Researchers Develop Innovative Nano-Capillary Rise Model to Decipher Fracking

In the last decades, hydraulic fracturing or “fracking,” a method of oil and gas extraction, has taken the global energy industry by storm. In this technique, small gas and oil deposits that are trapped inside stone formations are drawn out by fracturing the rock.

The fracturing is carried out by passing a highly pressurized liquid, that is, “fracking fluid,” which is mixture of water including sand suspended in thickening agents.

Once the water molecules in the fracking fluid get injected into the stone formations, they expand upward inside the stone walls of the small channels through which they flow. Then, they are subjected to “imbibition,” that is, a kind of diffusion in which the molecules are absorbed through nano-pores into the adjoining pockets, where the gas and oil are located.

The absorption of the water molecules results in the displacement of the gas and oil molecules, which can eventually be pumped to the surface. The capillary force between oil and water paves the way for such an activity, causing a tension at the point or interface at which the two fluids interact.

Researchers typically use the Lucas-Washburn equation to compute the anticipated increase in the capillary level under such circumstances. The Lucas-Washburn equation is a mathematical model with its earliest parameters initially devised nearly 100 years ago. However, the problem with this equation is that it has not proven to be completely accurate in predicting the actual increase observed in nano-capillary laboratory experiments.

The height of the capillary rise that was observed in these experiments was lower than what the Lucas-Washburn model would have predicted. Understanding what was causing this deviation became an important point of focus for my colleagues and me.

Anqi Shen, Doctoral Student, Northeast Petroleum University

Shen works in collaboration with Yikun Liu, a professor at the university.

The scientists have reported the outcomes of their research this week in the Applied Physics Letters journal published by AIP Publishing.

“Many explanations have been offered for the lower-than-expected capillary rise. One area of discussion has focused on the viscosity of the fluid. Another has been the sticky layers of oil that form on the walls of the capillaries and narrow their diameter, which is an issue that we have also explored,” explained Shen, whose research is also funded by the Major Projects Program for the National Science and Technology of China.

“We looked at many factors and found that the surface roughness of the capillaries was the main reason for the lower-than-expected result. Specifically, we realized that the model could better determine the actual level of capillary rise if we adjusted the parameters to account for the frictional drag that is caused by the inherent roughness of the surface of the capillary walls. When we saw how this made the model more accurate, we knew that we could not ignore it,” stated Shen.

In addition, the nano-scale size of the capillaries suggests that even a slight increase in surface roughness can significantly affect the computations.

Factors that might be ignored in normal conditions can have significant effects on a micro or nano level. For instance, a relative roughness of 5 percent, in a tube with a radius of 100 cm where the obstacle height is 5 cm hardly affects the fluid flow in the tube. However, with a tube radius of 100 nm and obstacle height of 5 nm, it could significantly affect the fluid flow in the tube.

Anqi Shen, Doctoral Student, Northeast Petroleum University

Currently, very few laboratories exist that can perform the nano-capillary rise experiments. Consequently, Shen and her collaborators were able to compute using the results from only one laboratory in the Netherlands. In future, they propose to validate their mathematical formula by analyzing its effectiveness in simulating the outcomes of other experiments.

Despite the fact that Shen’s study concentrates on gas and oil development, she and her collaborators anticipate that their study can prove useful for researchers working in other areas of research.

“Capillary rise is a basic, physical phenomenon that occurs in soil, paper, and other biologically relevant realms,” stated Shen. “Understanding how it is potentially affected at the nano-capillary level by frictional drag could shed light in a variety of scientific disciplines.”