It is common for field models of tight gas reservoirs to include several wells with hydraulic fractures. These hydraulic fractures can be very long, extending for more than a thousand feet. A hydraulic fracture width is usually no more than about 0.02 ft. The combination of the above factors leads to the conclusion that there is a need to model hydraulic fractures in coarse grid blocks for these field models since it may be impractical to simulate these models using fine grids. In this dissertation, a method was developed to simulate a reservoir model with a single hydraulic fracture that passes through several coarse gridblocks. This method was tested and a numerical error was quantified that occurs at early time due to the use of coarse grid blocks. In addition, in this work, rules were developed and tested on using uniform fine grids to simulate a reservoir model with a single hydraulic fracture. Results were compared with the results from simulations using non-uniform fine grids.

This project is a research into the effect of gas condensate damage in hydraulically fractured wells. It is the result of a problem encountered in producing a low permeability formation from a well in South Texas owned by the El Paso Production Company. The well was producing a gas condensate reservoir and questions were raised about how much drop in flowing bottomhole pressure below dewpoint would be appropriate. Condensate damage in the hydraulic fracture was expected to be of significant effect. Previous attempts to answer these questions have been from the perspective of a radial model. Condensate builds up in the reservoir as the reservoir pressure drops below the dewpoint pressure. As a result, the gas moving to the wellbore becomes leaner. With respect to the study by El-Banbi and McCain, the gas production rate may stabilize, or possibly increase, after the period of initial decline. This is controlled primarily by the condensate saturation near the wellbore. This current work has a totally different approach. The effects of reservoir depletion are minimized by introduction of an injector well with fluid composition the same as the original reservoir fluid. It also assumes an infinite conductivity hydraulic fracture and uses a linear model. During the research, gas condensate simulations were performed using a commercial simulator (CMG). The results of this research are a step forward in helping to improve the management of gas condensate reservoirs by understanding the mechanics of liquid build-up. It also provides methodology for quantifying the condensate damage that impairs linear flow of gas into the hydraulic fracture.

Problems involving coupled thermo-poro-chemo-mechanical processes are of great importance in geothermal and petroleum reservoir systems. In particular, economic power production from enhanced geothermal systems, effective water-flooding of petroleum reservoirs, and stimulation of gas shale reservoirs are significantly influenced by coupled processes. During such procedures, stress state in the reservoir is changed due to variation in pore fluid pressure and temperature. This can cause deformation and failure of weak planes of the formation with creation of new fractures, which impacts reservoir response. Incorporation of geomechanical factor into engineering analyses using fully coupled geomechanics-reservoir flow modeling exhibits computational challenges and numerical difficulties. In this study, we develop and apply efficient numerical models to solve 3D injection/extraction geomechanics problems formulated within the framework of thermo-poro-mechanical theory with reactive flow. The models rely on combining Displacement Discontinuity (DD) Boundary Element Method (BEM) and Finite Element Method (FEM) to solve the governing equations of thermo-poro-mechanical processes involving fracture/reservoir matrix. The integration of BEM and FEM is accomplished through direct and iterative procedures. In each case, the numerical algorithms are tested against a series of analytical solutions. 3D study of fluid injection and extraction into the geothermal reservoir illustrates that thermo-poro-mechanical processes change fracture aperture (fracture conductivity) significantly and influence the fluid flow. Simulations that consider joint stiffness heterogeneity show development of non-uniform flow paths within the crack. Undersaturated fluid injection causes large silica mass dissolution and increases fracture aperture while supersaturated fluid causes mineral precipitation and closes fracture aperture. Results show that for common reservoir and injection conditions, the impact of fully developed thermoelastic effect on fracture aperture tend to be greater compare to that of poroelastic effect. Poroelastic study of hydraulic fracturing demonstrates that large pore pressure increase especially during multiple hydraulic fracture creation causes effective tensile stress at the fracture surface and shear failure around the main fracture. Finally, a hybrid BEFEM model is developed to analyze stress redistribution in the overburden and within the reservoir during fluid injection and production. Numerical results show that fluid injection leads to reservoir dilation and induces vertical deformation, particularly near the injection well. However, fluid withdrawal causes reservoir to compact. The Mandel-Cryer effect is also successfully captured in numerical simulations, i.e., pore pressure increase/decrease is non-monotonic with a short time values that are above/below the background pore pressure.

Hydraulic fracturing is an important and abundant process in both industrial applications and natural environments. The current work is the first systematic quantitative study of the effect of interaction in and between complex hydraulic fractures at different spatial scales. A mathematical model, based on the boundary collocation method, has been developed. The model has been employed for a typical field case, a highly segmented vein. This vein is well-mapped, and therefore, represents a well constrained example. The computed apertures are compared to the measured apertures. By using the simplest constitutive model, based on an ideal elastic material, and including the effect of interaction between the segments, it was possible to obtain an excellent match at all considered scales. It was also shown that the concept of effective fracture, as currently accepted in the literature, is not always applicable and may lead to unbounded inaccuracy. Unfortunately, in most cases, very little (if any) directly measured data on fracture and material properties is available. An important example of such a weakly constrained case, involving hydraulic fracturing, is diking beneath the seafloor at mid-oceanic ridges. In this study, it is shown that the commonly accepted scenario of a dike propagating from the center of the pressurized magma chamber to the ocean floor is not consistent with conventional fracture mechanics due to the fact that the chamber has the shape of a thin lens. Even at such a large scale (i.e., a kilometer or more), the mechanical principles of elastic interaction appear to be applicable. Since diking is likely to generate a region of high permeability near its margin, in addition to heat, the ongoing hydrothermal activity becomes localized. Our modeling suggests the probable positions of the propagating dikes. Consequently, comparing the observed locations of hydrothermal sites with respect to that of the magma chamber could be useful for constraining the mechanisms of magma lens evolution.

