CO2-induced dissolution of low permeability carbonates. Part I: Characterization and experiments

Advances in Water Resources xxx (2013) xxx–xxx

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CO2-induced dissolution of low permeability carbonates. Part I: Characterization and experiments Megan M. Smith ⇑, Yelena Sholokhova, Yue Hao, Susan A. Carroll Lawrence Livermore National Laboratory, 7000 East Avenue, L-231, Livermore, CA 94550, USA

a r t i c l e

i n f o

Article history: Available online xxxx Keywords: Carbonate permeability Carbon sequestration Enhanced oil recovery Carbonate dissolution Microtomography

a b s t r a c t The effect of elevated dissolved CO2 concentrations on compositionally and structurally distinct carbonate sample cores from the Weyburn–Midale CO2-enhanced oil recovery and storage site (Canada) was measured from analysis of 3-D sample characterization and fluid chemistry data from core-flood experiments. Experimental conditions (60 °C; 24.8 MPa confining pressure) and brine composition were chosen to mimic in situ reservoir conditions. Mineralogy and pore space distributions within the eight individual cores were characterized with X-ray computed microtomography and scanning electron microscopy both before and after exposure to brine with 0.5 6 pCO2 6 3 MPa, while solution chemistry and differential fluid pressures were monitored during experiments. Our experimental study aimed to quantify the relationship between fluid flow, heterogeneity, and reaction specific to carbon storage at the Weyburn–Midale field by integrating characterization imaging, pressure data, and solution chemistry. Through the use of non-invasive microtomographic imaging, a variety of dissolution behaviors were observed, with variable effects on the evolution of solution chemistry and permeability as a result of heterogeneity within these two relatively low permeability carbonate samples. Similar-sized, evenly distributed pores, and steadily advancing dissolution fronts suggested that uniform flow velocities were maintained throughout the duration of the higher permeability ‘‘Marly’’ dolostone core experiments. The development of unstable dissolution fronts and fast pathways occurred in the ‘‘Vuggy’’ sample experiments when fluid velocities varied widely within the sample (as a result of increased pore structure heterogeneity). The overall effect of fast pathway development was to increase bulk permeability values by several orders of magnitude, allowing CO2-acidified fluids to travel through the cores largely unmodified by carbonate mineral reaction, as indicated by a lack of change in later-time solution pH levels at the core outlet. Given the impact of heterogeneity within low permeability cores, effort should be taken to incorporate smaller-scale heterogeneity into predictive models and such an averaging approach (utilizing the data and observations discussed here) is the topic of our companion manuscript (see Hao et al., this issue). Solution chemistry results indicated that steady-state carbonate mass transfer conditions were attained in the Marly dolostone experiments and during the earlier (pre-pressure breakthrough) portions of the Vuggy limestone experiments. Steady-state calcium and magnesium concentrations coincided with outlet solutions that were calculated to be at or very near to equilibrium with respect to both calcite and dolomite, relative to available thermodynamic data and considering experimental data scatter. Carbonate mass transfer data were evaluated against a variety of proposed carbonate dissolution mechanisms, including both pH- and pCO2-dependent expressions as well as a simplified pH-independent formulation. Based on this analysis, the calcite reaction rate coefficient was estimated to be 17 times faster than that for dolomite dissolution under our experimental conditions. This ratio is consistent with the use of rate equations that depend on carbonate mineral saturation without specifying additional dependence on solution pH or CO2 levels, and may be a result of the narrow experimental pH range. In addition, solution chemistry data were combined with time-dependent pressure data to constrain the exponent in a power-law expression describing the relationship between evolving porosity and permeability within the Vuggy limestones. This relationship as well as proposed carbonate kinetic expressions are further evaluated in our companion paper (see Hao et al., this issue). Ó 2013 Elsevier Ltd. All rights reserved.

