A boundary-integral method applied to water coning in oil reservoirs

Abstract

In oil reservoirs, the less-dense oil often lies over a layer of water. When pumping begins, the oil-water interface rises near the well, due to the suction pressures associated with the well. A boundary-integral formulation is used to predict the steady interface shape, when the oil well is approximated by a series of sources and sinks or a line sink, to simulate the actual geometry of the oil well. It is found that there is a critical pumping rate, above which the water enters the oil well. The critical interface shape is a cusp. Efforts to suppress the cone by using source/sink combinations are presented.

Maximising output from oil reservoirs without water breakthrough

“…As soon as the interface is not fiat, the method of images is no longer applicable. To assess the errors introduced, Figure 2 compares interface solutions for a single sink at (0, 0,1) of strengths F = 0.5, 1.0, 1.5, 2.0 using both the Muskat model and the accurate integral equation solution of Lucas et al [4]. A similar graph can also be found in Blake and Kucera [2].…”

“…In the work of Lucas et al [4] and Lucas and Kucera [5], integral equation methods were developed to find the interface shape to high accuracy, both for axisymmetric and use, available at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S1446181100013456 [5] Maximising output from oil reservoirs without water breakthrough general three-dimensional sink distributions.…”

“…Many of these are referenced or described in Lucas et al [4], Lucas and Kucera [5] and Gunning et al [3], although this last paper is more interested in extending to dual completion problems. Zhang and coworkers [12,13] also considered the time-dependent evolution of the interface in a bounded domain, where no steady-state interface shape exists.…”

A note on axisymmetric supercritical coning in a porous medium

“…Earlier work [3,13,17] has concentrated on subcritical flows in which all of the extracted fluid comes from the layer adjacent to the [2] point sink. The critical flow rate is defined as the maximum rate at which only the fluid from the layer adjacent to the sink is withdrawn, and it is of great practical interest.…”

Withdrawal from the lens of freshwater in a tropical island: The two interface case

“…The computation of the critical coning behaviour of the interface is analogous to similar problems in unbounded domains, e.g. [4,6,7,10]. However, much of that work was based in unbounded domains and so there was no necessity to balance inflow and withdrawal to obtain steady flows.…”