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

This dissertation presents an experimental investigation of fluid flow, proppant settling and horizontal proppant transport in hydraulic fractures. The work is divided into two major sections: investigation of proppant settling in polymer-free surfactant-based viscoelastic (VES) fluids and development of a new method of proppant injection, referred to as Alternate-Slug fracturing. VES fluid systems have been used to eliminate polymer-based damage and to efficiently transport proppant into the fracture. Current models and correlations neglect the important influence of fracture walls and fluid elasticity on proppant settling. Experimental data is presented to show that elastic effects can increase or decrease the settling velocity of particles, even in the creeping flow regime. Experimental data shows that significant drag reduction occurs at low Weissenberg number, followed by a transition to drag enhancement at higher Weissenberg numbers. A new correlation is presented for the sphere settling velocity in unbounded viscoelastic fluids as a function of the fluid rheology and the proppant properties. The wall factors for sphere settling velocities in viscoelastic fluids confined between solid parallel plates (fracture walls) are calculated from experimental measurements made on these fluids over a range of Weissenberg numbers. Results indicate that elasticity reduces the retardation effect of the confining walls and this reduction is more pronounced at higher ratios of the particle diameter to spacing between the walls. Shear thinning behavior of fluids is also observed to reduce the retardation effect of the confining walls. A new empirical correlation for wall factors for spheres settling in a viscoelastic fluid confined between two parallel walls is presented. An experimental study on proppant placement using a new method of fracturing referred to as Alternate-Slug fracturing is presented. This method involves alternate injection of low viscosity and high viscosity fluids into the fracture, with proppant pumped in the low viscosity fluid. Experiments are conducted in Hele-Shaw cells to study the growth of viscous fingers over a wide range of viscosity ratios. Data is presented to show that the viscous finger velocities and mixing zone velocities increase with viscosity ratio up to viscosity ratios of about 350 and the trend is consistent with Koval’s theory. However, at higher viscosity ratios the mixing zone velocity values plateau signifying no further effect of viscosity contrast on the growth of fingers and mixing zone. The plateau in the velocities at high viscosity ratios is caused by an increase in the thickness of the displacing fluid and a reduction in the thin film of the displaced fluid on the walls of the Hele-Shaw cell. Fluid elasticity is observed to retard the growth of fingers and leads to growth of multiple thin fingers as compared to a single thick dominant finger in less elastic fluids. Observations show the shielding effect is reduced by fluid elasticity. Elastic effects are observed to reduce the thickness of thin film of displaced fluid on the walls of Hele-Shaw cell. The dominant wave number for the growth of instabilities is observed to be higher in more elastic fluids. At the onset of instability, the interface breaks down into a greater number of fingers in more elastic fluids. Experiments are performed in simulated fractures (slot cells) to show the proppant distribution using alternate-slug fracturing. Observations show alternate-slug fracturing ensures deeper placement of proppant through two primary mechanisms: (a) proppant transport in viscous fingers formed by the low viscosity fluid and (b) an increase in drag force in the polymer slug leading to better entrainment and displacement of any proppant banks that may have formed. The method offers advantages of lower polymer costs, lower pumping horsepower, smaller fracture widths, better control of fluid leak-off and less gel damage compared to conventional gel fracs. / text

The thesis considers three-dimensional analyses of fractures and wellbores in low-permeability petroleum/geothermal reservoirs, with a special emphasis on the role of coupled thermo-hydro-mechanical processes. Thermoporoelastic displacement discontinuity and stress discontinuity methods are elaborated for infinite media. Furthermore, injection/production-induced mass and heat transport inside fractures are studied by coupling the displacement discontinuity method with the finite element method. The resulting method is then used to simulate problems of interest in wellbores and fractures for related to drilling and stimulation. In the examination of fracture deformation, the nonlinear behavior of discontinuities and the change in status from joint (hydraulically open, mechanically closed) to hydraulic fracture (hydraulically open, mechanically open) are taken into account. Examples are presented to highlight the versatility of the method and the role of thermal and hydraulic effects, three-dimensionality, hydraulic/natural fracture deformation, and induced micro earthquakes. Specifically, injection/extraction operations in enhanced geothermal reservoirs and hydraulic/thermal stimulation of fractured reservoirs are studied and analyzed with reference to induced seismicity. In addition, the fictitious stress method is used to study three-dimensional wellbore stresses in the presence of a weakness plane. It is shown that the coupling of hydro-thermo-mechanical processes plays a very important role in low-permeability reservoirs and should be considered when predicting the behavior of fractures and wellbores.

We connect the Mimetic Finite Difference method (MFD) with the finite-volume two-point flux scheme (TPFA) for Voronoi meshes. The main effect is reducing the saddle-point system to a much smaller symmetric-positive definite matrix. In addition, the generalization allows MFD to seamlessly integrate with existing porous media modeling technology. The generalization also imparts the monotonicity property of the TPFA method on MFD. The connection is achieved by altering the consistency condition of the velocity bilinear operator. First-order convergence theory is presented as well as numerical results that support the claims. We demonstrate a methodology for using MFD in modeling fluid flow in fractures coupled with a reservoir. The method can be used for nonplanar fractures. We use the method to demonstrate the effects of fracture curvature on single-phase and multi-phase flows. Standard benchmarks are used to demonstrate the accuracy of the method. The approach is coupled with existing reservoir simulation technology. / text