This paper presents the basic elements of a conceptual model for the development of epikarst in US mid-continent, horizontally-bedded carbonates in which flow is largely confined to secondary and tertiary porosity. The model considers the development of epikarst regimes in carbonate sequences beginning shortly after non-carbonate rocks are eroded away to expose the underlying carbonates and follows this through capture of the shallow flow by deeper dissolution conduits with reorientation of the epikarst to a more vertical form. The model does not require an underlying zone of vadose flow and in many cases considers development of such a zone to depend on the water supply provided by prior development of the epikarst. It is not claimed that all epikarsts form in the accordance with this model; rather this paper presents a viable additional model for epikarst formation under appropriate starting conditions. Factors influencing the development of epikarst are a combination of: 1) the pre-karst topography and modifications to this as the system evolves, 2) the original distribution and aperture of fractures as well as the distance and orientation of physically favorable fractures relative to potential discharge points, such as existing dissolutionally-enhanced channels with low head or nearby valleys, 3) character of soil cover as this affects percolation of water to the rock, erodability of the soil, sediment filling of conduits, and transport of sediment 4) variations in availability of dissolutionally aggressive water with time and location, and 5) low solubility layers, such as shale or chert, that promote lateral flow until a penetration point can be found. These interact to form an epikarst and deeper karst system that progressively increases its capacity both by internal improvement of its flow routes and extension into adjacent areas. The availability of water needed to promote dissolution also often has a positive feedback relationship to epikarst, in which locations of most active dissolution modify their vicinity to progressively increase capture of water, which promotes further dissolution. In early stages, lateral flow through the overlying soils and along top-of-rock must dominate the groundwater flow because the relatively intact carbonates have insufficient transmissivity to convey the available recharge through the body of the rock. Top-of-rock runnels developed by a combination of dissolution of their floors and piping erosion of their roofs would carry a significant portion of the flow. Horizontally-oriented epikarst develops with discharge to local drainage. Cutters and pinnacles, collapse-related macropores, and areas of concentrated recharge would begin to form at this stage. Initial downward propagation of this system would occur mostly due to lateral flow. Mixing corrosion could occur in sumps in these lateral flow routes when fresh, percolating rainwater mixes with older water with a higher dissolved load. Should conditions be suitable, leakage from this system promotes the migration of deeper karst conduits into the area by Ewers multi-tiered headward linking. Other sources of water may also bring in such deeper conduits. Once such deeper conduits are present, the epikarst can evolve into a more vertically oriented system, at least in the vicinity of master drains into this deeper system. Former shallow epikarst routes may then plug with sediment. In some areas, deeper systems may never develop due to unfavorable conditions. The epikarst may be the only significant system in these cases. This includes the case of poor karst formers such as interbedded shales and carbonates that may have very shallow horizontal epikarst flow paths that channel shallow subsurface flows.

Sequential time-step images acquired using nuclear magnetic resonance (NMR) show the displacement of deuterated water (D2O) by fresh water within two limestone samples characterized by a porous and permeable limestone matrix of peloids and ooids. These samples were selected because they have a macropore system representative of some parts of the eogenetic karst limestone of the Biscayne Aquifer in southeastern Florida. The macroporosity, created by the trace fossil Ophiomorpha, is principally well connected and of centimeter scale. These macropores occur in broadly continuous stratiform zones that create preferential flow layers within the Hydrogeologic units of the Biscayne. This arrangement of porosity is important because in coastal areas, it could produce a preferential pathway for salt water intrusion. Two experiments were conducted in which samples saturated with D2O were placed in acrylic chambers filled with fresh water and examined with NMR. Results reveal a substantial flux of fresh water into the matrix porosity with a simultaneous loss of D2O. Specifically, we measured rates upward of 0.001 mL/h/g of sample in static conditions, and perhaps as great as 0.07 mL/h/g of sample when fresh water continuously flows past a sample at velocities less than those found within stressed areas of the Biscayne. These experiments illustrate how fresh water and D2O, with different chemical properties, migrate within one type of matrix porosity found in the Biscayne. Furthermore, these experiments are a comparative exercise in the displacement of sea water by fresh water in the matrix of a coastal, karst aquifer since D2O has a greater density than fresh water.

Heterogeneity is a salient feature of every natural geological formation. In the past decades a large body of literature has focused on the effects of heterogeneity on flow and transport problems. These works have substantially improved the understanding of flow and transport phenomena but still fail to characterize many of the important features of an aquifer. Among them, preferential flows and solute paths, connectivity between two points of an aquifer, and interpretation of hydraulic and tracer tests in heterogeneous media are crucial points that need to be properly assessed to obtain accurate model predictions. In this context, the aim of this thesis is twofold:

· to improve the understanding of the effects of heterogeneity on flow and transport phenomena
· to provide new tools for characterizing aquifer heterogeneity

First, we start by theoretically and numerically examine the relationship between two indicators of flow and transport connectivity. The flow connectivity indicator used here is based on the time elapsed for hydraulic response in a pumping test (e.g., the storage coefficient estimated by the Cooper-Jacob method, Sest). Regarding transport, we select the estimated porosity from the observed breakthrough curve (Φ est) in a forced-gradient tracer test. Our results allow explaining the poor correlation between these two indicators, already observed numerically by Knudby and Carrera (2005).

Second, a geostatistical framework has been developed to delineate connectivity patterns using a limited and sparse number of measurements. The methodology allows conditioning the results to three types of data measured over different scales, namely: (a) travel times of convergent tracer tests, ta, (b) estimates of the storage coefficient from pumping tests interpreted using the Cooper-a Jacob method, S est, and (c) measurements of transmissivity point values, T. The ability of the methodology to properly delineate capture zones is assessed through estimations (i.e. ordinary cokriging) and sequential gaussian simulations based on different sets of measurements.


Third, a novel methodology for the interpretation of pumping tests in leaky aquifer systems, referred to as the double inflection point (DIP) method, is presented. The real advantage of the DIP method comes when it is applied with all the existing methods independently to a test in a heterogeneous aquifer. In this case each method yields parameter values that are weighted differently, and thus each method provides different information about the heterogeneity distribution. In particular, the combination of the DIP method and Hantush method is shown to lead to the identification of contrasts between the local transmissivity in the vicinity of the well and the equivalent transmissivity of the perturbed aquifer volume.

Fourth, the meaning of the hydraulic parameters estimated from pumping test performed in leaky aquifers is assessed numerically within a Monte Carlo framework. A synthetic pumping test is interpreted using three existing methods. The resulting estimated parameters are shown to be space dependent and vary with the interpretation method, since each method gives different emphasis to different parts of the timedrawdown data. Finally, we show that by combining the parameter estimates obtained from the different analysis procedures, information about the heterogeneity of the leaky aquifer system may be inferred.
Fifth, an unsaturated highly heterogeneous waste rock pile is modeled using a simple linear transfer function (TF) model. The calibration of the parametric model provides information on the characteristic time of the flow through the matrix and on the fraction of the water that, within each section, is channeled through the macropores. An analysis of the influence of the scale on the results is also provided showing that at large scales the behavior of the system tends to that of an equivalent matrix reservoir masking the effects of preferential flow.