⇑ Corresponding author. Tel.: +1 (925) 423 7970. E-mail addresses: [email protected] (M.M. Smith), [email protected] (Y. Hao), [email protected] (S.A. Carroll). 0309-1708/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.advwatres.2013.09.008

Please cite this article in press as: Smith MM et al. CO2-induced dissolution of low permeability carbonates. Part I: Characterization and experiments. Adv Water Resour (2013), http://dx.doi.org/10.1016/j.advwatres.2013.09.008

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1. Introduction Transition of carbon dioxide-enhanced oil recovery (EOR) fields to long-term CO2 storage sites has the potential to increase storage capacity and reduce injection pressures. The common practice of alternating injections of CO2 and water (so-called wateralternating-gas, or WAG) to enhance hydrocarbon production generates new pore space and enhances permeability as fluids partially dissolve carbonate minerals until equilibrium is reached. Accurate observation and prediction of meaningful changes in porosity and permeability as well as the development of useful parameters relating flow, heterogeneity and reaction in carbonates has been an active area of research for acid stimulation processes and more recently for geologic CO2 storage or GCS [1–12]. The evolving relationship between porosity and permeability can be assessed using reactive-transport simulators that couple fluid advection, molecular diffusion, mineral dissolution kinetics, and thermodynamics. However, application of these models to carbonate systems is hampered by both the heterogeneous distribution of pores and reactive mineral surfaces (often spanning several orders of magnitude; e.g., [13–14]), as well as uncertainty in carbonate dissolution kinetics in CO2-rich waters. Continuumscale reactive transport models rely on the principle that averaged rock properties can be applied over a representative elementary volume defined by the grid spacing [15]. In practice, however, imaging and characterization techniques are capable of obtaining far more information (at a finer scale) than that which can be computationally managed within current continuum models. These experiments were undertaken in part to provide a robust dataset for the development and calibration of alternative scaling parameters and relationships in continuum models to better describe and predict the onset of the unstable dissolution features observed in these low permeability carbonate samples (as is discussed further in our companion paper [16]). The role of mineral and pore-scale heterogeneity was explored in this study by reacting samples from both relatively heterogeneous and homogeneous carbonate units from the Weyburn– Midale hydrocarbon reservoir, Saskatchewan, Canada. The Weyburn–Midale reservoirs are dominated by a carbonate (calcite and dolomite, with trace anhydrite and quartz) mineralogy that will partially dissolve as acidic CO2-rich waters used in EOR operations react with formation rock, altering porosity and permeability. We chose to study the porosity evolution using fluids equilibrated at pCO2 levels representative of site monitoring values and carbonate units possessing different initial mineral abundances, porosity distributions, and permeabilities [17–19]. We combined X-ray computed microtomography (XCMT) data with higher resolution scanning electron microscopy (SEM) images and statistical analysis to capture submicron pores to centimeterscale or larger vugs. This methodology was selected in an effort to use pore space and mineral characterization of the carbonate cores before and after reaction to identify the type and mechanism of dissolution fronts in reactive systems. Here we discuss the role of physical and chemical heterogeneity on the development of distinct reaction fronts relevant to enhanced oil recovery and carbon storage using this rich experimental dataset. Our companion paper utilizes these data to rigorously constrain parameter inputs to quantify relationships between dissolution and evolving porosity and permeability in reactivetransport simulations of CO2-carbonate interactions [16].

2. Methods We conducted core-flood experiments on well-characterized samples collected from the Midale ‘‘Marly M3’’ and ‘‘Vuggy V6’’

beds described by Wegelin [20] from wellbore 21/6-8-6-13W2, cored prior to CO2-EOR operations at the Weyburn–Midale fields (www.ptrc.ca/weyburn-midale). We refer to these units as Marly dolostones and Vuggy limestones, and to specific cores by a sample identifier name, which contains the core type and the brine pCO2 level with which the core was reacted (e.g., ‘‘V-3’’ refers to a Vuggy limestone core reacted with a 3 MPa pCO2 fluid). Briefly, the Vuggy limestone has a much higher abundance of calcite relative to dolomite and lower initial porosity and permeability compared to the Marly dolostone. 2.1. Characterization methods Each subcore was imaged by X-ray computed microtomography (XCMT) prior to reaction at the ID-19 beam line at the European Radiation Synchrotron Facility (ESRF; Grenoble, France), and at the 8.3.2 beam line at the Advanced Light Source (ALS; Berkeley, California) after reaction. Subcore dimensions (15 mm diameter and 30 mm length, drilled parallel to bedding) were selected as a compromise between lengths long enough to capture some natural formation variability and detect geochemical reaction fronts, and the greatest diameter that could be accurately characterized with the XCMT technique. Data from both high-resolution XCMT and environmental scanning electron microscopy (SEM) in back-scatter electron (BSE) mode were combined to quantify the threedimensional changes produced by carbonate mineral dissolution. Parameters used for XCMT data collection are listed in Table 1. Image reconstruction of each core before and after reaction resulted in a large stack of image slices perpendicular to the samples’ long axes (z-direction), comprising P100 GB when stored at 16-bit accuracy. Initial conditioning and image analysis procedures were put in place to reduce the image stacks to a computationally manageable size. The 16-bit data were first scaled to 8-bit accuracy and then the resolution of both datasets was rescaled to a final resolution of 14.8 lm/pixel using bilinear interpolation in ImageJ [21], reducing each stack size to a manageable 2 GB. The interpolation step was found to produce better final image results especially for non-integer scaling (necessary due to differing initial pixel resolutions). These steps did not reduce the quality of the data because grain-scale pores were already below the XCMT resolution, while disconnected macro-scale pores remained well characterized at the final working resolution. After initial conditioning of each image stack, more involved image analyses were performed. First, the XCMT images were segmented into porous or solid phases by thresholding the data (treating each pixel based on gray-scale values only, and burning/ building back pixels to reduce anomalous grayscale single pixels (artifacts resulting from possible sub-resolution phase mixtures). This more efficient technique was preferred over other more

