On the maximum width of oil stringers under hydrodynamic flow conditions

Abstract

An analysis is presented of the maximum thickness of a stationary buoyant oil-mass, trapped under an angled incline, when subjected to hydrodynamic, surface tension and buoyancy forces. For high water-flow speeds down the aquifer, with upward buoyancy forces dominantly combating hydrodynamic pressure, it is shown that the maximum oil thickness occurs at about 60% of the length of the oil stringer measured from the upward end. The length of the oil stringer then is roughly proportional to the square root of the oil-mass contained, as is the maximum thickness. For low water-flow speeds, in which buoyancy and surface tension are dominantly balanced (with only lesser contributions from hydrodynamic pressure), the oil length is effectively constant, whereas the maximum thickness grows proportionately to the 3/4 power of the contained oil mass at low oil masses, and proportionately to the oil mass at high mass values. As the water-flow velocity increases, the shaping of the oil stringer shifts from the small “bubble” form to the long oil stringer form. Analytic formulae are given to provide approximate methods from which to estimate oil and gas accumulations under more complex conditions.