Constitutive Law for Permeability Evolution of Sandstones During Depletion

Abstract

Abstract Permeability changes have been measured during triaxial tests performed on two sets of Vosgian sandstones. The obtained results led to the definition of a criterion in the p'-q plot (effective mean stress—deviatoric stress) for the evolution of permeability. Inside the domain defined by the criterion, the permeability change is nil or small whatever the loading path is. The results are generalized in a normalized p'*-q* plot. The normalized stresses p'*-q* were previously defined by Wong et al., and depend on the onset of grain crushing under hydrostatic loading. We suggest herein a simpler way to determine the normalizing stress. Furthermore, the experimental results are interpreted to propose an explicit law for the evolution of permeability as a function of the stress path. Introduction During the primary production of hydrocarbons the main mechanism is the fluid expansion resulting from the reservoir pressure decrease. The production thus induces a depletion that in turn induces variations of the in-situ stresses. These stress variations finally induce strains. These stress changes have been measured in situ, and Rhett and Teufel (1992) have shown that the ratio K of the effective horizontal stress variation (?s'h) to the effective vertical stress variation (?s'v) is constant. As a consequence the deviator stress change (?q=?s'v-?s'h) increases while the pore pressure decreases. For example, in the elastic domain (?pp negative, b Biot coefficient) : ?q=-b(1-K)?pp. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (1) The strains induced by reservoir depletion as well induce changes of the mechanical parameters and of the petrophysical characteristics of the rock. The permeability can thus drastically drop, reducing the well productivity, and the economics of the well production can even be endangered. However, at the contrary, examples of permeability increase have been reported from laboratory tests (Rhett and Teufel, 1992a; Zhu and Wong, 1997). Since Fatt & Davis pioneering works (1952), permeability variation due to the reservoir production has been much studied (David, 1994; Wilhelmi, 1967; Gray, 1963; Holt, 1990; Morita, 1984; Rhett and Teufel, 1992a; Teufel, 1987; Zhu and Wong, 1997; Yale, 1984; Yale and Crawford, 1998, Krishnan et al., 1996). We herein reinterpret previous results obtained in our lab (Ferfera et al., 1997; Sarda et al., 1998) in the light of Wong et al. work (1997). Lab Results: Criterion for Permeability Changes In order to better understand the role of the stress deviator during the post-elastic phase, strains and permeability changes have been simultaneously measured during triaxial loading experiments performed on two sets of Vosgian sandstone core samples characterized by their mean porosity: about 20% for one set (Ferfera, 1997; Ferfera et al., 1997), 17% for the other one (Sarda et al., 1998). Several loading paths have been investigated, the samples being loaded up to failure: constant confining pressure, constant mean stress, proportional loading. Attention was paid to the levels of confining pressure and pore pressure in order to emphasize the possible influence of the stress deviator q. The results were analyzed in order to evidence this influence and the influence of the Terzaghi effective mean stress p'.