The Impact of Input Parameters on the Thermal Power of Shallow Geothermal Systems: A Case Study of Kielce, Poland

Shallow geothermal energy is an efficient and low-emission alternative to conventional heating and cooling systems [1, 2]. Growing energy demand and limited fossil fuel resources contribute to geopolitical conflicts and price instability. Therefore, there is an increasing need to develop stable and renewable energy sources [3, 4]. In practice, the temperature of groundwater used in shallow geothermal systems is typically limited to 21‒23 ℃. Temperature increases usually do not exceed 5 ℃. Systems are generally implemented at depths of up to approximately 100 m to preserve aquifer sustainability and comply with regulatory thresholds in countries such as Italy, Switzerland, and Germany [5]. Shallow geothermal systems are expected to meet up to 28% of the European Union’s heating and cooling demand by 2050. They may also achieve energy savings of up to 50% and reduce CO₂ emissions by up to 85% [6]. Open-loop groundwater heat pump (GWHP) systems, which utilize groundwater directly, are particularly efficient and cost-effective in areas where water resources are readily available [7]. Kielce has significant groundwater resources, whereas its wind energy potential remains limited. Therefore, shallow geothermal energy should receive particular attention in this region. Effective utilization of shallow geothermal energy requires the application of heat pump installations. Their efficiency strongly depends on local hydrogeological conditions, and improper exploitation can lead to thermal disturbances and reduced system performance. Economic, informational, social, and legislative barriers may also limit the development of low-temperature geothermal systems [8, 9]. Compliance with geological, mining, water, environmental, and building regulations is a significant challenge. At the same time, installations that obtain heat directly from the ground face fewer procedures and are therefore more attractive to investors. Informational and educational barriers are also significant. Commonly available data are often promotional and lack detailed information on advantages, disadvantages, and technical requirements, especially for water-to-water heat pumps [10].

Determining the energy potential of a geothermal reservoir is generally a complex and uncertain process, primarily due to limited data availability [11]. Estimation of geothermal resources is often performed by calculating the stored heat capacity of the reservoir, based on temperature measurements and rock property data [12, 13]. The THERMAL method has been identified as a promising tool for managing shallow geothermal energy in urban environments. This method highlights the crucial role of temperature in system performance [6]. Using this method, thermal power in GWHP systems can be optimized through key input parameters such as groundwater temperature, cooled water temperature, flow rate, and operational thresholds. This optimization helps minimize thermal interference and improve system efficiency. To apply these concepts effectively at a local scale, site-specific hydrogeological analysis is required.

Current literature reveals significant variability in methods and values used, resulting in inconsistent and sometimes inaccurate power calculations [14]. The lack of standardized parameter selection complicates the reliable assessment of geothermal potential. Available maps of low-temperature geothermal resources cover only parts of Poland and are typically produced at regional scales, making local interpretation difficult [8]. The diverse geological and hydrogeological conditions of the Kielce district further limit the development of low-temperature geothermal investments using groundwater heat pumps [15]. Nevertheless, the future use of shallow geothermal energy for heating and cooling systems in the region is promising [1].

In the case of Kielce, a site-specific analysis adapted to local hydrogeological conditions is still lacking. Developing such an approach is essential to accurately determine the most probable parameter values, improve thermal power estimates, and enable more effective utilization of groundwater heat resources in local heat pump systems. Therefore, this study presents a novel, locally adapted methodology with the following objectives:

(i) to analyze and select the most probable set of calculation parameter values for determining the thermal power of shallow groundwater intakes;

(ii) to assess the potential of 63 groundwater intakes in the city of Kielce for heating purposes, including the estimation of their available thermal power.

The study is based on the following hypotheses:

(i) It is assumed that a most probable set of calculation parameters exists for accurate and efficient estimation of the thermal power of shallow groundwater intakes. This approach may also be applicable in regions with similar hydrogeological conditions;

(ii) The shallow groundwater intakes in Kielce have sufficient thermal potential to be effectively utilized for heating purposes;

(iii) The available thermal power of groundwater intakes in Kielce may provide significant support for the operation of the local district heating system.

The results showed that the water temperature calculated using Eq. (1) differs from the value obtained with Eq. (2), even when the same average annual air temperature for the Kielce area and the same depth of groundwater occurrence were assumed (Figure 1). This highlighted the important role of both the geothermal degree and the geothermal gradient in determining this parameter.

(a) Water temperature (T_w) calculated from Eq. (1)

(b) Water temperature (T_w) calculated from Eq. (2)

Figure 1. Water temperature at depth H calculated from Eqs. (1) and (2) in well No. 8150052 – limestone aquifer, λ = 2.8 W/(m·K); t_avg (average annual air temperature in a given region [℃]) = 7.6 ℃, 8.2 ℃, and 10 ℃

In the analyzed case, Eq. (2) yields lower estimates of water temperature. This equation is based on the geothermal gradient derived from terrestrial heat flux and the thermal resistance of aquifer rocks. In contrast, Eq. (1) produces higher temperature values. This results from the inclusion of a positive elevation correction factor (A) and the use of the geothermal degree. In the study area, this approach corresponds to a greater effective increase in temperature with depth than the gradient-based method.

