The use of Discrete Fracture Networks (DFNs) is becoming increasingly common in geomechanical practice in addition to their continuing role in hydrogeology. These models can serve as useful tools for estimating interconnectedness of fractures, leading to estimates of probable block sizes and shapes for a set of input parameters. However, the development of these models is reliant on assumptions made about collected field data and while constructing the model themselves. The implications of these biases and assumptions are not well documented. This work investigates the variables involved in building a Discrete Fracture Network model in order to provide insight into the decisions and assumptions made during the modeling process. Select assumptions required within the FracMan DFN software pertaining to model selection and construction are evaluated; biases and assumptions relating to field data and how it is collected that may impact the development of DFN input parameters are investigated and limits of the effects of these models on block sizes are determined. The parameters determined to be critical in determining the overall geometry of the fracture network are ranked according to their relative importance in DFN modelling and according to the relative accuracy of each parameter. / Thesis (Master, Geological Sciences & Geological Engineering) -- Queen's University, 2014-05-30 18:00:51.384

Neural networks (NNs) are widely used to investigate the relationship among variables in complex multivariate problems. In cases of limited data, the network behavior strongly depends on factors such as the choice of network activation function and network initial weights. In this study, I investigated the use of neural networks for multivariate analysis in the case of limited data. The analysis shows that special attention should be paid when building and using NNs in cases of limited data. The linear activation function at the output nodes outperforms the sigmoidal and Gaussian functions. I found that combining network predictions gives less biased predictions and allows for the assessment of the prediction variability. The NN results, along with conventional statistical analysis, were used to examine the effects of folding, bed thickness, structural position, and lithology on the fracture properties distributions in the Lisburne Formation, folded and exposed in the northeastern Brooks Range of Alaska. Fracture data from five folds, representing different degrees of folding, were analyzed. In addition, I modeled the fracture system using the discrete fracture network approach and investigated the effects of fracture properties on the flow conductance of the system. For the Lisburne data, two major fracture sets striking north/south and east/west were studied. Results of the NNs analysis suggest that fracture spacing in both sets is similar and weakly affected by folding and that stratigraphic position and lithology have a strong effect on fracture spacing. Folding, however, has a significant effect on fracture length. In open folds, fracture lengths in both sets have similar averages and variances. As the folds tighten, both the east/west and north/south fracture lengths increase by a factor of 2 or 3 and become more variable. In tight folds, fracture length in the north/south direction is significantly larger than in the east/west direction. The difference in length between the two fracture sets creates a strong anisotropy in the reservoir. Given the same fracture density in both sets, the set with the greater length plays an important role for fluid flow, not only for flow along its principal direction but also in the orthogonal direction.

Modeling and simulation of fluid flow in subsurface fractured systems has been steadily a popular topic in petroleum industry. The huge potential hydrocarbon reserve in naturally and hydraulically fractured reservoirs has been a major stimulant for developments in this field. Although several models have found limited applications in studying fractured reservoirs, still more comprehensive models are required to be applied for practical purposes. A recently developed Embedded Discrete Fracture Model (EDFM) incorporates the advantages of two of the well-known approaches, the dual continuum and the discrete fracture models, to investigate more complex fracture geometries. In EDFM, each fracture is embedded inside the matrix grid and is discretized by the cell boundaries. This approach introduces a robust methodology to represent the fracture planes explicitly in the computational domain. As part of this research, the EDFM was implemented in two of The University of Texas in-house reservoir simulators, UTCOMP and UTGEL. The modified reservoir simulators are capable of modeling and simulation of a broad range of reservoir engineering applications in naturally and hydraulically fractured reservoirs. To validate this work, comparisons were made against a fine-grid simulation and a semi-analytical solution. Also, the results were compared for more complicated fracture geometries with the