James V. Tracy | USGS Science

USGS2010

Flow through fractures

Flow through fractures is often idealized as flow between two parallel plates (plane Poiseuille flow). The opening or aperture between parallel plates is unambiguous and its relation to flowrate is well known. However, fractures in rock have uneven walls and a variable aperture. A model for flow in a fracture is proposed wherein the fracture is represented by a set of parallel plate openings with different apertures. The model leads to a modified Poiseuille equation for flow which includes an aperture frequency distribution for the fracture. Any arbitrary aperture distribution can be used; in order to simplify computation and demonstrate the properties of the model a log normal form of distribution is assumed. Even when an analytical form of the distribution is assumed, two parameters, rather than a single value representing ‘aperture size’ are required to determine flowrate. Models of aperture change for a fracture undergoing compression (fracture walls deforming) and extension (fracture walls separating) are developed which constrain the additional parameter and allow calculation of flowrate as a function of mean aperture. The theoretical relationships developed between mean aperture and flowrate can be used to interpret published laboratory data for single fractures.

Water Resources Research↗

USGS1977

Ground-water resources of the North Beach Peninsula, Pacific County, Washington

The anticipated water demand of 425 million gallons per year for the North Beach Peninsula, Pacific County, Wash., can be met by properly developing the ground-water supplies of the area's water-table aquifer. Of the approximately 77 inches of precipitation on the peninsula, an estimated 23 inches is lost to evapotranspiration, and approximately 36 inches is discharged by the water-table aquifer into the ocean and bay. The remaining water either runs off the surface or is leaked to a deeper aquifer that ultimately discharges to the ocean. In some areas of the peninsula, particularly those that are low lying and covered with poorly permeable soils, runoff is promoted by an artificial drainage system developed to alleviate waterlogging. In these areas, it is estimated that natural discharge through the aquifer would be less than that of the artificial drainage system. By a conservative estimate, at least 12 inches of the water that discharges naturally through the aquifer is available for additional development. This quantity of water is approximately equivalent to 860,000 gallons per day or 320 million gallons per year per mile of peninsula length. Under specified idealized conditions wells spaced at least 1,000 feet apart along the major axis of the peninsula and pumped at average rates of no more than 80 gallons per minute would ensure that water-level declines do not exceed 6 feet near the wells and 1 foot at the shoreline, thereby preventing seawater intrusion. Lowering of the water table may be beneficial in reducing waterlogging problems, but care must be taken not to lower the levels near cranberry bogs, which require a shallow water table. Treatment of the otherwise good quality water for iron may be required, as about 75 percent of the well water sampled from the aquifer had iron concentrations in excess of limits recommended by the U.S. Environmental Protection Agency.

Washington↗