Streamline-based models have shown great potential in reconciling high resolution geologic models to production data. In this work we extend the streamline-based production data integration technique to naturally fractured reservoirs. We use a dualporosity streamline model for fracture flow simulation by treating the fracture and matrix as separate continua that are connected through a transfer function. Next, we analytically compute the sensitivities that define the relationship between the reservoir properties and the production response in fractured reservoirs. Finally, production data integration is carried out via the Generalized Travel Time inversion (GTT). We also apply the streamline-derived sensitivities in conjunction with a dual porosity finite difference simulator to combine the efficiency of the streamline approach with the versatility of the finite difference approach. This significantly broadens the applicability of the streamlinebased approach in terms of incorporating compressibility effects and complex physics. The number of reservoir parameters to be estimated is commonly orders of magnitude larger than the observation data, leading to non-uniqueness and uncertainty in reservoir parameter estimate. Such uncertainty is passed to reservoir response forecast which needs to be quantified in economic and operational risk analysis. In this work we sample parameter uncertainty using a new two-stage Markov Chain Monte Carlo (MCMC) that is very fast and overcomes much of its current limitations. The computational efficiency comes through a substantial increase in the acceptance rate during MCMC by using a fast linearized approximation to the flow simulation and the likelihood function, the critical link between the reservoir model and production data. The Gradual Deformation Method (GDM) provides a useful framework to preserve geologic structure. Current dynamic data integration methods using GDM are inefficient due to the use of numerical sensitivity calculations which limits the method to deforming two or three models at a time. In this work, we derived streamline-based analytical sensitivities for the GDM that can be obtained from a single simulation run for any number of basis models. The new Generalized Travel Time GDM (GTT-GDM) is highly efficient and achieved a performance close to regular GTT inversion while preserving the geologic structure.

The current streamline formulation is limited to single-porosity systems and is then not suitable for application to naturally fractured reservoirs. Describing the fluid transport in naturally fractured reservoirs has been recognized as a main challenge for simulation engineers due to the complicated physics involved. In this work, we generalized the streamline-based simulation to describe the fluid transport in naturally fractured reservoirs. We implemented three types of transfer function: the conventional transfer function (CTF), the diffusion transfer function (DTF), and the empirical transfer function (ETF). We showed that these transfer functions can be implemented easily in the current single-porosity streamline codes. These transfer functions have been added as a source term to the transport equation that describes the saturation evolution along the streamlines. We solved this equation numerically for all types of transfer functions. The numerical solution of the continuity equation with DTF and ETF requires discretizing a convolution term. We derived an analytical solution to the saturation equation with ETF in terms of streamline TOF to validate the numerical solution. We obtain an excellent match between the numerical and the analytical solution. The final stage of our study was to validate our work by comparing our dual-porosity streamline simulator (DPSS) to the commercial dual-porosity simulator, ECLIPSE. The dual-porosity ECLIPSE uses the CTF to describe the interaction between the matrix-blocks and the fracture system. The dual-porosity streamline simulator with CTF showed an excellent match with the dual-porosity ECLIPSE. On the other hand, dual-porosity streamline simulation with DTF and ETF showed a lower recovery than the recovery obtained from the dual-porosity ECLIPSE and the DPSS with CTF. This difference in oil recovery is not due to our formulation, but is related to the theoretical basis on which CTF, DTF, and ETF were derived in the literature. It was beyond the scope of this study to investigate the relative accuracy of each transfer function. We demonstrate that the DPSS is computationally efficient and ideal for large-scale field application. Also, we showed that the DPSS minimizes numerical smearing and grid orientation effects compared to the dual-porosity ECLIPSE.

With increase of interest in exploiting shale gas/oil reservoirs with multiple stage fractured horizontal wells, complexity of production analysis and reservoir description have also increased. Different methods and models were used throughout the years to analyze these wells, such as using analytical solutions and simulation techniques. The analytical methods are more popular because they are faster and more accurate. The main objective of this paper is to present and demonstrate type curves for production data analysis of shale gas/oil wells using a Dual Porosity model. Production data of horizontally drilled shale gas/oil wells have been matched with developed type curves which vary with effective parameters. Once a good match is obtained, the well dual porosity parameters can be calculated. A computer program was developed for more simplified matching process and more accurate results. As an objective of this thesis, a type curve analytical method was presented with its application to field data. The results show a good match with the synthetic and field cases. The calculated parameters are close to those used on the synthetic models and field cases.