results obtained from EDFM implementation in the GPAS reservoir simulator. In all the examples, good agreements were observed. To further illustrate the application and capabilities of UTCOMP- and UTGEL-EDFM, a few case studies were presented. First, a synthetic reservoir model with a network of fractures was considered to study the impact of well placement. It was shown that considering the configuration of background fracture networks can significantly improve the well placement design and also maximize the oil recovery. Then, the capillary imbibition effect was investigated for the same reservoir models to display its effect on incremental oil recovery. Furthermore, UTCOMP-EDFM was applied for hydraulic fracturing design where the performances of a simple and a complex fracture networks were evaluated in reservoirs with different rock matrix permeabilities. Accordingly, it was shown that a complex network is an ideal design for a very low permeability reservoir, while a simple network results in higher recovery when the reservoir permeability is moderate. Finally, UTGEL-EDFM was employed to optimize a conformance control process. Different injection timings and different gel concentrations were selected for water-flooding processes and their impact on oil recovery was evaluated henceforth. / text

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Groundwater inflow is a challenge in construction of tunnels in fractured bedrocks since it affects the safety function of tunnels and leads to potential problems in the surrounding environment, such as subsidence, dropdown of the groundwater table. Quantification of groundwater inflow into the tunnel is also important for design of grouting in the construction of the tunnel. Modelling groundwater flow in fractured bedrocks currently remains a challenge. Commonly used groundwater models are based on continuum assumptions and they do not consider realistic structures of discrete fractures, which leads to high potential uncertainty in prediction of tunnel groundwater inflow. This thesis focuses on prediction of tunnel groundwater inflow, using a discreet fracture-matrix (DFM) model. The DFM model is evaluated and compared with the conventional continuum model based on Darcy’s law. This DFM model considers, in particular, multi-scale heterogeneity, e.g. fracture networks and variable fracture aperture structures. Applying this DFM model, the impact of variable fracture aperture structures on tunnel inflow is investigated through stochastic analysis. The results show that under the same boundary conditions, the traditional continuum model overestimates the inflow compared to the DFM model. The difference in equivalent permeability is 2 to 3 orders of magnitude. The sensitivity analysis shows that the discreet fracture model is sensitive to the variability of fracture aperture. The estimated equivalent permeability values by discreet fracture modelling is in the order of 5×10-6 to 1×10-7 m/s for a fracture density of 1.2 fractures per square meter. This study demonstrates that the DFM represents the more realistic features of fractured rock structures, which is useful and can be used to predict groundwater inflow in fractured rock tunnels. / Grundvatteninflöde är en utmaning vid byggnation av tunnlar i sprucken berggrund eftersom det påverkar tunnlarnas säkerhetsfunktion och leder till potentiella problem i den omgivande miljön, såsom sättningar och Grundvattennivåsänkning. Kvantifiering av grundvatteninflöde till tunneln är också viktig för utformning av injektering i tätning? byggandet av tunneln. Att modellera grundvattenflödet i sprucken berggrund är för närvarande en utmaning. Grundvattenmodeller man normalt använder är baserade på kontinuumantaganden, och de tar inte hänsyn till realistiska strukturer av diskreta sprickor, vilket leder till hög potentiell osäkerhet i uppskattning av tunnelgrundvatteninflöde. Denna avhandling fokuserar på förutsägelse av tunnelinläckage, med hjälp av en diskret sprickmatris (DFM) modell. DFM-modellen utvärderas och jämförs med den konventionella kontinuummodell vilken är baserad på Darcys lag. Denna DFM-modell tar särskilt hänsyn till multi-skala heterogenitet, till exempel spricknätverk och variabla dubbelkolla. Genom att tillämpa denna DFM-modell undersöks effekten av strukturer med variabel spricköppning på grundvatteninflödet genom stokastisk analys. Resultaten visar att under samma randvillkor överskattar den traditionella kontinuummodellen inflödet jämfört med DFM-modellen. Skillnaden i ekvivalent permeabilitet är 2 till 3 storleksordningar. Känslighetsanalysen visar att den diskreta sprickmodellen är känslig möt variationen i spricköppningen. De uppskattade ekvivalenta permeabilitetsvärdena med diskret sprickmodellering är i storleksordningen 5x10-6 till 1x10-7 m/s för en spricktäthet på 1,2 sprickor per kvadratmeter. Denna studie visar att DFM representerar de mer realistiska egenskaperna hos sprickiga bergstrukturer, vilket är användbart och kan användas för att uppskatta grundvatteninflöde i sprickiga bergtunnlar.

