Analytical solutions to well hydraulic problems have restrictive assumptions that often do not match real world conditions. Although numerical models more closely match reality, they either ran too slowly to be practical or lacked accuracy because of coarse grid spacing and large time steps. Advances in computer power over the last few decades now allow for accurate, fast numerical models that handle complex flow systems. The purpose of this dissertation was to develop flexible and accurate numerical modeling codes for the simulation of hydrologic tests. One of these numerical modeling codes, the Slug Test Simulator (STS), was designed for the mechanics of a single well test, or slug test. STS can handle a variety of conditions including unconfined flow, partial penetration, layered heterogeneities, and the presence of a homogeneous well skin like existing codes. This program also extends on the capabilities of earlier codes with its ability to simulate a heterogeneous skin where K can vary in both the radial and vertical directions. STS has a clear user interface, can display graphical results, and allows the user to determine hydraulic conductivity through a trial-and-error curve-matching process. Comparisons of STS to the Cooper-Bredehoeft-Papadopulos analytical solution and the Kansas Geological Survey (KGS) semi-analytical solution produced near-identical curves under a wide variety of conditions. Numerous analytical studies have shown that the well skin is an important factor in the underestimation of hydraulic conductivity in slug tests. STS allows for the exploration of the well skin issue under conditions too complex for analytical models. Model trials revealed two key discoveries: 1) if any layers within the skin have the same hydraulic conductivity as the surrounding formation, flow is concentrated within these conduits and the resultant head response approaches the case when no skin is present; and 2) the two most important properties in determining the overall influence of the skin are specific storage and skin thickness. The first discovery suggests that extensive development activities can essentially eliminate any well skin impacts. Other factors such as partial penetration, the placement of the well screen, and anisotropy play insignificant roles in resultant head responses. Recent research is focusing on alternative direct- push (DP) methodologies to determine hydrologic properties. DP offers advantages over traditional well tests, but may yield inaccurate results if the screen becomes clogged during pushing activities. The Kansas Geological Survey (KGS) developed a new DP technique, the Direct-Push Permeameter (DPP), to overcome this limitation. Existing analytical or numerical models cannot address the specialized nature of DPP tests so a second numerical modeling code, the Direct Push Permeameter Simulator (DPSS), was developed. DPPS was generated by modifying STS so both numerical codes are similar in many ways, particularly with their flexibility and accuracy. The codes differ in how they handle vertical layering, the boundary conditions at the well, and the spreadsheet interfaces. DPPS was able to produce near-identical curves in comparison to the Theis analytical solution. DPPS was also able to reasonably recreate DPP field data conducted at two sites with distinctly different media properties. The GEMS and Nauen sites had an average error of 14.2% and 3.1%, respectively between the field data and DPPS simulations.

Artificial recharge and rainwater harvesting methods are being applied for mitigating effects of groundwater depletions in severe over-drafting urban and rural situations. When the aquifer to be recharged is situated at some depth below the ground surface and topped by a semi-previous layer with a large resistance against vertical water movement, recharge wells are the most appropriate solution. Water is injected by free or forced recharge technique by maintaining constant or variable head or rate of injection in the recharge well. A review of literature, carried out in two parts, looks into the aspects and performance of the practical field applications of recharge wells all over the world in Chapter II, whereas available theoretical solutions are reviewed in chapter III. The review indicates that free recharge conditions are analysed using slug theories and mirror image type curve analysis is helpful in dealing with forced recharge cases. Many slug test and pumping test theories developed focus either on simplistic recharge conditions or homogeneous hydro-geological conditions. Also, separate developments exist in the areas of large diameter well and flow to multi-aquifer system. These developments are mainly concentrated on constant wellhead boundary conditions with no well loss. Many researchers have dealt effect of pumping on base flow numerically, but the study on the impacts of recharge on base flow has not been noticed. One more practical issue, which has not been studied, is the aquifer clogging during well injection, though related background research on filtration phenomena is comparatively well established. Analytical solution for recharge in a finite aquifer from a large diameter well under variable head is obtained in Chapter IV. Furthermore, issues of analytical solution difficulty, in the available solution with constant head boundary condition are resolved and extended using Discrete Kernel approach to variable heads. Usefulness of choosing the variable head boundary condition lies in the advantage that continuous pouring of water in to the recharge well is not a necessary condition. As well and aquifer clogging is minimum in hard rock terrains, present solution is useful for estimating the pressure heads and recharge rates in the well flooding techniques frequently used in hard rock regions. For the case of free recharge in confined aquifers, available slug test theories do not consider appropriate well storage and well loss, as these may not be significant in the case of short duration test with instantaneous slug. Also slug theories are not extendable to multi-aquifer wells. Analytical solutions are obtained for free recharge condition for both single and multiple layer aquifers in chapter V, also incorporating well loss, well storage and friction loss. Parametric studies are made to see the effect of hydro-geological parameter namely; transmissivity and storativity, on recharge rates and head buildups. Theis (1935) solution is provided with well storage