Spontaneous imbibition plays a very important role in the displacement mechanism of non-wetting fluid in naturally fractured reservoirs. We developed a new 2D two-phase finite element numerical model, as available commercial simulators cannot be used to model small-scale experiments with different boundary conditions as well as complex boundary conditions such as fractures and vugs. Starting with the basic equation of fluid flow, we derived the non-linear diffusion saturation equation. This equation cannot be put in weighted-integral weak variational form and hence Rayleigh-Ritz finite element method (FEM) cannot be applied. Traditionally, the way around it is to use higher order interpolation functions and use Galerkin FEM or reduce the differentiability requirement and use Mixed FEM formulation. Other FEM methods can also be used, but iterative nature of those methods makes them unsuitable for solving large-scale field problems. But if we truncate the non-linear terms and decouple the dependent variables, from the spatial as well as the temporal domains of the primary variable to solve them analytically, the non-linear FEM problem reduces to a simple weighted integral form, which can be put into its corresponding weak form. The advantage of using Rayleigh-Ritz method is that it has immediate effect on the computation time required to solve a particular problem apart from incorporating complex boundary conditions. We compared our numerical models with the analytical solution of this diffusion equation. We validated the FDM numerical model using X-Ray Tomography (CT) experimental data from the single-phase spontaneous imbibition experiment, where two simultaneously varying parameters of weight gain and CT water saturation were used and then went ahead and compared the results of FEM model to that of FDM model. A two-phase field size example was taken and results from a commercial simulator were compared to the FEM model to bring out the limitations of this approach.

Fluid flow mechanisms in a large naturally fractured heterogeneous carbonate reservoir were investigated in this manuscript. A very thin layer with high permeability that produces the majority of production from specific wells and is deemed the Super-K Zone was investigated. It is known that these zones are connected to naturally occurring fractures. Fluid flow in naturally fractured reservoirs is a very difficult mechanism to understand. To accomplish this mission, the Super-K Zone and fractures were treated as two systems. Reservoir management practices and decisions should be very carefully reviewed and executed in this dual continuum reservoir based on the results of this work. Studying this dual media flow behavior is vital for better future completion strategies and for enhanced reservoir management decisions. The reservoir geology, Super-K identification and natural fractures literature were reviewed. To understand how fluid flows in such a dual continuum reservoir, a dual permeability simulation model has been studied. Some geological and production iv data were used; however, due to unavailability of some critical values of the natural fractures, the model was assumed hypothetical. A reasonable history match was achieved and was set as a basis of the reservoir model. Several sensitivity studies were run to understand fluid flow behavior and prediction runs were executed to help make completion recommendations for future wells based on the results obtained. Conclusions and recommended completions were highlighted at the end of this research. It was realized that the natural fractures are the main source of premature water breakthrough, and the Super-K acts as a secondary cause of water channeling to the wellbore.

