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 Calcite is a mineral phase that frequently precipitates during subsurface remediation or geotechnical engineering processes. This precipitation can lead to changes in the overall behavior of the system, such as flow alternation and soil strengthening. Because induced calcite precipitation is typically quite variable in space and time, monitoring its distribution in the subsurface is a challenge. In this research, we conducted a laboratory column experiment to investigate the potential of complex conductivity as a mean to remotely monitor calcite precipitation. Calcite precipitation was induced in a glass bead (3 mm) packed column through abiotic mixing of CaCl2 and Na2CO3 solutions. The experiment continued for 12 days with a constant precipitation rate of ∼0.6 milimole/d. Visual observations and scanning electron microscopy imaging revealed two distinct phases of precipitation: an earlier phase dominated by well distributed, discrete precipitates and a later phase characterized by localized precipitate aggregation and associated pore clogging. Complex conductivity measurements exhibited polarization signals that were characteristic of both phases of calcite precipitation, with the precipitation volume and crystal size controlling the overall polarization magnitude and relaxation time constant. We attribute the observed responses to polarization at the electrical double layer surrounding calcite crystals. Our experiment illustrates the potential of electrical methods for characterizing the distribution and aggregation state of nonconductive minerals like calcite. Advancing our ability to quantify geochemical transformations using such noninvasive methods is expected to facilitate our understanding of complex processes associated with natural subsurface systems as well as processes induced through engineered treatments (such as environmental remediation and carbon sequestration).
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 Calcite is a mineral phase that frequently precipitates as a result of increases in pH and alkalinity during subsurface remediation or geotechnical engineering activities. In some cases, calcite precipitation is beneficial and even critical to the efficiency of the remediation or engineering action. For instance, recent research has explored the potential of biogenic calcite (1) as a mean of enhancing sequestration of divalent radionuclides (e.g., 90Sr) through coprecipitation [Davis et al., 1987; Curti, 1999; Fujita et al., 2004] and (2) to improve soil strength for engineering purposes [DeJong et al., 2006; Whiffin et al., 2007]. While the precipitation of calcite can be beneficial in some cases, it may be undesirable in others. For instance, during the remediation of groundwater using the zero valent iron (ZVI) permeable reactive barrier (PRB) technology, calcite precipitation jeopardizes the performance of the barrier by reducing iron reactivity and hydraulic performance through formation of insulating layers on iron surfaces and clogging the pore spaces, respectively [Agrawal and Tratnyek, 1996; Phillips et al., 2000; Wilkin et al., 2003; Jeen et al., 2007]. In the cases of bioremediation, which often involves the introduction of organic nutrients and concomitant changes of pH and alkalinity, calcite is one of the readily precipitated mineral phases. Together with other mineral phases and biomass produced during bioremediation, calcite precipitation can be significant enough to alter the hydraulic property of the soil matrix [Li et al., 2010]. This can lead to flow rerouting at the field scale [Englert et al., 2009], which may in turn impact the efficacy and sustainability of the remediation treatment itself. However, developing a full understanding of the feedbacks between biogeochemical transformations and flow characteristics is challenging using conventional monitoring approaches.
 Aqueous geochemical measurements obtained using wellbore groundwater samples are typically used to infer the evolution of biogeochemical responses to remediation treatments [Lovley et al., 1994]. However, given the spatially variable distribution of injected amendments and the complexity of the subsequent biogeochemical reactions [Scheibe et al., 2006; Li et al., 2009], it is often difficult to assess the efficacy of remediation treatments over time and space with reasonable confidence using wellbore measurements alone. This challenge is exacerbated when attempting to understand the in situ evolution and spatiotemporal distribution of induced precipitates using conventional wellbore-based sampling approaches because those methods do not measure the time evolution of solid phases.
