Table 2 Defined dimensionless parameters for numerical convection–diffusion calculations.

Dimensionless simulation time

10⁴

Dimensionless ratio o lower permeability layer thickness to wellbore radius (h_r)

6

Porosity ratio (\(\frac{{\phi_{2} }}{{\phi_{1} }}\))

5

Dimensionless dispersion coefficient (α_D)

20

Dimensionless radius (r_D)

200

Time difference (dt)

0.5

Difference in vertical direction (dz)

0.5

Difference in radial direction (dr)

5

Dimensionless diffusion coefficient in L2 (D_L2)

10⁻⁹

Dimensionless diffusion coefficient in L1 (D_L1)

10⁻⁵

Peclet number in L1

10⁴

Peclet number in L2

10

Number of grids in vertical direction for low permeable layer (N_{low_k})

10

Number of grids in radial direction for high permeable layer (N_{high_k})

20