Wentzell boundary condition problems for linear elliptic equations of second order have been studied by various methods. Over time, the condition has come to be understood as a description of a process occurring on the boundary of a domain and affected by processes inside the domain. Since Wentzell boundary conditions in the mathematical literature have been considered from two points of view (in the classical and neoclassical cases), the aim of this paper is to analyse the stochastic Wentzell system of filtration equations in a circle and on its boundary in the space of differentiable K-“noise”. In particular, we prove the existence and uniqueness of the solution that determines quantitative predictions of changes in the geochemical regime of groundwater in the case of non-pressure filtration at the boundary of two media (in the region and on its boundary).