 Time-lapse geophysical methods hold potential for providing information about remediation-induced biogeochemical changes in a minimally invasive manner because they are often sensitive to changes in pore fluid and matrix properties associated with the induced biogeochemical transformations. Several biogeophysical studies have been performed in recent years to test this hypothesis [Atekwana et al., 2006]. For example, Williams et al.  performed a laboratory-scale biostimulation experiment where time-lapse complex resistivity, seismic, and various geochemical signals were measured over the length of the columns during induced metallic sulfide precipitation in sand packed columns. They showed that changes in complex resistivity and seismic amplitude measurements corresponded to the onset and spatial distribution of microbial-mediated iron and zinc sulfide precipitation. Slater et al. , Ntarlagiannis et al. [2005a], and Personna et al.  also used laboratory experiments to demonstrate the sensitivity of complex resistivity to metal sulfide precipitation/dissolution processes. These experiments conclusively show that FeS precipitation produces a polarization signal associated with charge redistribution in the electrical double layer (EDL) under an external potential field. The polarization magnitude is controlled by the surface area of the mineral precipitates and the evolution of the relaxation time constant coincides with the changes of a characteristic length scale (isolated precipitates or encrusted bacterial cells) as a result of FeS precipitation.
 Moving beyond experimental studies, recent research by Chen et al.  has developed a numerical framework for quantitative estimation of biogeochemical parameters based on colocated geophysical and geochemical data sets. They applied the estimation framework to the Williams et al.  data sets and verified its capability to provide realistic parameters consistent with direct geochemical and imaging results. They proposed a dynamic petrophysical model to explain the time-lapse response of the polarization magnitude and time constant based on the concept of isolated precipitates evolving into bioaggregates. In the model, they attributed the decrease of polarization magnitude and increase of time constant to the formation of encrusted microbe cell clusters, which reduced the total surface area and increased the particle size [Chen et al., 2009]. Together, these experimental and numerical studies showed the potential of geophysical methods for the monitoring of mineral precipitation during biostimulation at column scales. Recent studies have also illustrated the potential of using time-lapse geophysical methods to track subsurface changes associated with bioremediation at the field scale [Lane et al., 2006; Hubbard et al., 2008; Williams et al., 2009].
 The studies described above were primarily focused on the geophysical detection of injected remedial amendments or the precipitation of single metallic mineral phase (e.g., FeS). The metallic mineral phases are promising targets for complex conductivity imaging due to their semiconductive nature. However, the precipitation profiles developed during subsurface remediation are normally complex with concurrent precipitation of several mineral phases that are frequently colocated. A prerequisite of successful applications of geophysical methods for monitoring complex precipitate profiles during remediation is the understanding of the geophysical signatures from each of the individual mineral phases, including nonconductive calcite. Unlike metal sulfides, the understanding of geophysical responses due to calcite precipitation has been limited despite its ubiquitous presence in many natural systems, as well as its tendency to be an important product during in situ subsurface manipulations. As a step toward a better understanding of geophysical responses from systems with complex mineral precipitations, we performed laboratory studies to explore geophysical responses and mechanisms associated with calcite precipitation using complex conductivity method.
 Complex conductivity (σ*) is an electrical geophysical method that investigates charge transfer and polarization behavior under an external current. At low frequencies, σ* of natural soil can be expressed as:
where ω is the angular frequency, σ′ is the measured real part of σ*(ω), representing the conduction (energy loss) component, σ″ is the measured imaginary part of σ*(ω), which represents the polarization (energy storage) component. Two major electrical charge transport behaviors exist in saturated natural sediments: An electrolytic conductivity (σel) that occurs via the interconnected, fluid-filled pore space (a purely real term) and a complex interfacial conductivity (σ*int), which represents conduction and polarization processes that occur at the grain/electrolyte interface. While the measured σ′ depends on σel and σ*int, σ″ is only dependent on σ*int (i.e., it primarily depends on the interfacial properties of soil). A phenomenological model, called the Cole-Cole model [Pelton et al., 1978] is typically adopted to describe σ*(ω) of soils (see Dias  for review). In the Cole-Cole model, the frequency (ω) dependence of σ* is modeled as [Jones, 2002],
where σ0 is the conductivity at DC frequency, τ is the mean relaxation time, c is a shape exponent (typically 0.1–0.6) and m is the chargeability, a measure of the polarization magnitude (m = 1 − σ0/σ, where σ is the conductivity at high frequency). The three Cole-Cole parameters of most interest are σ0, mn (=m × σ0) and τ, representing global measures of electrical conductivity, induced polarization (IP) magnitude and a length scale measure related to particle size, respectively [Lesmes and Frye, 2001].
