## 4 Results and Discussion  
The proposed methodology serves to carry out computational experiments, where we used the following values of the initial parameters: \(\mu=10^{-1}\) Pa\(\cdot\)s, \(\beta^{*}=10^{-9}\) Pa\(\ {}^{-1}\), \(k_{1}=10^{-12}\div 2.5\cdot 10^{-12}\) m\({}^{2}\), \(k_{2}=5\cdot 10^{-13}\div 10^{-12}\) m\({}^{2}\), \(p_{c}=1000\) Pa, \(p_{0}=0\) Pa, \(T=3600\) s, \(h_{1}=0.01\) m, \(h_{2}=0.005\) m, \(\tau=0.1\) s, \(a=0.5\) m, \(b=1.5\) m.  
In Figures 2 and 3 we present surfaces \(c_{1}\), \(c_{2}\) and \(p\) for the classic case, i.e., ignoring anomalous effects. It is easy to notice the spread of surfaces along the directions \(x\) and \(r\). On the common border of the two zones, \(\Omega_{1}\) and \(\Omega_{2}\), i.e., at \(r=a\) one can observe a kink of surfaces, which means a discontinuity in concentration gradients on \(r=a\). It means that \(\left.\frac{\partial c_{1}}{\partial r}\right|_{r=a-0}\
eq\left.\frac{ \partial c_{2}}{\partial r}\right|_{r=a+0}\). This phenomenon is characteristic for macroscopically inhomogeneous media, where on the boundary of two media gradients of many characteristics break. One can notice the progress of the surfaces in the directions \(x\) and \(r\) with increasing the time \(t\). The same phenomena occur with the pressure distribution (Figure 3).  
Using pressure distribution (Figure 3) according to (1), (2) filtration velocity fields are determined. On Figure 4 we present filtration velocity contour lines. Filtration velocity is expressed through \(v_{1}=\sqrt{v_{1r}^{2}+v_{1x}^{2}}\), \(v_{2}=\sqrt{v_{2r}^{2}+v_{2x}^{2}}\), where \(v_{1}\) and \(v_{2}\) are filtration velocity modules in \(\Omega_{1}\) and \(\Omega_{2}\), respectively.  
One can observe that filtration velocities in \(\Omega_{1}\) and \(\Omega_{2}\) are considerably differ. On the common boundary of \(\Omega_{1}\) and \(\Omega_{2}\) we have a drastically change of the filtration velocity due to different values of permeabilities in \(\Omega_{1}\) and \(\Omega_{2}\).  
Figures 5 and 6 show the surfaces of \(c_{1}\) and \(c_{2}\) for values \(\gamma_{1}^{*}\) and \(\gamma_{2}^{*}\), less than 2. From the presented material, one can notice an increase in diffusion effects in the direction \(x\) in both zones, when \(\gamma_{1}^{*}\) takes values less than 2. When \(\gamma_{2}^{*}\) decreases from 2, \"fast diffusion\" is observed mainly in the zone \(\Omega_{2}\). In addition, surface \(c_{1}\) in \(\Omega_{1}\) do not undergo much change. Thus, the results obtained show that the transport characteristics of the solute mainly depend on the distribution of concentration and other hydrodynamic parameters of the zone \(\Omega_{1}\). The transport characteristics in \(\Omega_{2}\) are determined depending on the characteristics of \(\Omega_{1}\).  
Numerical experiments show that the decreasing of \(\gamma_{1}\) and \(\gamma_{2}\) from \(1\) leads to the \"fast diffusion\" in the radial direction similar to that as in \(x\) direction. The smaller values of \(\gamma_{2}\) than \(1\) that \(\gamma_{1}=1\) leads to the \"fast diffusion\" almost only in \(\Omega_{2}\), whearase in decreasing of \(\gamma_{1}\) from \(1\) we can observe \"fast diffusion\" in both zones \(\Omega_{1}\) and \(\Omega_{2}\). In other words, solute transport characteristics in the micropore are influenced by the corresponding characteristics of the macropore.