Accurately characterizing the distribution of hydraulic parameters is critical for any site investigation, particularly those dealing with solute or contaminant transport. Despite the fact that many tools are currently available for both characterizing (e.g. soil core analysis, slug and pumping tests, direct push techniques, etc.,) and modeling (e.g. geostatistical interpolators, construction of geological models, etc.,) heterogeneous aquifers, this still remains a challenge. In this thesis, hydraulic tomography (HT), a recently developed tool for characterizing and modeling heterogeneous aquifers is evaluated under both laboratory and field conditions. To date, both steady state hydraulic tomography (SSHT) and transient hydraulic tomography (THT) have been demonstrated at the laboratory scale, however, only SSHT has been rigorously validated through the prediction of independent tests (those not used for estimating the distribution of hydraulic parameters), and comparison to other characterization/modeling techniques. Additionally, laboratory and field validations of HT using comparisons other than the prediction of independent pumping tests (e.g. prediction of solute transport) are lacking. The laboratory studies performed in this thesis address some of these gaps by: i) rigorously validating THT through the prediction of independent pumping tests, and comparison to other characterization techniques; ii) using HT estimated parameter distributions to predict the migration of a conservative tracer in a heterogeneous sandbox aquifer; and, iii) predicting the flow of water to a well in a heterogeneous, unconfined, sandbox aquifer. For all three cases, HT was compared to more traditional characterization/modeling approaches, such as; the calculation of homogeneous effective parameters, kriging of point data, or the creation and calibration of a geological model. For each study the performance of HT was superior to the other characterization methods. These laboratory experiments demonstrated both the ability of HT to map aquifer heterogeneity, and the critical need for accurately understanding heterogeneity in order to make accurate predictions about a system. In this regard, HT is a powerful tool at the laboratory scale where the forcing functions (i.e., boundary conditions, flow rates, etc.,) are accurately known. While several field scale HT studies have been reported in the literature, none attempt to validate 3D THT through the prediction of independent pumping tests, or through comparison to known geology. The application of THT at the field scale presents unique challenges not faced in the laboratory setting. For example, boundary conditions are not accurately known and it is not possible to instrument a field site as densely as a sandbox aquifer. In the field studies conducted as part of this thesis, THT was validated by comparing estimated hydraulic parameter fields to known geology (borehole data) and simulating 9 pumping tests that were performed at the site. The THT analysis was able to capture the salient features of the aquifer (the presence of a double aquifer separated by an aquitard), and was able to reasonably reproduce most of the pumping tests. For comparison purposes, a homogeneous model and three additional heterogeneous models were created: i) permeameter estimates of hydraulic conductivity from soil cores were interpolated via kriging; ii) the transition probability/Markov Chain approach was used to interpret material classifications from borehole logs; and iii) a stratigraphic model was created and calibrated to pumping test data. Of these cases, THT and the calibrated stratigraphic model performed best, with THT performing slightly better. This work indicates that it is possible to interpret multiple pumping tests using hydraulic tomography to estimate the 3D distribution of hydraulic parameters in heterogeneous aquifer systems. Also, since hydraulic tomography does not require the collection and analysis of a large number of point samples, it is likely comparable in cost to other characterization/modeling approaches.