 We focused on complex conductivity method in this study because it is sensitive to the solid/liquid interfacial properties that are critical to the understanding of reaction mechanisms during precipitation. The experiment described here aims to (1) investigate the sensitivity of complex conductivity method to calcite precipitation, (2) understand the underlying polarization mechanisms, and (3) develop quantitative correlation between calcite precipitation and complex conductivity signals. Our study provides the necessary knowledge to help interpret time-lapse geophysical field data in terms of subsurface processes, such as the evolution of induced transformations or the impact of the transformations on flow characteristics. These processes are typically heterogeneous over space and time and are very challenging to sufficiently quantify using conventional (wellbore-based) sampling methods; advancement in our ability for remote quantification is expected to facilitate improved understanding of complex and often coupled subsurface processes.
 Laboratory experiments were conducted to explore the complex conductivity responses to calcite precipitation using instrumented flow-through columns. The column design included three sections (Figure 1). The two end sections of the column had inner diameters (I.D.) of 0.9 cm and housed both the current injection (A/B) and potential measurements (M/N) electrodes. Both current injection and potential measurement electrodes were made from silver (Ag) wires (∼1 mm thickness) coated with silver chloride (AgCl) and were coupled with the column through fluid filled polycarbon tubes installed on the column wall. The middle section, which had an I.D. of 2.54 cm, hosted column material. A layer of plastic mesh was installed at each end of the middle section to confine the solid material. The purpose of this design was to prevent the zone of reaction from expanding out of the measurement area between the two potential electrodes, thus allowing quantitative control on the establishment of petrophysical relationship between the mass of the precipitation and the electrical signals.
 The experiment was designed to induce calcite precipitation abiotically to achieve a well controlled reaction rate and to eliminate confounding biological effects [Ntarlagiannis et al., 2005b; Davis et al., 2006]. A fluid injection port equipped with flow control valve was installed on the middle section close to the bottom for fluid delivery. The column was set up vertically and the middle section was packed with large transparent glass beads (3 mm diameter, Fisher Scientific) (porosity = 49%) to (1) provide a simple background matrix with zero baseline polarization, (2) allow visual observation of the precipitation process over time, and (3) maintain a sufficiently high permeability thus minimizing pore clogging. A solution of 26.2 mM CaCl2 was injected into the column from the bottom to establish an equilibrated baseline state. Following this, a second stream of 29 mM Na2CO3 solution was introduced into the column from the injection port at the middle section to initiate calcite precipitation, as follows:
Note that the ionic concentrations were diluted once inside the column due to the equal volume mixing of these two solutions. The flow rate of both solutions was kept at 36 μl/min for the duration of the experiment, which continued for 12 days past injection of Na2CO3.
 Effluent aqueous samples were collected on regular basis for subsequent analysis of fluid conductivity (Orion 5 star meter, Thermal Scientific), alkalinity (Mettler Toledo DL 50 Graphix titrator) and Ca2+ concentrations (ICP-MS, Perkin Elmer). Scanning electron microscopy (SEM) (TM-1000, Hitachi) imaging was also carried out on column samples collected during postmortem analysis to characterize the morphology of the precipitates. Due to the destructive nature of this analysis, SEM imaging was only carried out at the end of the experiment; as such, a time evolving image series is not available. Surface area of calcite coated glass beads samples collected from the top and bottom sections of the column were measured with a seven point Brunauer, Emmett, and Teller (BET) method [Brunauer et al., 1938] using AUTOSORB-1 from Quantachrome Instruments (Boynton Beach, Florida). The measurable surface area of the uncoated 3 mm glass beads is below the detection limit of the instrument, thus the background surface area of the glass beads was not measured. Theoretical calculation results in 7.5 E-4 m2/g specific surface area of the uncoated glass beads, assuming smooth surfaces (verified with SEM).
