## 2 Data  
Our subsurface dataset from the Bekes Basin consists of Gamma-Ray (GR) logs of both Mezobereny geothermal wells (Figure 2a), along with production logs and permeability from pressure build-up testing in both wells, as well as other data provided by the municipality of Mezobereny. The production logs will be used to estimate the permeability of each sandstone layer in the production intervals of both wells. In addition, three core fragments from the Ujfalu Fm. were retrieved from the MOL Plc. core repository: two from the Gyoma-1 well (F3 and F4); one (F1) from the Kond-1 well (Figure 1). GR logs of both these wells are shown in Figure 2b. As is illustrated, both these wells have several cored intervals, typically of ~5 m vertical extent. Core recovery from these wells was very low because of the poor consolidation of the Ujfalu Fm, only un-slabbed slices of the cored intervals being available. From the available fragments in the repository, the most sandstone-rich pieces were selected (Figure 3).  
During production logging in well VS-1, the total production rate (Q\({}_{\mathrm{I}}\)) was kept constant at 460 L/min. The log in Figure 2a shows the contributions to the production flow from individual sandstone sections. Twelve production screens have been placed in the production interval of this well, connected by a blind production liner. The log shows that only the ten sandstone layers with lowest GR log readings contribute to the production flow, with individual contribution ranging from 10 to 140 L/min, the combined thickness of all producing layers being 43.3 m. In well T-1 four production screens are installed, of which only three intervals of combined thickness 12.5 m contributed to the production flow. The total production flow was 350 L/min during production logging of this well, the contributions of the three productive layers ranging from 100 to 130 L/min.  
Table 1 summarizes these production logging outcomes. The percentage of flow that each layer contributes to the total is presented in the column with header F\({}_{\mathrm{i}}\). In addition to production logging, gas-lift production tests were performed with pressure build-up measurements after shut-in periods of ~2 h. This time was too short to determine the skin factor, and only allows rough estimation of the average permeability K\({}_{\mathrm{a}}\) across the total production interval in each well: 89 mD in well VS-1 and 196 mD in well T-1. Utilizing these values, we estimated the permeability of each production layer assuming a modified version of the standard Theis [30] steady state radial flow equation. Thus:  
\[\mathrm{Q_{i}}=\mathrm{F_{i}}\,\mathrm{Q_{t}} \tag{1}\]  
where Q\({}_{\mathrm{i}}\) is the flow rate from layer i, and F\({}_{\mathrm{i}}\) is the fraction of the total flow rate (Q\({}_{\mathrm{I}}\)) from that layer, and:  
\[\mathrm{K_{i}}=\mathrm{F_{i}}\,\mathrm{K_{a}}\,\frac{\mathrm{h_{i}}}{\mathrm{h _{t}}} \tag{2}\]  
where K\({}_{\mathrm{i}}\) and h\({}_{\mathrm{i}}\) are the permeability and thickness of layer i, and h\({}_{\mathrm{t}}\) is combined thickness of all the producing layers (Table 1).  
Figure 3: Descriptions of recovered core fragments.  
Figure 2: Gamma Ray logs of Békes Basin wells. (**a**) Mezöberény geothermal production well T-1 (well B-115) and re-injection well VS-1 (well K-116), with production data also shown. (**b**) Hydrocarbon wells Kond-1 and Gyoma-1.