Table 1 Parameters used in X-ray computed microtomography data collection and analysis. XCMT parameters

ALS, LBNL

ESRF, grenoble

Beam geometry Beam light mode Lens Field of view (mm) Energy (keV) Beam size (lm) Scintillator Filters (width, mm) Camera Camera size Resolution (lm/pixel) Angular increment Projections per core

Parallel White 2X Mitutoyo + 1X tube 17.7 30 (M3); 40 (V6) 220  30 CsWO4 Cu – 0.92; Al – 1.6 Cooke PCO4000 4008  2672 4.44 0.125 1440

Parallel Pink N/A 15.1 60 135  25 Gd2O5S W – 0.25 FreLon 3250  3250 5.04 0.12 1500

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M.M. Smith et al. / Advances in Water Resources xxx (2013) xxx–xxx Table 2 Run parameters common to all experiments. Experimental parameter

Value

Brine temperature (°C) Core temperature (°C) Fluid flow rate (mL min1) Core confining pressure (MPa) Fluid outlet pressure (MPa) Fluid inlet pressure (MPa) Pre-CO2 brine pH Brine composition (mole kg H2O1)

60 ± 1 60 ± 1 0.05 ± 0.003 24.8 ± 0.1 12.4 ± 0.07 19.6–12.4 6.9 ± 0.2 [NaCl] = 1.01 m [NaHCO3] = 0.00792 m [Na2SO4] = 0.0369 m [CaCl2] = 0.0353 m [MgCl2] = 0.0159 m 4.3; 0.33 m 4.5; 0.22 m 4.8; 0.11 m 4.9; 0.055 m

3 MPa pCO2 brine pH; CO2(aq) (mole kg H2O1) 2 MPa pCO2 brine pH; CO2(aq) (mole kg H2O1) 1 MPa pCO2 brine pH; CO2(aq) (mole kg H2O1) 0.5 MPa pCO2 brine pH; CO2(aq) (mole kg H2O1)

sophisticated segmentation algorithms because the data lacked grain-scale resolution. Because phase contrast was lower in postreaction tomography datasets, these image stacks were simply thresholded between void and solid, evaluated for the production of new solid phases (none was noted), and then segmented to create masks, which were registered and applied to pre-reaction images. Each pre-reaction sample dataset was further divided into several different gray-scale ‘‘matrices,’’ defined by a specific grayscale range and representing a distinct mixture of minerals and pore space. Gray-scale values within XCMT images provided an indication of the combined density within a particular pixel resulting from relative amount of phases (i.e., pore space, calcite, or dolomite). Polished thin sections of each core were used to collect at least 25 higher-resolution SEM images from each of four identified gray-scale matrices in Vuggy samples or randomly selected in the case of the Marly samples (as less overall gray-scale variation was noted in these samples). After mineral identification/confirmation via energy dispersive X-ray (EDX) spectroscopy analysis, indicator Kriging segmentation was employed to segment the SEM images into distinct phases [22] and then statistically estimate micropore size, mineral abundance, and accessible surface area from each SEM image. The average properties reported in Tables 3 and 4 were computed from application of a sample-specific SEM/XCMT grayscale calibration to the full extent of each Marly sample’s image stack, or in the case of the Vuggy samples, application of up to four different ‘‘matrix’’ calibrations to specifically identified gray-scale regions within each full image stack. The application of this grayscale calibration to the XCMT image stack was performed using a

