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 [Formula: see text] 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 [Formula: see text] is easy to estimate from density and velocity of acoustic (elastic) waves. We studied [Formula: see text] and [Formula: see text] of chalk from the reservoir zone of the Valhall field, North Sea, and found that [Formula: see text] and [Formula: see text] vary with differential stress (overburden stress-pore pressure). For Valhall reservoir chalk with 40% porosity, [Formula: see text] 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, [Formula: see text] ranges between 0.85 and 0.70 and decreases by 5% due to a similar increase in differential stress. Our data indicate that [Formula: see text] measured from sonic velocity data falls in the same range as for [Formula: see text], and that [Formula: see text] is always below unity. Stress-dependent behavior of [Formula: see text] is similar (decrease with increasing differential stress) to that of [Formula: see text] 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, [Formula: see text] increases with stress while [Formula: see text] decreases.
We present results from a study of dynamic and static Young’s moduli of North Sea chalk based on laboratory tests on both dry and water-saturated chalk. We obtained static moduli by using both strain gauge and linear voltage displacement transducer (LVDT) measurements. We investigated the influence of pore fluid on static and dynamic Young’s moduli and evaluated the two methods for obtaining static Young’s modulus. We obtained good agreement between dynamic and static Young’s moduli from strain gauge measurements on dry chalk, but for water-saturated chalk the dynamic Young’s modulus was larger than the measured static Young’s modulus. This difference may be caused in part by the influence of the difference in frequencies of static and dynamic measurements. Another reason for the observed difference may be a practical experimental problem that causes the measured static Young’s modulus for water-saturated chalk to be lower than the true modulus. When we compared dynamic Young’s modulus for dry chalk with that for water-saturated chalk, the dry modulus was larger than the water-saturated modulus, probably owing to shear weakening of the chalk. Young’s modulus from LVDT measurements does not relate to dynamic Young’s modulus for dry or water-saturated rock because the LVDT is not able to accurately measure the small deformations of the samples during loading at relatively low stresses.
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