Evolution of microstructure and elastic wave velocities in dehydrated gypsum samples

Authors


Abstract

[1] We report on changes in P and S-wave velocities and rock microstructure induced by devolatilization reactions using gypsum as a reference analog material. Cylindrical samples of natural alabaster were dehydrated in air, at ambient pressure, and temperatures between 378 and 423 K. Dehydration did not proceed homogeneously but via a reaction front moving sample inwards separating an outer highly porous rim from the remaining gypsum which, above approximately 393 (±5) K, concurrently decomposed into hemihydrate. Overall porosity was observed to continuously increase with reaction progress from approximately 2% for fully hydrated samples to 30% for completely dehydrated ones. Concurrently, P and S-wave velocities linearly decreased with porosity from 5.2 and 2.7 km/s to 1.0 and 0.7 km/s, respectively. It is concluded that a linearized empirical Raymer-type model extended by a critical porosity term and based on the respective time dependent mineral and pore volumes reasonably replicates the P and S-wave data in relation to reaction progress and porosity.

1. Introduction

[2] Dehydration reactions exert significant effects on rock transport properties due to concurrent volumetric changes of the solid and fluid phases involved. As hydrated minerals are abundant both within the continental and oceanic lithosphere this type of mineral transformation is likely to play a key role for fluid transport, fluid budget, and seismicity in metamorphic environments and particularly in subduction zones [e.g., Hacker et al., 2003; Milsch and Scholz, 2005; Brantut et al., 2011]. Unlike a number of experimental investigations on mechanical and hydraulic effects associated with such reactions (see, e.g., Brantut et al. [2012]for reviews) only 3 studies were identified where direct measurements of dehydration induced changes in P and S-wave velocity were performed [Kern, 1982; Popp and Kern, 1993; Brantut et al., 2012]. Ultimately, such laboratory-scale process studies are of paramount importance for any seismic or seismological interpretation in metamorphic environments, e.g., for tomographic imaging of active continental margins and subduction zones [e.g.,Nolet, 1986].

[3] Gypsum has repeatedly been used as an analog material principally for its abundance and its low dehydration temperature. It is well accepted [e.g., Ballirano and Melis, 2009], that up to temperatures of approximately 403 K gypsum (CaSO4·2H2O) dehydrates to γ-anhydrite (CaSO4) via an intermediate step forming hemihydrate (bassanite, CaSO4·0.5H2O) first. However, it was also observed that the ultimate reaction end member, either bassanite or anhydrite, strongly depends on the water vapor partial pressure [e.g., McAdie, 1964]. When comparing the molar volumes of the educt and the solid reaction products one notices that, at ambient conditions and assuming no compaction, the solid volume decreases by approximately 29% (for bassanite) and 39% (for anhydrite) and so increases porosity. In turn, changes in mineralogical content and porosity significantly affect P and S-wave velocities due to changes in the elastic moduli and densities of both the solid and fluid components of the rock [e.g.,Mavko et al., 2009].

2. Sample Material and Experimental Procedures

2.1. Sample Material, Sample Dehydration, and Porosity Measurements

[4] Table 1 shows a summary of all samples tested including reaction temperature and time as well as the types of subsequent measurements and investigations, if applicable. Cores of natural alabaster gypsum from Volterra, Italy with 25 mm in diameter and 50 mm in length were used in this study. The average starting mass of the samples was m0,av = 55.9 ± 0.2 g. Four dehydration temperatures, T = 378, 388, 398, and 423 K, were selected and dehydration was performed by heating the samples at a given temperature level for certain time periods in a preheated Memmert UNB400 universal oven, in air, and at ambient pressure. After heating, the samples were weighed again (mt) and the mass difference (m0mt) then was the basic quantity to derive the reaction progress as outlined in Milsch et al. [2011].

