On the Poroelastic Biot Coefficient for a Granitic Rock

Abstract

The Biot coefficient is a parameter that is encountered in the theory of classical poroelasticity, dealing with the mechanics of a fluid-saturated porous medium with elastic grains and an elastic skeletal structure. In particular, the coefficient plays an important role in the partitioning of externally applied stresses between the pore fluid and the porous skeleton. The conventional approach for estimating the Biot coefficient relies on the mechanical testing of the poroelastic solid, in both a completely dry and a fully saturated state. The former type of tests to determine the skeletal compressibility of the rock can be performed quite conveniently. The latter tests, which determine the compressibility of the solid material constituting the porous skeleton, involve the mechanical testing of the fully saturated rock. These tests are challenging when the rock has a low permeability, since any unsaturated regions of the rock can influence the interpretation of the compressibility of the solid phase composing the porous rock. An alternative approach to the estimation of the solid grain compressibility considers the application of the multi-phasic theories for the elasticity of composite materials, to estimate the solid grain compressibility. This approach requires the accurate determination of the mineralogical composition of the rock using XRD, and the estimation of the elasticity characteristics of the minerals by appealing to published literature. This procedure is used to estimate the Biot coefficient for the Lac du Bonnet granite obtained from the western region of the Canadian Shield.

Poroelastic properties of rocks with a comparison of theoretical estimates and typical experimental results

“…6 that, on average, for sandstones and limestones the Biot coefficient is equal to 0.75 and for the marbles-granite group the Biot coefficient can be lower and in the range 0.2 to 0.5. This observation is consistent with results obtained recently for the Lac du Bonnet granite recovered from the Canadian Shield 79 .

Figure 6 Biot coefficient versus porosity.

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“…If the Biot coefficient is known from experimental data 10 , 43 , 44 , 50 , 51 , 78 , 79 , the fraction of open interfaces can be estimated from ( 11 ) as …”

Cavity Flow Permeability Testing of an Intact Granite

“…An air flow technique was applied to estimate the permeability of low permeability materials such as cement grout, concrete and ceramics; further references and a review of the experimental techniques are given in [178][179][180][181][182][183] . Transient techniques are complicated because other properties relevant to the interpretation of the tests have to be determined, including the compressibility of the porous skeleton, the compressibility of the solid material composing the porous skeleton, the compressibility of water, the porosity of the porous medium, the Biot coefficient (see [178][179][180][181][182][183][184][185][186][187] ), the air voids that can be present in the fluid region that is pressurized to attain the transient flow, and the appropriate mathematical formulation and modelling (i.e. the diffusion equation approach or a poroelasticity approach) used to interpret the experiments.…”

A Reference Thermal-Hydrologic-Mechanical Native State Model of the Utah FORGE Enhanced Geothermal Site

“…Mechanical properties of the granitoid reservoir rocks were determined from laboratory analysis of core plugs from Well 58-32, geophysical logs, and values reported in the literature [11,41]. Young's modulus and Poisson's ratio were determined from laboratory testing on the two core sections and also measured from well logs.…”

“…Mechanical properties inferred from the logging operations were corrected using the laboratory measurements [11]. The Biot coefficient of the granitoid was taken from the literature [41]. Granitoid mechanical properties are summarized in Table 2.…”