Doctor of Philosophy (PhD)


Petroleum Engineering

Document Type



Non-Darcy flows are expected to be ubiquitous in near wellbore regions, completions, and in hydraulic fractures of high productivity gas wells. Further, the prevailing dynamic effective stress in the near wellbore region is expected to be an influencing factor for the completion conductivity and non-Darcy flow behavior in it. In other words, the properties (fracture permeability and β-factor) can vary with the time and location in the reservoir (especially in regions close to the wellbore). Using constant values based on empirical correlations for reservoirs/completions properties can lead to erroneous cumulative productivity predictions. With the recent advances in the imaging technology, it is now possible to reconstruct pore geometries of the proppant packs under different stress conditions. With further advances in powerful computing platforms, it is possible to handle large amount of computations such as Lattice Boltzmann (LB) simulations faster and more efficiently. Calculated properties of the proppant pack at different confining stresses show reasonable agreement with the reported values for both permeability and β-factor. These predicted stress-dependent permeability and β-factors corresponding to the effective stress fields around the hydraulic fractured completions is included in a 2D gas reservoir simulator to calculate the productivity index. In image-based flow simulations, spatial resolution of the digital images used for modeling is critical not only because it dictates the scale of features that can be resolved, but also because for most techniques there is at least some relationship between voxel size in the image data and numerical resolution applied to the computational simulations. In this work we investigate this relationship using a computer-generated consolidated porous medium, which was digitized at voxel resolutions in the range 2-10 microns. These images are then used to compute permeability and tortuosity using lattice Boltzmann (LB) and compared against finite elements methods (FEM)simulation results. Results show how changes in computed permeability are affected by image resolution (which dictates how well the pore geometry is approximated) versus grid or mesh resolution (which changes numerical accuracy). For LB, the image and grid resolution are usually taken to be the same; we show at least one case where effects of grid and image resolution appear to counteract one another, giving the mistaken appearance of resolution-independent results. For FEM, meshing can provide certain attributes (such as better conformance to surfaces), but it also adds an extra step for error or approximation to be introduced in the workflow.



Document Availability at the Time of Submission

Release the entire work immediately for access worldwide.

Committee Chair

Tyagi, Mayank