Table 1. Summary of Samples, Measurements and Resultsa
SampleTemperature (K)Heating Time (h)Maximum Transformed Fraction (1)cPorosity (%)vp [Series 1](m/s)vp | vs [Series 2]f (m/s)
9_1293002.6------
10_1293001.9------
16_1293002.3d5221---
35_1293002.2d---4984 | 3085
36_1293001.7d---5001 | 2370
       
3737860.105.0e---4362 | 2239
38378220.5417.0e---3105 | 1844
36_2378320.7221.0e---2829 | 1034
35_2378500.9325.0e---1629 | 771
393787181.3030.0e---1142 | 696
223788001.2829.91006---
 
18b388160.5418.43360---
26b388390.9625.51377---
 
10_2b39840.209.13748---
839870.3111.43797---
9_2398100.4415.12750---
7b398160.8123.01942---
12398701.2930.0d1079---
 
24423421.3128.21167---
234231021.3128.41035---

[5] Porosity measurements were performed with a Micromeritics AccuPyc helium (He) pycnometer at the Technical University Berlin. Porosity was measured for a number of selected samples to establish a reference curve against which all remaining samples were calibrated based on their reaction progress [Milsch et al., 2011] (Table 1).

2.2. Microstructural Investigations

[6] In the present study, a total of four samples were investigated microstructurally. The samples reflect four different degrees of reaction progress where two samples each were dehydrated at 388 K and 398 K, respectively (Table 1). These specimens were saturated with blue epoxy and were then saw-cut dry along the vertical axis into two equal halves. For each sample one of these halves was used for thin section preparation under water-absent conditions. The thin sections were finally investigated optically and with a Scanning Electron Microscope (SEM, Carl Zeiss Ultra 55 Plus) in Secondary Electron (SE) mode. Each of the second halves was used for color photographs of the cross-sectional sample area.

2.3. P and S-Wave Velocity Measurements

[7] Two sets of measurements were performed at the GFZ-Potsdam (1) and the University of Kiel (2), respectively as indicated inTable 1. In (1) P-wave velocityvp was measured along the sample axis with two commercial Panametrics ultrasonic transducers at 1 MHz and ambient conditions. One transducer acted as an emitter the other one as a receiver and the signal travel time t0 through the sensors was determined in a calibration run. The received signal was recorded with respect to the excitation using an oscilloscope and the wave travel time tthrough the sample was then directly read from the screen at the first P-wave arrival. The time resolution of the oscilloscope is 0.1μs which implies a reproducibility of individual velocity measurements within ±1.5% or better. P-wave velocity was finally calculated according tovp = L/(t-t0), where L is the sample length.

[8] In (2) the procedure was generally similar, however, both P and S-wave velocities,vp and vs, were determined with Geotron ultrasonic transducers at 350 kHz and ambient conditions. In addition to one P and S-wave measurement each along the sample axis cross-sample traces were recorded: 5 for P, 5 for SH, and 5 for SV at half the sample length and with a circumferential distance of 45°. Horizontally (SH) and vertically (SV) polarized S-waves were discriminated by rotating the sensors 90° within their fixtures. Again, wave velocities were determined manually by picking travel times at the first P and S-wave arrival, respectively.

3. Results and Discussion

3.1. Microstructure and Reaction Mechanism

[9] Irrespective of reaction temperature and time (Table 1) the bulk volume of the samples did not change by dehydration as evidenced by length measurements. Consequently, porosity φ was measured to continuously increase with reaction progress (Table 1). Starting from approximately 2 ± 0.5% (pure gypsum) porosity increased to 30% for completely dehydrated samples. Based on a mass balance it showed that the ultimate reaction end member, in fact, is anhydrite [Milsch et al., 2011] (Table 1). Due to the existence of unconnected pore space the measured maximum porosity underestimates the calculated true porosity of end member samples by 9% [Milsch et al., 2011].

