Water Resources Research

Characteristics of acoustic emissions induced by fluid front displacement in porous media

Authors


Corresponding author: F. Moebius, Department of Environmental Sciences, ETH Zurich, Universitaetstr. 16, CH-8092 Zurich, Switzerland. (franziska.moebius@env.ethz.ch)

Abstract

[1] The dynamics of fluid displacement in porous media often affect phase entrapment and shape macroscopic transport properties and thus are of considerable interest for a range of natural and engineering applications. The macroscopic motion of a displacement front is composed of numerous abrupt pore-scale invasion events that involve rapid interfacial jumps and reconfigurations with associated mechanical and interfacial energy release detectable as acoustic emissions (AE). We conducted systematic experiments of fluid displacement and measured associated AE during passage of fluid fronts (primarily drainage) within assemblies of glass beads of different sizes. Results indicated distinct acoustic signatures associated with different displacement processes, reflecting dependency on porous media pore size, displacement flow rate, and liquid properties. The rich AE signals associated with front dynamics exhibited power law relationships between the number of AE events and their amplitudes, reminiscent of avalanche-like invasion processes. In addition to AE signals emanating from rapid emptying or filling of pores (Haines jumps), other processes such as redistribution and interfacial reconfigurations behind a drainage front and grain rearrangement may generate AE. Characteristic AE signatures generated by displacement processes in different media and under various boundary conditions offer a promise for remote detection of pore-scale fluid interfacial dynamics in porous media that may shape macroscopic transport properties (e.g., linked with phase entrapment).

1. Introduction

[2] Immiscible fluid displacement in porous media such as drainage, imbibition, and evaporation are of considerable interest for applications ranging from study of infiltration and evaporation in soils, to quantifying drying of food products and construction materials, or oil reservoir operation or geologic carbon sequestration [e.g., Aker et al., 2000a; Culligan et al., 2006]. Fluid front morphology and dynamics during displacement processes are shaped by pore space geometry, fluid properties, and by boundary conditions [Meheust et al., 2002]. Even minute variations in fluid velocity or pressure gradient may trigger instabilities altering fluid phase displacement pattern thereby affecting macroscopic transport properties such as hydraulic and electrical conductivity and gaseous diffusion [Jury et al., 2003; Chau and Or, 2006; Lovoll et al., 2011]. Advances in measurement and imaging methods motivated interest in characterizing the role of (the often dismissed) “Haines jumps” and other pore-scale aspects of fluid displacement processes [Måløy et al., 1992; Wildenschild et al., 2002; Culligan et al., 2004].

[3] The seemingly continuous and regular motion of imbibition and drainage fronts involve numerous pore-scale abrupt interfacial reconfigurations and rapid pore invasion events in response to local interfacial instabilities. Such interfacial invasion processes may resemble an avalanche when a group of pores abruptly empties or fills in response to instability induced by a single meniscus. The resulting rapid advance and pressure fluctuation are referred to as Haines jumps or rheons [Haines, 1930; Melrose and Brandner, 1974; Aker et al., 2000b; DiCarlo et al., 2003; Crandall et al., 2009]. These and other abrupt interfacial reconfiguration processes such as “snap-off” resulting from the spontaneous filling of angular pores or irregular pore throats [Blunt and Scher, 1995; Tuller et al., 1999] are often associated with interfacial energy release [Ransohoff et al., 1987] observable with the acoustic emission technique. A relatively understudied aspect of abrupt interfacial snap-off and related jumps is their potential impact on fluid phase entrapment that subsequently shape transport properties through the partially saturated region behind a displacement (drainage) front.

[4] Acoustic emission signals (AE) emanate from abrupt and localized release of mechanical and interfacial energy that triggers generation of elastic waves [Scruby, 1987]. The high-frequency (>kHz) waves propagate as compression or shear waves through solids (or as compression waves through fluids) and carry information regarding the source location and characteristics of the source of energy release. AE transducers (typically piezoelectric sensors) detect minute surface vibrations and provide a means for determining AE characteristics such as amplitude, rise time, duration or simply counting hits above a threshold (as shown inFigure 1). The AE technique has been used extensively in recent decades in diverse applications, e.g., characterization and nondestructive testing of materials, such as fiber-reinforced plastics [Barre and Benzeggagh, 1994]; fatigue testing of structural elements or real-time monitoring and localization of crack formation in critical structures [Johansen and Sornette, 2000]; process monitoring [Dornfeld, 1992]; motion of solid particles in loose porous media; the study of soil movement in earth dams [Lord and Koerner, 1975] and for study of mechanical processes in geologic media [Michlmayr et al., 2012].

Figure 1.

Characteristics of a typical acoustic emission signal.

[5] Some of the mechanisms responsible for generating elastic waves are discussed in more detail, with the primary processes of interest in this study are those linked with interfacial processes induced by evaporation, imbibition, drainage or bubble coalescence [DiCarlo et al., 2003; Chotard et al., 2006, 2007; Manasseh et al., 2008]. This link between individual displacement events and measurable acoustic emissions holds a promise for noninvasive and data-rich exploration of pore-scale displacement processes.

[6] DiCarlo et al. [2003] measured acoustic emissions during motion of fluid interfaces in sand which they attributed to “Haines jumps” occurring during fluid front displacement. The acoustic events were recorded using microphones and hydrophones in a frequency range of up to 20 kHz. Evidence suggests that different displacement processes (drainage or imbibition), pore sizes and flow rates may result in different AE patterns. Chotard et al. [2007] focused on event numbers and AE rate evolution during evaporation processes from a porous ceramic and found a correlation between the frequency of hits and evaporative mass loss rates.

