Relation Between Width and Length of Compaction Bands in Porous Sandstones

Compaction bands are narrow, roughly planar zones of reduced porosity that form perpendicular to the maximum compressive stress. Because both laboratory and field studies have shown that these bands strongly impede fluid flow, their presence in situ can adversely affect usage of the formation for applications involving fluid injection or withdrawal. The most extensive field study of the bands [Sternlof, PhD Thesis, 2006; Sternlof et al., JGR, 2005] shows that the midpoint width of the bands does not increase in proportion to the length as would be expected for self-similar or crack-like spreading. Plotting these data with points from laboratory compression tests and a few additional points from other field studies on a log-log plot reveals the data can be fit by a straight line over nearly four orders of magnitude of band half-length L. This fit indicates the width w varies approximately as the square root of the band half-length. More specifically w=AL^{a},where A is a (dimensional) constant and a equals 0.42. This variation is consistent with an anti-crack/dislocation model of the band in which the inelastic compaction (corresponding to the measured width w) is specified over the central portion of the band -b≤ x≤ b. A uniform traction, equal to the difference of the farfield compressive stress and the local resistance to closure, acts over the remainder of the band of total length 2L. This traction is chosen to eliminate the singularity in stress at x=± b. If it is assumed that propagation of the band requires a critical value of energy released per unit area of advance, Gcrit, then w is proportional to √{L} (for a fixed ratio of b/L). In addition, for small b/L, consistent with the field observations, the coefficient,corresponding to A, is given to a good approximation by √{8Gcrit(1-ν )/π μ }, where μ is the shear modulus and ν is Poisson's ratio. For Gcrit=40 kJ/m2, comparable to values inferred for both field and laboratory specimens and values of ν (0.2) and μ (8.3 GPa), representative of Sternlof's field site, A=0.0313 cm^{1/2} compared with 0.0302.cm^{1/2} for the observations. This agreement supports the relevance of the model and suggests that the propagation of compaction bands has common features in different rock types and loading conditions. The discrepancy of the exponent inferred from the data from 0.5 suggests that propagation may not occur at fixed b/L.