custom MATLAB script. Table 5 provides descriptions of these identified Vuggy-specific matrices and their properties. ‘‘Macropores’’ (macroporosity, Table 3) are defined as clearly identifiable pore space in XCMT images occupying a 3-D reconstructed volume of greater than 10 voxels (a spherical equivalent would possess a diameter of at least 40 microns). Pore space and mineral areas were quantified as fractions of each entire 2-D SEM image, which were then related to volume fractions according to the protocols of [4,23]. Pore space pixels with edges neighboring solid phases were counted and summed to compute the total 2-D pore perimeter. These pore perimeter pixels were sorted according to the mineral with which they were in contact; the number of pore-mineral boundary pixels divided by the total pore perimeter is a fraction representing each mineral’s ‘‘accessibility’’ in each of the 2-D images. To obtain a total specific surface area value (TSSA, units of L1), the ratio of the pore perimeter to the pore space area was multiplied by a factor of 4/p, according to stereological principles for an isotropic medium [23,24]. Individual specific surface areas for both calcite and dolomite were computed by multiplying TSSA by mineral accessibility values, and are shown in Table 4. In addition to these XCMT-derived data, one representative sample each of Vuggy limestone and Marly dolostone (cores of similar dimensions, collected within 5 cm of cores used in experiments) was subjected to mercury intrusion porosimetry (Micromeritics; Norcross, GA) to obtain an independent estimate of pore throat size distributions. 2.2. Experimental materials Reagent grade salts (NaCl, Na2SO4, MgCl2, CaCl2, and NaHCO3) and milli-pure filtered water were used to prepare a concentrated brine solution, which was designed to be in or near chemical equilibrium with calcite and dolomite at 60 °C (see Table 2 for brine composition). All prepared brine solutions were purged with N2(g) within the brine/CO2 mixer vessel to remove dissolved oxygen from the starting solution before introduction to the cores. Rock subcores were lightly washed and oven-dried overnight at 60 °C but otherwise used as received after coring. All wetted surfaces in contact with brine solution were either grade 4 titanium or C-276 alloy material. 2.3. Experimental methods The experimental assembly is shown in Fig. 1 (similar to that utilized in [25]), and the experimental methodology was based

Table 3 Sample depth, average mineral and pore space abundances (determined from pre-reaction tomography and SEM analyses) and permeability (determined from differential fluid pressures recorded prior to CO2 introduction). Sample ID

Depth (m)

Calcite

Dolomite

Anhydrite

Totala porosity

Macrob porosity

Initial permeability (mD)

0 0 0 0 0 0 Trace 0 Trace 0 Trace 0

36 ± 4 31 ± 3 31 ± 8 35 ± 5 15 39 16 20 13 15 15 22

3.5 0.6 3.2 1.1 1.5 27 3.3 7.5 2.2 4.6 1.2 7.5

1.7 1.2 0.92 1.7 0.032 N/a 0.032 N/a 0.024 N/a 0.0091 N/a

% of total core volume M-3 core M-2 core M-1 core M-0.5 core V-3 core V-3 wormholec V-2 core V-2 wormhole V-1 core V-1 wormhole V-0.5 core V-0.5 wormhole a b c

1445.9 1446.0 1446.5 1446.1 1462.8 1462.8 1463.0-1 1463.0-1 1463.0-2 1463.0-2 1463.2 1463.2

19 ± 7 7.7 ± 4 20 ± 17 14 ± 9 59 35 55 52 63 62 56 49

45 ± 4 61 ± 4 49 ± 11 52 ± 7 26 26 27 27 24 23 29 29

Total porosity = sum of all observable pore space. Macroporosity is defined as voids occupying more than 10 voxels, or having an equivalent sphere diameter of greater than 40 lm. Mineral abundances and porosities for wormhole regions are reported normalized to the volume occupied by wormhole, post-reaction.

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M.M. Smith et al. / Advances in Water Resources xxx (2013) xxx–xxx Table 4 Pore-accessible specific surface areas determined prior to CO2/brine reaction. Sample ID

Total specific surface area (cm1)

Calcite specific surface area (cm1)

Dolomite specific surface area (cm1)

M-3 core M-2 core M-1 core M-0.5 core V-3 core V-2 core V-1 core V-0.5 core

6559 8290 9846 7606 36,565 37,740 39,900 29,000

2450 2106 2491 2330 28,666 22,300 24,573 24,920

4109 6184 7355 5276 7900 15,437 15,326 4078

Table 5 Average composition and specific surface areas for identified Vuggy matrices.