This dissertation presents the development of a method for quantitative integration of seismic (elastic) anisotropy attributes with reservoir performance data as an aid in characterization of systems of natural fractures in hydrocarbon reservoirs. This new method incorporates stochastic Discrete Feature Network (DFN) fracture modeling techniques, DFN model based fracture system hydraulic property and elastic anisotropy modeling, and non-linear inversion techniques, to achieve numerical integration of production data and seismic attributes for iterative refinement of initial trend and fracture intensity estimates. Although DFN modeling, flow simulation, and elastic anisotropy modeling are in themselves not new technologies, this dissertation represents the first known attempt to integrate advanced models for production performance and elastic anisotropy in fractured reservoirs using a rigorous mathematical inversion. The following new developments are presented: . • Forward modeling and sensitivity analysis of the upscaled hydraulic properties of realistic DFN fracture models through use of effective permeability modeling techniques. . • Forward modeling and sensitivity analysis of azimuthally variant seismic attributes based on the same DFN models. . • Development of a combined production and seismic data objective function and computation of sensitivity coefficients. . • Iterative model-based non-linear inversion of DFN fracture model trend and intensity through minimization of the combined objective function. This new technique is demonstrated on synthetic models with single and multiple fracture sets as well as differing background (host) reservoir hydraulic and elastic properties. Results on these synthetic control models show that, given a well conditioned initial DFN model and good quality field production and seismic observations, the integration procedure results in convergence of both fracture trend and intensity in models with both single and multiple fracture sets. Tests show that for a single fracture set convergence is accelerated when the combined objective function is used as compared to a similar technique using only production data in the objective function. Tests performed on multiple fracture sets show that, without the addition of seismic anisotropy, the model fails to converge. These tests validate the importance of the new process for use in more realistic reservoir models.

The advancement of both electronics and instrumentation technology has fostered the development of multi-physics platforms that can probe the earth’s subsurface. Remote, non-destructive testing techniques have led to the increased deployment of electromagnetic waves in sensor technology. Electromagnetic wave techniques are reliable and have the capacity to sense materials and associated properties with minimal perturbation. However, meticulous data analyses and mathematical derivations reveal inconsistencies in some formulations. Thus, revisiting the fundamental physics that underlies both electrical impedance experimental setups and electromagnetic properties are paramount. This study aims to unravel inherent limitations in the understanding of the relationships between electromagnetic and non-electromagnetic properties that are relevant to the characterization of fluids in porous media. These correlations pervade porosity, permeability, specific surface, pore size distribution, tortuosity, fluid discrimination, diffusion coefficient, degree of saturation, viscosity, temperature, phase transformation, miscibility, salinity, and the presence of impurities. The focus is on the assessment of liquids, soils, rocks, and colloids using broad spectral frequency complex permittivity, conductivity, magnetic permeability, and nuclear magnetic resonance relaxometry. Broadband electrical properties measurement for saturated porous media can provide multiple physical phenomena: Ohmic conduction, electrode polarizations, Maxwell-Wagner spatial polarizations, rotational, and segmental polarizations. Liquids dominate the electromagnetic signatures in porous media as dry minerals are inherently non-polar and non-conductive. Results reveal that voltage drops due to the discontinuity of charge-carrier at the electrode-electrolyte interface named electrode polarization inherently affect the low-frequency electrical measurements both in two- and four-probe configurations. Rotational polarizations that occur in MHz-GHz ranges are defined by the electrical dipole moment and effective molecular volume. Both viscosity and effective molecular volume govern the NMR transverse relaxation time. An engineered soil suspension with ferromagnetic inclusions exhibits excellent characteristics for drilling fluid application. Overall, the study highlights the complementary nature of conductivity, permittivity, and NMR relaxation for the advanced characterization of fluid saturated geomaterials.

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.

