Effect of Partial Water Saturation on Attenuation Characteristics of Low Porosity Rocks

Attenuation increases as the porosity increases because the water content in a pore becomes larger at the same degree of water saturation. Higher porosity rocks can have more opportunity of interaction between fluid and rock frame in the cracks than lower porosity rocks. Specifically, Fig. 1a shows that the attenuation of a high porosity rock (when n = 30%, Q ⁻¹ = 0.0046) is approximately nine times larger than that of a low porosity rock (when n = 1%, Q ⁻¹ = 0.0005) at a saturation degree of 98–99%, which is the saturation degree required for a maximum attenuation value.

For low permeability rocks, the pressure gradient induced by wave propagation dissipates slowly and there are minimal flows of fluid in the pores and pore throats. Meanwhile, for higher permeability rocks, fluids can move more freely, and consequently cause greater loss of energy during the wave propagation. It is found that permeability has the strongest impact on the magnitude of the attenuation than porosity and pore size, affecting approximately one order of magnitude increase of attenuation by an order of magnitude increase of the permeability, as shown in Fig. 1b.

The pore size parameter is an indicator of the geometric characteristics of the pore space. As shown in Fig. 1c, when the rock has the same porosity and permeability, the attenuation increases as the pore size parameter decreases. It implies that the wave loses more energy in smaller-sized pores at the same porosity.

The attenuation (Q ⁻¹) is normalized by the maximum attenuation (Q _max ⁻¹ ), which is the attenuation value for nearly full water-saturated conditions (i.e., S ≈ 99%). The normalized value enables us to examine how the curve tendency and shape depend on the various parameters of low porosity rocks. The attenuation-water saturation (Q ⁻¹ /Q _max ⁻¹  − S) curves (hereafter, attenuation curve) are superimposed in Fig. 2 to highlight the effect of changes in the permeability and pore size parameter. Porosity is excluded as a variable because it has a negligible effect on the attenuation curve tendency. Figure 2 shows that the attenuation curve shape with water saturation can be convex, linear, or concave depending on the permeability. A high permeability (k ≥ 10⁻⁵ m/s in the presented study) produces a concave attenuation curve. In contrast, the attenuation curve is convex when the permeability is lower than 10⁻⁵ m/s. It is worth to note that a small pore size parameter produces a linear curve: the attenuation curve is almost linear with water saturation when the pore size parameter is less than 1 μm (also refer to Fig. 1c).

Four cylindrical rock specimens were prepared, representing unique low porosity characteristics of deep bed-rock formations in Korea: two weathered granite and two mudstone specimens. All the specimens had a diameter of 5 cm, a length of 10 cm, and a porosity value of less than 3%. The dry density of the specimens was measured after drying them in an oven at 50°C for 72 h, while the water-saturated density was measured after submerging them until the measured masses converged to a certain value. The effective porosity, which is a measure of connected pores, but not closed pores, was estimated from a dry density and a fully water-saturated density. A standard method suggested by the International Society for Rock Mechanics (ISRM; Brown 1981) was used to determine the specific gravity of each specimen. The properties of the specimens tested are summarized in Table 1.

To determine water content, porosity, density, absorption, and related properties, saturating and drying processes were performed by following the procedures suggested by ISRM (Brown 1981). A saturating process was performed by completely immersing a specimen in a water bath. The water bath was agitated to remove any trapped air. After a saturating procedure, the specimen was dried in an oven at a constant temperature of 50°C in order to prevent any damage induced by thermal shock. As time elapses, the degree of water saturation was periodically evaluated by measuring the mass, and the attenuation was simultaneously measured.

The attenuation of a rock specimen was obtained by a free–free resonant column (FFRC) test (Vaghela and Stokoe 1995; Kim et al. 1997; Cha and Cho 2007). The FFRC method measures the attenuation of the longitudinal wave mode (i.e., also called as rod wave or bar wave). A typical result of the FFRC test at the time domain is shown in Fig. 3a. The damping ratio (D) is obtained by fitting the frequency response curve of a single degree of freedom system to the measured data as shown in Fig. 3b. The attenuation is expressed in terms of the inverse quality factor (Q ⁻¹) calculated by the relationship, Q ⁻¹ = 2D.

Attenuation is highly affected by frequency and confining pressure. All the measurements were taken under atmospheric pressure and a room temperature of 25°C. The FFRC measurements were conducted within the regime of the resonant frequency between 6 and 27.5 kHz. The signals were captured regularly until the measured mass of the specimen converged to a certain value, where the specimen was considered as fully water-saturated. We subsequently subjected the saturated specimens to a drying process in an oven and repeated the same elastic wave and mass measurement procedure.