[7] Motivated by results from these recent studies and by advances in AE measurement technology, our primary objective was to systematically characterize acoustic emissions generated during a range of fluid front displacement regimes in well-defined porous media, focusing on differences in AE generation during imbibition and drainage within the same porous medium. In our experimental studies we varied pore spaces, mean front velocity and liquid properties (surface tension and viscosity) and examined their impacts on measured AE event rates and amplitudes. These results provide the experimental basis for attempting to link AE characteristics with factors affecting their generation during displacement in porous media toward potential using the AE method for noninvasive characterization of fluid displacement processes.

2. Sources of Acoustic Emission During Fluid Front Displacement

[8] Detailed quantification of the wide scope of AE generating mechanisms is beyond the scope of this experimental study, nevertheless we present a brief overview of potential AE generation mechanisms associated with interfacial displacement in porous media. The primary mechanisms considered here include (1) rapid interfacial invasion into pores (Haines jumps or rheons), (2) air entrainment and oscillating bubbles, (3) liquid bridge rupture, (4) interfacial snap-off, and (5) capillary-induced grain rearrangement and collisions. Estimates on timescales, energy values and wave frequencies of the different processes associated with advancing drainage and imbibition fronts, and redistribution processes behind a drainage front are presented in the following.

2.1. Rapid Pore Invasion (Haines Jumps)

[9] Drainage is associated with nonwetting phase (air) invading wetting phase filled pores. The pore-scale interfacial motions exhibit pinning-jumping behavior where segments of a drainage front may become pinned until a meniscus at the largest throat (lowest capillary barrier) becomes unstable and abruptly invades the pore body. The ensuing interfacial jump occurs at significantly higher velocity than mean front velocity and is often associated with significant inertia and subsequent pressure relaxation [Moebius and Or, 2012]. As drainage rates increase, the pinning-jumping behavior becomes complex and may involve simultaneous invasion of several pores in an avalanche-like process. Rapid changes in interfacial configurations are associated with attainment of unstable states (e.g., passage through a pore throat) and involve minimization of interfacial energy. During the moment before rapid breakthrough of the instable meniscus, the interfacial area along the entire front is “stretched” (into the pore throats). Rapid breakthrough and associated drawback of the neighboring menisci lead to reduction in interfacial area and associated energy release which are of the order of μJ and are considered as potential sources for elastic energy release detectable as acoustic emission.

[10] For interfacial jumps at time scales shorter than viscous dissipation of interfacial motions [Quere, 1997], excess interfacial energy (released during rapid configuration) may induce short bursts of elastic waves [Scruby, 1987] detected as acoustic emissions. A characteristic time for the inertial regime during initial stages of capillary rise is given by

display math

with the density ρ, surface tension σ, contact angle θ, radius r of the capillary and height of the meniscus h [Fries and Dreyer, 2008]. For example, a purely inertial capillary rise through 0.5 mm beads may last 0.2 ms with meniscus velocity in the range of 1.3 m s−1 (for water). Such rapid and highly inertial interfacial motions are considered as potential sources of AE signals. This motion may be followed by interfacial oscillations. An estimate of energy dissipation rates is deduced from the characteristic decay time for inertial interfacial oscillations [Quere et al., 1999; Lorenceau et al., 2002] given as

display math

where r is the radius of the capillary, ρ the density and η the viscosity. The time scale associated with such oscillations is in the range of 1–10 ms for water in pores of sizes 10–100 μm. Although these oscillation frequencies are lower than typical AE frequencies often in the range 10–1000 kHz [Scruby, 1987; Lockner, 1993], they may excite oscillations and resonance within entrained air bubbles as discussed next.

[11] Differences in details of pore filling or emptying during imbibition and drainage are reflected in their respective AE signatures. During imbibition, the liquid is drawn into pore throats by capillary forces. For large pore throats and bodies it results in moderate invasion menisci velocity closely linked with supply (flow) rate. For narrow pore throats, invasion process accelerates into purely inertial regime with time scales and velocities of the order given by equation (1) [Quere et al., 1999; Lorenceau et al., 2002; Fries and Dreyer, 2008].

2.2. Entrainment of Bubbles and Oscillating Bubbles

[12] Rapid contact line motions are often associated with failure and associated air entrainment into liquids. Similarly bulk flow instabilities may also lead to air bubbles entrainment [Cohu and Benkreira, 1998]. In industrial applications, the critical contact line velocity for entrainment is estimated as Vc = 1.14 (σ/ η)0.77 [Burley and Jolly, 1984] approximately 30 m s−1 for water. Nevertheless, the motion of contact lines on rough surfaces may become irregular and give rise to fingering and instabilities that may enhance occurrence of bubble entrainment even at lower velocities.

