## 3 Methods
Because only a few hundred individual fractures were available for evaluation, a unique pair of parameters (E, F) could be calculated for the entire well, while the spatial variation of the length distribution could not be followed. As the studied A-1 well was not oriented, no primary information concerning the real geographical position of the bore cores was available. For this reason, the fracture orientation data, dip, and dip angle measured by a borehole televiewer (BHTV) in a neighbouring well were used for the simulation. Figure 4: Discriminant functions to distinguish (**a**) undeformed host rock (white bars) from fault rocks (black bars) and (**b**) fault breccia, cataclasite and gouge based on the discriminant functions \(F(1\)-\(2)\), \(F3\) and \(F4\) calculated using Discriminant Function Analysis on well-log data from the Szeghalom area (modified after [19]). Red dots denote the fault rocks of the studied A-1 well. Considering all the above information, in the fracture network simulation, the fracture density was computed as a fractal dimension (\(D\)) for each 3-m-long interval, fracture lengths were characterised by a unique (E, F) pair for the whole well and fracture orientation data, which should have been statistically identical for the entire rock body, were applied during the simulation. For fracture network modelling, we used the newly developed Infress software, which applies the modified algorithms of the previous RepSim code [17]. This is a fractal geometry-based discrete fracture network (DFN) modelling system, in which each fracture is represented by a circle. The simulated 3D network had the same statistical parameters as the original natural network concerning spatial density (fractal dimension of fracture midpoints) as well as fracture size (diameter), distribution, and orientation (dip and dip angle). Moreover, the simulation was a stochastic process, meaning that any number of different models of identical probability could be generated using the same initial set of parameters. In the present case, 10 near-well fracture models were produced around the well and evaluated for a \(30\times 30\) m\({}^{2}\) column. As a result, interconnected fracture sub-systems as well as their spatial positions were determined for all 10 models. Further details on the mathematical background of the simulation procedure have been discussed in many previous papers [32; 33; 34; 35]. Considering the vein-filling mineral phases, all, except for the final laumontite, represent ancient mineralisation processes, as shown previously [22]. Thus, hereinafter, only the conditions of laumontite formation will be focused on. In the first step, zeolites separated from five distinct depths were measured by X-ray diffraction to check whether other zeolite phases occurred in the veins. Zeolite separates were handpicked, powdered, and analysed by a Philips PW1710 automated diffractometer using Cu-Ka radiation at the University of Bern (Switzerland). The chemical compositions of laumontite crystals from three different depths were analysed using a Cameca SX-50 electron microprobe at the University of Bern. Synthetic and natural standards were used, and the conditions included a 15 kV electric potential and a 20 nA beam current. Natural minerals [36] were used as standards. To model the stability conditions (pressure, temperature, and fluid composition) of the vein-filling laumontite, the THERIAK-DOMINO thermodynamic system was applied [37; 38], which calculates equilibrium mineral paragenesis for any \(P_{0}\)-\(T_{0}\) point. When modelling fluid-bearing systems, an appropriate \(T\)-\(X_{i}\) (\(P\)-\(X_{i}\)) field should be modelled instead. In this study, the \(T\)-\(X_{CO2}\) field (at constant pressure) will be applied. As input, the bulk, chemical composition of the vein-filling mineral paragenesis and an internally consistent thermodynamic database are required. In this project, the Berman [39] system, completed with data of some Ca-zeolites (laumontite, heulandite, stilbite, and wairakite), was used.