According to Biot model, the wave does not dissipate under a dry condition (i.e., 0% saturation); hence, the attenuation is expected to be null (Q ⁻¹ → 0 when S → 0). However, attenuations are unexceptionally measured for natural rock specimens under a dry condition (e.g., GN1: 0.048, GN2: 0.071, MS1: 0.006, and MS2: 0.010). These experimental measurements represent pure material damping without fluid effect, where the material damping is decided by frictional energy loss between cracks (or mineral grain boundaries) during elastic wave propagation (Winkler and Nur 1982). As shown in Fig. 4, granite specimens have higher attenuations under a dry condition than the mudstone specimens do because the mudstone specimens are much stiffer and have a smaller particle size than the granite specimens. It indicates that the energy loss due to internal heterogeneity-induced wave scattering, such as micro-cracks, is greater in the granite specimens than in the mudstone specimens.

Attenuation curve tendency can be considered to have two distinctive regimes: low saturation regime and mid-to-high saturation regime. In the low saturation regime, the attenuation behavior as a function of saturation is dominated by the microscopic fluid flow mechanism (e.g., as explained by the squirt flow model; Cadoret et al. 1998). On the other hand, attenuation behavior in the mid-to-high saturation range is governed by a macroscopic mechanism (e.g., as explained by Biot model).

In a low water saturation regime, as shown in Fig. 4, attenuation of the low porosity rocks hardly or slightly increases with water saturation. This region covers the saturation from 0 to approximately 10 or 20%. In contrast, in high-porosity rocks (e.g., Murphy 1982; Cadoret et al. 1998), the region that provides no or slight increase in attenuation with increasing water saturation covers a wider range of water saturation, i.e., from 0 to approximately 60 or 70%. This phenomenon is due to the fact that the high porosity rock requires more water to reveal Biot effect, which causes water–solid coupling and decoupling.

In the mid-to-high water saturation regime, Biot model can be applicable for predicting the attenuation tendency and comparing it to measurements because Biot model is based on a macroscopic mechanism. Typical attenuation-water saturation curves are shaped as convex, linear, or concave (see Fig. 2). The attenuation curves of the granite specimens are convex, while the curves of the mudstone specimens are linear in the mid-to-high water saturation regime, as shown in Fig. 4. The linearity of the attenuation curves of the mudstone specimens is attributed to the small pore size of the mudstone specimen. In contrast to low porosity rocks, it has been presented in previous studies (e.g., Murphy 1982; Cadoret et al. 1998) that the attenuation curves of high-porosity rocks (n > 23%) are presumed to be concave in the mid-to-high saturation regime. This concave shape of the attenuation curve in high-porosity rocks is consistent with the calculations in Biot model, as shown in Fig. 2 (i.e., when permeability k is larger than 10⁻⁵ m/s and the pore size parameter a is larger than 10 μm).

A hysterical loop of attenuation during the saturating and drying processes is generally evident in tests on high porosity rocks due to different water distribution conditions (Cadoret et al. 1998). In contrast, the fluid distribution during the saturating and drying processes of low porosity rock has little effect on the attenuation. Figure 4 shows that the attenuation values during the saturation process are almost the same as those of the drying process for low porosity rocks.

The attenuation values of the tested specimens when fully saturated are nearly two to five times greater than the values under a dry condition as shown in Table 2 and Fig. 4. In particular, Fig. 4 indicates that the granite specimens are strongly influenced by a saturation level. GN2 (the softest rock in the presented study) has larger difference in attenuation between dry and saturation conditions than does MS1 (the hardest rock in the presented study). This means that a soft rock (e.g., a rock with low stiffness and slow wave velocity) is easily affected by fluid flow during saturation.

It is worth noting that high porosity rocks demonstrate attenuation drops in a fully water saturated condition (refer to the data in Murphy 1982; Cadoret et al. 1998). This drop is because no patchy water distribution and no squirt flow occur when water fully saturates the pores in a rock; as a result, the pore fluid cannot easily squeeze or flow into adjacent pores. Thus, the energy loss decreases. However, this phenomenon is not observed in the low porosity rock specimens tested (refer to Fig. 4). This result implies that low porosity rocks are unlikely to be fully water-saturated under a natural atmospheric environment without some additional pressure due to water surface tension on the micro-cracks and closed pores, both of which form during rock diagenesis. This condition is expected in various near-surface grounds.