Pressure and Depth - Pros and cons of fluid pressure gradient plots

Tim Wynn

Tim Wynn

Principal Geology & Geomechanics at TRACS International

Published Aug 6, 2019

Measuring, calculating, plotting and understanding pressures are core activities for most subsurface professionals. However, there are some differences between how different groups approach the same data. In general, Reservoir Engineers, Petrophysicists and Geologists tend to plot pressure vs depth. Conversely, Drilling Engineers and Geomechanics Engineers often plot pressures vs depth as densities such as pounds per gallon (ppg) or they can be expressed as pressure gradients such as psi/ft. You can convert ppg to psi/ft just by multiplying by 0.052 so they are fundamentally the same.

I will use psi/ft here as it is widely used and explicitly couples pressure and depth in the units used. For fluid pressures (as discussed here) it is common to use ftTVDss as a depth datum. Drillers usually require ftTVDrkb because of the extra column weight of drilling fluid from the drill floor to sea level.

Pressures vs Depth - oil and water

Before we look at the differences in the two approaches, let's assess what causes different fluid pressures in the earth. Fluid pressures at depth are a function of two main things:

  1. Density of the fluid. As a rule of thumb, formation water densities are around 0.447 psi/ft, oil density is around 0.3 psi/ft and gas density (at most reservoir depths) is around 0.1 psi/ft. A normal or hydrostatic pressure gradient is given by a column of formation water in the rock pores that is continuously connected back to sea level. This is the reference pressure line and important to know.
  2. Overpressure comes from various mechanisms such as disequilibrium compaction (as the sediments are buried, fluids can't escape and pressure builds up). In some cases, these processes can cause many thousands of psi of excess pressure above the hydrostatic pressure gradient. In general, within a permeable unit such as a sandstone, overpressures cause a constant shift in the fluid pressure to higher values.

The first plot below shows a typical plot for fluid pressure vs depth in a water, oil and gas system with 1000 psi of overpressure in the water leg with respect to the hydrostatic pressure reference line. It can be seen that the hydrostatic and water leg lines are parallel as they have the same fluid density of 0.447 psi/ft. However, the pressure lines in the oil and gas legs become progressively steeper because of the lower fluid densities of 0.3 psi/ft in the oil and 0.1 psi/ft in the gas. More on this later.

No alt text provided for this image

Under static conditions (no production), where lighter oil sits above denser water the two fluids have the same pressure at the contact - see left hand plot. This pressure equilibration at the contact occurs because the less dense oil typically migrates into a reservoir laterally or from underneath until it reaches a seal and then gradually fills the reservoir from the top downwards. Therefore the oil-water contact moves downwards as more oil comes in. This stops when the oil stops migrating or the structure is completely filled.

As you move upwards from the oil-water contact through the lighter oil column the pressure is higher in the oil than it would be in the water. How can a lighter fluid like oil have a higher pressure than water at a shallower depth? The reason for this is that the density of the fluid column in the oil or gas legs is less than the water. So, as you get shallower the pressure can't 'unload' as quickly as it would in denser water. You feel this unloading effect in your ears when diving down and back up in 2 metres of water vs no noticeable effect when walking up and down 2 metres on stairs that are in air. This higher pressure at shallower depths within lighter fluids (oil or gas) is called the buoyancy pressure.

All the principles defined above also hold for free gas above water or free gas above oil as shown in the example here. Hopefully the above description explains how pressures occur in typical hydrocarbon columns. Now let's look at representing the pressures as gradients.

Pressure Gradients

The second plot below shows those same pressures as the first plot but converted to instantaneous pressure gradients (pressure / depth). The hydrostatic pressure line has a constant gradient of 0.447 psi/ft as it is connected all the way back to zero pressure at zero depth (sea level). Lets look at the gradient changes starting at the bottom (check both the plots to avoid getting lost in numbers!).

No alt text provided for this image

  1. WATER. The water leg has a presssure offset of 1000 psi but the same fluid density as the hydrostatic line. At the oil-water-contact is at 10,000 ftTVDss this means the total pressure gradient becomes 0.447 + 1000/10,000 ftTVDss = 0.547 psi/ft but at 12,000 ftTVDss it is 0.447 + 1000/12,000 = 0.530 psi/ft. So a constant pressure offset in the water leg with the same fluid density as the hydrostatic column becomes a non constant instantaneous pressure gradient. It is non-intuitive but correct because of the different depths of calculation with the same 1000 psi pressure offset.
  2. OIL. At the gas-oil contact the pressure has become 1294 psi above hydrostatic because of the buoyancy pressure of the oil column of 294 psi that is added to the 1000 psi overpressure. This means the total instantaneous pressure gradient increases again to 0.609 psi/ft from both the buoyancy pressure increase and the shallower depth of 8000 ftTVDss.
  3. GAS. Finally, at 7000 ftTVDss, at the top of the gas leg in the reservoir, our system has reached the maximum pressure of 1641 psi. This is made up of 346 psi buoyancy pressure in the gas leg plus 294 psi buoyancy pressure in the oil leg plus the overpressure of 1000 psi. This combination of buoyancy pressure increases and the shallowest depth causes the total pressure gradient to reach 0.681 psi/ft.

Summary

  1. The pressures in reservoir fluid systems at depth are comprised of overpressure offset and the buoyancy pressure components.
  2. For any fluid system other than a hydrostatic column (where pressure reduces to zero at zero depth), the instantaneous pressure gradients will increase upwards. This is the case even where there is a single fluid and constant pressure offset relative to a hydrostatic column.
  3. It is often hard to look at a fluid pressure instantaneous gradient plot and quickly determine where the contacts are and what is controlling the different fluid pressures. However, these plots can be interpreted with practice, especially when used in conjunction with traditional pressure plots.

Finally, pressure gradient or fluid density plots are particularly useful in drilling because the pressure at depth in a well being drilled is primarily controlled by the drilling fluid density (static mud weight). In general you want the mud weight, expressed as a pressure gradient or density, to be above the pore pressure (to stop fluid influxes and blow-outs) but below the pressure that will fracture the rock to prevent mud losses. At the top of some long gas columns the pore pressure and frac gradients can converge leaving a very narrow window within which to target the mud weight. That's another topic though!

For any queries, clarifications or corrections please contact me on LinkedIn or at tim.wynn@tracs.com

Others also viewed

Explore topics