 A dynamic signal analyzer (DSA) from National Instrument (NI 4461) was used to perform the electrical measurements (Figure 1). Spectral electrical data were collected from 0.1 to 10,000 Hz. The background data set was collected after the initial equilibration with CaCl2 and showed an average phase error of less than 3 mrads at 10,000 Hz. The data quality was excellent, displaying 0.1 mrad error or less over the majority of the frequencies (Figure 2). The spectral electrical data collected during the experiment was inverted with the Cole-Cole model [Pelton et al., 1978] described above using a Bayesian approach, which has been shown to improve parameter estimates and decrease uncertainty [Ghorbani et al., 2007; Chen et al., 2008].
 Complex conductivity measurements were carried out on daily basis together with geochemical monitoring of the effluents. The effluent geochemistry data are plotted in Figure 3.
 The fluid conductivities of the original CaCl2 and Na2CO3 solutions were 0.635 S/m and 0.567 S/m, respectively. Effluent fluid conductivity decreased significantly (from 0.635 S/m to ∼0.4 S/m) upon the introduction of Na2CO3 due to calcite precipitation that significantly reduced the total dissolved solids (TDS) of the pore fluid. The effluent conductivity stayed relatively constant for the rest of the experiment indicating a stable precipitation rate. Effluent calcium concentration decreased significantly from 13.1 mM to <2 mM upon calcite precipitation, and effluent alkalinity data showed similar changes decreasing from 29 meq/l to <5 meq/l and confirming the precipitation of calcite. Based on effluent geochemistry, equation (3), and the experimental flow rate, the precipitation rate was calculated at ∼0.6 milimole/d with a total mass of ∼7 milimoles (0.7 g) for the 12 day duration of the experiment. The total precipitate volume was 0.26 cm3 using a density of 2.71 g/cm3 for calcite. No measurable change of porosity was observed during the experiment due to the small amount of calcite precipitation relative to the total pore volume (<1%). The specific surface area of the calcite coated glass beads from the top and bottom of the column was measured at 0.03 and 0.033 m2/g, respectively, representing an increase of more than forty times relative to uncoated samples (7.5 E-4 m2/g). Note that these values are likely higher than the true values because (1) certain amounts of precipitate fall off the surface of glass beads during sample desiccation, a necessary step for BET analysis, especially those from the bottom of the column that have more precipitates and (2) some calcite aggregates shattered during sample preparation and desiccation, mostly for the samples from the bottom of the column. These disturbances are more significant for the samples from the bottom of the column, which may lead to an overestimation of the BET value, and thus the specific surface area, for the bottom glass beads.
 The spectral σ″, σ′ and σ″ at select frequencies, as well as Cole-Cole parameters of interest (mn and τ) are plotted in Figure 4. The spectral σ″ data (Figure 4a) at day 0 (i.e., before calcite precipitation was initiated) was essentially zero across most of the frequencies indicating neglectable surface polarization from the glass beads pack. During calcite precipitation, there was a consistent pattern of changes of σ″ with continuous increase for the first 9 days (Figure 4a) followed by a continuous decrease thereafter from days 9 to 12 (Figure 4b). The magnitude change of the σ″ was accompanied by a consistent pattern of shifts of critical frequencies (peak frequencies) with a gradual decrease for the first 9 days followed by a continuous increase thereafter. The σ′ at 1 Hz (Figure 4c) decreased significantly upon the precipitation of calcite, similar to the changes of effluent conductivity (Figure 3). This decrease indicates simply the dominant control of fluid conductivity on the bulk conductivity of the column. The changes of σ″ at selected frequencies (1, 10, 100 at 1000 Hz) are also plotted on Figure 4c and are consistent with the observations from the spectral data showing continuous increases for the first 9 days followed by decreases thereafter. Note that due to the small sizes of the calcite precipitates (a few to tens of μm), the polarization changes were most significant at higher frequencies. The estimated mean value of the Cole-Cole parameters (Figure 4d) revealed a continuous increase of both mn and τ before day 9 and decrease thereafter consistent with the observations from the spectral data (Figures 4a and 4b).
