Numerical Simulation of Microscopic Oil-Water Two-Phase Flow Mechanisms in Porous Media Using the Volume of Fluid (VOF) Method

Imagine trying to clean a giant, messy sponge that is soaked in thick, sticky honey. Now, imagine that the sponge isn't just one big block, but a complex maze of tiny tunnels, some wide and some so narrow you can barely see them. This is essentially what happens inside an oil reservoir deep underground. The "sponge" is the rock, the "honey" is the crude oil, and the "water" is what we pump in to push the oil out. But here's the tricky part: the rock isn't just a boring, uniform sponge. It has a personality. Sometimes the rock walls love water (water-wet), and sometimes they prefer to hug the oil (oil-wet). This preference, called "wettability," changes how the fluids move. If you push the water in too fast, it might just blast through the easy tunnels, leaving the honey trapped in the hard-to-reach corners. If you push too slow, the water might get stuck. Scientists have been trying to figure out the perfect way to push this water to get every last drop of oil without wasting a single drop of water themselves.

This is where a team of researchers from Yangtze University stepped in. Instead of drilling into the ground and guessing, they built a tiny, digital world inside a computer. They used a clever math trick called the "Volume of Fluid" (VOF) method, which is like a super-accurate digital camera that can watch the boundary between oil and water as it moves, pixel by pixel. They created microscopic models of rock pores, some with cracks (fractures) and some without, and simulated what happens when water is injected at different speeds and under different "moods" of the rock. They wanted to see: Does speed matter? Does the rock's preference for oil or water change the game? And is there a smarter way to pump water than just turning the tap on full blast and leaving it there?

The Race Through the Rock Maze

The researchers set up a digital race. They built four different types of "sponges" (porous media models) to see how the water and oil interacted. Some were uniform, like a perfectly organized grid of marbles, while others were messy and chaotic, with big gaps and tiny pinholes. They then watched what happened when they pushed water through these models at different speeds.

They found that speed is a double-edged sword. When they pushed the water slowly (at 0.005 m/s), the water was like a cautious explorer. It felt the tiny capillary forces—the sticky pull of the rock walls—and took the time to squeeze into the small, hard-to-reach pockets. It was sensitive to the local bumps and bruises of the rock structure. However, when they cranked up the speed to 0.01 m/s, the water turned into a reckless sprinter. The force of the push (viscous force) became so strong that it overpowered the rock's sticky pull. The water ignored the small, tricky tunnels and blasted straight through the wide, easy highways.

Here's the twist: being fast wasn't always better. In one of their messy, heterogeneous models (Model C), speeding up the water actually reduced the amount of oil they could get out. At the slower speed, they recovered about 51.2% of the oil. But when they sped up, that number dropped to 47.0%. Why? Because the fast water created "highways" that bypassed the oil trapped in the side streets. It was like a flood rushing down a main street, leaving the houses in the alleyways untouched. The simulation suggested that if you push too hard, you might just sweep the easy stuff and leave the rest behind.

The Rock's Mood Swing: Who Does the Wall Like?

Next, the team asked a question about the rock's personality: Does it like water or oil? In the real world, rocks aren't just one way; they are often "mixed-wet," meaning some parts of the rock love water while others love oil. The researchers simulated four different "moods" for their digital rock:

1. MWL: Big pores love oil, small pores love water.
2. MWS: Small pores love oil, big pores love water.
3. FW: A mix of both everywhere.
4. OW: The whole rock loves oil.

They discovered that the "MWS" mode (where the tiny, hard-to-reach pores love water) was the superstar. When they injected water at a moderate speed of 0.01 m/s, this setup allowed the water to sneak into the tiny pores and pull the oil out like a magnet. It recovered about 68.6% of the oil. In contrast, the "OW" mode (where the whole rock hates water) was a disaster. The water couldn't get into the rock at all; it just rushed through the cracks and left the oil behind, recovering only about 25.6%.

But even the best mood had a limit. When they pushed the water even faster (0.015 m/s) in the MWS model, the recovery rate dropped to 63.7%. The simulation showed that going too fast made the water ignore the rock's helpful little pores and just zoom through the main cracks again. It seems there is a "Goldilocks" speed—not too slow, not too fast—that lets the water do its job of sucking the oil out of the rock's tiny pores.

The Art of the Pump: Stop, Start, and Vary

Finally, the researchers tackled the question of how to pump the water. In the real world, oil companies usually just pump water at a constant rate, like a steady stream from a hose. But the team wondered: What if we played with the rhythm? They tested three strategies:

1. Constant Rate: Pumping at a steady 0.01 m/s.
2. Periodic Intermittent: Pumping for a bit, then stopping completely (shut-in), then pumping again.
3. Periodic Variable-Rate: Pumping at a slow speed, then switching to a fast speed, then back.

The results were surprising. The "stop-and-start" method (Periodic Intermittent) was the most efficient. When the pump stopped, the water didn't just sit there; it had time to relax and seep sideways into the oil-filled corners that the fast stream had missed. This "rest period" allowed the water to redistribute and grab more oil.

By the end of their simulation (at 0.06 seconds), the intermittent method had recovered about 36% of the oil. The variable-rate method did slightly better at 40%, but it used more water to get there. The constant-rate method recovered 37%, but it was the least efficient with water.

The most important number here is the "water cost." To get 35% of the oil out, the constant-rate method needed a normalized cumulative injected volume (Ninj) of 5.25. The intermittent method only needed 2.93. That means the stop-and-start method used about 44% less water to get the same amount of oil! The variable-rate method was also a winner, using about 31% less water than the constant method.

The Takeaway

This study didn't just guess; it simulated the microscopic dance between oil and water in great detail. The findings suggest that in tight, complex rocks, blasting water in at high speeds might actually hurt your oil recovery by creating shortcuts that skip the hard-to-reach oil. Instead, a moderate speed combined with the right rock "mood" (where small pores love water) seems to work best. Even better, changing the rhythm of the pump—stopping and starting or varying the speed—can save a massive amount of water while still getting the oil out.

Of course, these are results from a computer simulation of 2D models. The real world is 3D, messy, and full of surprises. The authors note that these results show relative trends and need to be tested with real core samples and field experiments before being used in actual oil wells. But the message is clear: sometimes, in the race to get oil out of the ground, it's not about how hard you push, but how smartly you play the game.