Static and dynamic effective stress coefficient of chalk

Deformation of a hydrocarbon reservoir can ideally be used to estimate the effective stress acting on it. The effective stress in the subsurface is the difference between the stress due to the weight of the sediment and a fraction (effective stress coefficient) of the pore pressure. The effective stress coefficient is thus relevant for studying reservoir deformation and for evaluating 4D seismic for the correct pore pressure prediction.

The static effective stress coefficient n is estimated from mechanical tests and is highly relevant for effective stress prediction because it is directly related to mechanical strain in the elastic stress regime. The corresponding dynamic effective stress coefficient α is easy to estimate from density and velocity of acoustic (elastic) waves.

We studied n and α of chalk from the reservoir zone of the Valhall field, North Sea, and found that n and α vary with differential stress (overburden stress-pore pressure). For Valhall reservoir chalk with 40% porosity, α ranges between 0.98 and 0.85 and decreases by 10% if the differential stress is increased by 25 MPa.

In contrast, for chalk with 15% porosity from the same reservoir, α ranges between 0.85 and 0.70 and decreases by 5% due to a similar increase in differential stress. Our data indicate that α measured from sonic velocity data falls in the same range as for n, and that n is always below unity. Stress-dependent behavior of n is similar (decrease with increasing differential stress) to that of α during elastic deformation caused by pore pressure buildup, for example, during waterflooding.

By contrast, during the increase in differential stress, as in the case of pore pressure depletion due to production, n increases with stress while α decreases.