 In order to establish the quantitative correlation between polarization signatures and calcite precipitation during the experiment, we plotted the changes of σ″ at selected frequencies (10, 100 and 1000 Hz) and the Cole-Cole parameter (mn) against cumulative calcite precipitation in Figure 5. Figure 5 shows that despite the last few data points (discussed in the following section), σ″ and mn increase linearly over time with the evolved calcite precipitates (R2 > 0.95).
 Both visual observations/photographic imaging and SEM imaging were carried out to characterize precipitation geometry and pore structure changes at both macroscales and microscales (Figure 6). Visual observations revealed two characteristic phases with respect to the pore structure changes during precipitation (Figures 6a–6d): (1) an early phase of discrete precipitation before day 9 and (2) a later phase of partial aggregation and pore clogging from days 9 to 12. In contrast to the transparency of the column observed at the beginning of the experiment (Figure 6a), the column became opaque due to the precipitation of calcite during the early stage of phase one (Figure 6b). Later in phase one (Figure 6c), additional precipitation of calcite accumulated on the glass beads, especially near the bottom portion of the material section where the two solutions initially mixed. During this stage, the accumulation of calcite primarily occurred on individual glass beads with limited deposition in the pore spaces. However, during phase two, the continued precipitation of calcite started to fill the pore spaces between the calcite coated glass beads (Figure 6d).
 SEM images of glass beads collected from various locations after column shut down revealed differences in precipitation size and geometry (Figures 6e–6g). Calcite precipitation collected from the top portion of the glass beads pack showed a well distributed single layer of calcite crystals with crystal sizes primarily <5 μm (Figure 6e). Glass beads from the middle of the column were more extensively covered by calcite with the size of the crystals ranging from a few to about 20 μm (Figure 6f). Glass beads from the bottom of the column (closest to the initial mixing point) revealed much more significant accumulation and aggregation of calcite and larger average crystal sizes (∼20 μm) (Figure 6g) compared to the other locations. Because of the destructive nature of the sample acquisition required for SEM imaging, a time course series of SEM images associated with precipitation was not available. However, because the precipitation progressed from the bottom of the column to the top, we assume that the samples from the top of the glass bead pack likely represent the precipitation pattern during the early phase of the experiment. In fact, SEM images of glass beads collected after conducting a short (<1 day) experiment (using the experimental protocol described earlier) showed very similar precipitation pattern to those from the top of the glass beads pack in the main experiment which supports this assumption.
 Our experiment documented the spectral electrical geophysical signatures associated with calcite precipitation induced through abiotic mixing of calcium and carbonate solutions under controlled conditions. The glass beads used in the experiment were large and uniform in size, which provided the simplest and ideal baseline geophysical response with zero phase responses over a board frequency range (0.1 to 10,000 Hz). Note that a recent study has established a electrochemical model describing the polarization phenomena associated with spherical glass beads (tens to a hundred μm in diameter) and a phase response as high as 10 mrads was observed in their experiments [Leroy et al., 2008]. This large background phase response was not observed in our experiment due to the much larger bead size (3 mm) and smaller sample holder size, i.e., much smaller total polarizable surface area.
 Although calcite is a nonconductive mineral phase, the spectral electrical response collected during the experiment was similar to those observed during the introduction or evolution of zero valent iron and metal sulfides [Williams et al., 2005; Wu et al., 2005, 2008]. Specifically, the spectral electrical response from calcite precipitation shows a Cole-Cole type of dispersion with its magnitude related the total volume of the precipitates similar to those from metallic mineral precipitation [Williams et al., 2005; Wu et al., 2005; Slater et al., 2007]. Furthermore, the existence of characteristic critical frequencies and their evolution over time are similar to the observations with metallic mineral precipitates. However, it is noteworthy that the critical frequencies (hence, the relaxation time constant) of calcite precipitation (several hundreds to over one thousand Hz) is much higher comparing to those associated with granular ZVI and FeS precipitation (normally <100 Hz), reflecting probably the differences in particle sizes.