[13] In addition to rapid reconfigurations of the gas-fluid-solid interfacial line or gas-fluid interface, the rapid attachment of contact lines at solid surfaces (at the next grain) during advancing wetting front may also entrain small air bubbles. The coupling of pressure jumps and induced oscillations associated rapid interfacial jumps with entrained gas bubbles may mechanically excite the bubbles and induce acoustic emissions at characteristic frequencies. In the context of sound generation by bubbles,Manasseh et al. [2008] discussed two key processes leading to passive sound emission: (1) when “bubbles are pinched off from an underwater orifice connected to a large, parent body of gas” and (2) when bubbles are created by the entrapment of air from a free surface. Similar processes and bubble coalescence have been observed along displacement fluid fronts in porous media [Kovscek and Radke, 2003]. Although direct calculations of the role of these processes on analyses of AE measured from displacement fronts is not yet quantitatively feasible, it is instructive to introduce a limiting case of naturally oscillating bubbles in liquid (in response to external impulse) giving rise to the so-called Minnaert frequency [Minnaert, 1933]. An expression resulting from balancing potential and kinetic energy for a bubble with initial radius r0 in water excited by an external force is given as [Minnaert, 1933; Devaud et al., 2008]:

display math

where P0 is the liquid pressure, ρ liquid density, and γis the adiabatic index for air (∼1.4). An approximation for the Minnaert frequency for an air bubble in water with radius of 1 mm under standard conditions would be 3 kHz. Similar arguments are envisioned for sound generation for entrained bubbles during snap-off processes at a displacement front, and for geometrical constrains imposed by pore sizes on “bubble” size and associated AE signature [Manasseh et al., 2008]. As air bubble size ranges from 1 μm (contact line entrained) to 1 mm (snap-off) the expected resonance frequency ranges from 3 to 3000 kHz. The measurement range and characteristics of AE sensors determine which of these signals are detectable, nevertheless, during fluid displacement bubble oscillations are likely to represent a significant part of measured AE signals.

2.3. Liquid Bridge Rupture

[14] The rupture of liquid bridges between grains is another process associated with rapid interfacial reconfiguration. As fluid front recedes, the remaining (trapped) liquid bridges gradually shrink below a critical volume resulting in their abrupt rupture [Orr et al., 1975]. Liquid bridge rupture energy is dependent on both capillary and viscous forces as shown experimentally by Pitois et al. [2001]. Simons et al. [1994] have shown that the interfacial energy release is of the order of μJ (similar to rapid changes of interfacial area during Haines jumps). Liquid bridge dynamics were also studied by Zhang et al. [1996], who found the breakage time to be in a range of 1 to 20 ms [Michlmayr et al., 2012]. We also need to consider an opposite and similarly rapid process of liquid drop coalescence and formation of liquid bridges at rates of the order of 10 ns after drops are brought into contact [Paulsen et al., 2011].

2.4. Snap-Off Processes

[15] Snap-off processes are an integral component of the processes during the so called transient state region [Tallakstad et al., 2009a]. Pore spaces in granular media would invariably satisfy the geometrical condition of rt/rp < 0.5 (with rt and rpthroat and pore radius respectively) necessary for the onset of snap-off [Kovscek and Radke, 1996]. Snap-off processes were extensively studied by Gauglitz et al. [Ransohoff et al., 1987; Gauglitz et al., 1988; Gauglitz and Radke, 1989, 1990]. Results propose inertial breakup at low Ohnesorge numbers (ratio of viscous forces to inertial and surface forces) (<10−2) and viscous processes above. For water as the wetting fluid this leads to the condition that inertial breakup occurs for throats larger than 0.14 mm. The dimensionless breakup time for inertial process is in the order of 104 or larger which is about ∼16 ms for 0.5 mm. It was further found the dimensionless breakup time being proportional to the local Capillary number (representing the ratio of viscous and capillary forces) to the power of −2 [Gauglitz and Radke, 1989].

2.5. Grain Collision

[16] Capillary forces and pressure waves may induce grain motion and associated solid surface friction and particle collisions during fluid front displacement. A recent review by Michlmayr et al. [2012] lists a range of AE producing mechanical processes, for example, the estimated impact time for 1 mm glass beads moving at 0.05 m s−1 would be about 13 μs, some 3 orders faster than interfacial reconfigurations described above. Separation of AE signals by grain friction or collision from those generated by fluid interfacial reconfigurations at the front remain a challenge. In most consolidated porous media such solid phase mechanical interactions would make a minor contribution to the total AE, practically, the displacement experiments reported herein were conducted within confined grain assemblies to reduce the impact of solid phase AE generation to a minimum.

[17] The phenomena above provide an overview of potential sources for rapid energy release resulting in acoustic emissions during front displacement through porous media. The energy release, AE source location and rates of excitation result in AE signals with different characteristic values. The focus here is flow related AE signatures without attempting to resolve individual AE generation mechanisms.

3. Experimental Methods

3.1. Experimental Setup

[18] We conducted fluid front displacement experiments in vertical Hele-Shaw cells packed with uniform-sized glass beads (using different mean bead size for various experiments). Cell dimensions were 260 × 75 × 10 mm, and the beads were confined by compressing a plastic block on the top surface to reduce relative bead motion and friction between glass beads. A schematic of the experimental setup is shown inFigure 2. The port for injection and withdrawal of the wetting liquid was mounted at the bottom of the cell (at the center of the base) while nonwetting fluid (air) entered from the top surface (an ample gap was left between the confining block and the walls as to not restrict air entry). The flow rate of the wetting liquid was controlled using a syringe pump (KDS210, KD Scientific, Holliston, USA) capable of injecting or withdrawing liquid with accuracy of less than ±1%.

Figure 2.

Experimental setup. (left) Hele-Shaw cell with glass beads and tube to the syringe pump. (right) Acoustic emission sensor, preamplifier, and AE board (Vallen Systeme, Icking, Germany).