Artificial drainage networks established throughout peatlands during the peat extraction process often remain active following abandonment, maintaining a water table relatively far from the surface of the peat and hindering the survival and reestablishment of Sphagnum mosses. Since cutover peatlands are characterized by low (negative) soil water pressures, sufficient internal water storage and balanced water fluxes are critical for the physiological function of spontaneously regenerated Sphagnum mosses. The relative importance of water exchanges between spontaneously regenerated Sphagnum moss cushions and their surroundings are addressed through investigation of the sensitivity of moss moisture dynamics to a range of environmental variables. Precipitation waters are poorly retained within the cushions, which indicated that rain event water can only be relied upon by the mosses for a short period of time. An imbalance between water inputs and losses from moss cushions identified that additional (small) sources of water, such as dewfall and distillation, are potentially important for physiological processes under dry conditions, common in disturbed peatland ecosystems. As an initial restoration effort, rewetting of the peatland by blocking drainage ditches consequently reduced the runoff efficiency and caused the site-average water table to rise by 32 cm. Higher water tables and a blocked drainage network created conditions more favourable for Sphagnum survival through increasing the moisture content and soil-water pressures within the remnant peat deposit. The hydrologic connectivity between moss cushions and the remnant peat was strong when conditions were wet and the water table was within 30 cm of the surface of the cutover peat but weakened as conditions became drier, as reflected by weakened upward hydraulic gradients in the unsaturated zone below the moss cushions. Runoff variability increased following rewetting, and displayed a greater dependence upon antecedent conditions (capacity to retain additional water on-site) and event-based precipitation dynamics. Evapotranspiration rates were 25% higher following rewetting (3.6 mm day-1) compared to pre-restoration ET rates of 2.7 mm day-1. Total storage changes were restricted following rewetting, as a factor of the reduced runoff losses limiting water table drawdown, thereby constraining peat compression and preventing undue drying of the unsaturated zone. Changes to the system hydrology following rewetting of the peatland by blocking drainage ditches created conditions more favourable for Sphagnum survival through increasing the moisture content and soil-water pressures within the remnant peat deposit; although restoration efforts should aim to constrain water table fluctuations to within the upper 30 cm.

A digital position servo controller for the Electro-hydraulic system is proposed based on robust integral structure control (RISC) scheme. The main aims of the proposed system are to enhance the performance while driving the servo machine rod to track a sine-wave or step command. According to the state feed-back theorems, a simplified plant model of the Electro-hydraulic is conducted. Close-loop characteristic function of the control system will be assigned on the stable plane to ensure the state variables so that it can rapidly converge to stable point. The design steps and theoretical analysis will be described in detail. Both simulation and experimental results are shown for proving the performance.

One of the most critical parameters in the success of a hydraulic fracturing treatment is to have sufficiently high fracture conductivity. Unbroken polymers can cause permeability impairment in the proppant pack and/or in the matrix along the fracture face. The objectives of this research project were to design and set up an experimental apparatus for dynamic fracture conductivity testing and to create a fracture conductivity test workflow standard. This entirely new dynamic fracture conductivity measurement will be used to perform extensive experiments to study fracturing fluid cleanup characteristics and investigate damage resulting from unbroken polymer gel in the proppant pack. The dynamic fracture conductivity experiment comprises two parts: pumping fracturing fluid into the cell and measuring proppant pack conductivity. I carefully designed the hydraulic fracturing laboratory to provide appropriate scaling of the field conditions experimentally. The specifications for each apparatus were carefully considered with flexibility for further studies and the capability of each apparatus was defined. I generated comprehensive experimental procedures for each experiment stage. By following the procedure, the experiment can run smoothly. Most of dry runs and experiments performed with sandstone were successful.

The distributions of pore pressure and stresses around a fracture are of interest in conventional hydraulic fracturing operations, fracturing during water-flooding of petroleum reservoirs, shale gas, and injection/extraction operations in a geothermal reservoir. During the operations, the pore pressure will increase with fluid injection into the fracture and leak off to surround the formation. The pore pressure increase will induce the stress variations around the fracture surface. This can cause the slip of weakness planes in the formation and cause the variation of the permeability in the reservoir. Therefore, the investigation on the pore pressure and stress variations around a hydraulic fracture in petroleum and geothermal reservoirs has practical applications. The stress and pore pressure fields around a fracture are affected by: poroelastic, thermoelastic phenomena as well as by fracture opening under the combined action of applied pressure and in-situ stress. In our study, we built up two models. One is a model (WFPSD model) of water-flood induced fracturing from a single well in an infinite reservoir. WFPSD model calculates the length of a water flood fracture and the extent of the cooled and flooded zones. The second model (FracJStim model) calculates the stress and pore pressure distribution around a fracture of a given length under the action of applied internal pressure and in-situ stresses as well as their variation due to cooling and pore pressure changes. In our FracJStim model, the Structural Permeability Diagram is used to estimate the required additional pore pressure to reactivate the joints in the rock formations of the reservoir. By estimating the failed reservoir volume and comparing with the actual stimulated reservoir volume, the enhanced reservoir permeability in the stimulated zone can be estimated. In our research, the traditional two dimensional hydraulic fracturing propagation models are reviewed, the propagation and recession of a poroelastic PKN hydraulic fracturing model are studied, and the pore pressure and stress distributions around a hydraulically induced fracture are calculated and plotted at a specific time. The pore pressure and stress distributions are used to estimate the failure potentials of the joints in rock formations around the hydraulic fracture. The joint slips and rock failure result in permeability change which can be calculated under certain conditions. As a case study and verification step, the failure of rock mass around a hydraulic fracture for the stimulation of Barnett Shale is considered. With the simulations using our models, the pore pressure and poro-induced stresses around a hydraulic fracture are elliptically distributed near the fracture. From the case study on Barnett Shale, the required additional pore pressure is about 0.06 psi/ft. With the given treatment pressure, the enhanced permeability after the stimulation of hydraulic fracture is calculated and plotted. And the results can be verified by previous work by Palmer, Moschovidis and Cameron in 2007.

