The effect of the permeability heterogeneity on the extension of wellhead protection area based on synthetic simulation and a case study in Hungary

Sustainable water extraction and the vulnerability of aquifers require the accurate definition of wellhead protection area (WHPA) around both production and injection wells. Although the WHPA definition is different in every country, they have a common feature that the protected area is defined by groundwater travel time. The assumption of a homogeneous medium is the general simplification in modelling of WHPA, although, heterogeneity can have a significant effect on its size in the hydrogeological environment.

In this study, we investigated the effect of permeability heterogeneity on the size of the WHPA in synthetic two- and three-dimensional finite element models with COMSOL Multiphysics software at the time points used in the Hungarian legislation (t=20 d, 180 d, 5 yr, 50 yr). Heterogeneous permeability distributions with different heterogeneity scales (i.e. correlation length R=5 m, 10 m, 20 m) were created in SGeMS geostatistics software using unconditional Sequential Gaussian Simulation (SGS). 20–20 realizations were generated for each value of R in order to get statistically stable solutions for the simulations. The temporal evolution of the concentration front (minimum - r_min, average - r_av and maximum - r_max distances from well) was used to monitor the size of the WHPA at the respective time points.

Among the results, the following main conclusions can be drawn based on 2D simulations. Although the average distance (r_av) in heterogeneous media is approximately equal to the homogeneous solution, the maximum distance (r_max) is significantly greater in heterogeneous media, because the water travels larger distances in a heterogeneous medium through the channels of zones with good permeability. Therefore, a larger protection area should be expected compared to the homogeneous approach. Water travels up to 25–75% farther depending on the scale of heterogeneity, where the increment rate decreases over time. Based on the 3D simulations, only small differences are detected between the 2D and 3D results. The maximum distances (r_max) in 3D models are 1.05–1.47 times greater than those in 2D models. Besides, the ratio decreases with time, which indicates that the differences are relevant especially on short time scales, and there is no significant difference after 50 years.

The research provides useful results in terms of the size of the WHPA, which is important for geothermal applications and sustainable water management. In this light, the findings from synthetic model calculations are used in a geothermal project area in Hungary where the heterogeneity scale is estimated from seismic attributes (sweetness, amplitude anomaly) and a 3D hydrodynamic model of the heterogeneous hydrogeological environment is evaluated in FEFLOW software.

Project no. KT-2023-900-I1-00000975/0000003 has been implemented with the support provided by the Ministry of Culture and Innovation of Hungary from the National Research, Development and Innovation Fund, financed under the KDP-2023 funding scheme.