Figure 2. Overview of the thermal power for the example intake (8150023) according to the selected calculation variants

Table 3. Assessment of the possibility of the given values of calculation parameters for evaluating the thermal power of intakes according to formula (4) and the criteria for selecting the most probable variant

It was also observed that higher assumed average annual air temperatures generally led to higher groundwater temperature values. In addition, groundwater occurrence depth (H) had a significant influence on the final results. Careful selection is necessary to obtain reliable and representative temperature estimates. Figure 2 illustrates the thermal power of the example intake (8150023) for each calculation variant. The results showed significant differences depending on the assumed parameter values, highlighting the importance of selecting the most probable calculation scenario, as each parameter directly influenced the final thermal power estimates.

To support these calculations, the thermal power of groundwater intakes was determined using selected parameters that were not directly measured, including the cooled water temperature (T_c) and groundwater temperature (T_w). Since direct measurements were unavailable, a likelihood scale for these temperature values was adopted based on assumptions derived from the literature. Table 3 presents the probabilities assigned to the different variants. A three-point scale was applied, where 1 indicated the least probable variant, 2 indicated an uncertain variant, and 3 indicated the most probable variant.

The thermal potential of the groundwater intakes in Kielce was calculated using the most probable parameter values adopted in accordance with the methodology described above. These included the water temperature at the intake, calculated using Eq. (1) and taking into account the average temperature in Kielce in 2023, and the depth of the stabilized water table, as well as the cooled water temperature assumed to be 5 ℃. The presented data correspond to calculation variant H according to Table 2, which was adopted as the most probable case. The obtained results are summarized in Figure 3.

The total thermal power of all considered wells amounted to 23,339.97 kW, of which 13,878.44 kW came from active wells and 9,461.53 kW from inactive wells, representing approximately 60% and 40% of the total, respectively. Considering only the 29 active wells, the results were as follows:

• The largest share (24%) consisted of wells with a power greater than 1000 kW (7 wells).

• Wells with a power below 15 kW accounted for about 10% (3 wells), which is the same as wells in the 500–1000 kW range.

• The 50–100 kW and 100–250 kW ranges included 2 wells each (approximately 7%).

• There were 5 wells (approximately 17%) in the 15–30 kW range, and 6 wells (approximately 21%) in the 30–50 kW range.

• One well (about 4%) fell into the 250–500 kW range.

The analysis showed that the wells in Kielce exhibited considerable variation in thermal power. The largest group of wells with potential for use as a low-temperature heat source was in the 100–250 kW range, comprising 13 wells. The smallest groups corresponded to the 250–500 kW range (3 wells) and below 15 kW (4 wells). In the 15–30 kW range, there were 10 wells, while the 30–50 kW, 50–100 kW, and 500–1000 kW ranges each included 8 wells. There were 9 wells with a thermal power above 1000 kW (Figure 3). The most favourable wells in terms of thermal potential were located in the Białogon Valley (Nos. 8150017, 8150127, 8150024, 8150033, 8150034, 8150101, 8150118, 8150134, 8150144, 8150147, 8150037, 8150145, 8150052, 8150081). However, most of these wells are operated by Wodociągi Kieleckie, which limits their potential use for heat pump installations.

In summary, Kielce does not have sufficient potential for large-scale investment in shallow geothermal energy as a primary heat source. Nevertheless, individual wells within the city could be utilized for small- to medium-scale heating systems with water-to-water heat pumps.

The observed agreement of the results with the literature highlighted the critical importance of the proper selection of input parameters used for estimating thermal power. Parameters such as the hydraulic variant, water temperature, and the degree of cooling directly affected the final calculation results. Due to the archival nature of the data, direct experimental validation was not possible. Existing geothermal maps developed by the Polish Geological Institute – National Research Institute (PIG-PIB) did not yet cover this location [22]. In addition, the available data on rock thermal conductivity provided through the portal were limited, although they were consistent with the values used in this study. The estimated groundwater temperatures were consistent with those reported in the literature. For Kielce, Devonian formations were reported to have temperatures in the range of 10–20 ℃ [23].

The analysis, therefore, introduced a significant degree of novelty, providing detailed estimates of thermal conductivity and geothermal potential for a previously poorly documented area. These results may serve as a valuable basis for further research and for planning geothermal investments. It is worth emphasizing that the applied computational methodology is not limited to local conditions and can also be applied in other geothermal regions, provided that hydrogeological differences are taken into account. Proper selection of input parameters allows results consistent with the actual geothermal potential of the analyzed area.

Additional confirmation of the reliability of the results was provided by the estimated thermal power for the most probable variant. Within the analyzed group of intakes, the highest power of 1,922.67 kW was recorded for well no. 8150101, located in the Białogon Valley. This value was consistent with the literature data. For the Białogon area, a realistically achievable thermal power of approximately 1,700 kW had been reported for a water temperature reduction of about 2 °C [23]. This agreement confirms both the high energy potential of the area and the reliability of the calculations.

It should be noted that for several intakes in the analyzed set (including wells 8150017, 8150127, 8150024, 8150033, 8150034, 8150101, 8150118, 8150134, 8150144, 8150147, 8150037, 8150145, 8150052, and 8150081), no data on realistically exploitable resources were available. These wells are not currently used for district heating purposes.

Many of the most promising wells are already used by the local water utility. At present, only about half of their resources are utilized, which limits the possibility of additional exploitation for district heating purposes. However, partially unused resources may still allow for additional abstraction or the development of new intakes in this area.

This work is supported by the Kielce University of Technology, Grant NO.: 05.0.12.00/1.02.001/SUBB.IKGT.26.002.