[19] Three piezoelectric AE sensors (VS30-V, Vallen Systeme, Icking, Germany) were mounted on the outer surface of a 6 mm thick glass of the Hele-Shaw cell spaced along the height of the cell (Figure 2). An additional AE sensor was placed on the column holder or the table serving as a reference sensor for background AE signals. The sensors are characterized by relatively flat acoustic response within a wide frequency range of 25 to 80 kHz (which may not cover the full range of possible AE frequencies). The sensors were connected via preamplifier to the acoustic emission measurement system (AMSY-5, Vallen Systeme, Icking, Germany) recording at 10 MHz sampling frequency. The threshold amplitude was set at 30 dB based on background noise.

3.2. Experimental Parameters and Boundary Conditions

[20] The fluid front displacement experiments examined a wide range of parameters considering different pore sizes, flow rates and liquid properties toward assembling a systematic matrix of key factors linking displacement regimes and AE characteristics. Five sizes of glass beads ranging from 0.5 to 4.4 mm in diameter (0.5–0.75 mm, 1.00–1.30 mm, 2.00–2.40 mm, 2.85–3.45 mm, 3.80–4.40 mm) were used resulting in estimated average porosities of 0.40 for small and 0.43 for larger beads, and span a range of pore sizes. In the following we refer to the lower limit of beads sizes as 0.5, 1.00, 2.00, 2.85, and 3.80 mm. As a first approximation of pore-related AE events, we assumed that the number of pores was similar to the number of beads in the sample resulting in values of 6.36 × 105, 1.0 × 105, 1.4 × 104, 4.7 × 103, and 2.1 × 103pores for the five different glass bead sizes (along the 180 mm path length in the Hele-Shaw cell marked by solid lines inFigure 2). We varied the volumetric flow rate q from 5 to 80 mL min−1, resulting in mean displacement front velocities in the range of 0.25 to 4.6 mm s−1, respectively, according to

display math

where A is the cross section area of the column (750 mm2) and ε the porosity. Note that these front velocity estimates do not consider effects of phase entrapment emerging at higher front velocities.

[21] The effects of liquid properties on AE behavior was studied across a range of liquids with different viscosity and surface tension using distilled water, silicon oil (η= 10 mPa s at 25°C, Silicon oil DC 200, Sigma-Aldrich), and water with different amounts of surfactant Triton X-100 (Sigma-Aldrich) that modifies water-air surface tension with minimal effects on viscosity and density [Hodgson and Berg, 1988; Labajos-Broncano et al., 2006]. Concentrations of 1.9 × 10−6 mol L−1 and 1.5 × 10−4 mol L−1of Triton X-100 in distilled water result in surface tension values of 53 mN m−1 and 33 mN m−1 [Labajos-Broncano et al., 2006]. The visualization of the wetting liquid was greatly enhanced by adding minute amounts of brilliant blue (<0.5 g L−1) to water (also with Triton X-100) and methyl red to silicon oil. The range of Capillary numbers (Ca; ratio of viscous forces to surface tension) induced by flow rates in experiments with water ranged between 6.2 × 10−4 and 1 × 10−2 (indicating dominance of capillary forces), and the Bond numbers (Bo; gravitational forces to surface tension) varied in the range from 5.9 × 10−3 to 2.5 × 10−1, suggesting significant gravitational forces for experiments with beads larger than 2.0 mm. A criterion for front displacement regimes proposed by Meheust et al. [2002] using the generalized Bond number (Bo* = BoCa) predicts that air displacing water in the smallest beads for volumetric flow rate of 80 mL min−1 would yield an unstable displacement front with significant viscous fingering. The length scales used to calculate both Capillary and Bond number were about 1/3 of beads diameter.

[22] A series of measurements consisting of several imbibition and drainage runs were performed using different glass beads sizes for each series. We initiated the experiments with an imbibition front advancing through initially dry pack of beads at a volumetric flow rate of 20 mL min−1, followed by drainage and imbibition runs at increasing flow rates for columns with beads larger than 2.0 mm where liquid phase entrapment was relatively minor (less than 5%). Due to high values of phase entrapment in the two small glass bead sizes (diameters of 0.5 and 1.0 mm), to remove ambiguities we initiated all imbibition runs into initially dry beads, and all drainage experiments started with fully saturated columns. The impact of prewetted glass bead surface relative to initially dry beads is discussed in section 4. The reproducibility of experimental results was evaluated by repeating all displacement processes with larger glass beads with water at flow rates of 40 and 80 mL min−1. An overview over the performed and analyzed experiments is shown in Table 1.

Table 1. Overview of Combination of Experiments Performed With Respect to Grain Sizes, Flow Rates, and Liquidsa
Flow Rate (mL min−1)Glass Bead Diameter (mm)
0.501.002.002.853.80
wtswtswtswtswts
  • a

    Abbreviations: w, water; t, solutions with Triton X-100; s, silicon oil.

5YYYYYYYYYY  YYY
10Y  Y  Y  Y  Y  
20YYYYYYYYYY  YYY
40Y  Y  Y  Y  Y  
80YY YY YYYY  YYY

4. Results and Discussion

[23] Measured AE signals during the experiments were characterized by their amplitude, energy content, rise time, duration and hit counts (exceeding a prescribed threshold). We limit the AE data analyses to the number of events (or pores involved per measured AE event), and to measured AE signal amplitudes. These two attributes are the simplest and most common in AE analyses, and are expected to bear the signatures of different imbibition and drainage processes, pore sizes, and possibly flow rates. To address the role of signal attenuation and its impact on inferred AE behavior we studied aspects of attenuation from knowledge of displacement front position relative to locations of various AE sensors. The measurement reproducibility was evaluated by comparing data for runs with same boundary conditions and experimental parameters (for simplicity, reproducibility was expressed in terms of number of AE events).