[10] A cross section view of the samples in Figure 1a evidently shows that dehydration progresses via a reaction front that moves sample inwards leaving behind a porous network in which the epoxy could penetrate. Macroscopically, it can be seen on Figure 1a that the reaction front is very sharp for the samples dehydrated at 388 K (Samples 18 and 26) whereas it appears rather fuzzy for Samples 7 and 10 dehydrated at 398 K as indicated by the arrows. Also, the remaining inner portion of the sample appears more transparent in the former and whitish opaque in the latter case. This implies significant differences in the overall transformation mechanism with some transition between 388 and 398 K.

Figure 1.

(a) Cut samples and corresponding thin-sections for optical and SEM analysis. Left to right: Sample 10 (398 K), 18 (388 K), 7 (398 K), 26 (388 K). Reaction progresses via a reaction front from the sample outside to the inside. Arrows indicate differences in the rim structure at 398 K dehydration temperature as compared to 388 K. (b) Optical micrograph of Sample 18 (388 K). The reaction front is sharp with bassanite at the sample margin and unaltered gypsum in the sample interior. (c) Optical micrograph of Sample 10 (398 K). Again, the reaction front is sharp but gypsum is decomposed into numerous subgrains. SEM micrographs of (d) Sample 18 (388 K) and (e and f) Sample 7 (398 K). For both samples, in the upper margins of Figures 1d and 1e a highly porous network formed within the rim matrix. Towards the center of the sample (Figure 1f) bassanite fibers emerge from gypsum implying a change in the reaction mechanism as compared to Figure 1d where gypsum is stable and unaltered.

[11] These observations are confirmed microstructurally in Figures 1b–1f. Figure 1b shows an optical micrograph under crossed Nicols of Sample 18 (388 K). One notices a fine grained matrix in the upper half which is the dehydrated rim. The lower half (the inner core) evidently is the unaltered gypsum. In Figure 1c(Sample 10, 398 K, crossed Nicols), the outer rim appears identical to Sample 18 but the sample core looks strikingly different. The original gypsum has decomposed into numerous subgrains with fiber or needle-like crystals appearing in addition. This needle-like morphology is typical for bassanite [e.g.,Ko et al., 1997]. The SEM-image inFigure 1d (Sample 18, 388 K) additionally shows that the outer rim consists of a highly porous network and that the unaltered gypsum in the core is very dense. Finally, the SEM cross section in Figures 1e and 1f (Sample 7, 398 K) highlights the transition from the porous rim to gypsum this time containing dispersed bassanite fibers.

[12] The absence of bassanite in the gypsum core of all samples dehydrated at 388 K and its concurrent occurrence at 398 K was evidenced by X-ray diffraction (XRD) point measurements. The spectra are shown in Figure S1 in theauxiliary material. However, regarding the formation of anhydrite the spectra of the four samples in Figure 1are inconclusive. This supports the two-stage mechanism outlined inSection 1 where anhydrite forms after all gypsum has been converted to bassanite.

[13] In addition to temperature three factors can be discussed to affect the transformation mechanism: (1) Alabaster from Volterra was shown to be relatively heterogeneous on the mm to cm-scale [e.g.,Fusseis et al., 2012]. However, as observed by Milsch et al. [2011] the samples are very homogeneous regarding the reproducibility of the reaction kinetics. (2) Heating the center of the samples to target temperature was numerically modeled to take approximately 20 min with no significant temperature dependence [Milsch et al., 2011]. This implies that the heat wave propagates always significantly faster than the reaction front. Therefore, any effect of thermal damage should not yield temperature dependent reaction mechanisms. (3) Figure S2 in the auxiliary material shows that there is no evidence for bassanite grain growth during the longer reaction time of sample 7 (16 h) as compared to sample 10 (4 h). This indicates that the occurrence of bassanite in the high temperature field is rather independent of reaction time as it emerges very early once the target temperature has been reached. However, the density of bassanite fibers was observed to increase with time.

