33 \\ Halite & 2170 & NaCl \(\rightarrow\) Cl\({}^{-}\) + Na\({}^{+}\) & 1.586 \\ Sylvite & 1990 & KCl \(\rightarrow\) Cl\({}^{-}\) + K\({}^{+}\) & 0.915 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Potash salt mineral densities and dissolution properties (modified from [PERSON] et al. [6]). Figure 5: Initial and boundary conditions: the inflow region is prescribed by a Dirichlet boundary (blue line); all other boundaries are impermeable (green lines); the models are initialized as dry with homogeneous potash salt (red, mineralogical composition shown) and halite inclusions according to Figure 6 (modified from [PERSON] et al. [6]).