 The experiment revealed two distinctive stages with respect to the observed IP data: (1) phase one (approximately days 0–9) that showed continuous increase of IP effect and shift of critical frequency from high (>2 K Hz) to low (∼500 Hz) values during accumulation of calcite precipitates on the glass bead surfaces; and (2) phase two (∼days 9–12) that revealed consistent decreases of the IP effect and concurrent shift of critical frequency from low (∼500 Hz) to high values (∼1.5 K Hz) with aggregation of evolved calcite crystals on the grain surface and within the pore spaces.
 For nonconductive minerals, typically clay, membrane polarization is one of the proposed polarization mechanisms [Marshall and Madden, 1959; Titov et al., 2002]. This mechanism contributes the polarization phenomena to selective ion passage/blockage at the pore throats under external potential field, which creates temporal electric dipole moments (i.e., a form of charge storage). Because of the nonconductive nature of the calcite precipitates and their small sizes (a few to tens of μm), membrane polarization might initially be considered the dominant mechanism for the observed data. However, multiple evidences show that this might not be the case here. First, SEM images showed that during the early stage of phase one (i.e., when the precipitation was still at relatively low level) the precipitation and attachment of calcite to the large glass beads were discrete and well distributed and not likely to create the amount of pore throat effects significant enough to generate the observed polarization signals. Second, although the pore clogging of calcite during phase two could potentially create more significant pore throat effects (i.e., increase the observed IP response), we observed a decrease in polarization during this phase. In addition, the SEM images revealed the lack of submicro pores with the precipitates, a prerequisite for pore throat polarization, excluding membrane polarization as a major contributor. Last, we also find it difficult to explain the very characteristic critical frequency shift phenomena with the membrane polarization theory.
 Maxwell-Wagner polarization is a polarization mechanism associated with charge accumulation at the interfaces of two material of different dielectric properties, and has been used to explain the polarization phenomena associated with glass beads at high frequencies (>1000 Hz) [Leroy et al., 2008]. Although this is a polarization phenomena commonly occur in binary systems, e.g., discrete and dispersed particles in a continuous fluid, we consider this a minor contribution to the polarization observed in this experiment because (1) the majority of the data show critical frequencies at <1000 Hz, i.e., a relaxation timescale reasonably associated with dipole-related polarization in stead of the Maxwell-Wagner effect, (2) the decease of phase response at high frequency at 10,000 Hz, contradictive to the increase observed by Leroy et al. , and (3) a continuous and consistent shift of the critical frequencies that extended to as low as a few hundred Hz that cannot be explained by the Maxwell-Wagner polarization theory.
 We attribute the σ″ response to electrochemical polarization occurring at the electrical double layer (EDL) surrounding the calcite grains. Under an applied potential field, charges diffuse tangentially around the particles in the direction of the potential field, resulting in temporal distortions of the previously balanced EDL charge field around the particles [Schwarz, 1962]. This charge redistribution creates temporal dipole moments (i.e., polarization or charge storage). Once the external potential field is shut off, the distorted EDL charge structures relax back to restore the previous balanced structures, resulting in the measured IP effects. This EDL polarization is a diffusion limited process with the diffusion coefficients of the charged ions in the EDL being the critical factor controlling the timescale of the polarization process (given the fixed grain sizes and surface charge density distributions) [Schwarz, 1962]. During dynamic processes involving continuous crystal growth, the length scale and relaxation time are directly controlled by the size of the particles. The EDL polarization involves charge movement in both the fixed and the diffused layers of the EDL structure; and although we did not evaluate the relative contributions of each component in this experiment, previous research has suggested that the fixed layer polarization is dominant in sedimentary rocks [Lesmes and Morgan, 2001].