4.1. AE Signals Induced by Displacement of Fluid Fronts

[24] Prior to fluid front motion, no acoustic activity was measured by the AE sensors mounted on the cell. AE activity begun at the onset of fluid front motion through the porous medium similar to other studies [DiCarlo et al., 2003]. The AE signals generated by the moving front were detected by three sensors. Effects of signal attenuation with distance from the sensor were evidenced by AE event density and maximum of amplitude as a function of sensor distance from the moving front. The slope of the cumulative distribution of AE signals (AE events per displacement length) detected by the three sensors versus position of imbibition front is shown in Figure 3. The position of the front was determined by projecting the time information from displacement runs on the length scale using duration of displacement processes (beginning and end of runs were marked by manual tackles on cell, causing high-amplitude events) and total displacement length of about 180 mm. The AE event slopes detected by the different sensors vary significantly during passage of the front and reach a maximum right after front passage of the sensors placed at 25, 75, and 150 mm from the column's bottom reference level. The results show AE energy dissipation near the front (rapid drop in events over short displacement distance).

Figure 3.

Cumulative number of AE events versus imbibition front position for initially dry beads (0.50 mm) and flow rate of 5 mL min−1 (∼0.3 mm s−1). The data were smoothed by moving average considering 5000 data points.

[25] The response frequency band of the AE sensors used in this study was between 20 and 80 kHz corresponding to acoustic signal wavelengths of 280 to 70 mm in glass. These wavelengths are significantly larger than glass beads sizes thereby suggesting homogeneous propagation of the elastic waves with little scattering [Jia, 2004]. Theoretical signal attenuation values indicate, that AE signals would be damped in glass and air and thus propagate preferentially through the water phase (the respective attenuation coefficients are: αair = 1.2 × 10−2 dB cm−1, αwater = 1.4 × 10−5 dB cm−1, αglass=1.7 × 10−1 dB cm−1; for frequency of f = 80 kHz [Kaye and Laby, 1995]) and also through the Hele-Shaw glass walls. Considering attenuation effects on AE signals traveling along large distances, we restricted subsequent analysis to AE signals detected by sensor 2 (middle height) during passage of a displacement front within a 60 mm window centered around the sensor position (corresponding to a third of the total displacement length). Extraction of corresponding data sets was made.

4.2. Effects of Pore Size and Flow Rates on AE Signatures

[26] Five different glass bead sizes ranging from 0.5 to 4.4 mm in diameter were used to study the effect of pore size (and number of pores per volume) on AE activity during fluid front displacement at velocities ranging from 0.25 to 4 mm s−1. Figure 4 depicts the number of AE events detected during drainage (solid symbols) and imbibition (open symbols) of water across all glass bead sizes (marked by different symbols) and flow rates. The higher number of AE events during front displacement through smaller pores (with large number of pores per volume) is clearly visible. For the range of glass bead sizes used, we distinguish two different AE responses with respect to displacement velocity between small beads (0.5 mm and 1.0 mm) and large beads (2.0 mm and larger). In contrast with nearly exponential decrease in the number of AE events with increasing flow rate in the small beads, the total number of AE events remained nearly constant across all flow rates in columns with large beads.

Figure 4.

Effects of glass bead size and flow rate on AE events during imbibition and drainage of water in Hele-Shaw cells. Open symbols refer to imbibition processes, and solid symbols indicate values for drainage processes. Additional (open black) data points show number of events detected during imbibition through initially dry beads at flow rate of 20 mL min−1. (Data points are plotted at 22 mL min−1 for improved visibility.)

[27] Different displacement rates resulted in significant wetting phase entrapment of up to 27% of the water volume for drainage through smallest bead size, which reduce the number of drainable pores involved in the displacement process. Nevertheless, phase entrapment alone cannot explain the significant difference of nearly 2 orders of magnitude in the total number of AE events. The average number of pores involved per AE event versus flow rate is shown in Figure 5. The values were estimated by independently considering the total volume of beads in the cell volume (over length of 180 mm) and the void space from the volume of wetting liquid injected into initially dry beads (no air entrapment). The number of beads was inferred from their mean radii and the total number of pores was assumed to be similar to the number of beads. Note that for rapid withdrawal rates a considerable volume of liquid phase remained entrapped behind the front, this volume was subtracted from the calculation of the total number of pores. The number of pores involved per AE event is a crude estimate based on the ratio of number of pores to the number of AE events detected during a complete displacement experiment. The results presented in Figure 5 highlight differences between AE response for front displacement in small and large beads. Interestingly, for low flow rates (<20 mL min−1) pore/bead size had little effect on the number of pores per AE event (the value remained near 10 pores/AE event). For the small beads the number of pores associated with measured AE event increased nearly exponentially with increasing flow rate (up to 1000 pores/AE event). The fitted function a·ebx to drainage data (solid symbols) in Figure 5 yield exponents b = 0.05 for 0.5 mm, and 0.03 for 1 mm beads (with prefactors a of 41.4 and 7.7, for 0.5 and 1 mm, respectively). Despite relatively poor exponential fit for imbibition, the results show higher exponents for the wetting processes. The origins of the large differences in the number of AE events during displacement through the small beads over the range of flow rates remain unclear. We suspect the increased importance of viscous resistance with higher flow rates and smaller pores that may give rise to larger number of pores draining per event, but more work is needed to quantify the relations. The lower number of events for slow displacement process through 1 mm beads in comparison to 0.5 mm beads is addressed in section 4.4.