[14] Two macroscopic overall transformation mechanisms can therefore be distinguished that only depend on the respective temperature field at otherwise identical reaction conditions. At temperatures below approximately 393 (±5) K, in air, and at ambient pressure gypsum only transforms from the sample margin to its center yielding a sharp reaction front. This reaction front progresses whenever the water released in the narrow front region can dissipate outwards through the porous network leaving behind new porosity. This is in agreement with the observations and interpretations made by Fusseis et al. [2012]who performed very similar dehydration experiments at 388 K using concurrent X-ray tomographic imaging. Above approximately 393 K, concurrently, the remaining gypsum decomposes into bassanite. In this temperature field, apparently, gypsum becomes unstable throughout the sample. At the sample margin the released water is easily dissipated to the atmosphere via the porous network that progressively forms. In the sample interior the released water is trapped and a higher water vapor partial pressure decelerates the reaction rate. With progressing reaction a transition zone forms (Figure 1e) where the outer rim and the isolated bassanite fibers in the core coalesce. Through this extended pore network the epoxy in Figure 1a could more effectively penetrate the sample from outside yielding the fuzzy appearance of the rim. In conclusion, the overall reaction mechanism depends primarily on a combination of reaction temperature and water vapor partial pressure.

3.2. P and S-Wave Velocities

[15] Results of the two measurement series (1) and (2) are compiled in Figure 2and are labeled accordingly. In series (1) P-wave velocityvp was measured on 11 samples (Table 1) and was observed to generally decrease with an increase in sample porosity (Figure 2, dots). The overall trend is linear with velocities ranging from 5.2 km/s at 2% (pure gypsum) to 1.0 km/s at 30% (pure anhydrite). For pure, polycrystalline and isotropic gypsum aggregates and zero porosity the available elasticity [e.g., Bass, 1995] and density data [e.g., Deer et al., 1992] yields: vp = [(4/3 G + K)/ρ]1/2 = 5.28 km/s with K, the bulk modulus = 43 ± 1 GPa, G, the shear modulus = 16 ± 1 GPa, and ρ, the density = 2.31 g/cm3. This upper bound value is in reasonable proximity to the P-wave velocity measured for the starting material having a porosity of 2%. The dots are labeled with the respective temperature at which dehydration was performed for a particular sample. The overall trend is independent of dehydration temperature but evidently depends on reaction progress which is unequivocally related to porosity [Milsch et al., 2011]. The scatter of the 4 data points for intermediate porosities between approximately 8% and 20% therefore should reflect reaction temperature independent microstructural differences of the samples, e.g., the preexistence of microcracks which disappear at high porosities when the samples are close to being fully converted.

Figure 2.

P and S-wave velocitiesvp and vsas a function of porosity for series (1) and (2) samples. The series (1) data (dots) are labeled with the respective reaction temperature. Values averaged over the full data set of an individual sample are shown. Scatter of the data and measurement uncertainties are symbolized by the error bars. The blue dashed lines indicate the confidence region for the S-wave data. The solid red and blue lines indicate the replication of the data for the P and S-wave velocities, respectively, by means of a velocity-porosity model outlined inSection 3.3.

[16] For series (1) samples theoretical simulations of the P-wave velocity dependence on porosity with effective medium bounds [e.g.,Mavko et al., 2009] were performed. We tested a modified Raymer model [Raymer et al., 1980], the Wyllie equation as well as the upper and lower Hashin-Shtrikman bounds [e.g.,Arns et al., 2002]. The Raymer model was linearized according to vp= [(1 -φ) vps + φpf], where vps and vpfare the P-wave velocities in the solid and the fluid phase, respectively. This relationship can be regarded as the corresponding upper bound Wyllie equation, which is 1/vp= [(1 -φ)/vps + φ/vpf]. Air at ambient pressure (0.1 MPa) and temperature (293 K) with K = 0.1 MPa, ρ = 0.0012 g/cm3 and vp = 0.343 km/s was assumed as the pore fluid. An evaluation of these bounds was performed with one mineral phase: gypsum with properties as above or anhydrite as the reaction end member with K = 55 GPa, G = 29 GPa [Bass, 1995], ρ = 2.98 g/cm3 [Deer et al., 1992], and vp= 5.61 km/s. In conclusion, none of these models adequately replicates the experimentally determined velocity-porosity relationship as shown in theauxiliary material in Figure S3.

