Calculating Reservoir Pressure and Temperature

The initial reservoir pressure and temperatures is one of the most important parameters we need in petroleum engineering. From initial reservoir pressure and temperatures we can determine fluid properties with correlations, estimate the amount of hydrocarbons in place, and predict an overall recovery factor from a well. How do we estimate reservoir pressure and temperature?? Lucky for you, I’m going to give you some rules of thumb that you can use to predict reservoir temperature and pressure easily with very little knowledge of the formation.

Pore Pressure

Pore pressure refers to the pressure of the fluid held within the pore space of the rock at a given depth (This includes hydrocarbons!!). In essence, pore pressure is the key to calculating reservoir pressure because it’s also the pressure that hydrocarbons feel in the subsurface. The pore pressure is derived from geological processes and is essentially the hydraulic gradient of the regional water gradient multiplied by the true vertical depth of the formation. I repeat the hydraulic gradient of water, not oil (remember this!!). The table below shows some normal pore pressure gradients for various drilled areas:

Table 1: Normal formation pressure gradients for several drilling locations [1]

Location	Pressure Gradient (psi/ft)
West Texas	0.433
Gulf of Mexico Coastline	0.465
North Sea	0.452
Malyasia	0.442
Mackenzie Delta	0.442
West Africa	0.442
Anadarko Basin	0.433
Rocky Mountains	0.436
California	0.439

It is important to note, that the pressure gradient of freshwater (you know the stuff you drink everyday) is $0.433 \frac{psi}{ft}$ (Store this number in your brain because it will show up constantly). From the table above it is clear that some of the regions have an identical pressure gradient to freshwater. So within reason, you can use the pressure gradient of freshwater to calculate reservoir pressure. The general equation used to calculate formation pressure at a given depth is given by the following expression:

(1) $\begin{equation*} P_f = (0.433 \frac{psi}{ft})SG_{localwater}(TVD) \end{equation*}$

where:

$TVD$ = true vertical depth, $ft$

$SG$ = specific gravity of water, $unitless$

** Note: the specific gravity of water is equivalent to 1.0***

Based on the data above, I would recommend the following:

Use Pressure Gradients between 0.433 and 0.470 $\frac{psi}{ft}$ when predicting reservoir pressure

Temperature

Temperature is easy to estimate because we assume it varies linearly with depth. The temperature at a given depth is given by the following expression:

(2) $\begin{equation*} T_z = T_{surf} + \frac{dT}{dZ} Z \end{equation*}$

where:

$T_z$ = the temperature at the depth $Z$ , $^\circ F$

$T_{surf}$ = the temperature at the surface, $^\circ F$

$\frac{dT}{dZ}$ = the temperature gradient, $\frac{{^\circ} F}{ft}$

$Z$ = the depth, $ft$

The average thermal gradient of crustal rocks is $1.41 ^\circ F/100 ft$ . If you don’t know the surface temperature, use $68 ^\circ F$ . If your offshore, use $32^\circ F$ at the the ocean bottom. So in general use the following if you lack all information about temperature:

Use a temperature gradient of $1.41 ^\circ F/100ft$ . For onshore wells use $T_{surf} = 68 ^\circ F$ . For offshore wells, start at the ocean bottom and use $T_{surf}= 32 ^\circ F$ .

That’s it, it is really simple to estimate reservoir temperature and pressure. Just understanding these two simple concepts will take you a long way in you petroleum engineering studies.

(3) $\begin{align*} x^2 + y^2 &= 1 \\ y &= \sqrt{1 - x^2} \end{align*}$

References

[1] Bourgoyne, A., Bmillheim, K. , and et. al. Applied Drlling Egineering, Society of Petroleum Engineers. 1991.