Single-And Two-Phase Flow in Natural Fractures, and Other Aspects of Scale-Up of Two-Phase Flow in Porous Medium




Kumar, Arun T. A.

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The first objective of this dissertation is to understand flow through fractured media by performing experiments to characterize the aperture spatial distribution in a rock fracture, develop a microscopic network model for relative permeabilities in a fracture, and test the model implications with simulations. Nuclear magnetic resonance imaging (NMRI) techniques were developed for the accurate modeling of spatial distributions of apertures and two-phase fluid distributions in rock fractures. Rock models of known apertures were used to validate the NMRI technique. NMRI aperture values were in fair agreement with nominal and hydraulic aperture values. The fracture signal was isolated by NMRI. Individual fractures can be represented as two-dimensional networks of locations of wide and narrow aperture. Using the Effective Medium Approximation (EMA), the effects of aperture distribution and of gravity on these relative permeability curves is illustrated. Simultaneous two-phase flow is possible if the wetting-phase flow occurs along the fracture wall. Zones of zero aperture, locations where the fracture walls close, reduce relative permeabilities; the manner of this reduction depends on spatial distribution of the zones of zero aperture. Simple EMA models for non-Newtonian single-phase flow through fractures were developed. Shear-thinning non-Newtonian fluids make the fracture appear to be wider than in Newtonian flow. The substantial effect of fracture relative permeabilities on reservoir performance is illustrated using the waterflood case of the Sixth SPE Comparative Simulation Project as a basis of comparison. The second objective of this dissertation is to develop computational tools to scale up petrophysical properties in a spatially periodic, mixed-wet, heterogeneous rock and apply the algorithms to realistic reservoir descriptions comprising more than J06 fine-grid data points from a sandstone oil field. Two-phase effective relative-permeabilities and capillary pressure were obtained by scale-up from plug scale to gridblock scale. The steady-state approximation was used for two-phase scale-up, which has the potential to be a computationally significant improvement over unsteady-state scale-up methods that require extensive fine-grid simulation. The results also illustrate differences between scaled-up horizontal and vertical relative-permeability curves and rock curves corresponding to average permeability and porosity. Effective properties are compared using direct pressure solution and averaging techniques for the limiting cases of low and high capillary number. The effect of wettability and lithology variations on the scaled-up relative permeabilities is illustrated. For the sandstone field descriptions tested, the calculated capillary-number-dependent effective horizontal relative-permeability curves were close to the high-capillary-number limit at realistic reservoir flow rates.


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