This research utilizes the imbibition experiments and X-ray tomography results for modeling fluid flow in naturally fractured reservoirs. Conventional dual porosity simulation requires large number of runs to quantify transfer function parameters for history matching purposes. In this study empirical transfer functions (ETF) are derived from imbibition experiments and this allows reduction in the uncertainness in modeling of transfer of fluids from the matrix to the fracture. The application of the ETF approach is applied in two phases. In the first phase, imbibition experiments are numerically solved using the diffusivity equation with different boundary conditions. Usually only the oil recovery in imbibition experiments is matched. But with the advent of X-ray CT, the spatial variation of the saturation can also be computed. The matching of this variation can lead to accurate reservoir characterization. In the second phase, the imbibition derived empirical transfer functions are used in developing a dual porosity reservoir simulator. The results from this study are compared with published results. The study reveals the impact of uncertainty in the transfer function parameters on the flow performance and reduces the computations to obtain transfer function required for dual porosity simulation.

We propose a rigorous approach for well drainage volume calculations in gas reservoirs based on the flux field derived from dual porosity finite-difference simulation and demonstrate its application to optimize well placement. Our approach relies on a high frequency asymptotic solution of the diffusivity equation and emulates the propagation of a 'pressure front' in the reservoir along gas streamlines. The proposed approach is a generalization of the radius of drainage concept in well test analysis (Lee 1982), which allows us not only to compute rigorously the well drainage volumes as a function of time but also to examine the potential impact of infill wells on the drainage volumes of existing producers. Using these results, we present a systematic approach to optimize well placement to maximize the Estimated Ultimate Recovery. A history matching algorithm is proposed that sequentially calibrates reservoir parameters from the global-to-local scale considering parameter uncertainty and the resolution of the data. Parameter updates are constrained to the prior geologic heterogeneity and performed parsimoniously to the smallest spatial scales at which they can be resolved by the available data. In the first step of the workflow, Genetic Algorithm is used to assess the uncertainty in global parameters that influence field-scale flow behavior, specifically reservoir energy. To identify the reservoir volume over which each regional multiplier is applied, we have developed a novel approach to heterogeneity segmentation from spectral clustering theory. The proposed clustering can capture main feature of prior model by using second eigenvector of graph affinity matrix. In the second stage of the workflow, we parameterize the high-resolution heterogeneity in the spectral domain using the Grid Connectivity based Transform to severely compress the dimension of the calibration parameter set. The GCT implicitly imposes geological continuity and promotes minimal changes to each prior model in the ensemble during the calibration process. The field scale utility of the workflow is then demonstrated with the calibration of a model characterizing a structurally complex and highly fractured reservoir.

Naturally fractured reservoirs (NFR) represent an important percentage of the worldwide hydrocarbon reserves and production. Reservoir simulation is a fundamental technique in characterizing this type of reservoir. Fracture properties are often not available due to difficulty to characterize the fracture system. On the other hand, well test analysis is a well known and widely applied reservoir characterization technique. Well testing in NFR provides two characteristic parameters, storativity ratio and interporosity flow coefficient. The storativity ratio is related to fracture porosity. The interporosity flow coefficient can be linked to shape factor, which is a function of fracture spacing. The purpose of this work is to investigate the feasibility of estimating fracture porosity and fracture spacing from single well test analysis and to evaluate the use of these two parameters in dual porosity simulation models. The following assumptions were considered for this research: 1) fracture compressibility is equal to matrix compressibility; 2) no wellbore storage and skin effects are present; 3) pressure response is in pseudo-steady state; and 4) there is single phase flow. Various simulation models were run and build up pressure data from a producer well was extracted. Well test analysis was performed and the result was compared to the simulation input data. The results indicate that the storativity ratio provides a good estimation of the magnitude of fracture porosity. The interporosity flow coefficient also provides a reasonable estimate of the magnitude of the shape factor, assuming that matrix permeability is a known parameter. In addition, pressure tests must exhibit all three flow regimes that characterizes pressure response in NFR in order to obtain reliable estimations of fracture porosity and shape factor.