Today everyone seems to agree that ultra-low permeability and shale reservoirs have become the potentials to transform North America's oil and gas industry to a new phase. Unfortunately, transient flow is of long duration (perhaps life of the well) in ultra-low permeability reservoirs, and traditional decline curve analysis (DCA) models can lead to significantly over-optimistic production forecasts without additional safeguards. Stretched Exponential decline model (SEDM) gives considerably more stabilized production forecast than traditional DCA models and in this work it is shown that it produces unchanging EUR forecasts after only two-three years of production data are available in selected reservoirs, notably the Barnett Shale. For an individual well, the SEDM model parameters, can be determined by the method of least squares in various ways, but the inherent nonlinear character of the least squares problem cannot be bypassed. To assure a unique solution to the parameter estimation problem, this work suggests a physics-based regularization approach, based on critical velocity concept. Applied to selected Barnett Shale gas wells, the suggested method leads to reliable and consistent EURs. To further understand the interaction of the different fracture properties on reservoir response and production decline curve behavior, a series of Discrete Fracture Network (DFN) simulations were performed. Results show that at least a 3-layer model is required to reproduce the decline behavior as captured in the published SEDM parameters for Barnett Shale. Further, DFN modeling implies a large number of parameters like fracture density and fracture length are in such a way that their effect can be compensated by the other one. The results of DFN modeling of several Barnett Shale horizontal wells, with numerous fracture stages, showed a very good agreement with the estimated SEDM model for the same wells. Estimation of P90 reserves that meet SEC criteria is required by law for all companies that raise capital in the United States. Estimation of P50 and P10 reserves that meet SPE/WPC/AAPG/SPEE Petroleum Resources Management System (PRMS) criteria is important for internal resource inventories for most companies. In this work a systematic methodology was developed to quantify the range of uncertainty in production forecast using SEDM. This methodology can be used as a probabilistic tool to quantify P90, P50, and P10 reserves and hence might provide one possible way to satisfy the various legal and technical-society-suggested criteria.

Numerical modeling of fluid flow and dissolved species transport in the subsurface is a challenging task, given variability and measurement uncertainty in the physical properties of the rock, the complexities of multi-fluid interaction, and limited computational resources. Nonetheless, this thesis seeks to expand our modeling capabilities in the context of contaminant hydrogeology. We describe the numerical simulator CompFlow Bio and use it to model invasion of a nonaqueous phase liquid (NAPL) contaminant through the vadose zone and below the water table in a fractured porous rock. CompFlow Bio is a three-phase, multicomponent, deterministic numerical model for fluid flow and dissolved species transport; it includes capillary pressure and equilibrium partitioning relationships. We have augmented the model to include randomly generated, axis-aligned, discrete fracture networks (DFNs). The DFN is coupled with the porous medium (PM) to form a single continuum. The domain is discretized using a finite-volume scheme in an unstructured mesh of rectilinear control volumes (CVs). Herein we present the governing equations, unstructured mesh creation scheme, algebraic development of fracture intersection CV elimination, and coupling of PM CVs over a fracture plane to permit asperity contact bridged flow. We include: small scale two-phase water-air and NAPL-water simulations to validate the practice of intersection CV elimination; small scale simulations with water-air, NAPL-water, and NAPL-water-air systems in a grid refinement exercise and to demonstrate the effect of asperity contact bridged flow; intermediate scale 3D simulations of NAPL invading the saturated zone, based on the Smithville, Ontario, site; intermediate scale 2D and 3D simulations of NAPL invading the vadose zone and saturated zone with transient recharge, based on the Santa Susana Field Laboratory site, California. Our findings indicate that: the formulation provides a practical and satisfactory way of modeling three-phase flow in discretely fractured porous rock; numerical error caused by spatial discretization manifests itself as several biases in physical flow processes; that asperity contact is important in establishing target water saturation conditions in the vadose zone; and simulation results are sensitive to relative permeability-saturation-capillary pressure relationships. We suggest a number of enhancements to CompFlow Bio to overcome certain computational limitations.