Figure 5.

Effects of glass bead size and flow rate on number of pores involved per AE event during imbibition and drainage of water in Hele-Shaw cells. Open symbols refer to imbibition processes, and solid symbols indicate values for drainage processes. The lines indicate exponential trend. The exponent for 0.50 mm beads was 0.05 and for 1.00 mm beads was 0.03. The exponent decreases with increasing pore size and is around zero for larger pores.

[28] Note, that beads were initially dry for small sizes, and initially wet for beads larger than 2.0 mm before imbibition. We have added three data points in Figure 4 for AE events during imbibition through initially dry large beads for flow rate of 20 mL min−1 (black open symbols shifted to 22 mL min−1 for improved visibility). We observe that imbibition processes through initially dry beads slightly exceeded the number of AE signals detected during displacement process through prewetted beads and its acoustic richness is comparable with a drainage process with the same boundary conditions. We attribute the difference resulting between initially dry and prewetted beads to the higher degree of contact line pinning and subsequent rapid contact line jumps with more entrainment of micro air bubbles relative to prewetted surfaces. A similar conclusion on capillary pinning forces on initially dry and wetted beads was found by Chatterjee et al. [2012].

[29] We also note that the motion of drainage front is acoustically richer than imbibition front invading prewetted beads (Figure 4). The ratio of AE events between imbibition and drainage varies with flow rate and is difficult to explain due to the likewise varying phase entrapment. Nevertheless, Figure 5 shows that number of pores involved per AE event varies more significantly for imbibition than for drainage.

4.3. Power Law Statistics of Amplitudes Versus Number of AE Events

[30] Considering the invasion percolation nature of drainage fronts and that AE events are likely to be linked with pore-scale invasion bursts, the power law statistics of pore invasion events [Måløy et al., 1992; Aker et al., 2000b] are likely to induce similar statistical behavior of associated AE events. Figure 6 depicts a representative summary of AE number of events versus AE amplitude (in units mV) for a drainage process through 0.5 mm beads clearly exhibiting a power law relationship similar to results obtained by other studies [DiCarlo et al., 2003]. Anomalies are discussed in section 4.4. The AE data permits representation of present amplitude values in units of decibels (a logarithmic unit for level) as well. The equation for the conversion between both units writes to

display math
Figure 6.

The statistics of AE amplitudes versus number of events exhibiting power law relationships shown here for passage of drainage front through 0.50 mm glass beads at volumetric flow rate of 5 mL min−1 (0.3 mm s−1). The parameters for power law fit on amplitude values (in mV) result in α = 0.78 and β = −1.3.

[31] To avoid confusion among the various units, we employ the following notation:

display math

inline image and

display math

inline image, with N being the number of AE events detected. The exponent β describes the slope in double logarithmic scale and was determined for AE events as a function of amplitude in units of electric potential (mV) for all data sets consisting of appropriate number of events. The β values are listed in Tables 2 and 3. The amplitude distributions are plotted in units of decibels; the conversion of the exponent and prefactor is inline image and inline image. Imbibition shows steeper slopes, in agreement with literature values that found AE amplitude-event exponent for drainage in sand to be −1.7, and for imbibition the exponent value was −2.6 [DiCarlo et al., 2003].

Table 2. Exponents β of Power Law Fits to Drainage With Water (AE Event Versus Amplitude (mV), inline image) and Number of Events With Amplitude of 30 dB (Determined From Data Fit)
Flow Rate (mL min−1)Glass Bead Diameter (mm)
0.50–0.751.00–1.302.00–2.402.85–3.203.80–4.20a
βN30dBβN30dBβN30dBβN30dBβN30dB
  • a

    The number of signals detected with 3.80 mm beads and during displacement experiments with highest flow rate applied (80 mL min−1) is low, possibly not showing a clear power law trend. The exponent values β and number of events with amplitude of 30 dB N30dB are listed here but are not included in the discussion in section 4.

5−1.301103−0.99424−0.4925−0.4412−0.232
10−1.39751−1.05503−0.5022−0.327−0.252
20−1.30330−0.95270−0.4521−0.316−0.162
40−1.0960−0.84145−0.4923−0.377−0.322
80a−0.324−0.7239−0.4722−0.326−0.222
Table 3. Exponents β of Power Law Fits to Imbibition With Water (AE Event Versus Amplitude (mV), inline image) and Number of Events With Amplitude of 30 dB (Determined From Data Fit)
Flow Rate (mL min−1)Glass Bead Diameter (mm)
0.50–0.751.00–1.302.00–2.402.85–3.203.80–4.20a
βN30dBβN30dBβN30dBβN30dBβN30dB
  • a

    The number of signals detected with 3.80 mm beads and during displacement experiments with the highest flow rate applied (80 mL min−1) is low, possibly not showing a clear power law trend. The exponent values β and number of events with amplitude of 30 dB N30dB are listed here but are not included in the discussion in section 4.