This research utilizes the imbibition experiments and X-ray tomography results for modeling fluid flow in naturally fractured reservoirs. Conventional dual porosity simulation requires large number of runs to quantify transfer function parameters for history matching purposes. In this study empirical transfer functions (ETF) are derived from imbibition experiments and this allows reduction in the uncertainness in modeling of transfer of fluids from the matrix to the fracture. The application of the ETF approach is applied in two phases. In the first phase, imbibition experiments are numerically solved using the diffusivity equation with different boundary conditions. Usually only the oil recovery in imbibition experiments is matched. But with the advent of X-ray CT, the spatial variation of the saturation can also be computed. The matching of this variation can lead to accurate reservoir characterization. In the second phase, the imbibition derived empirical transfer functions are used in developing a dual porosity reservoir simulator. The results from this study are compared with published results. The study reveals the impact of uncertainty in the transfer function parameters on the flow performance and reduces the computations to obtain transfer function required for dual porosity simulation.

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.

Fluid flow process in fractured reservoirs is controlled primarily by the connectivity of fractures. The presence of fractures in these reservoirs significantly affects the mechanism of fluid flow. They have led to problems in the reservoir which results in early water breakthroughs, reduced tertiary recovery efficiency due to channeling of injected gas or fluids, dynamic calculations of recoverable hydrocarbons that are much less than static mass balance ones due to reservoir compartmentalization, and dramatic production changes due to changes in reservoir pressure as fractures close down as conduits. These often lead to reduced ultimate recoveries or higher production costs. Generally, modeling flow behavior and mass transport in fractured porous media is done using the dual-continuum concept in which fracture and matrix are modeled as two separate kinds of continua occupying the same control volume (element) in space. This type of numerical model cannot reproduce many commonly observed types of fractured reservoir behavior since they do not explicitly model the geometry of discrete fractures, solution features, and bedding that control flow pathway geometry. This inaccurate model of discrete feature connectivity results in inaccurate flow predictions in areas of the reservoir where there is not good well control. Discrete Fracture Networks (DFN) model has been developed to aid is solving some of these problems experienced by using the dual continuum models. The Discrete Fracture Networks (DFN) approach involves analysis and modeling which explicitly incorporates the geometry and properties of discrete features as a central component controlling flow and transport. DFN are stochastic models of fracture architecture that incorporate statistical scaling rules derived from analysis of fracture length, height, spacing, orientation, and aperture. This study is focused on developing a methodology for application of DFN to a shale gas reservoir and the practical application of DFN simulator (FracGen and NFflow) for fracture modeling of a shale gas reservoir and also studies the interaction of the different fracture properties on reservoir response. The most important results of the study are that a uniform fracture network distribution and fracture aperture produces the highest cumulative gas production for the different fracture networks and fracture/well properties considered.

This thesis is aimed to calculate the effective permeability tensor and to simulate the fluid flow in naturally fractured reservoirs. This requires an understanding of the mechanisms of fluid flow in naturally fractured reservoirs and the detailed properties of individual fractures and matrix porous media. This study has been carried out to address the issues and difficulties faced by previous methods; to establish possible answers to minimise the difficulties; and hence, to improve the efficiency of reservoir simulation through the use of properties of individual fractures. The methodology used in this study combines several mathematical and numerical techniques like the boundary element method, periodic boundary conditions, and the control volume mixed finite element method. This study has contributed to knowledge in the calculation of the effective permeability and simulation of fluid flow in naturally fractured reservoirs through the development of two algorithms. The first algorithm calculates the effective permeability tensor by use of properties of arbitrary oriented fractures (location, size and orientation). It includes all multi-scaled fractures and considers the appropriate method of analysis for each type of fracture (short, medium and long). In this study a characterisation module which provides the detail information for individual fractures is incorporated. The effective permeability algorithm accounts for fluid flows in the matrix, between the matrix and the fracture and disconnected fractures on effective permeability. It also accounts for the properties of individual fractures in calculation of the effective permeability tensor. The second algorithm simulates flow of single-phase fluid in naturally fractured reservoirs by use of the effective permeability tensor. This algorithm takes full advantage of the control volume discretisation technique and the mixed finite element method in calculation of pressure and fluid flow velocity in each grid block. It accounts for the continuity of flux between the neighbouring blocks and has the advantage of calculation of fluid velocity and pressure, directly from a system of first order equations (Darcy???s law and conservation of mass???s law). The application of the effective permeability tensor in the second algorithm allows us the simulation of fluid flow in naturally fractured reservoirs with large number of multi-scale fractures. The fluid pressure and velocity distributions obtained from this study are important and can considered for further studies in hydraulic fracturing and production optimization of NFRs.

