Elastic behaviour of North Sea chalk: A well‐log study

Abstract

We present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk. We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate. The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.

A compaction front in North Sea chalk

“…Taking this correction into account, the effective stress leading to failure should be of the order [Lawn, 1993] of s eff = (1 − ') ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi E=r max p ∼16-22 MPa, where g = 0.2 J m −2 is the interfacial energy of calcite [Røyne et al, 2011], E = 12.9-24 GPa is the Young's modulus for ' = 0.25 [Gommesen et al, 2007]. Here, ' = 0.25 and r max = 5.5 mm are the porosity and maximum pore size at the onset of compaction (from Figure 4).…”

“…The Young's modulus is derived from well log measurements of shear stress and Poisson ratio in the Ekofisk, Tor, and Hod formations, and the ratio between the maximum and minimum Young's modulus was ≈5. However, estimates of the Young's modulus based on other methods of measurement [Vajdova et al, 2004;Bell et al, 1999;Gommesen et al, 2007] cover a much larger range, with a maximum-tominimum ratio of ≈1000.…”

Rock physics interpolation used for velocity modeling of chalks: Ontong Java Plateau example

“…Biots coefficient relates to the pore space compressibility as it is the ratio of pore volume change to bulk volume change at constant pore pressure [9]. As has been pointed out by Gommesen et al [7], this parameter is important for describing the elastic behaviour of chalks. Saberi et al [10] considered the diagenetic model of Fabricius [6], to model the elastic parameters of chalks by defining different pore-models at various diagenetic stages (ooze, chalk, limestone).…”

“…The relationship between P-wave velocity, porosity, and burial depth has been discussed widely by other authors (e.g. [3][4][5][6][7][8]). …”

How depositional texture and diagenesis control petrophysical and elastic properties of samples from five North Sea chalk fields

“…where (g cm 3 ) is bulk density and v P (km s 1 ) is P-wave velocity; and Gommesen et al (2007) pointed to the significance of Biot's coefficient. For a given porosity, Biot's coefficient, , is an indicator of pore stiffness and may be supposed to decline with increasing cementation.…”