The use of temperature logging for identifying water flow through fractures in sedimentary rock has declined since the 1960’s and 70’s primarily because of low sensor resolution and cross-connected flow along the borehole. Although sensor resolution has improved to the order of 10-3 C for several decades, temperature logging has not experienced a notable increase in popularity. This thesis studies these and other fundamental limitations to the application of borehole temperature logging for identifying flow through fractured rock, and tests the hypothesis that the limitations can be overcome, presents new methods for accomplishing that goal, and increases the applicability of the technology. Although some conventional open-hole testing (e.g. flow meters) rely on vertical cross-connected flow in the borehole annulus to identify transmissive fractures, the flow is recognized to both distort open-hole temperature logs and facilitate chemical cross contamination. Removable polyurethane coated nylon liners have recently been developed to seal boreholes and minimize cross-contamination. High sensitivity temperature logs collected in the stagnant water column of lined boreholes under different hydrogeologic conditions herein show the degree to which cross connected flow can mask important flow conduits and thereby distort the interpretation of which fractures control flow. Results from the lined holes consistently lead to identification of more hydraulically active fractures than the open-hole profiles and an improved qualitative ranking of their relative importance to flow consistent with contaminant distributions observed in rock core. The identification of flow in fractures with temperature logs depends on the presence of a temperature contrast between the water and the rock matrix to create an aberration in the otherwise gradually varying profile. Atmospherically driven thermal disequilibrium commonly only extends several tens of meters from surface and dissipates with depth, making temperatures logs a variable assessment of flow that is depth limited to the heterothermic zone. The active line source (ALS) method, a series of temperature logs measured before and within a day after the water column of a lined borehole is placed into thermal disequilibrium with the broader rock mass with a heating cable, is shown to provide two advantages. First, the method eliminates the depth limitation allowing flow zones to be identified below the hetro-homothermic boundary and second, the qualitative assessment of ambient water flow in fractures is improved throughout the test interval. The identification of the flow conduits is supported by the combined evidence from visual inspection of core, rock contamination profiles, acoustic televiewer logs and tests for hydraulic conductivity using straddle packers. A new device, the thermal vector probe (TVP) is presented. It measures the temperature of the borehole fluid with four high sensitivity temperature sensors arranged in a tetrahedral pattern which is orientated using three directional magnetometers. Based on these, the total thermal gradient, its horizontal and vertical components as well as the direction and inclination are determined, typically at less than 0.01m intervals. Comparison of TVP data collected in lined boreholes under ambient conditions (thermal and hydraulic) as well during thermal recovery after ALS heating demonstrate the reproducibility of the results and superior characterization of thermal aberrations indicative of flow relative to single sensor temperature data. A detailed comparison of subdivisions in the thermal field to the vertical changes in the hydraulic gradient measured from three nearby high detail (12-14 port) multi-level installations demonstrates the interrelationship between hydraulic and thermal fields and thereby the potential benefit of the TVP in hydrogeologic investigations. Developing confidence in the use of both the TVP and ALS techniques in lined holes relies on demonstrating the reproducibility of results, consistency with observations from other technologies, and numerical simulation. Comparisons of field data with highly detailed numerical simulations using the program SMOKER shows that the influence of water flow in a fracture around a lined borehole on the temperature patterns is complex and factors such as convection likely influence the shape of the thermal aberrations observed. Model results suggest that the temperature aberrations are related to the volumetric water flow, a distinct lower resolution limit exists (approximately 5.6x10-7 m3/sec per metre across the fracture, m2/s), and although flow above 10-4 m2/s is readily detectable, prospects for quantification of higher flows are poor. Some field data indicate the numerically determined lower limit is conservative and the details of the limit require additional study. The aspects of temperature logging historically limiting applicability for detecting and comparing flow through discrete or groups of fractures in rock are hereby better understood and consistently overcome. The high level of detail achieved in the data highlights the complexity of the system and offers opportunities for further refinement. The TVP and ALS technique applied in a lined borehole promise both new insights into, and potential for quantification of ambient groundwater flow through fractures in rock.

Two factorsrole duality and school sizeimpact teaching principals abilities to fulfill their roles and responsibilities. Principals with significant teaching loads experience role duality a situation in which one person fills two distinct roles. Teaching principals experience role tension and conflicts between professional teaching concerns, leadership demands and management issues. Further tensions are created when policymakers demands fail to recognize complexities around the roles of a teaching principal working in a unique context (Dunning, 1993; Wilson & McPake, 2000). Specifically, though the tensions of role duality are known to be more challenging in small schools, exceptionally small schools are a different context altogether. My autoethnographic study examined the complexity of my teaching principals role in an exceptionally small rural school. It was guided by a central question: How does the context of an exceptionally small, rural school impact upon a teaching principal's role(s)? Sub questions included: (a) How do stakeholder expectations (school staff, community, division, Ministry) impact a teaching principals roles and responsibilities in an exceptionally small rural school? and (b) What challenges and opportunities does a teaching principal face in an exceptionally small rural school? Documentation from two daily personal journals and my what I do log during the 2009 2010 school year provided research data. My analysis focused on three themes: fractured roles, capacity to meet expectations and establishing relationships. This study added to current research rich narratives describing the impact of an exceptionally small school on a teaching principals role.