 The length scale and relaxation time of this polarization is also affected by the thickness, the charge density, and the charge mobility at the EDL because these parameters dictate the rate and magnitude of the charge redistribution under the external potential field [Schwarz, 1962; Vinegar and Waxman, 1984; Schön, 1996; Lesmes and Frye, 2001]. During our experiment, effluent geochemical data (Figure 3) indicated a stable stage throughout the experiment shortly after the experiment started. Because the charge density, mobility and thickness at the EDL is mostly controlled by pore fluid properties which was stable throughout the experiment, the impact of these parameters on time lapse polarization responses was minimal. However, in situations with evolving pore fluid chemistry, these parameters could play significant roles in controlling the polarization.
 The overall polarization magnitude is related to the total surface area of the particles available, similar to that observed for clay and metallic particles [Slater et al., 2006]. This EDL polarization phenomenon is similar to one of the mechanisms described by Wong  and Slater et al.  to explain polarization processes associated with metal particles. Although this polarization mechanism exists in both conductive and nonconductive materials, in the case of electronically conductive/semiconductive metallic particles (such as ZVI or iron sulfide) the external potential field not only causes the polarization of the charged ions in the EDL, but it also induces the redistribution of free charges (electrons) inside the particles. This redistribution exaggerates the overall charge imbalance around the particles, resulting in more significant IP effects.
 The polarization mechanism can be used to explain the responses observed during the first and second phases of the experiment. During phase one, the experiment started with the precipitation of individual calcite particles at an average size <5 μm based on SEM images (Figure 6e). These particles were well sorted in size and well distributed on the surfaces of the glass beads. As the experiment continued, additional calcite precipitation covered more beads surfaces and started to form aggregates primarily on top of the glass beads due to gravitational settling. The longer growth time also resulted in the increase of the sizes of early precipitated crystals. At this stage, individual calcite precipitates of varying sizes coexisted with aggregates and resulted in an increased average particle size which increases continuously as the crystals as well as the aggregates grew larger. Manifested in the electrical data, this accumulation of calcite precipitation resulted in the occurrence and subsequent increase of the IP effect due to the increase of the total surface area from calcite over time (>40 times increase based on BET measurements). The increased average size of the calcite precipitation caused the increase of the average diffusion length and relaxation time as indicated by the decrease of the critical frequency and the increase of estimated time constant (τ) over time (Figures 4a and 4d).
 During phase two of the experiment, excessive calcite precipitation filled the pore spaces and led to the formation of large calcite aggregates extending across multiple glass beads. This occurred primarily at the bottom portion of the glass bead pack (i.e., near the initial mixing point, Figure 6d). The formation of large calcite aggregates caused pore clogging, which in turn reduced the total calcite surface area compared to those previously isolated calcite particles. This aggregation-induced reduction in surface area resulted in the decrease of the polarization magnitude. This is similar to those described by Chen et al.  to explain the changes of polarization magnitude associated with FeS precipitation and bioaggregation. Because of the coexistence of small calcite crystals that were dispersive primarily at the top portion of the glass beads pack and large crystals mostly at the bottom, the average particle size was dependent on the relative volume of each component. The formation of large calcite aggregates at the bottom of the column could significantly reduce the number of large crystals. Although the particle size increases, the much large rate of quantity decrease resulted in a decrease of the averaged particle size and caused the decrease of overall relaxation time and shift of the critical frequencies to higher values according to the EDL polarization mechanism discussed above.
