There was an interesting study I read a few years ago. The were many smallish oil fields discovered on Texas railroad lands in the decades prior to the 1930's. When the big discovery made in East Texas drove the prices down, many of these older, small fields were shut in. Some of them sat for decades. Others had sporatic re-development. In a few wells, there were recorded reservoir pressure measurements prior to long shut in intervals. When prices spiked in the late 1970's, a few of these wells were re-entered and re-logged (primarily looking for bypassed, or behind pipe reserves). But lo! and behold!, reservoir pressures were found to be much higher than when shut in, and some almost back to original (estimated) pressures. There were only a couple of possibilities, of which natural recharge was one.
I'm not a petroleum engineer, but the geolgical concepts behind recharge are sound. It is however, a dynamic equation. Time is the crucial factor. Also, proximity to an active petroleum system (in oil field lingo - how close you are to the "kitchen") is essential.
Many oil and gas reservoirs are connected to large aquifers -- large accumulations of water in the surrounding porous and permeable rock that may stretch for many miles away from the reservoir. When the oil or gas is produced from the reservoir, the pressure in the reservoir declines. The body of surrounding water then slowly expands and pushes water through the reservoir rock into the field, thereby recharging reservoir pressure over a period of years.
This natural water drive is a more likely explanation for reservoir pressure recovery in shut-in wells than the recharge of oil. A rapid recharge of oil to a reservoir would be an unusual, non-typical case.