Reservoir geomechanics is a production induced phenomena that is experienced in large number of fields around the world. Hydrocarbon production changes the pore pressure which in turn alters the in-situ stress state. For reservoirs that are either stress sensitive or where rock is soft and unconsolidated, stresses have appreciable effect on rock properties like porosity and permeability. Anisotropic and isotropic permeability changes affect flow direction and movement of flood front thereby influencing well performance and reservoir productivity. Coupling of geomechanical calculation with multi-phase flow calculation is needed to make prudent predictions about the reservoir production and recovery. The post processing tools provided with the simulators cannot monitor flood front movement and fail to capture important information like flow directionality and dominant phase in a flow. Geomechanical simulation is combined with streamline tracing to aid in better understanding of the reservoir dynamics through visualization of flow patterns in the reservoir. Streamline tracing is a proved reservoir engineering tool that is widely used by industry experts to capture information on flood movement, injector-producer relations and swept area. In the present research, we have incorporated total velocity streamlines and phase streamlines for coupled geomechanical simulation and compared the results with streamline tracing for conventional reservoir simulator to explain geomechanics behavior on reservoir flow processes in a more detailed and appealing manner. Industry standard simulators are used for coupled geomechanical simulation and conventional simulation and streamline tracing has been done through in-house tracing code. The research demonstrates the benefits and power of streamline tracing in visualizing flow patterns through work on two cases; first, a synthetic case for studying water injection in a five spot pattern and second, a SPE 9th comparative study. The research gives encouraging results by showing how geomechanics influences reservoir flow paths and reservoir dynamics through visualization of flow. The streamlines captures flow directionality, information regarding appearance and disappearance of gas phase and the connectivity between injector and producer.

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The goal of any data assimilation or history matching algorithm is to enable better reservoir management decisions through the construction of reliable reservoir performance models and the assessment of the underlying uncertainties. A considerable body of research work and enhanced computational capabilities have led to an increased application of robust and efficient history matching algorithms to condition reservoir models to dynamic data. Moreover, there has been a shift towards generating multiple plausible reservoir models in recognition of the significance of the associated uncertainties. This provides for uncertainty analysis in reservoir performance forecasts, enabling better management decisions for reservoir development. Additionally, the increased deployment of permanent well sensors and downhole monitors has led to an increasing interest in maintaining 'live' models that are current and consistent with historical observations. One such data assimilation approach that has gained popularity in the recent past is the Ensemble Kalman Filter (EnKF) (Evensen 2003). It is a Monte Carlo approach to generate a suite of plausible subsurface models conditioned to previously obtained measurements. One advantage of the EnKF is its ability to integrate different types of data at different scales thereby allowing for a framework where all available dynamic data is simultaneously or sequentially utilized to improve estimates of the reservoir model parameters. Of particular interest is the use of partitioning tracer data to infer the location and distribution of target un-swept oil. Due to the difficulty in differentiating the relative effects of spatial variations in fractional flow and fluid saturations and partitioning coefficients on the tracer response, interpretation of partitioning tracer responses is particularly challenging in the presence of mobile oil saturations. The purpose of this research is to improve the performance of the EnKF in parameter estimation for reservoir characterization studies without the use of a large ensemble size so as to keep the algorithm efficient and computationally inexpensive for large, field-scale models. To achieve this, we propose the use of streamline-derived information to mitigate problems associated with the use of the EnKF with small sample sizes and non-linear dynamics in non-Gaussian settings. Following this, we present the application of the EnKF for interpretation of partitioning tracer tests specifically to obtain improved estimates of the spatial distribution of target oil.

Many real-world engineering problems require large amounts of data in order to accurately model and predict outcomes. However, this data is often noisy, sampled and discontinuous, making the data difficult to process and giving rise to incorrect models. In order to address this issue, different interpolation techniques are commonly used to make the data continuous. This can then followed by a filtering process in order to reduce noise and further reduce discontinuities. In this report, our approach to filtering is the use of convolution kernels, which smooths out the data. By doing so, a better visual representation of the limited data available can be obtained. For instance, in the specific case of studying streamlines and vortices, filtering techniques have been used to produce more realistic plots. While the use of filters can be beneficial, it is important to note that the choice of filter and its parameters can greatly impact the results obtained. In particular, we found that, for the filters we studied, applying these to analytical functions can actually increase the error. On the other hand, when filters are applied to discontinuous functions, they can improve the accuracy of the data. Overall, when analyzing stream functions with filters, significant improvements can be seen in the quality of the data. This underscores the importance of careful selection and application of filtering techniques in engineering problems that involve large amounts of noisy and discontinuous data.

<p>The topic of this thesis is streamline-based integration of dynamic data for porous media systems, particularly in petroleum reservoirs. In the petroleum industry the integration of dynamic data is usually referred to as history matching. The thesis starts out by giving an introduction to streamline-based history-matching methods. Implementations and extensions of two existing methods for streamline-based history matching are then presented.</p><p>The first method pursued is based on obtaining modifications for streamline-effective properties, which subsequently are propagated to the underlying simulation grid for further iterations. For this method, two improvements are proposed to the original existing method. First, the improved approach involves less approximations, enables matching of porosity, and can account for gravity. Second, a multiscale approach is applied for which the data integration is performed on a hierarchy of coarsened grids. The approach proved robust, and gave a faster and better match to the data.</p><p>The second method pursued is the so-called generalized travel-time inversion (GTTI) method, which earlier has proven very robust and efficient for history matching. The key to the efficiency of this method is the quasilinear convergence properties and the use of analytic streamline-based sensitivity coefficients. GTTI is applied together with an efficient multiscale-streamline simulator, where the pressure solver is based on a multiscale mixed finite-element method (MsMFEM). To make the history matching more efficient, a selective work-reduction strategy, based on the sensitivities provided by the inversion method, is proposed for the pressure solver. In addition, a method for improved mass conservation in streamline simulation is applied, which requires much fewer streamlines to obtain accurate production-response curves. For a reservoir model with more than one million grid blocks, 69 producers and 32 injectors, the data integration took less than twenty minutes on a standard desktop computer. Finally, we propose an extension of GTTI to fully unstructured grids, where we in particular address issues regarding regularization and computation of sensitivities on unstructured grids with large differences in cell sizes.</p> / Paper I reprinted with kind permission of Elsevier, sciencedirect.com