Elemental sulphur (S0) is produced from processing bitumen from the oil sands region, Alberta. Long term storage of this S0 is under consideration. The objective of the current study was to determine the controls on water migration in variably saturated S0 blocks. Based on visual observations of S0 blocks, they were characterized as a hydrophobic fractured porous media. Thus, measurements of the hydraulic characteristics, including porosity (n) and hydraulic conductivity (K) of the matrix and the fractured media, were undertaken. These data were used to create characteristic relationships of unsaturated K (Kunsat) and volumetric moisture content (è) change with change in positive injection pressure (Ø).<p>Analyses showed that the mean total matrix n (nm) was 0.094 ± 0.035 (n = 280), the mean n available for water migration (na) was 0.065 ± 0.044 (n = 8) and the mean (geometric) K for the matrix was 2.0 x 10-6 ± 2.1 x 10-6 ms-1. In the case of vertical fractures, the aperture frequencies were measured to be 2.5, 10.0 and 21.0 m-1 for fractures with apertures > 1.4, 1.4 to 0.6 and < 0.6 mm respectively while the frequency of horizontal fractures, were measured to be 1.7 and 3.7 m-1 for with apertures > 1.4, and < 1.4 mm respectively. The fracture n (nf) was determined to be 0.0135. è Ø relationships were determined for both the fractured and non fractured media. From these plots, water entry values of 9 mm and 1 m were determined for the fracture pore space and the matrix pore space, respectively.<p>Simulations of packer tests resulted in a bulk saturated K (Kb) values ranging from 8.5 x 10-5 to 2 x 10-4 ms-1 above 9 m depth and 3 x 10-6 to 1.5 x 10-5 ms-1 below 9 m depth. Coupled Kunsat Ø and è Ø relationships were used to conceptually describe water migration in S0 blocks under different precipitation and mounding conditions. These plots also showed that the Kb is dominated by the fractures.

Elemental sulphur (S0) is produced from processing bitumen from the oil sands region, Alberta. Long term storage of this S0 is under consideration. The objective of the current study was to determine the controls on water migration in variably saturated S0 blocks. Based on visual observations of S0 blocks, they were characterized as a hydrophobic fractured porous media. Thus, measurements of the hydraulic characteristics, including porosity (n) and hydraulic conductivity (K) of the matrix and the fractured media, were undertaken. These data were used to create characteristic relationships of unsaturated K (Kunsat) and volumetric moisture content (è) change with change in positive injection pressure (Ø).<p>Analyses showed that the mean total matrix n (nm) was 0.094 ± 0.035 (n = 280), the mean n available for water migration (na) was 0.065 ± 0.044 (n = 8) and the mean (geometric) K for the matrix was 2.0 x 10-6 ± 2.1 x 10-6 ms-1. In the case of vertical fractures, the aperture frequencies were measured to be 2.5, 10.0 and 21.0 m-1 for fractures with apertures > 1.4, 1.4 to 0.6 and < 0.6 mm respectively while the frequency of horizontal fractures, were measured to be 1.7 and 3.7 m-1 for with apertures > 1.4, and < 1.4 mm respectively. The fracture n (nf) was determined to be 0.0135. è Ø relationships were determined for both the fractured and non fractured media. From these plots, water entry values of 9 mm and 1 m were determined for the fracture pore space and the matrix pore space, respectively.<p>Simulations of packer tests resulted in a bulk saturated K (Kb) values ranging from 8.5 x 10-5 to 2 x 10-4 ms-1 above 9 m depth and 3 x 10-6 to 1.5 x 10-5 ms-1 below 9 m depth. Coupled Kunsat Ø and è Ø relationships were used to conceptually describe water migration in S0 blocks under different precipitation and mounding conditions. These plots also showed that the Kb is dominated by the fractures.

Two factorsrole duality and school sizeimpact teaching principals abilities to fulfill their roles and responsibilities. Principals with significant teaching loads experience role duality a situation in which one person fills two distinct roles. Teaching principals experience role tension and conflicts between professional teaching concerns, leadership demands and management issues. Further tensions are created when policymakers demands fail to recognize complexities around the roles of a teaching principal working in a unique context (Dunning, 1993; Wilson & McPake, 2000). Specifically, though the tensions of role duality are known to be more challenging in small schools, exceptionally small schools are a different context altogether. My autoethnographic study examined the complexity of my teaching principals role in an exceptionally small rural school. It was guided by a central question: How does the context of an exceptionally small, rural school impact upon a teaching principal's role(s)? Sub questions included: (a) How do stakeholder expectations (school staff, community, division, Ministry) impact a teaching principals roles and responsibilities in an exceptionally small rural school? and (b) What challenges and opportunities does a teaching principal face in an exceptionally small rural school? Documentation from two daily personal journals and my what I do log during the 2009 2010 school year provided research data. My analysis focused on three themes: fractured roles, capacity to meet expectations and establishing relationships. This study added to current research rich narratives describing the impact of an exceptionally small school on a teaching principals role.

