# Why do we consider hydrostatic pressure and lithostatic pressure separately?

In petroleum geology, why do we consider hydrostatic pressure and lithostatic pressure separately? Surely the pressure at any point, whether fluid or rock, at depth is simply equal the weight of all the fluid and rock overlying it? Hence why isn't pressure for fluids and solids equal at a particular depth?

• Underground rock stresses are not two dimensional. In addition to the vertical rock stresses (in the z direction), there are two horizontal (or lateral) stresses (in the x & y directions). As to why lithostatic and hydrostatic pressures aren't equal at depth, because they have different pressure gradients. See the graph for Pressure/Stress Gradients.
– Fred
Oct 25 '18 at 2:30
• The difference between these pressures is important in glaciology since water is more dense than ice. See the diagram under "Controls on crevasse depth" about halfway down the page. Oct 25 '18 at 2:57

I think (but I'm not an expert on the topic) that your assumption is wrong! The pore fluid pressure and effective pressure exerted on the rock are not identical. And during log measurements, it is only the pore fluid pressure that is measured, $$\sigma_\text{pore}=\rho_\text{water}gz$$. As long as the water is connected through pores to the earth's surface and it is assumed to be hydrostatic (not-flowing), the measured pressure in the pores will create a pressure to push up the overlying water only -- the rocks will take care of carrying the overlying rocks themselves! If you'd drill a borehole, the water-filled column would be filled with water exactly to the earth's surface. The effective pressure on the whole system is then $$\sigma_\text{effective}=\sigma_\text{lithostatic}-\sigma_\text{pore}$$.

However, once a seal is formed (e.g., a shale formation overlies a formation), the pore water suddenly has to also carry the overlying rock formation! The pressure will then increase significantly, and the pore water pressure that you measure becomes more similar to the effective pressure.

The pore water pressure thus increased below a seal because it is stuck. Once you drill a hole from the surface to this formation, you allow water to flow freely to the surface, and it is clear that it is under overpressure with respect to the lithostatic pressure, because it will blow out!

• Yes, the pore pressure and lithographic pressures are different. In certain rock formations the lithographic pressures can crush high strength steel casing ,although the steel casing can withstand the hydrostatic pressure by itself. PS - I never heard of an oil or gas well where the formation waters were allowed to escape , unless some one screwed -up big time. Also , water is not allowed to flow from one formation through the annulus to another formation .That is why there are drilling/casing engineers. Sep 4 '19 at 1:56

It took me a while to get it (and I'm not a geologist or petroleum engineer or anything, just someone who knows basic physics and has been reading a geology textbook), but I think I understand Erik's answer: It's based on buoyancy.

Consider a column of permeable rock and soil that has a zone of aeration above a zone of saturation. (I'm gonna talk about water, but it would also work for oil or air or any other fluid less dense than the local rock/soil.) If any weight from the soil/rock were pushing down on the water in the zone of saturation, it would just push the water up and out of the way and raise the water table, while lowering some of the rock/soil. This is because the rock/soil is denser than water, so gravitational potential energy goes down when rock/soil goes down and pushes an equal volume of water up.

Water with an impermeable layer above it can support some of the weight of the rock because the buoyancy force this would create can't push the water up through the impermeable layer. If a hole were made in said impermeable layer, displaced water could move up through that hole to allow the supported rock to settle a little lower (which is how artesian wells work).

If the water is supporting some of the weight of the rock, this fraction of that weight (this fraction of the lithostatic pressure) will have to be supported by pressure that is locally (approximately) hydrostatic (equal in all directions), because that's the only way stationary fluids can exert pressure. This means the water pressure can also push sideways, which seems like it should matter when strata are tilted or curved so that part of the permeable bed is open to the surface while the rest is overlied by an impermeable bed, as in a typical aquifer, and it does:

As you move sideways (on a surface of constant gravitational potential(pot. energy÷mass)/geopotential) the hydrostatic pressure in the water must be stay constant; otherwise, the water would flow sideways to equalize it. (Actually, this isn't entirely true, as can be determined from my geology textbook, which notes that "pores ... provide resistance to flow", related to permeability of the rock/soil and viscosity of the fluid I guess, and that "pressure is lost through fractures (leaks)", presumably in the "imperable" layers, but it's a good starting approximation.) As you move down through the water, the pressure goes up according to how much more weight (weight of the water and possibly a bit of the rock) the water at that point needs to support. (Reverse as you go up.)

Now, remember that the water at the top of the water table in the area with a zone of aeration above it, and atmosphere above that, cannot support any lithostatic pressure. As you go straight down from here, let's assume only the weight of the water above being supported by the water, not any rock/soil. (I think that's true, but I'm not sure. In any case, it doesn't significantly affect my point if not.) As you move sideways from a point below the permable zone of aeration to a point below an impermable bed, the height of water above you has to drop from the height of the water table to the height of the bottom of the impermable bed (whenever this gets lower than the water table under air). More importantly, this generally means there is less weight of (contiguous) water pushing down on the water where you are. (I'm just noticing that, since much or most of the volume underground is rock/soil, volume and therefore weight of water in a column is only proportional to height in rock/soil of constant porosity, but that approximation basically works within a single permable bed.) However, the hydrostatic pressure must stay (approximately) the same. The only way to accomplish this is for the water to push up some of the rock and support enough of the lithostatic pressure to (approximately) equal the weight of water lost. (Actually resistance to flow and leaks mean the pressure goes slightly down as you move further sideways away from an area below air, which is why the "artesian-pressure surface"/"potentiometric surface" above an aquifer slopes down as you move away from the "recharge area" rather than being flat.)

I imagine a little extra complexity is added when your dealing with gasses rather than liquids (so the density of the fluid is highly dependent on the hydrostatic pressure it's under), when fluids are in motion rather than stationary, or when you consider the permeability of rocks quantitatively rather than as just "permeable" and "impermeable".

• I've just realized that wet soild takes up more volume than dry soil, and I think removing water even from soil and rock that was never capped with impermeable layers can cause subsidence (as in Mexico city, where most of the city is built on what used to be a lakebed before the water was pumped out of the lake). This implies to me that the water must somehow be supporting some of the lithostatic pressure in wet soils, contradicting my buoyancy argument. Maybe this is related to Van der Waals forces between water and grains, i.e., related to that "resistence to flow"? Maybe I'm just wrong? Jul 8 at 23:46
• Maybe I should have thought more about my concept of buoyancy. Rock is negatively buoyant in water (denser than water), so water pressure can't actually push a rock up alone, but the water pressure is still higher near the bottom of a rocky grain than the top, so it might still exert an upward force, which will remove some of the load on the grains below. This reduction in lithostatic pressure could cause grains to expand or to reduce their tendency to settle lower and pack down tighter. Jul 9 at 0:07