Development of a modular geo-statistical framework for the evaluation of novel aquifer analysis techniques

Groundwater is an important natural resource. A quarter of the total water supply in Germany is groundwater and more than 70% of the local drinking water is obtained from it. Groundwater supports agricultural activities, contributes to industrial processes, and acts as a natural filter, reducing pollutants, and improving water quality. However, this vital resource is increasingly threatened by contamination from these agricultural and industrial sources as well as persistent droughts and is therefore of great interest to environmental research. Hydrogeology faces two main challenges: first, there is only sparse information on key quantities to characterize subsurface processes such as porosity or permeability, which are often limited in both spatial and temporal resolution. Second, the heterogeneous distribution of these properties, caused by complex geological processes, creates large variability from local to regional scales. Together, these factors complicate the accurate assessment of subsurface flow. An approach to supplement the sparse point measurements of these quantities is to perform hydrological tests that capture the response behavior of an aquifer under specific conditions, such as pumping tests in groundwater wells. This thesis presents an integrated framework for the analysis of groundwater flow in heterogeneous aquifers by combining advanced geo‐statistical methods, (semi) analytical solutions, and numerical simulations to improve the interpretation of pumping test data. Building on classical formulations such as Thiem's and Theis' solutions for pumping tests in homogeneous porous media, we derived the extended Generalized Radial Flow (eGRF) model, which can be applied to effective transmissivity representations and allows non-integer flow dimensions. We used this eGRF model on a set of effective transmissivity formulations that integrate several characteristics of heterogeneity to demonstrate its capabilities. Furthermore, we applied type curves derived from the eGRF model to estimate parameters of heterogeneity at two hydrological field sites, validating its practical applicability. The heterogeneity of the subsurface is characterized using geo-statistical parameters derived from two-point statistics, specifically the mean, variance, and correlation length of the logarithmic hydraulic conductivity, as well as a shape parameter in the variogram function to explicitly account for field roughness. In particular, we utilized a truncated power-law variogram framework to introduce an integral variogram function as a superposition of simpler models that accounts for sub-scale variability of the transmissivity distribution. From this we derived a novel formulation for effective transmissivity that can be used with the above-mentioned eGRF model. The results show that the effective drawdown in persistent (rather smooth) fields is only slightly affected by roughness, while in antipersistent (rather rough) fields the head response quickly converges towards the classical Thiem and Theis solutions for increasing roughness. This fills a long-standing gap in the literature on the effect of roughness on pumping test data. To validate these theoretical developments and facilitate their practical application, we have developed a modular open source software suite written in Python that integrates welltestpy for pumping test analysis, AnaFlow for (semi) analytical groundwater flow solutions, ogs5py for finite element groundwater flow simulations, and GSTools as a geo-statistical toolbox for random field generation and variogram analysis. This comprehensive virtual laboratory enables automated workflows from data processing and parameter estimation to ensemble simulation, thereby reducing uncertainty in aquifer characterization and providing robust tools for groundwater management. By performing ensemble simulations of pumping tests on well-specified transmissivity fields, we were able to prove the correctness of the eGRF model, the effective integral transmissivity function, and the implemented estimation routines to justify the conclusions drawn. In addition, a special database for geo-statistical parameters was compiled through extensive literature research, in which typical value ranges for various geological conditions are cataloged. These parameters, such as correlation lengths, variances, and anisotropy ratios, provide a solid reference for the initialization and calibration of hydrogeological models. By systematically processing this information, the dissertation not only ensures reproducibility but also provides a practical resource for both researchers and practitioners who wish to integrate sound geo-statistical findings into their own groundwater investigations. Overall, our work bridges the gap between theoretical geo-statistics and practical hydrogeological applications, offering a significant advancement in the understanding and modeling of subsurface flow in complex, heterogeneous media.