Calcite (% of total core volume) Dolomite (% of total core volume) Porosity (% of total core volume) Total specific surface area (cm1) Calcite specific surface area (cm1) Dolomite specific surface area (cm1)

Matrix 1

Matrix 2

Matrix 3

Matrix 4

21 ± 8 55 ± 9 24 ± 5 26490 10280 16210

35 ± 7 45 ± 8 19 ± 3 39650 22660 16990

69 ± 7 9±5 22 ± 6 38700 35600 3100

96 0 4 71250 71250 0

on several previously published core-flooding procedures [26–28]. Each core was aligned between two endcaps (radially counterbored to distribute fluid) and jacketed with heat-shrinkable VitonÒ tubing, creating a water-tight seal prohibiting bypass flow. Any large visible pores or vugs along the core walls were packed with PTFE tape to avoid overstressing the flexible jacket. Jacketed cores were oriented and plumbed into the reactor pressure vessel, and then brought to the experimental confining pressure (24.8 MPa) by means of a dedicated syringe pump and heated to 60 °C. Thermocouples at the base of the reactor allowed the confining pressure fluid temperature to be controlled via a furnace controller, and thermocouples emplaced within each endcap allowed core temperatures to be reliably monitored within 0.1 °C. All experiments were conducted at 60 °C and 24.8 MPa confining pressure. Flow was maintained at a constant rate of

0.05 mL min1 (±0.003 mL min1) under a constant fluid outlet pressure of 12.4 MPa (Table 2). System pressures (confining reactor vessel, brine mixer vessel, fluid inlet, fluid outlet, and core differential), temperatures (mixer vessel brine, sample inlet, and sample outlet) and flow rates were collected once per minute via a customized software system. Fluid pressures into and out of the core were monitored using both absolute pressure transducers and a higher-resolution 30-psi differential transducer plumbed into a bypass loop. Slug tracer tests were not conducted prior to introduction of CO2-equilibrated brine; our experimental setup did not allow for the addition of a tracer solute to the fluid reservoir after the initial saturation period but before preparation of CO2-equilibrated brine within the sealed and pressurized brine mixer vessel. Each experiment consisted of two phases: brief brine-only (CO2-free) flow, and reactive CO2/brine flow under defined pCO2

Fig. 1. Experimental set-up for core-flooding experiments. G = gauge; D/PT = differential/pressure transducer; TC = thermocouples.

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M.M. Smith et al. / Advances in Water Resources xxx (2013) xxx–xxx

conditions. Cores were saturated overnight with CO2-free brine and CO2-free brine flow extended an additional 24–72 h. During this time, up to four fluid samples were collected, and the flow rate was varied to obtain initial permeability measurements. At the end of this period, both cylinders of the dual piston pump were completely filled with CO2-free brine and set to a lower flow rate (0.008 mL min1 or lower) to maintain flow and pressure during overnight CO2/brine equilibration. To produce brine/CO2 mixtures of desired pCO2 (3; 2; 1; and 0.5 MPa), the remaining brine was isolated and saturated with 99.9% pure CO2 at 60 °C and pressure conditions determined via temperature- and pressure-corrected equilibrium constants [29] and CO2/brine solubility predictions from [30]. Small pressure changes in the brine mixer vessel diminished significantly after six to eight hours, providing an indication that steady-state brine/CO2 saturation was achieved during overnight (12+ hours) equilibration (in agreement with recent estimates of supercritical CO2 mass transfer rates [31]). However, it was not possible to directly sample input fluid from the sealed brine/CO2 vessel to confirm chemical equilibrium. After each pump cylinder delivered its last volume of CO2-free brine, pump cylinders were manually refilled with freshly CO2-equilibrated brine. At this time, constant flow of CO2-equilibrated brine was initiated (referred to as time t = 0). Vuggy experiments were allowed to continue under constant flow rate for approximately twice as long as the time required for the initial differential pressure difference across the core (from 400 to 1100 psi, depending on the sample) to decrease to a negligible amount defined in our experimental set-up as 5 psi difference. We refer to this sample-specific time period as ‘‘pressure breakthrough’’ in the remainder of the text. In the case of the Marly experiments where initial differential pressures were often too low to permit accurate measurement of declining pressure, experiments were run for not more than two days to limit the impact of expected frontal dissolution predicted by preliminary modeling and confirmed by sample failures. At the end of each experiment, fluid and confining pressures were gradually decreased before introducing a stream of low-pressure N2 gas to displace remaining brine, requiring 30 min for total take-down. Cores were dried at 60 °C before reimaging. 2.4. Geochemical sampling During each sampling event, three consecutive brine fluid samples were collected from the back-pressure regulator outlet and filtered through 0.2 lm polypropylene filters before storage and analysis. Diluted and acidified aliquots were analyzed for major and trace elements using inductively coupled plasma-mass spectroscopy (ICP-MS). A second aliquot was diluted for ion chromatograph (IC) analysis of chloride and sulfate as well as ion-specific electrode analysis of sodium. The third sample was collected via glass syringes with gas-tight Luer-lock fittings pre-loaded with 3 mL of 1 N NaOH to capture CO2 gas. These samples were analyzed for total inorganic carbon (TIC) analysis by phosphoric acid digestion in a total carbon analyzer. Sample pH was only directly measured during CO2-free brine flow (times t < 0) because CO2 exsolution at the fluid outlet (under atmospheric pressure) interfered with measurement of in situ pH values. 2.5. Geochemical data analysis Where collection times between element/ion and total inorganic carbon (TIC) samples differed by P2 h, a linear interpolation with time was used to adjust elemental concentrations to the TIC collection time. Correction of elemental data rather than TIC values was preferred because higher TIC concentrations had a greater impact on pH calculation (see below). This procedure was necessary