[17] The series (2) P-wave results (red squares) fit well into the ones of series (1) (black dots). We observed no systematic difference between measurements along and across the core axis with variations symbolized by the error bars. For the S-waves (blue diamonds), again, the velocities decrease with increasing porosity and follow a linear trend from 2.7 km/s at 2% to 0.7 km/s at 30% on average. Calculating S-wave velocity in pure, polycrystalline and isotropic gypsum aggregates for zero porosity according tovs = [G/ρ]1/2 with elastic properties as above yields vs= 2.63 km/s in reasonable agreement with the measured average value at 2% porosity. As for the P-waves, no systematic difference between measurements along and across the core axis was observed. Also, no systematic difference in vertically and horizontally polarized S-wave velocities was detected. The significant shape-preferred orientations observed byFusseis et al. [2012]for alabaster gypsum therefore cannot account for the wave velocity variations at intermediate porosities reported above. S-wave first arrival picking showed to be significantly more imprecise than for P-waves with errors amounting to ± 0.2 km/s as indicated by the error bars at values averaged over the full data set for an individual sample. The blue dashed lines thus indicate the approximate confidence region for the S-wave data. Any anisotropy in S-wave velocity therefore is suggested to be smaller than errors related to the measurement itself.

3.3. Relationships Between Wave Velocities, Microstructure, and Reaction Progress

[18] The data assembled in Figure 2provides the basis for testing an improved velocity-porosity model which will be outlined in the following. Similar to the modified Raymer model that provides a linear relationship as shown above the P or S-wave velocitiesvp,s in the different mineral and fluid phases (gypsum (Gp), bassanite (Bs) or anhydrite (Anh), and air) are weighted according to their different, time dependent volumetric proportions V:

display math

where t is the reaction time. In the following the simulation is performed with anhydrite as the reaction end member. A test of this assumption was conducted as outlined further below. Based on the microstructural observations in Section 3.1, assuming a constant bulk volume and a shrinking gypsum cylinder as reaction progresses, neglecting the presence of bassanite in the gypsum core for tests in the high temperature field, and finally assuming a constant maximum porosity of φmax = 30% throughout the rim matrix one obtains:

display math
display math
display math

with vp,s (Air) = 0.34 and 0 km/s as well as vp,s (Gp) = 5.28 and 2.63 km/s, respectively. For vp,s (Anh, φmax) we applied the critical porosity (φc) concept introduced by Nur et al. [1991]: vp (Anh, φmax) = [{4/3 G(φmax) + K(φmax)}/ρ(φmax)]1/2 and vs (Anh, φmax) = [G(φmax)/ρ(φmax)]1/2, with K(φmax) = K[1-(φmax/φc)], G(φmax) = G[1-(φmax/φc)], and ρ(φmax) = ρ[1-φmax] as well as φc = 31%. With anhydrite elastic (K, G) and density (ρ) properties as noted in Section 3.2 one finally obtains vp,s (Anh, φmax) = 1.21 and 0.67 km/s, respectively.

[19] The result of this model is shown in Figure 2for both P (red solid line) and S-waves (blue solid line). Evidently, with a critical porosity of 31% as assumed above, the model provides a reasonable replication of the measured data within the limits of experimental precision and sample homogeneity that can be assumed. The simulation was also conducted with bassanite elastic and density properties (K = 70 GPa, G = 30 GPa, and ρ = 2.73 g/cm3) [Brantut et al., 2012] replacing the term for anhydrite in equation (1) and resulting in virtually no difference in the result as shown in Figure S4 in the auxiliary material. This implies that (1) the assumption to neglect the presence of bassanite in the gypsum core was reasonable and (2) that, in fact, the significantly altered effective elastic properties of the transformed mineral matrix dominate the dependence of the wave velocities on porosity.

