Doctoral Dissertations

Date of Award

8-2018

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

Joan R. Lind

Committee Members

Michael W. Berry, Michael W. Frazier, Kenneth Stephenson

Abstract

Spontaneous imbibition (SI) is a capillary-driven flow process, in which a wetting fluid enters a porous medium displacing a preexisting non-wetting fluid. In low-porosity rocks SI generally occurs slowly within the matrix. However, fractured low-porosity rocks allow pathways for rapid SI to occur which can directly influence oil and gas recovery, fracturing fluid loss, leakage from deep waste storage repositories, and the degradation of building materials. Previous research has typically focused on the measurement and modeling of SI in high porosity systems, with little attention given to low-porosity rocks. Furthermore, SI models generally idealize a fracture as a gap formed between parallel flat surfaces, disregarding fracture roughness. Here, a new analytical model was derived for the early-time SI behavior within a fracture bounded by parallel rough fractal surfaces. The model was tested by fitting it to experimental data for the SI of deionized water into air-filled fractures collected on a suite of low-porosity rocks (Burlington Limestone, Crossville Sandstone, Mancos Shale, Sierra White Granite, Vermilion Bay Granite, and Westerly Granite). The SI data were obtained using dynamic neutron radiography at ORNL’s Neutron Imaging Facility (beam CG-1D, HFIR). Height of wetting versus time was delineated using change point analysis. The fracture aperture width and fracture sorptivity were also quantified. Among all rock types, geometric mean aperture widths ranged from 84 to 205 µm, with igneous cores producing larger apertures than sedimentary cores. Wetting fronts within the fractures generally exhibited a square-root of time behavior. Fracture sorptivity values ranged from 13.2 to 33.7 mm·s-0.5 with sedimentary cores yielding higher values than igneous cores. Differences in fracture surface roughness explained the majority of the variance in the fracture sorptivity values. The newly-derived fractal model fitted the experimental SI data very well for all cores investigated. Inversely estimated surface fractal dimensions, D, all fell within the theoretical bounds of 2 ≤ D < 3, thereby validating this modeling approach for fractured low-porosity rocks. Future research should focus on forward prediction of SI through independent measurements of D and extension of the fractal SI model to late-times through the inclusion of gravity.

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