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for 620% of the data (mainly those samples collected during periods of rapid change, such as immediately after introduction of CO2-equilibrated brine), and resulted in differences of less than 10% between original and adjusted data. Mineral saturation indices and in situ pH reported in following sections were calculated via charge balance on species H+ from measured solution compositions (after adjusting sodium concentrations as a constant equivalent of IC-measured chloride concentrations), using the EQ3/6 geochemical speciation code [32] and the data.shv thermodynamic database [33] to correct for experimental pressure and temperature. Sodium concentrations were not expected to vary as a result of CO2-induced reactions in these materials, and selected analyses showed that sodium remained roughly constant in relation to measured chloride concentrations. Assuming a constant Na/Cl ratio removed the effects of analytical IC error from the pH calculation and linked modeled solution pH more strongly to variations in measurements of introduced total inorganic carbon. We chose to focus our modeling and interpretation efforts on those geochemical components that directly reflected carbonate and/or anhydrite mineral reactions. We included only calcium, magnesium, sodium, chloride, sulfate, and TIC (encompassing 2 HCO 3 , CO3 , and CO2(aq)) data in the EQ3/6 pH and saturation index calculations. Other components with concentrations that may have been sensitive to carbonate reactions (e.g., iron, manganese, strontium) were present at levels three or more orders of magnitude lower and were not considered. A sample-free blank run was also conducted to examine the experimental system’s transition from CO2-free to CO2-equilibrated (3 MPa pCO2) brine. After transitioning this experiment from CO2-free to CO2-equilibrated brine (as described above in Section 2.3), two additional hours (the turnover time for one pump cylinder) beyond estimates of travel time through experimental tubing (see Fig. 1) were required to achieve TIC C/C0 = 0.5 at the solution sampling outlet. Delays such as this, also observed to some extent in the core-flood experiments, are suggestive of an experimental artifact related to initial in-line or withincylinder dilution of the first cylinder’s worth of CO2-equilibrated brine by remaining CO2-free brine. An experimental artifact is favored rather than diffusive transport and immobilization of CO2 within sample porewaters or in a residual hydrocarbon phase because the required volumes of porewater or hydrocarbon are far larger than possibly available in these cores. The heat-shrink jacket material surrounding the core samples should not allow significant losses of aqueous CO2 or other dissolved carbonate species and thus this mechanism is also not expected to contribute to delay in transport of TIC relative to other dissolved species. However, these processes were not explicitly investigated. Delays between the onset of increases in TIC and calcium concentrations were generally less than one hour, with the exceptions of experiments V-3 and V-2, which experienced shorter brine/CO2 equilibration periods.