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

There have been many attempts to use mathematical method in order to characterize shale gas/oil reservoirs with multi-transverse hydraulic fractures horizontal well. Many authors have tried to come up with a suitable and practical mathematical model. To analyze the production data of a shale reservoir correctly, an understanding and choosing the proper mathematical model is required. Therefore, three models (the homogeneous linear flow model, the transient linear dual porosity model, and the fully transient linear triple porosity model) will be studied and compared to provide correct interpretation guidelines for these models. The analytical solutions and interpretation guidelines are developed in this work to interpret the production data of shale reservoirs effectively. Verification and derivation of asymptotic and associated equations from the Laplace space for dual porosity and triple porosity models are performed in order to generate analysis equations. Theories and practical applications of the three models (the homogeneous linear flow model, the dual porosity model, and the triple porosity model) are presented. A simplified triple porosity model with practical analytical solutions is proposed in order to reduce its complexity. This research provides the interpretation guidelines with various analysis equations for different flow periods or different physical properties. From theoretical and field examples of interpretation, the possible errors are presented. Finally, the three models are compared in a production analysis with the assumption of infinite conductivity of hydraulic fractures.

A large percentage of oil and gas reservoirs in the most productive regions such as the Middle East, South America, and Southeast Asia are naturally fractured reservoirs (NFR). The major difference between conventional reservoirs and naturally fractured reservoirs is the discontinuity in media in fractured reservoir due to tectonic activities. These discontinuities cause remarkable difficulties in describing the petrophysical structures and the flow of fluids in the fractured reservoirs. Predicting fluid flow behavior in naturally fractured reservoirs is a challenging area in petroleum engineering. Two classes of models used to describe flow and transport phenomena in fracture reservoirs are discrete and continuum (i.e. dual porosity) models. The discrete model is appealing from a modeling point of view, but the huge computational demand and burden of porting the fractures into the computational grid are its shortcomings. The affect of natural fractures on the permeability anisotropy can be determined by considering distribution and orientation of fractures. Representative fracture permeability, which is a crucial step in the reservoir simulation study, must be calculated based on fracture characteristics. The diagonal representation of permeability, which is customarily used in a dual porosity model, is valid only for the cases where fractures are parallel to one of the principal axes. This assumption cannot adequately describe flow characteristics where there is variation in fracture spacing, length, and orientation. To overcome this shortcoming, the principle of the full permeability tensor in the discrete fracture network can be incorporated into the dual porosity model. Hence, the dual porosity model can retain the real fracture system characteristics. This study was designed to develop a novel approach to integrate dual porosity model and full permeability tensor representation in fractures. A fully implicit, parallel, compositional chemical dual porosity simulator for modeling naturally fractured reservoirs has been developed. The model is capable of simulating large-scale chemical flooding processes. Accurate representation of the fluid exchange between the matrix and fracture and precise representation of the fracture system as an equivalent porous media are the key parameters in utilizing of dual porosity models. The matrix blocks are discretized into both rectangular rings and vertical layers to offer a better resolution of transient flow. The developed model was successfully verified against a chemical flooding simulator called UTCHEM. Results show excellent agreements for a variety of flooding processes. The developed dual porosity model has further been improved by implementing a full permeability tensor representation of fractures. The full permeability feature in the fracture system of a dual porosity model adequately captures the system directionality and heterogeneity. At the same time, the powerful dual porosity concept is inherited. The implementation has been verified by studying water and chemical flooding in cylindrical and spherical reservoirs. It has also been verified against ECLIPSE and FracMan commercial simulators. This study leads to a conclusion that the full permeability tensor representation is essential to accurately simulate fluid flow in heterogeneous and anisotropic fracture systems. / text

Different methods have been proposed for history matching production of shale gas/oil wells which are drilled horizontally and usually hydraulically fractured with multiple stages. These methods are simulation, analytical models, and empirical equations. It has been well known that among the methods listed above, analytical models are more favorable in application to field data for two reasons. First, analytical solutions are faster than simulation, and second, they are more rigorous than empirical equations. Production behavior of horizontally drilled shale gas/oil wells has never been completely matched with the models which are described in this thesis. For shale gas wells, correction due to adsorption is explained with derived equations. The algorithm which is used for history matching and forecasting is explained in detail with a computer program as an implementation of it that is written in Excel's VBA. As an objective of this research, robust method is presented with a computer program which is applied to field data. The method presented in this thesis is applied to analyze the production performance of gas wells from Barnett, Woodford, and Fayetteville shales. It is shown that the method works well to understand reservoir description and predict future performance of shale gas wells. Moreover, synthetic shale oil well also was used to validate application of the method to oil wells. Given the huge unconventional resource potential and increasing energy demand in the world, the method described in this thesis will be the "game changing" technology to understand the reservoir properties and make future predictions in short period of time.