En los últimos años, el análisis numérico de problemas acoplados, como los procesos de degradación de materiales y estructuras relacionados con los efectos medioambientales, ha cobrado especial importancia en la comunidad científica de la mecánica del hormigón. Problemas de este tipo son por ejemplo el ataque químico, el efecto de altas temperaturas o la retracción por secado.Tradicionalmente, los análisis acoplados existentes en la literatura se han realizado a nivel macroscópico, considerando el material como un medio continuo y homogéneo. Sin embargo, es bien conocido que el origen de la degradación observada a nivel macroscópico, a menudo es debida a la interacción entre los áridos y el mortero, sobre todo cuando se dan cambios de volumen diferenciales entre los dos componentes. Esta es la razón por la que el análisis mesomecánico está emergiendo como una herramienta potente para estudios de materiales heterogéneos, aunque actualmente existen escasos modelos numéricos capaces de simular un problema acoplado a esta escala de observación.En esta tesis, la aplicabilidad del modelo meso-mecánico de elementos finitos, desarrollado en el seno del grupo de investigación durante los últimos quince años, se extiende al análisis de problemas acoplados higro-mecánicos y químico-mecánicos, con el fin de estudiar la retracción por secado y el ataque sulfático externo en muestras de hormigón. La generación numérica de mesogeometrías y mallas de elementos finitos con los áridos de mayor tamaño rodeados de la fase mortero se consigue mediante la teoría de Voronoï/Delaunay Adicionalmente, con el fin de simular las principales trayectorias de fisuración, se insertan a priori elementos junta de espesor nulo, equipados con una ley constitutiva basada en la mecánica de fractura no lineal, a lo largo de todos los contactos entre árido y matriz, y también en algunas líneas matriz-matriz.La aportación principal de esta tesis es, conjuntamente con la realización de análisis acoplados sobre una representación mesoestructural del material, la simulación no solo de la formación y propagación de fisuras, sino también la consideración explícita de la influencia de éstas en el proceso de difusión.Los cálculos numéricos se realizan mediante el uso de los códigos de elementos finitos DRAC y DRACFLOW, previamente desarrollados en el seno del grupo de investigación, y acoplados mediante una estrategia staggered. Las simula-ciones realizadas abarcan, entre otros aspectos, la evaluación del compor-tamiento acoplado, el ajuste de parámetros del modelo con resultados experimentales disponibles en la bibliografía, diferentes estudios del efecto de los áridos en la microfisuración inducida por el secado y las expansiones debidas al ataque sulfático, así como el efecto simultáneo de los procesos gobernados por difusión y cargas de origen mecánico. Los resultados obtenidos concuerdan con observaciones experimentales de la fisuración, el fenómeno de spalling y la evolución de las deformaciones, y muestran la capacidad del modelo para ser utilizado en el estudio de problemas acoplados en los que la naturaleza heterogénea y cuasi-frágil del material tiene un papel predominante.

A naturally fractured reservoir (NFR) is a reservoir with a connected network of fractures created by natural processes such as diastrophism and volume shrinkage (Ordonez et al. 2001). There are two models to simulate this kind of reservoirs: the discrete fracture model and the dual porosity model. In the dual porosity model, the matrix blocks occupy the same physical space as the fracture network and are identical rectangular parallelepipeds with no direct communication between isotropic and homogeneous matrix blocks. However, each fracture and matrix property is defined separately in the discrete fracture model. Another feature of this thesis is tracer testing. In this process, a chemical or radioactive element is injected to the reservoirs, and then it can be traced using the devices, which are designed to detect the tracers. Tracer tests have several advantages such as determining residual oil saturation, identifying barriers or high permeability zones in reservoirs, and providing the information on flow patterns. Limited number of research studies has been done on performing tracer tests in naturally fractured reservoirs. Also because there is not enough information about the advantages and disadvantages of the discrete fracture and the dual porosity models, researchers and engineers lack the expertise to confidently select either the discrete fracture or the dual porosity models to simulate the different types of NFRs. In this thesis, we compared the oil and water productions, and tracer concentration curves in various reservoir conditions, using both the discrete fracture and the dual porosity models. We used the ECLIPSE, which is a commercial software package in the area of petroleum industry, to model a naturally fractured reservoir. We performed a simple waterflooding with two conservative tracers on the reservoirs. The results presented in each section include the graphs of the oil production rate, water production rate, and tracer concentration. In