effects for the entire period of recharge, using Duhamel’s convolution theorem. Comparison with Cooper et al. (1967) shows, that the present solution could be useful for long-term non-instantaneous free recharge data analysis. Relationship between diffusivity and time to decay has been developed, which is useful for aquifer parameter estimation using recharge test data. Similar improvement is feasible for other existing type curves also including leaky aquifers. Analytical solutions for free recharge with constant well loss, variable well loss and losses due to friction have been developed. Comparison indicates better solution with losses due friction, which is also a more easily measurable physical parameter as compared to other well loss constants. Free recharge solutions provide unique opportunity to estimate the recharge rates in the individual aquifers of single and multi-layered aquifer. Well bore interaction has been accounted through recharge well injecting water to multi-aquifers. Specific analytical solutions are developed for the cases of free recharge in hard rock multi-layered aquifers. Present state of the art for recharge well considers forced recharge as mirror image of the pumping test solutions, type curves of which are found more difficult to fit in to the recharge test data. Again, deviation in type curve match lies in considering well storage, well clogging and aquifer clogging effects. In chapter VI analytical forced recharge solutions are developed for constant and variable rate of injection. Mirror image Theis (1935) solution is coupled with well storage during the recharge period to improve the existing solution and make it suitable for recharge computation after comparing it with Popodopulos and Cooper (1967) solution. Well bore interaction in case of multi-layered aquifer has been considered. Similar exercises are possible with existing solutions other than Theis (1935) including those for leaky aquifers. Type curves for recharge for various diffusivity ratios have been developed. Constant and variable well loss is considered for forced recharge in single as well as multi-layered aquifer. Results say that present solutions are more accurate in terms of well storage, which has significant influence on well injection as compared to well pumping. In the case of pumping, well storage effects are dominant in the initial times, where as it effects the entire recharge cycle, also depend upon the aquifer diffusivity and the recharge column dimensions. Significant influence of well loss in case of forced well recharge has been taken care of by considering linear trend of deteriorating well condition between times dependant Walton’s well loss constant. In Chapter VII, aquifer clogging, changing with time has been analysed using numerical modelling technique and applying the results of the filtration experiments reported in the literature. Inclined initial piezometric water table condition is found effective towards observation well water level and is considered for simulation of the observation well water level of Hansol project. The methodology is transferable for analyzing other injection project also. Base flow on regional scale is affected by the location, rate of injection and number of wells. In the case of Bamnod injection well project, base flow retained in the aquifer, is reducing with the increase in the quantity of injected water. This conclusion may not always be same everywhere, however, this aspect needs to be investigated. Chapter VIII summaries and highlights the conclusions drawn out of the present research study. It has been summarized that the Chapters IV, V and VI develop analytical solutions for recharge rates under unsteady wellhead condition by coupling existing groundwater flow solution with Duhamel’s convolution theorem. It provides the well storage effects throughout the recharge cycle, which unlike in pumping cases, could be significant in recharge cases. Second foremost specific requirement for a well recharge may be the consideration of head loss. In free recharge cases friction factor per unit diameter of recharge well is found a better physically computable parameter, where as well loss constants suggested by Walton (1962) could bring the head loss effects in the developed solutions for forced recharge. Free and forced recharge solutions developed for single aquifer are further extended to multi-aquifer system with respective head loss effects and well bore interaction. This is an useful contribution owing to the fact that no multi-aquifer solution considers aquifer interactions through recharge well and equivalent single aquifer theory worked for the multi-aquifer system without head loss All the solutions in Chapters IV, V and VI are found sensitive towards well radius and could analyze recharge behavior at the well face with horizontal initial piezometric surface. Simulation of the response in an observation well situated 50 m away from the recharge well is found inappropriate with the present solution. Therefore in the Chapter VII, to solve the solution difficulty, analysis is extended for the observation well, some distant away from the recharge well face, using numerical solution technique. Heterogeneity in the flow medium between the recharge well and the observation well is considered as per the time dependant aquifer clogging, based upon theory of filtration. Recharge well in general has been considered as a technology, which would increase the groundwater storage. With a case study it is found that groundwater regime also plays a crucial role in this respect. Present thesis also provides specific solution to practical issues like; estimation of diffusivity from time to decay of recharge, friction loss in the recharge well, time variant well loss as per recharge well condition, effect of sudden pump shut down, control of injection rates against recharge well over flooding, recharge rates to individual aquifers of a multi-aquifer system and multiple well recharge options. Though the scope of the present research is confined to aquifer-aquiclude system only, it could easily be extended to various other hydro-geological setups also. Unique feature of the applied analytical solution technique lies in the flexibility of transformation between head and flux boundary conditions. This provides an opportunity to compute recharge rates and corresponding heads simultaneously with any kind of boundary conditions.

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