Fluid flow mechanisms in a large naturally fractured heterogeneous carbonate reservoir were investigated in this manuscript. A very thin layer with high permeability that produces the majority of production from specific wells and is deemed the Super-K Zone was investigated. It is known that these zones are connected to naturally occurring fractures. Fluid flow in naturally fractured reservoirs is a very difficult mechanism to understand. To accomplish this mission, the Super-K Zone and fractures were treated as two systems. Reservoir management practices and decisions should be very carefully reviewed and executed in this dual continuum reservoir based on the results of this work. Studying this dual media flow behavior is vital for better future completion strategies and for enhanced reservoir management decisions. The reservoir geology, Super-K identification and natural fractures literature were reviewed. To understand how fluid flows in such a dual continuum reservoir, a dual permeability simulation model has been studied. Some geological and production iv data were used; however, due to unavailability of some critical values of the natural fractures, the model was assumed hypothetical. A reasonable history match was achieved and was set as a basis of the reservoir model. Several sensitivity studies were run to understand fluid flow behavior and prediction runs were executed to help make completion recommendations for future wells based on the results obtained. Conclusions and recommended completions were highlighted at the end of this research. It was realized that the natural fractures are the main source of premature water breakthrough, and the Super-K acts as a secondary cause of water channeling to the wellbore.

Fractured reservoirs have been traditionally idealized using dual-porosity models. In these models, all matrix and fractures systems have identical properties. However, it is not uncommon for naturally fractured reservoirs to have orthogonal fractures with different properties. In addition, for hydraulically fractured reservoirs that have preexisting natural fractures such as shale gas reservoirs, it is almost certain that these types of fractures are present. Therefore, a triple-porosity (dual-fracture) model is developed in this work for characterizing fractured reservoirs with different fractures properties. The model consists of three contiguous porous media: the matrix, less permeable micro-fractures and more permeable macro-fractures. Only the macro-fractures produce to the well while they are fed by the micro-fractures only. Consequently, the matrix feeds the micro-fractures only. Therefore, the flow is sequential from one medium to the other. Four sub-models are derived based on the interporosity flow assumption between adjacent media, i.e., pseudosteady state or transient flow assumption. These are fully transient flow model (Model 1), fully pseudosteady state flow model (Model 4) and two mixed flow models (Model 2 and 3). The solutions were mainly derived for linear flow which makes this model the first triple-porosity model for linear reservoirs. In addition, the Laplace domain solutions are also new and have not been presented in the literature before in this form. Model 1 is used to analyze fractured shale gas horizontal wells. Non-linear regression using least absolute value method is used to match field data, mainly gas rate. Once a match is achieved, the well model is completely described. Consequently, original gas in place (OGIP) can be estimated and well future performance can be forecasted.

Hydraulic fracturing has recently been the completion of choice for most tight gas bearing formations. It has proven successful to produce these formations in a commercial manner. However, some considerations have to be taken into account to design an optimum stimulation treatment that leads to the maximum possible productivity. These considerations include, but not limited to, non-Darcy flow and multiphase flow effects inside the fracture. These effects reduce the fracture conductivity significantly. Failing to account for that results in overestimating the deliverability of the well and, consequently, to designing a fracture treatment that is not optimum. In this work a thorough investigation of non-Darcy flow and multi-phase flow effects on the productivity of hydraulically fractured wells is conducted and an optimum fracture design is proposed for a tight gas formation in south Texas using the Unified Fracture Design (UFD) Technique to compensate for the mentioned effects by calculating the effective fracture permeability in an iterative way. Incorporating non-Darcy effects results in an optimum fracture that is shorter and wider than the fracture when only Darcy calculations are considered. That leads to a loss of production of 5, 18 percent due to dry and multiphase non-Darcy flow effects respectively. A comparison between the UFD and 3D simulators is also done to point out the differences in terms of methodology and results. Since UFD incorporated the maximum dimensionless productivity index in the fracture dimensions design, unlike 3D simulators, it can be concluded that using UFD to design the fracture treatment and then use the most important fracture parameters outputs (half length and CfDopt) as inputs in the simulators is a recommended approach.