Many hydraulically fractured shale gas horizontal wells in the Barnett shale have been observed to exhibit transient linear behavior. This transient linear behavior is characterized by a one-half slope on a log-log plot of rate against time. This transient linear flow regime is believed to be caused by transient drainage of low permeability matrix blocks into adjoining fractures. This transient flow regime is the only flow regime available for analysis in many wells. The hydraulically fractured shale gas reservoir system was described in this work by a linear dual porosity model. This consisted of a bounded rectangular reservoir with slab matrix blocks draining into adjoining fractures and subsequently to a horizontal well in the centre. The horizontal well fully penetrates the rectangular reservoir. Convergence skin is incorporated into the linear model to account for the presence of the horizontal wellbore. Five flow regions were identified with this model. Region 1 is due to transient flow only in the fractures. Region 2 is bilinear flow and occurs when the matrix drainage begins simultaneously with the transient flow in the fractures. Region 3 is the response for a homogeneous reservoir. Region 4 is dominated by transient matrix drainage and is the transient flow regime of interest. Region 5 is the boundary dominated transient response. New working equations were developed and presented for analysis of Regions 1 to 4. No equation was presented for Region 5 as it requires a combination of material balance and productivity index equations beyond the scope of this work. It is concluded that the transient linear region observed in field data occurs in Region 4 – drainage of the matrix. A procedure is presented for analysis. The only parameter that can be determined with available data is the matrix drainage area, Acm. It was also demonstrated in this work that the effect of skin under constant rate and constant bottomhole pressure conditions is not similar for a linear reservoir. The constant rate case is the usual parallel lines with an offset but the constant bottomhole pressure shows a gradual diminishing effect of skin. A new analytical equation was presented to describe the constant bottomhole pressure effect of skin in a linear reservoir. It was also demonstrated that different shape factor formulations (Warren and Root, Zimmerman and Kazemi) result in similar Region 4 transient linear response provided that the appropriate f(s) modifications consistent with lAc calculations are conducted. It was also demonstrated that different matrix geometry exhibit the same Region 4 transient linear response when the area-volume ratios are similar.

The application of carbon-dioxide injection for enhanced oil recovery and/or sequestration purposes has gained impetus in the last decade. It is known that well test analysis plays a crucial role on getting information about reservoir properties, boundary conditions, etc. Although there are some studies related to the well test analysis in the fractured reservoirs, most of them are not focused on the carbon dioxide injection into the reservoir. Naturally fractured reservoirs (NFR) represent an important percentage of the worldwide hydrocarbon reserves and current production. Reservoir simulation is a fundamental technique in characterizing this type of reservoirs. Fracture properties are often not clear due to difficulty to characterize the fracture systems. On the other hand, well test analysis is a well known and widely applied reservoir characterization technique. Well testing in NFR provides two significant characteristic parameters, storativity ratio (&omega / ) and interporosity flow coefficient (&lambda / ). The storativity ratio is related to fracture porosity. The interporosity flow coefficient can be linked to the shape factor which is a function of fracture spacing. In this study, the effects of fracture and fluid flow factors (geometry, orientation and flow properties) on pressure and pressure derivative behavior are studied by applying a reservoir simulation model. Model is utilized mainly for the observation of multiphase flow effects in CO2 flooded fractured reservoirs. Several runs are conducted for various ranges of the aforementioned properties in the CO2 flooded reservoir. Results of well test analysis are compared to the input data of simulation models on a parameter basis.

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