Closed form flow model of a damped slug test in a fractured bedrock borehole

- We model fractured bedrock response to slug tests with geophysical logs.
- Closed form model accommodates lognormally distributed apertures.
- Applied to boreholes in fracture zone of Dedham Granite in eastern Massachusetts.
- Compressibility, mean and median apertures are calibrated.
- Permeability, transmissivity, porosity, and storativity can be calculated from results.

SummaryAn existing closed form model is modified to describe the damped response of groundwater in a fractured bedrock borehole with variable apertures and dips to a slug test. The existing theory, which requires single sized horizontal fractures, is accurately calibrated by slug test data from three uncased bedrock boreholes in the Dedham Granite and an observation well screened just below the contact surface with a till drumlin. Apertures and dips vary however, so the ability of the modified theory to accommodate different sizes and inclinations improves upon the physical validity of its predecessor when fracture information accompanies slug test data. Geophysical logs identify a large number and dip of fractures in the uncased boreholes in the Dedham Granite in this regard. A lognormally distributed, horizontal aperture calibration of the slug tests in the uncased boreholes retains the accuracy of the single size model, and yields aperture statistics more consistent with literature values. The slug test in the screened observation well is accurately calibrated with the modified horizontal theory for discrete (two) sizes, based upon the average fracture spacing found in the uncased boreholes. All four results yield comparable compressibility estimates, which depend on fracture spacing but not size or dip. The calibrated aperture size and calculated fracture porosity and permeability decrease with length of the borehole into the Dedham Granite. The measured dip and aperture for flowing and nonflowing fractures in one of the boreholes accurately calibrates the modified theory. The inclusion of dip reduces the calibrated permeability because of the increased ellipsoidal area at the interface of the borehole and the inclined fractures.