Capillary pressure is the pressure difference that occurs across the interface between two immiscible fluids (like water and oil, or air and water) when they’re in contact within a narrow space, such as the tiny pores of a rock or soil. It’s caused by the interplay of surface tension, the force that holds the surface of a liquid together, and the geometry of the space, like how curved the interface becomes in those tight confines.
Capillary Pressure Formula
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\( P_c \;=\; \dfrac{ 2 \cdot \sigma \cdot cos(\theta) }{ r } \) (Capillary Pressure) \( \sigma \;=\; \dfrac{ P_c \cdot r }{ 2 \cdot cos(\theta) }\) \( cos(\theta) \;=\; \dfrac{ P_c \cdot r }{ 2 \cdot \sigma } \) \( r \;=\; \dfrac{ 2 \cdot \sigma \cdot cos(\theta) }{ P_c } \) |
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| Symbol | English | Metric |
| \( P_c \) = Capillary Pressure | \(lbf \;/\; in^2\) | \(Pa\) |
| \( \sigma \) (Greek symbol sigma) = Fluid Interfacial Tension | \(lbf \;/\; in\) | \(dyn \;/\; cm\) |
| \( \theta \) = Angle of Wettability | \(deg\) | \(rad\) |
| \( r \) = Radius of Capillary | \(in\) | \(cm\) |
Surface Tension - It’s the cohesive force at the surface of a liquid that makes it act like a stretched membrane. When two fluids, like water and oil meet, surface tension at their interface resists mixing and creates a pressure difference. The stronger the surface tension, the higher the capillary pressure.
Wettability - This is about how much one fluid prefers to stick to a solid surface over the other. If a surface (like a rock pore) is water-wet, water spreads out and hugs it, while oil gets pushed aside. If it’s oil-wet, the reverse happens. Wettability shapes the curvature of the fluid interface, which directly affects the pressure difference.
Pore Size and Geometry - The smaller the space, like a tiny pore or capillary tube, the more pronounced the effect. When the interface between the fluids curves sharply in a narrow space, the pressure difference spikes. This is why capillary pressure is a big deal in fine-grained materials like clay or tight rocks, but less so in wide-open spaces.
Fluid Properties - The difference in densities or viscosities between the two fluids can influence how they behave under capillary forces. For instance, a denser fluid might resist displacement more, tweaking the pressure balance.
Interfacial Curvature - Tied to all the above, the shape of the boundary between the fluids matters. In a capillary tube or pore, this boundary (called the meniscus) curves based on wettability and pore size. The tighter the curve, the greater the capillary pressure, as described by the Young-Laplace equation: pressure scales inversely with the radius of curvature.
Capillay Pressure Applications
Reservoir Characterization - Capillary pressure helps geologists and engineers figure out the structure of reservoir rocks, like sandstones or carbonates. By measuring how oil, water, or gas distribute in the pores under different pressures, they can estimate pore size distribution, permeability, and how much of each fluid the rock can hold. This is often done with lab tests on core samples, using techniques like mercury injection or centrifuge methods.
Fluid Saturation and Distribution - In a reservoir, oil, water, and gas coexist, and capillary pressure governs where they sit. Water, usually the wetting phase, clings to smaller pores, while oil or gas occupies larger ones. This determines the irreducible water saturation (water that won’t budge) and the residual oil saturation (oil left behind after production), critical for predicting how much hydrocarbon can be extracted.
Oil and Gas Migration - Capillary pressure influences how hydrocarbons move into and get trapped in reservoirs. During formation, oil and gas push against water in tight rock pores. If capillary pressure in a seal rock (like shale) is high enough, it stops hydrocarbons from escaping, forming a trap. Understanding this helps locate drillable reserves.
Enhanced Oil Recovery - Techniques like waterflooding or gas injection rely on manipulating capillary pressure. Injecting water pushes oil out of pores, but capillary forces can trap some oil in smaller spaces. Engineers tweak injection pressures or add surfactants to lower surface tension, reducing capillary pressure and freeing more oil.
Relative Permeability Studies - Capillary pressure ties into how easily oil, water, and gas flow through rock together. By studying it, engineers model “relative permeability,” how each fluid’s flow changes as saturation shifts, which is essential for optimizing production rates and designing well systems.
Height of Transition Zones - Above the free water level in a reservoir (where water pressure balances oil pressure), there’s a transition zone where oil and water mix. Capillary pressure dictates its height, thinner in coarse rocks, thicker in fine ones. This affects how much oil sits above the water and where wells should tap in.