5−1.792947−1.26650−0.5212−0.566−0.192
10−1.691427−1.21936−0.489−0.465−1.316
20−1.62438−1.31515−0.5210−0.414−1.237
40−1.1446−1.14172−0.5011−0.465−1.106
80a−0.809−0.6912−0.5010−0.445−1.337

[32] The significance of the slope of the power law relates to the relatively large (but rare) amplitudes at the tail of the distribution, indicating occurrence of more frequent large amplitudes during drainage than during imbibition. The differences between AE power law slopes for imbibition and drainage become less pronounced for front displacement through larger bead sizes.

[33] The nature of power law relationship is strongly influenced by bead size showing a consistent increase in the (absolute) value of β with decreasing bead/pore size as depicted in Figure 7. Higher values of the exponent (slope) are indicative of dominance of many small amplitude AE events in the small glass beads with only a few high-amplitude events. The AE amplitude-event number relations are less affected by variations in displacement flow rates exhibiting a nearly constant exponentβ (Tables 2 and 3). Only with onset of unstable flow regimes (drainage) with negative generalized Bond number [Meheust et al., 2002] that we observe reduced value for β (Figure 8).

Figure 7.

Distribution of amplitudes after drainage processes through three sizes of beads with q = 5 mL min−1. The slope (power law exponent) varies with particle/pore size and is −1.30, −0.99, and −0.49 for 0.5, 1.0, and 2.0 mm beads. The arrow indicates an apparent change in power law slope around 40 dB for AE data during drainage through 1.00 mm.

Figure 8.

Power law relationships between AE amplitude and event numbers during drainage through 0.5 mm beads with three different mean front velocities. Black, green, and red symbols refer to volumetric flow rates of 5, 20, and 80 mL min−1. The resulting power law exponents are −1.30 for the 5 and 20 mL min−1 rates and −0.32 for the unstable drainage regime with an 80 mL min−1 rate.

4.4. Anomalies in AE Power Law Relationships With Bead Sizes

[34] AE measurements for displacement through glass beads with 1.0 mm and for the slowest imbibition rate in 0.5 mm beads exhibited some anomalies relative to the overall AE trends. We observed a bend in the power law statistics occurring near 40 dB casting certain doubts on the simple power law fit (Figure 7). This behavior was consistent upon repeated tests with new setup and beads. At present it stays a challenge to explain the origins of these anomalies but we can say, that signal energy, duration, and rise time of the signal fall especially for 1 mm likewise out of alignment. However, the other data sets for small beads show minor bending and could also hint to crossover behavior which is not closer observed. Further, the total number of AE events detected during displacement processes (drainage and imbibition) with flow rate of 5 mL min−1 is lower for 1 mm beads than for 0.5 mm beads and contradicts the assumption of a distinct relation between number of pores and number of AE events detected.

4.5. AE Characteristics Affected by Liquid Properties

[35] Complementing the studies on the effects of pore sizes and flow rates on AE signatures during water front displacements, we conducted similar experiments using different liquids focusing on the roles of viscosity and surface tension on AE activity. Displacement experiments were conducted using silicon oil and solutions of water with Triton X-100 with lower surface tension than pure water (solution A resulting to surface tension of 53 mN m−1 and B to 33 mN m−1). Measured AE activity during displacement processes were compared with observations made with distilled water for similar displacement rates and bead sizes. Figure 9 and Table 4 depict amplitude statistics for all four liquids used during imbibition through initially dry 0.5 mm glass beads at a flow rate of 20 mL min−1. These particular conditions were selected for comparison to avoid potential influences of or irritation by phase entrapment. We also focused on smallest beads to provide comparisons with a large number of AE signals.

Figure 9.

AE amplitude-event distribution for imbibition process with water (blue circles), surfactant A (σ = 53 mN m−1, red squares), and surfactant B (σ = 33 mN m−1, green diamonds) and silicon oil (black triangles) for q = 20 mL min−1 and a glass bead size of 0.5 mm.

Table 4. Exponents β of Power Law Fits to Imbibition and Drainage With Surfactants and Silicon Oil (AE Event Versus Amplitude (mV), inline image)
 Glass Bead Diameter >0.50–0.75 mm
Drainage (5 mL min−1) 
 Solution A−1.46
 Solution B−1.34
 Silicon oil−1.24
Imbibition (20 mL min−1) 
 Solution A−1.43
 Solution B−1.41
 Silicon oil−1.20

[36] While differences in the AE power law exponent were relatively minor, the total number of acoustic events varied significantly between the different liquids used. Surprisingly, results suggest that the effect of surface tension on AE generation was relatively minor. Surface tension was expected to exert a much larger influence due to the strong link between time scales, energy release during rapid interfacial reconfigurations and surface tension. The rate of interfacial configuration (and AE energy release) is determined primarily by liquid viscosity that consequently plays a more significant role in AE generation than surface tension. AE generated during displacement of silicon oil through the smallest glass beads exhibited only 15% of the AE activity detected during passage of water-air front. We thus conclude that interfacial reconfigurations of silicon oil are significantly slower than water (viscosity ratio of 10) resulting in lower AE activity. Additionally, entrained air bubble oscillations are likely to be strongly attenuated by the high viscosity of silicon oil.

