Formation Pressure Dynamics

The pressure distribution in subsurface porous media and its evolution in time in response to various disturbances are proved to honour diffusion equation very accurately.

This means that interaction forces behind the pressure diffusion process propagate at infinite speed, namely:

There are few major disclaimers on the above.

Disclaimer 1

Pressure Speed Statement does not mean that pressure dynamics in one well is totally synchronised with 

Disclaimer 2

The fluid flow in porous media only starts above a certain pressure gradient threshold.

This means that even in infinite pressure propagation speed there will be some areas away from disturbing well which will never respond to the disturbance.

In practical terms this effect can only be captured at very high distances between wells or at regular cross-well distances but in low mobility formations ( usually low permeability and / or high viscosity oil ).

Disclaimer 3

The actual physical process behind pressure diffusion  in porous media is density impulse transport which propagates at speed of sound in fluid-filled porous rocks (thousands of m/s ).

In practical petroleum applications the time travel of density impulse between wells is so small (seconds or fractions of seconds) that it is never measured by gauges and not worth modelling.

That totally justifies describing the pressure dynamics with diffusion equation.

Disclaimer 4

The actual reservoir where pressure dynamic is studied is not an isolated physical object.

It is connected to wellbore and overlying/underlying rocks which represent inertial forces.

This introduces some delay in pressure response which in practical applications can measure up to minutes, can be recorded by gauges and can carry some useful information on the formation-well system and is worth modelling.

This area of knowledge is developed in non-linear Pressure Rheology Theory and linear Pressure Relaxation Theory.