 Numerous early studies have documented a correlation between the size of the minerals and the time constant of the spectral electrical data [Wait, 1959; Pelton et al., 1978; Wong, 1979; Olhoeft, 1985], and most of the correlations were developed for conductive or semiconductive mineral phases (such as metal sulfides). These studies suggested an exponential correlation between time constant and particle sizes [Schwarz, 1962; Pelton et al., 1978]. Our data showed clearly the shift of critical frequency and time constant over time (Figure 4), indicating the existence of the particle size/time constant relationship for well crystallized single mineral phases that are nonconductive in nature. Although we could not acquire accurate average particle sizes during the various stages of the experiment, rough estimates from the SEM images revealed a 3–4 fold increase in average particle size (from <5 μm to ∼20 μm) coincident with the 3–4 fold increase in τ (from ∼0.15 milisecond to ∼0.48 milisecond) preceding significant pore clogging (Figure 4d). Our data suggest a positive and near linear correlation between time constant and particle size similar to those observed in saturated and unsaturated sandstones [Binley et al., 2005]. The time constant values in this experiment are much smaller than those normally observed in natural sediments and mineralized rocks (∼0.01 to hundreds of seconds) due to the very small sizes of the calcite crystal precipitates (a few to tens of μm). Although various studies have repeatedly shown the exponential correlation between time constant and particle size (R), τ ∝ Rc, the exponent value (c) is case specific and impacted by both solid phases properties (such as texture and mineralogy) as well as those of the pore fluids. Note that time constant, as well as other parameters associated with the phenomenological Cole-Cole model, is a fitted parameter that does not have any fundamental significance with respect to the physical mechanisms of the IP effects [Wong, 1979]. Recent studies have developed a theoretical model connecting spectral IP phenomena to the electrochemical processes occurring at the EDL in a spherical glass beads system, a step forward toward a better understanding of the fundamental physical basis of polarization phenomena associated with EDL [Leroy et al., 2008].
 Previous research on simultaneous precipitation of calcite and magnetite in ZVI systems showed that calcite primarily acts as an insulating phase that can coat mineral grains and reduce the polarization property of the samples [Wu et al., 2009]. Although our experiment revealed the polarizable nature of calcite precipitation, these findings do not contradict these previous results. Rather, the polarization phenomenon reported here occurred when calcite was precipitated on nonpolarizable or weakly polarizable siliceous background material. In systems that have large background polarization, such as ZVI, the precipitation of calcite could likely have a masking effect on the polarization relative to that associated with calcite alone. This highlights the importance of considering the polarization of the host material when interpreting the dominant mechanism, which was a primary reason for our choice of glass beads.
 Our experiment shows that regardless of the electronically nonconductive nature of the mineral phase, the EDL polarization is observable in calcite. This suggests the potential of using spectral electrical methods for monitoring nonconductive mineral phase precipitation often encountered during subsurface remediation and engineering manipulations. Based on existing laboratory characterization of calcite precipitates generated microbially [Rivadeneyra et al., 1998; Stocks-Fischer et al., 1999] and abiotically using microbial enzymes [Sondi and Salopek-Sondi, 2005], we expect that both volume/surface area relationships and multiscale pore throat distributions may differ dramatically from the abiotic case explored here. However, we hope that relationships based on characteristic length scales will generalize across the more complex morphologies commonly observed in bacterial systems relevant to site remediation. Although it is important to consider other factors that could also influence the electrical signatures during treatment in natural subsurface systems (such as the polarization of the host material, the effect of redox reactions, the evolution of coprecipitates, biofilms, and pore fluid TDS), this study demonstrates that calcite precipitation produces characteristic polarization signatures directly related to volume fraction and grain size. Advancing our ability to interpret geophysical signatures in terms of geochemical transformations paves the way for the use of these methods to remotely monitor complex processes associated with engineered treatments (such as environmental remediation or carbon sequestration) or natural systems (such as active limestone dissolution/precipitation karst processes).
 Funding for this study was provided by the U.S. Department of Energy, Biological and Environmental Research Program contract DE-AC0205CH11231 to the project entitled “Field Investigations of Microbially Facilitated Calcite Precipitation for Immobilization of Strontium-90 and Other Trace Metals in the Subsurface” (PI: Robert Smith, University of Idaho) and to the LBNL Sustainable Systems Scientific Focus Area. We thank Joern Larsen and Kathryn Flynn (both at LBNL) for conducting calcium and alkalinity analysis. We thank Xavier Comas (Florida Atlantic University) and an anonymous reviewer for providing useful comments.