Multiple transverse fracturing along a horizontal well is a relatively new technology that is designed to increase well productivity by increasing the contact between the reservoir and the wellbore. For multiple transverse fractures, the performance of the well system is determined by three aspects: the inflow from the reservoir to the fracture, the flow from the fracture to the wellbore, and the inflow from the reservoir to the horizontal wellbore. These three aspects influence each other and combined, influence the wellbore outflow. In this study, we develop a model to effectively formulate the inter-relationships of a multi-fracture system. This model includes a reservoir model and a wellbore model. The reservoir model is established to calculate both independent and inter-fracture productivity index to quantify the contribution from all fractures on pressure drop of each fracture, by using the source functions to solve the single-phase gas reservoir flow model. The wellbore model is used to calculate the pressure distribution along the wellbore and the relationship of pressure between neighboring fractures, based on the basic pressure drop model derived from the mechanical energy balance. A set of equations with exactly the same number of fractures will be formed to model the system by integrating the two models. Because the equations are nonlinear, iteration method is used to solve them. With our integrated reservoir and wellbore model, we conduct a field study to find the best strategy to develop the field by hydraulic fracturing. The influence of reservoir size, horizontal and vertical permeability, well placement, and fracture orientation, type (longitudinal and transverse), number and distribution are completely examined in this study. For any specific field, a rigorous step-by-step procedure is proposed to optimize the field.

Hydraulic fracturing of a naturally-fractured reservoir is a challenge for industry, as fractures can have complex growth patterns when propagating in systems of natural fractures in the reservoir. Fracture propagation near a natural fracture (NF) considering interaction between a hydraulic fracture (HF) and a pre-existing NF, has been investigated comprehensively using a two dimensional Displacement Discontinuity Method (DDM) Model in this thesis. The rock is first considered as an elastic impermeable medium (with no leakoff), and then the effects of pore pressure change as a result of leakoff of fracturing fluid are considered. A uniform pressure fluid model and a Newtonian fluid flow model are used to calculate the fluid flow, fluid pressure and width distribution along the fracture. Joint elements are implemented to describe different NF contact modes (stick, slip, and open mode). The structural criterion is used for predicting the direction and mode of fracture propagation. The numerical model was used to first examine the mechanical response of the NF to predict potential reactivation of the NF and the resultant probable location for fracture re-initiation. Results demonstrate that: 1) Before the HF reaches a NF, the possibility of fracture re-initiation across the NF and with an offset is enhanced when the NF has weaker interfaces; 2) During the stage of fluid infiltration along the NF, a maximum tensile stress peak can be generated at the end of the opening zone along the NF ahead of the fluid front; 3) Poroelastic effects, arising from fluid diffusion into the rock deformation can induce closure and compressive stress at the center of the NF ahead of the HF tip before HF arrival. Upon coalescence when fluid flows along the NF, the poroelastic effects tend to reduce the value of the HF aperture and this decreases the tension peak and the possibility of fracture re-initiation with time. Next, HF trajectories near a NF were examined prior to coalesce with the NF using different joint, rock and fluid properties. Our analysis shows that: 1) Hydraulic fracture trajectories near a NF may bend and deviate from the direction of the maximum horizontal stress when using a joint model that includes initial joint deformation; 2) Hydraulic fractures propagating with higher injection rate or fracturing fluid of higher viscosity propagate longer distance when turning to the direction of maximum horizontal stress; 3) Fracture trajectories are less dependent on injection rate or fluid viscosity when using a joint model that includes initial joint deformation; whereas, they are more dominated by injection rate and fluid viscosity when using a joint model that excludes initial joint deformation.

