Browsing by Subject "Geometric Approximation"
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Item A Novel Approach for the Rapid Estimation of Drainage Volume, Pressure and Well Rates(2012-11-12) Gupta, Neha 1986-For effective reservoir management and production optimization, it is important to understand drained volumes, pressure depletion and reservoir well rates at all flow times. For conventional reservoirs, this behavior is based on the concepts of reservoir pressure and energy and convective flow. But, with the development of unconventional reservoirs, there is increased focus on the unsteady state transient flow behavior. For analyzing such flow behaviors, well test analysis concepts are commonly applied, based on the analytical solutions of the diffusivity equation. In this thesis, we have proposed a novel methodology for estimating the drainage volumes and utilizing it to obtain the pressure and flux at any location in the reservoir. The result is a semi-analytic calculation only, with close to the simplicity of an analytic approach, but with significantly more generality. The approach is significantly faster than a conventional finite difference solution, although with some simplifying assumptions. The proposed solution is generalized to handle heterogeneous reservoirs, complex well geometries and bounded and semi-bounded reservoirs. Therefore, this approach is particularly beneficial for unconventional reservoir development with multiple transverse fractured horizontal wells, where limited analytical solutions are available. To estimate the drainage volume, we have applied an asymptotic solution to the diffusivity equation and determined the diffusive time of flight distribution. For the pressure solution, a geometric approximation has been applied within the drainage volume to reduce the full solution of the diffusivity equation to a system of decoupled ordinary differential equations. Besides, this asymptotic expression can also be extended to obtain the well rates, producing under constant bottomhole pressure constraint. In this thesis, we have described the detailed methodology and its validation through various case studies. We have also studied the limits of validity of the approximation to better understand the general applicability. We expect that this approach will enable the inversion of field performance data for improved well and/or fracture characterization, and similarly, the optimization of well trajectories and fracture design, in an analogous manner to how rapid but approximate streamline techniques have been used for improved conventional reservoir management.Item Exploring an Unstructured Lattice Representation for Carbonate Reservoir Characterization(2014-05-19) Pasumarti, LakshmiCarbonates for flow simulation purposes are typically characterized as grid-blocks of varying permeability, with a finer grid employed where heterogeneity is greatest. However, this manner of representation is more suited to sandstone reservoirs, as transport in carbonate reservoirs is usually far more un-geometric due to the complex types of carbonate rock pore-spaces. Far from simply flow between inter-granular pore-spaces, diagenetic processes produce carbonate reservoirs with permeability heterogeneity mainly within three distinct but yet interacting geologic features - Matrix, Vugs and Fractures ? very often with each feature occurring at various length scales. This project will explore the merits of an unstructured means of representing carbonates via a lattice-network of pore-volumes connected in space in directions and connectivity properties driven by the rock fabric, as opposed to being limited by the rigid geometry of grid-blocks. With this goal in mind, some aspects related to a lattice-based characterization will be studied. Firstly, the geologic context that motivates a non-grid based approach to carbonate reservoir modeling will be discussed in the literature review. Secondly, convective and diffusive calculations on a grid will be compared to their equivalents on a lattice in order to establish the applicability of the lattice-system. Convective time-of-flight on a grid is calculated using Pollock?s method, while an approximation using the average pore-volumes between nodes will be employed on the lattice. Diffusive time-of-flight on a grid is populated using the Fast Marching Method (FMM), whereas Dijkstra?s Algorithm is more appropriate for a lattice. Thirdly, ?-CT-scan data of a rock sample from an outcrop will be used to build an equivalent unstructured lattice-representation of the media at that length scale, and explored for convective and diffusive flow properties. This will be performed by using the AVIZO Suite to first binarize the ?-CT data into pore space and non-pore space, and then skeletonizing it to convert the pore-space into an unstructured set of nodes ? carrying volumes ? and bonds ? each carrying a mean length and radius. These properties will then be used to calculate the transmissibility and diffusive time-of-flight across each bond. Once these are known, convective and diffusive floods can be initiated and the appropriate responses studied to learn about the rock properties. This project is envisaged also as laying the groundwork for a long term goal of unstructured lattice-based carbonate reservoir characterization.