The topic of this thesis is streamline-based integration of dynamic data for porous media systems, particularly in petroleum reservoirs. In the petroleum industry the integration of dynamic data is usually referred to as history matching. The thesis starts out by giving an introduction to streamline-based history-matching methods. Implementations and extensions of two existing methods for streamline-based history matching are then presented. The first method pursued is based on obtaining modifications for streamline-effective properties, which subsequently are propagated to the underlying simulation grid for further iterations. For this method, two improvements are proposed to the original existing method. First, the improved approach involves less approximations, enables matching of porosity, and can account for gravity. Second, a multiscale approach is applied for which the data integration is performed on a hierarchy of coarsened grids. The approach proved robust, and gave a faster and better match to the data. The second method pursued is the so-called generalized travel-time inversion (GTTI) method, which earlier has proven very robust and efficient for history matching. The key to the efficiency of this method is the quasilinear convergence properties and the use of analytic streamline-based sensitivity coefficients. GTTI is applied together with an efficient multiscale-streamline simulator, where the pressure solver is based on a multiscale mixed finite-element method (MsMFEM). To make the history matching more efficient, a selective work-reduction strategy, based on the sensitivities provided by the inversion method, is proposed for the pressure solver. In addition, a method for improved mass conservation in streamline simulation is applied, which requires much fewer streamlines to obtain accurate production-response curves. For a reservoir model with more than one million grid blocks, 69 producers and 32 injectors, the data integration took less than twenty minutes on a standard desktop computer. Finally, we propose an extension of GTTI to fully unstructured grids, where we in particular address issues regarding regularization and computation of sensitivities on unstructured grids with large differences in cell sizes. / Paper I reprinted with kind permission of Elsevier, sciencedirect.com

Seismic data have been established as a valuable source of information for the construction of reservoir simulation models, most commonly for determination of the modeled geologic structure, and also for population of static petrophysical properties (e.g. porosity, permeability). More recently, the availability of repeated seismic surveys over the time scale of years (i.e., 4D seismic) has shown promising results for the qualitative determination of changes in fluid phase distributions and pressure required for determination of areas of bypassed oil, swept volumes and pressure maintenance mechanisms. Quantitatively, and currently the state of the art in reservoir model characterization, 4D seismic data have proven distinctively useful for the calibration of geologic spatial variability which ultimately contributes to the improvement of reservoir development and management strategies. Among the limited variety of techniques for the integration of dynamic seismic data into reservoir models, streamline-based techniques have been demonstrated as one of the more efficient approaches as a result of their analytical sensitivity formulations. Although streamline techniques have been used in the past to integrate time-lapse seismic attributes, the applications were limited to the simplified modeling scenarios of two-phase fluid flow and invariant streamline geometry throughout the production schedule. This research builds upon and advances existing approaches to streamline-based seismic data integration for the inclusion of both production and seismic data under varying field conditions. The proposed approach integrates data from reservoirs under active reservoir management and the corresponding simulation models can be constrained using highly detailed or realistic schedules. Fundamentally, a new derivation of seismic sensitivities is proposed that is able to represent a complex reservoir evolution between consecutive seismic surveys. The approach is further extended to manage compositional reservoir simulation with dissolution effects and gravity-convective-driven flows which, in particular, are typical of CO2 transport behavior following injection into deep saline aquifers. As a final component of this research, the benefits of dynamic data integration on the determination of swept and drained volumes by injection and production, respectively, are investigated. Several synthetic and field reservoir modeling scenarios are used for an extensive demonstration of the efficacy and practical feasibility of the proposed developments.

Texture evolution is a vital component of many computational tools that link structure, properties and processes of polycrystalline materials. By definition, this evolution process involves the manipulation, via rotation, of points in orientation space. The computational requirements of the current methods being used to rotate crystalline orientations are a significant limiting factor in the drive to merge the texture information of materials into the engineering design process. The goal of this research is to find and implement a practical rotation algorithm that can significantly decrease the computation time required to rotate macroscopic and microscopic crystallographic textures. Three possible algorithms are considered in an effort to improve the computational efficiency and speed of the rotation process. The first method, which will be referred to as the Gel'fand method, is based on a paper, [1], that suggests a practical application of some of Gel'fand's theories for rotations [2]. The second method, which will be known as the streamline method, is a variation on the Gel'fand method. The third method will be known as the principal orientation method. In this method, orientations in Fourier space are written as linear combinations of points on the convex surface of the microstructure hull to reduce the number of points that must be rotated during each step in the texture evolution process. This thesis will discuss each of these methods, their strengths and weaknesses, and the accuracy of the computational results obtained from their implementation.

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