This thesis presents a methodology based on Proppant Number approach for optimal fracture treatment design of natural gas wells considering non-Darcy flow effects in the design process. Closure stress is taken into account, by default, because it is the first factor decreasing propped pack permeability at in-situ conditions. Gel damage was also considered in order to evaluate the impact of incorporating more damaging factors on ultimate well performance and optimal geometry. Effective fracture permeability and optimal fracture geometry are calculated through an iterative process. This approach was implemented in a spreadsheet. Non-Darcy flow is described by the β factor. All β factor correlations available in the literature were evaluated. It is recommended to use the correlation developed specifically for the given type of proppant and mesh size, if available. Otherwise, the Pursell et al. or the Martins et al. equations are recommended as across the board reliable correlations for predicting non-Darcy flow effects in the propped pack. The proposed methodology was implemented in the design of 11 fracture treatments of 3 natural tight gas wells in South Texas. Results show that optimal fracture design might increase expected production in 9.64 MMscf with respect to design that assumes Darcy flow through the propped pack. The basic finding is that for a given amount of proppant shorter and wider fractures compensate the non-Darcy and/or gel damage effect. Dynamic programming technique was implemented in design of multistage fractures for one of the wells under study for maximizing total gas production. Results show it is a powerful and simple technique for this application. It is recommended to expand its use in multistage fracture designs.

Many oceanographers have postulated that internal wave form inversion would take place at the turning point where the thickness of the upper and bottom layer are equal in a stratified two-layer fluid system. This implies that an internal wave of depression may convert into elevation as the wave propagates over a continental margin comprising continental slope and shelf. Laboratory experiments were conducted on the propagation of a depression ISW over a trapezoidal obstacle in a stratified two-layer fresh/brine water system in a steel framed wave tank of 12m long with cross section of 0.7m high by 0.5m wide. The relative difference in water depth between the upper and lower layer and the initial ISW amplitude were the main controlling parameters, among others. The water depth in the stratified two-layer system on the horizontal plateau of the trapezoid obstacle fell into one of the following case: (1) the upper layer larger than lower (H1>¢Ö2'); or (2) equal depth in the upper and lower layer (H1=¢Ö2'); or (3) the upper layer less than lower layer (H1<¢Ö2'). In addition of the depth ratio, the difference in the length of the horizontal plateau and the thickness of the phycnocline above if were also parameters affecting the outcome of the experiments. In these experiments, three different type of the height and length of the trapezoidal obstacle were used, including long (4.8x0.37m), medium (1x0.35m) and short (0.5x0.35m) types. A full account on the characteristics of the ISW evolution observed during this experimental study is presented in this thesis. As an ISW propagated on the fronting slope, were run-down, vortex motion, internal hydraulic jump (IHJ) and run-up were occurred. Once the wave passed the turning point (where the depth of upper and lower layer equal), the wave form became elevation on the plateau above the obstacle. Based on the laboratory data available, the effect on internal wave evolution can be evaluated by the relative fluid thickness (H1/¢Ö2') on the plateau. The outcome can be classified into three categories: (1) H1>¢Ö2', the relative layer thickness on the plateau unfits for depression ISW propagation and waveform behaves like elevation type; (2) H1=¢Ö2', wave boluses containing mixed fluid propagating on the plateau after breaking on the slope; (3) H1<¢Ö2', ISW propagated over trapezoidal obstacle subjected to shoaling and viscosity effect, without change in waveform. As a depression ISW propagated over the variable length of the plateau, another important factor affecting the intensity of the internal hydraulic jump was the water volume drawn from the plateau. In the case of long horizontal plateau, the interaction range was large, and the IHJ was strong. Consequently, the thickness of the increased which caused the IHJ to move upward along the fronting slope. However, the amplitude and phase speed of the resulting internal wave decreased as if propagated further.

Dissertation (Ph.D.)--University of Toledo, 2009. / Typescript. "Submitted as partial fulfillment of the requirements for the Doctor of Philosophy degree in Mechanical Engineering." Bibliography: leaves 203-209.