## 1. Introduction

[2] The *in situ* detection and delineation of toxic contaminants is an on-going challenge for scientists responsible for environmental site remediation. Dense non-aqueous phase liquids or DNAPLs are a class of fluids which include several problematic industrial contaminants including the chlorinated solvent trichloroethylene (TCE) [*Pankow and Cherry*, 1996]. Multiple geophysical techniques have been proposed for DNAPL detection in shallow subsurface environments [*Romig*, 2000]. However, most methods lack the spatial resolution and/or sensitivity for the characterization of small DNAPL lenses or pools. High-resolution borehole seismic methods may have sufficient resolution in some geological scenarios when appropriate source frequencies and experiment geometries are used. While previous seismic imaging experiments have targeted regions of DNAPL contamination [*Temples et al.*, 2001], to date no core-scale ultrasonic measurements have been performed on DNAPL-saturated aquifer materials, a prerequisite for the calibration of relevant rock-physics models.

[3] We present the results of four experiments investigating the ultrasonic properties of granular materials partially saturated with TCE. These measurements provide constraints on the seismic signature of partial DNAPL saturation. Two natural aquifer samples and two synthetic glass bead packs of differing porosities were examined. All samples were initially water saturated before being subjected to an axial injection of TCE. TCE is a colorless fluid with a high density (1464 kg/m^{3}), a low P-wave velocity (1050 m/s [*Nath and Saini*, 1990]), and a low viscosity (0.56 × 10^{−3} Poise [*Mercer and Cohen*, 1990]) with respect to water at 20°C. TCE has a low aqueous solubility (1100 mg/L [*Montgomery*, 1991]) but is tightly regulated by the EPA with a maximum allowable concentration of 0.005 mg/L in drinking water.

[4] Ultrasonic pulse transmission measurements were acquired during the injection of TCE into the granular samples allowing determination of P-wave velocity as a function of DNAPL saturation. Maximum TCE saturation varied between 22% and 59% for the four samples. Since only water and TCE were used as saturating fluids, our results are most relevant to characterization of DNAPLs in the saturated zone. The resulting velocity estimates show a reduction in P-wave velocity as a function of DNAPL saturation. The largest observed velocity decrease was 15% at a TCE saturation of 59%. A combination of Gassmann fluid substitution and Hill's equation was used to estimate the effects of DNAPL saturation but underpredicted the observed decrease in velocity at high TCE levels. A linear model, expressed in terms of volumetric contaminant fraction, provided an excellent empirical fit to our measurements across all samples.

### 1.1. Principles

[5] The key parameters for determining the seismic signature of fluid saturation are the fluid's compressional wave velocity and density (*ρ*_{fl}) which can be directly related to fluid bulk modulus (*K*_{fl} = Fluids with a high bulk modulus stiffen porous materials; at higher frequencies viscous losses can be generated due to motion of the saturating fluid with respect to the porous matrix. Biot-Gassmann theory [*Biot*, 1956] describes the effects of pore fluids on the bulk elastic properties of porous materials. The theory does not attempt to predict rock properties from *ab initio* information concerning phase properties and geometric distribution but limits itself to the effect of fluids. For this investigation, we use a simplified conceptual model where the sample is treated as a three phase composite consisting of grain material, water, and TCE. The saturated composite can be described by three parameters, compressional wave velocity shear wave velocity and bulk density (*ρ*_{sat}) or equivalently as *ρ*_{sat} and wet shear and bulk moduli (*μ*_{sat} and *K*_{sat}).

### 1.2. Previous Laboratory Investigations

[6] Several experimental studies have examined the impact of NAPL saturation on ultrasonic properties of synthetic soils. *Geller and Myer* [1995] investigated the relationship between NAPL saturation, P-wave velocity, and attenuation at effective pressures of 140 kPa using 1,1,2-trichloro-1,2,2-trifluro-ethane (freon-113), n-dodecane, and iso-octane as model contaminants using a pulse-transmission apparatus operating at 500 kHz. Reductions in V_{p} of up to 40.3% were observed for sands fully saturated with freon-113. *Seifert et al.* [1999] performed a similar set of measurements with a focus on varying fluid viscosity and wetting properties. V_{p} and Q_{p} were measured while saturating samples with two different grades of silicone oil (10 and 100 cs), castor oil, and n-dodecane at effective pressures of 690 kPa. Both sets of experiments were performed with ultrasonic pulse transmission systems operating between 500 and 1000 kHz. Both *Geller and Myer* [1995] and *Seifert et al.* [1999] made measurements on synthetic samples consisting of medium sub-rounded quartz sand (212-250 microns) with porosities between 35% and 42%.

### 1.3. A Model For Fluid Substitution

[7] Past efforts to develop rock-physics models for NAPL saturation have met mixed success; methods considered include the Kuster-Toksoz scattering model [*Geller and Myer*, 1995] and the dynamic composite elastic medium model (DYCEM) [*Seifert et al.*, 1999]. *Carcione et al.* [2003] proposed a model for the seismic properties of contaminated sediments based on an extension of Biot-Gassmann theory with the addition of patchy saturation and viscodynamic effects related to clay content.

[8] We adopt a model which combines Gassmann fluid substitution [*Gassmann*, 1951; *Mavko et al.*, 1998] and Hill's equation [*Hill*, 1963] to estimate the seismic signature of TCE injection into water saturated granular media. This approach, sometimes referred to as the Biot-Gassmann-Hill model (BGH) [*Johnson*, 2001], assumes a macroscopic patchy distribution of fluids in contrast to formulations requiring fluid mixing on the pore scale. Although the BGH model neglects dynamic Biot effects, numerical tests indicate that such processes, while present, are small yielding a maximum difference in V_{p} of 1.2%.

[9] We follow the BGH formulation described by *Dvorkin et al.* [1999] and *Johnson* [2001]. We calculate the bulk and shear moduli of the water saturated fluid/solid composite using measured and values and a literature estimate of the wet V_{p}/V_{s} ratio at a similar pressure; we use a value of 5 obtained from measurements on clean sands carried out by *Zimmer et al.* [2002] at low pressure (<1 MPa). We then estimate the frame bulk modulus (*K*_{fr}) using the Gassmann model. The Gassmann model assumes that fluids do not effect rock shear properties i.e. *μ*_{fr} = These frame properties, derived from the water-saturated case, serve as a starting point for our model predictions.

[10] Hill's equation [*Hill*, 1963] provides an exact formulation for the properties of a multi-phase composite where all components have identical shear moduli but possibly different bulk moduli. The general form of Hill's equation, which is independent of the geometry of the constituent phases, can be expressed as,

where *x*_{i} and *K*_{i} are the volume fraction and bulk modulus of the *i*th phase respectively. In our case, the phases chosen are not the pure fluid or mineral components but different regions where Gassmann's model holds for a single fluid; phase 1 is a fully water saturated composite while phase 2 is fully saturated with TCE. The fraction of phase 1 and 2 are controlled by the measured TCE saturation. The properties of the water/TCE/mineral composite are then estimated by computing the phase 1 and 2 properties using the Gassmann model and the previously estimated frame properties, followed by application of equation 1.