addition, we presented the oil saturation profiles of a cross-section, which includes the production and injection wells. The results illustrated that both the discrete fracture and the dual porosity models are in good agreement, except for a few special cases. Generally, the oil production using the dual porosity model is more than in the discrete fracture model. The major disadvantage of the dual porosity model is that the fluid distribution in the matrix blocks is changing homogenously during the waterflooding period. In other words, ECLIPSE shows a constant value of the oil and water saturations in each time step for the matrix blocks. However, the dual porosity model is 3 to 4 times faster than the discrete fracture model. In the discrete fracture model, the users have complete control in defining the reservoirs. For example, the fracture aperture, fracture spacing, and fracture porosities can be set by the user. The disadvantage of this model is that millions of grid blocks are needed to model a large reservoir with small fracture spacing. / text

Naturally fractured reservoirs (NFRs) hold a significant amount of the world's hydrocarbon reserves. Compared to conventional reservoirs, NFRs exhibit a higher degree of heterogeneity and complexity created by fractures. The importance of fractures in production of oil and gas is not limited to naturally fractured reservoirs. The economic exploitation of unconventional reservoirs, which is increasingly a major source of short- and long-term energy in the United States, hinges in part on effective stimulation of low-permeability rock through multi-stage hydraulic fracturing of horizontal wells. Accurate modeling and simulation of fractured media is still challenging owing to permeability anisotropies and contrasts. Non-physical abstractions inherent in conventional dual porosity and dual permeability models make these methods inadequate for solving different fluid-flow problems in fractured reservoirs. Also, recent approaches for discrete fracture modeling may require large computational times and hence the oil industry has not widely used such approaches, even though they give more accurate representations of fractured reservoirs than dual continuum models. We developed an embedded discrete fracture model (EDFM) for an in-house fully-implicit compositional reservoir simulator. EDFM borrows the dual-medium concept from conventional dual continuum models and also incorporates the effect of each fracture explicitly. In contrast to dual continuum models, fractures have arbitrary orientations and can be oblique or vertical, honoring the complexity and heterogeneity of a typical fractured reservoir. EDFM employs a structured grid to remediate challenges associated with unstructured gridding required for other discrete fracture models. Also, the EDFM approach can be easily incorporated in existing finite difference reservoir simulators. The accuracy of the EDFM approach was confirmed by comparing the results with analytical solutions and fine-grid, explicit-fracture simulations. Comparison of our results using the EDFM approach with fine-grid simulations showed that accurate results can be achieved using moderate grid refinements. This was further verified in a mesh sensitivity study that the EDFM approach with moderate grid refinement can obtain a converged solution. Hence, EDFM offers a computationally-efficient approach for simulating fluid flow in NFRs. Furthermore, several case studies presented in this study demonstrate the applicability, robustness, and efficiency of the EDFM approach for modeling fluid flow in fractured porous media. Another advantage of EDFM is its extensibility for various applications by incorporating different physics in the model. In order to examine the effect of pressure-dependent fracture properties on production, we incorporated the dynamic behavior of fractures into EDFM by employing empirical fracture deformation models. Our simulations showed that fracture deformation, caused by effective stress changes, substantially affects pressure depletion and hydrocarbon recovery. Based on the examples presented in this study, implementation of fracture geomechanical effects in EDFM did not degrade the computational performance of EDFM. Many unconventional reservoirs comprise well-developed natural fracture networks with multiple orientations and complex hydraulic fracture patterns suggested by microseismic data. We developed a coupled dual continuum and discrete fracture model to efficiently simulate production from these reservoirs. Large-scale hydraulic fractures were modeled explicitly using the EDFM approach and numerous small-scale natural fractures were modeled using a dual continuum approach. The transport parameters for dual continuum modeling of numerous natural fractures were derived by upscaling the EDFM equations. Comparison of the results using the coupled model with that of using the EDFM approach to represent all natural and hydraulic fractures explicitly showed that reasonably accurate results can be obtained at much lower computational cost by using the coupled approach with moderate grid refinements. / text