4.6. AE Activity Associated With Interfacial Configurations Behind a Drainage Front

[37] Macroscopically, the motion of imbibition fronts seem relatively regular, and for initially dry porous media, pore space behind an imbibition front becomes fully saturated independent of flow rate. Drainage front morphology and dynamics are more complex, specifically with respect to AE activity and phase entrapment behind the front. The amount of liquid phase left behind a drainage front could be related to the front stability as classified by the generalized Bond number [Meheust et al., 2002; Lovoll et al., 2005]. The disconnected liquid phase may subsequently reorganize due to local capillary gradients or film flow down by gravity resulting in interfacial reconfiguration and potential reconnection to the continuous phase. The dynamics of the two phase flow or mobility of the phases behind the front in the transition zone depends on the degree of saturation and is strongly related to the displacement process Capillary number [Knudsen and Hansen, 2006].

[38] AE activity during and after cessation of imbibition and drainage front motion through columns with 0.5 mm beads is illustrated in Figure 10. Measured AE events (symbols) and their average rates (red line) as a function of time are depicted. Immediately after cessation of an imbibition experiment (after the front was stopped), a small number of AE events were detected possibly reflecting liquid redistribution due to capillary forces at the front (Figure 10a). The injected fluid volume allows assuming non to minor nonwetting phase entrapment. In opposite, the amount of wetting fluid behind the drainage front was between 14 and 27% after the performed drainage process through 0.5 mm beads. Note that only a part of this volume is disconnected from the wetting phase and can be considered as residual entrapment (at equilibrium). The main fraction of the entrapped phase may not be in equilibrium and abrupt interfacial configurations may be driven by capillary and gravitational forces. A significantly high acoustic activity is clearly visible long after the end of drainage experiments, an activity attributed to interfacial reconfigurations behind the front (driven by capillary and gravitational forces). We observed a decrease in AE activity with time after stopping the drainage fronts (Figures 10b and 10c). There was correlation between the amount of liquid entrapped behind the front and subsequent acoustic activity (higher intensity and longer duration of relaxation following rapid drainage rates). In some cases, the acoustic activity behind the front was even higher than during motion of the displacement front especially for unstable front displacement regimes (Figure 10c). The relaxation regime behind a drainage front is referred to as transition regime [Tallakstad et al., 2009b] reflecting transition from transient displacement to minimum energy steady state configuration. AE signals could be generated by snap-off processes and liquid bridge rupture behind the drainage front (due to film drainage of trapped liquid), in some cases with large entrapped liquid clusters, we expect rapid pore invasions (Haines jumps) driven by imbalance of capillary and gravitational forces.

Figure 10.

Acoustic activity after stopping imbibition and drainage fronts in a Hele-Shaw cell with the amplitudes of individual AE events (symbols) and AE event rate (red solid line) for (a) imbibition (20 mL min−1), (b) drainage at a flow rate of 20 mL min−1, and (c) drainage at a high flow rate of 80 mL min−1 (unstable displacement regime). The vertical lines indicate time where the advancing front was stopped. The glass bead size is 0.50 mm. The data were obtained from the sensor closest to the front's end position, namely, S1 for imbibition, and S3 for drainage.

5. Summary and Conclusions

[39] We conducted a systematic study of fluid front displacement at different flow rates through columns with different size of glass beads to characterize acoustic emissions (AE) signatures. Evidence suggests that AE measurements could be used for noninvasive monitoring of rapid pore-scale invasion events and interfacial reconfigurations during motion of drainage and imbibition fronts. Modern acquisition systems yield data-rich AE measurements that contain signatures of key flow attributes linking the number of AE events and pore sizes, or the emergence of power law relationships between AE amplitudes and event numbers reminiscent of pore-scale avalanche-like invasion regime documented during front displacement [Aker et al., 2000b]. Imbibition through initially dry surfaces resulted in higher AE activity (more events) relative to prewetted surfaces reflecting the large number of contact line pinning release events, and the higher propensity for air bubble entrainment during rapid contact line jumps.

[40] The number of AE events was correlated with the displacement regime, with larger number of small AE amplitude for imbibition and more AE signals with larger amplitudes for drainage. AE events were affected by pore size or number of pores per volume. We observed that flow rate exerted an effect on AE events for front displacement in small beads, but had virtually no effect on AE signals detected during displacement in glass beads larger than 2.0 mm in diameter. The number of pores involved per AE event is of similar order of magnitude for all glass bead sizes at low flow rates but changes significantly with increasing flow rate for small bead sizes. A surprising and unexpected result was the significant AE activity associated with interfacial reconfiguration during redistribution behind a drainage front. The extent of activity and duration were related to the amount of liquid entrapped behind a front.

[41] The origins of AE during interfacial motions are linked with Haines jumps, snap-off and gas entrainment, liquid bridge rupture, attachment and detachment of contact lines with embedding of bubbles, and friction and grain collisions. Establishing direct links between AE activity with a porous medium and particular interfacial phenomena is a far more complex problem than the fluid invasion problem under study and remains a challenge. Nevertheless, the study shows significant differences in acoustic signatures and particular attributes of the porous medium and the flow process suggesting potential for remote interrogation of these highly dynamic pore-scale displacement processes at the fluid front. The results provide a necessary first step toward using AE for in situ monitoring of multiphase flow toward gaining new insights into phase entrapment and redistribution.

Acknowledgments

[42] The authors gratefully acknowledge funding of for the project Multi-scale Interfaces in Unsaturated Soil (MUSIS) by the German Research Foundation DFG (FOR 1083). We are grateful for the many constructive comments offered by Renaud Toussaint and by two anonymous reviewers.