Petroleum Related Rock Mechanics, 2nd Edition

So far, we have assumed that any change in applied stress is followed instantaneously by the corresponding deformation. Quite often, however, it is observed that the deformation of rocks continues for a long time after a change in the applied stress. The time-dependent effects can be divided into two groups: consolidation and creep. Consolidation is due to pore pressure gradients induced by a change in the stress state, and the fact that it takes time to re-establish pore pressure equilibrium. Creep is related to visco-elastic behaviour of the solid framework. In the following, consolidation and creep are discussed separately. In practice, however, it is sometimes difficult to distinguish between genuine creep and consolidation effects.
Consolidation theory describes the transient process, where pore pressure equilibrium is reestablished after a change in the stress state. This process involves a flow of the pore fluid through the porous rock. Viscous flow in porous rocks is described by Darcy s law, which states that the fluid flow rate
(fluid volume per unit time flowing through a surface), is proportional to the pore pressure gradient ? p f:
Here A is the surface through which the fluid flows, and ? f is the dynamic viscosity of the fluid. k is the permeability of the rock. Normally, k is measured in the unit Darcy, defined as the permeability which gives a flowrate of one centimetre per second of a fluid with viscosity one centipoise...