# Software for Estimation of Stochastic Model Parameters for a Compacting Reservoir
## 5 Discussion and Conclusions  
The obtained fitting of the deformation field profile to the modeled values differs along the profile (Figure 7). The biggest discrepancy was observed in the initial part of the cross-section in the Kocki fault area (Figure 5), which constitutes a natural hydrogeological window for waters from the Jurassic horizon. This zone is responsible for the asymmetric shape of the depression cone (Figure 6), which may cause overestimation of vertical deformations in that area. The maximum values of the observed and modeled subsidence are similar, i.e., about 0.56 m, and they can be found in the mine shaft area where the aquifer depression was biggest. The modeled values are underestimated in the section between 7.5 km and 9.5 km of the profile. This is the second shaft drainage area of considerable depression in the reservoir. Due to the lack of piezometric boreholes in that area, the assumed pressure gradient may significantly differ from the real values, which are unknown. This could lead to underestimation of the observed vertical deformation values. The overestimation of modeled values in the eastern part of the mining area may stem from incomplete information about pressure gradients in that part. In the last part of the subsidence trough, where the modeled and observed values are similar, a piezometric well is located. The proposed method of parameter determination requires the establishment of reservoir elements with the ascribed geometrical information on \(\Delta p\) and \(H\). The pressure gradient in a single element will affect the attained calculation accuracy. An example of a deposit divided into uniform elements with square bases is presented in Section 4. The possibility of using elements with various base sizes is very useful. As shown in the example (Figure 6), this is purposeful, especially in an area of strong local variability of pressure depletion (\(\Delta p\)). Such a solution is possible, and the presented software assumes that reservoir elements may vary in size. However, the proposed model does not assume chemical interactions such as non-equilibrated brines [48]. If it were possible to express the chemical interactions in space (as compaction in Equations (1) and (2)), the model could be expanded. The chemical interactions of rock weakening or chemical effects could be added to the model, and this could be a direction for future research. The presented SubCom v1.0 software may be used to determine the parameters of a prediction model for areas where groundwater, oil, and gas are extracted. It applies the Scilab open-source environment, in which the graphical interface features of SubCom v1.0 software were created. This software may be used in all locations where a compaction process has been observed. For the sake of calculation, the reservoir has to be divided into reservoir elements which are ascribed a depth and pressure decrease. Initial data for the surface includes subsidence measurement results, which can  
Figure 7: Fitting the model to the A-A deviating trough profile with a plot of differences. be obtained with methods such as classic leveling surveys, GNSS, or InSAR. The proposed solution assumes the interpretation of results based on the subsidence trough profile. However, the presented algorithm also allows calculations to be made in a grid of distributed points (3D); although this is not in the scope of the present paper, it may be a starting point for further work on the software and development by users. The source-code for SubCom v1.0 is available from [[https://github.com/wwwitkow/SubCom](https://github.com/wwwitkow/SubCom)]([https://github.com/wwwitkow/SubCom](https://github.com/wwwitkow/SubCom)). Research concept, W.T.W. and R.H.; methodology, W.T.W. and R.H.; software, W.T.W., validation, W.T.W., writing--original draft preparation, W.T.W. ; writing--review and editing, R.H. All authors have read and agreed to the published version of the manuscript.