[20] In equation (1) the choice of the critical porosity value then controls the slope of the simulated curves in Figure 2. A sensitivity analysis with varying values for φc was conducted and the results are shown in the auxiliary materialin Figure S5. When choosing a porosity difference of 1% between the maximum porosity measured (30%) and the critical porosity (thus 31%) the simulation reasonably replicates the data. When increasing this difference the simulated curves flatten. When decreasing this difference to zero the rim matrix becomes a suspension and only the fluid (air) filled portion of the sample transmits (P-) waves. In this limit the concept breaks down and becomes physically meaningless. In conclusion, a porosity difference of 1% suggests that the rim matrix is suspension-like but still load bearing to some degree.

[21] Based on this model (equation (1)), an effective vp/vs ratio can be derived. One obtains a value of approximately 2.0 ± 0.1 independent of porosity or reaction progress and therefore a Poisson’s ratio of 0.33. When combining equation (1) above with equation 3 in Milsch et al. [2011]and the reaction-kinetic results reported therein this finally yields, for each temperature individually, the time dependent evolution of the wave velocities, thusvp,s = f(t, T), where t is reaction time and T is reaction temperature.

4. Conclusions

[22] We investigated the effect of dehydration on rock microstructure and P and S-wave velocities using gypsum as an analog material. Dehydrating the samples in air and at ambient pressure excluded compaction and yielded unequivocal relationships between reaction progress, porosity, and the elastic wave velocities. It showed that at the present environmental conditions polycrystalline gypsum first transforms to bassanite but ultimately dehydrates to anhydrite regardless of temperature contrasting previous investigations with water as the pore fluid [e.g.,Ko et al., 1997; Hildyard et al., 2011]. Reaction progresses via a reaction front moving sample inwards but two temperature fields were distinguished where significant differences in microstructure point to different overall transformation mechanisms with a transition at approximately 393 (±5) K. This particularly concerns the concurrent formation of bassanite within the gypsum core which was only observed at 398 K and above.

[23] The P and S-wave velocities were measured to linearly decrease with increasing porosity. For modeling this dependence, common two phase effective medium bounds, e.g., Hashin-Shtrikman, showed to be deficient. A linearized empirical Raymer-type model extended by a critical porosity term reasonably replicated both the P and S-wave data and suggests that the reaction products are constantly in a suspension-like state. It is concluded, that measured P and S-wave velocities are effective ones and when modeled the different time dependent volumetric proportions of the solid and fluid phases have to be taken into account.

[24] As sample compaction was precluded and the samples were nominally dry the present experimental procedure evidently yielded different relationships between P and S-wave velocities and reaction progress than those reported byPopp and Kern [1993] and Brantut et al. [2012]. In their experiments water wet conditions and elevated pressures resulted in significantly higher velocities as reaction proceeded but also in a departure from the linear velocity-porosity/reaction progress relationship observed here. The present study thus provides an upper bound reference data baseline for dehydration-induced changes in P and S-wave velocities as a function of reaction progress and porosity. With this baseline established further investigations are suggested that relate the effects of water and elevated stresses to dehydration induced dynamic changes of rock transport properties.

Acknowledgments

[25] We thank Stefan Gehrmann, Ansgar Schepers, Helga Kemnitz, and Rudolf Naumann for substantial technical and analytical assistance. Permission to use the ultrasonic equipment at the University of Kiel, Institute of Geosciences was given by Thomas Meier and is greatly acknowledged. Constructive reviews by Christoph Schrank and one anonymous reviewer helped to improve the paper.

[26] The Editor thanks Christoph Schrank and an anonymous reviewer for their assistance in evaluating this paper.

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