3. Results and discussion 3.1. Pre- and post-reaction characterization Reaction of CO2-rich brines with the Marly dolostone and the Vuggy limestone yield two distinct dissolution fronts. In this section we summarize the physical properties of these rocks that likely contributed to the development of stable dissolution fronts in the Marly dolostone and unstable dissolution fronts in the Vuggy limestone when reacted under the same geochemical and flowrate conditions. Specifically we discuss the relative abundance, available (or effective) surface area, spatial distribution and

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reactivity of calcite and dolomite, as well as porosity and permeability in the two carbonate rocks. 3.1.1. Marly dolostones The Marly dolostone cores were relatively homogeneous with evenly distributed proportions of dolomite, calcite, and pores (Table 3), with the exception of the M-1 sample which was predominantly calcite along one half of the core in the z-direction (long axis of sample). Total porosity in these four cores varied between 31% and 36%, with bulk analysis revealing that over 90% of pore throat sizes varied by only one order of magnitude (0.5–5 lm; Fig. 2(a)). ‘‘Macropores’’ were more rare but possessed a similar size distribution ranging up to approximately 1 mm among all four Marly samples (Fig. 2(c)). Measured permeability for these cores varied between 0.9 and 1.7 mD, in agreement with similarly low measurements obtained by Durocher et al. [17]. Dolomite was 2.4–8 more abundant than calcite in all four samples on a normalized volumetric basis. A representative Marly texture is shown at both the core- and pore-scale in Fig. 3. Although slight variations in texture were observed from tomography data and further scanning electron microscopy especially between M-1 and the remaining three cores, the Marly samples were overall highly

Fig. 2. Pore size cumulative distribution functions. (a) Pore size data obtained from mercury intrusion cumulative porosimetry performed on neighboring Marly and Vuggy cores not used in experiments. (b, c) Macroporosity size distributions determined from XCMT pre-reaction data on Vuggy and Marly cores, respectively.

similar in mineral and pore morphology, and no further textural distinctions were made (in contrast to the Vuggy samples, see Section 3.1.2 below). Dolomite crystals in these samples were usually small, euhedral rhombs, less than 20 lm in diameter, with effective surface areas (bordering pore space) ranging from 4000 to 7400 cm1 (Table 4). Although calcite was present as finely crystalline masses, its effective surface area was smaller (2100–2500 cm1) as a result of the extremely low porosities in such dense masses. Comparison of microtomographic images of Marly cores before and after reaction with CO2-rich brine (over reaction periods of 11– 50 h) showed relatively homogeneous dissolution fronts (Fig. 4). The majority of dissolution was limited to a region of enhanced porosity concentrated within the first few millimeters from the inlet, with final porosities of 60–70%. Some diffuse fingering is evident within the dissolution front, most notably in sample M-1, but is minor compared to the preferential pathways that developed in the Vuggy cores (discussed below in Section 3.1.2). We suspect only limited changes in bulk permeability as a result of such dissolution, although resulting pressure changes were generally too small to be reliably measured by our pressure transducers. Generally the calcite dissolution front extended slightly further into the core than the dolomite dissolution front. This observation is qualitatively consistent with faster kinetic dissolution rate constants for calcite than dolomite. The width in the z-direction (along the long axis of each core) of the dissolution region did not depend on the pCO2 of the reacting brine; however, this lack of dependence could be attributable also to variable experimental runtimes for these samples. However, CO2-induced reaction within the M-1 MPa sample did lead to the development of a slightly different reaction front which extended further into the dolomite-rich and more porous half of the core compared to the other Marly samples. The observations of similar-sized and evenly distributed pores within Marly cores, as well as relatively high permeabilities (with no regions of contrasting lower permeability, with the exception of sample M-1) are consistent with the development of well-defined plug-like reaction fronts, if reaction kinetics proceed rapidly compared to fluid advection. 3.1.2. Vuggy limestones In contrast to the Marly dolostone, the Vuggy limestone displayed far greater heterogeneity in both pore space and mineral composition, with cores V-3 and V-0.5 possessing relatively more pore space heterogeneity than cores V-1 and V-2 (Fig. 2(a) and (b)). Total porosity in Vuggy cores was lower (13–16%; Table 3) in comparison to the Marly samples, and bulk Vuggy pore throat analyses showed a much wider size range (nearly 3.5 orders of magnitude, 0.05–100 lm; Fig. 2(a)) between d10 to d90 (describing the median 80% of pore throat sizes). Macropore distributions obtained from XCMT analysis of the four Vuggy cores also exhibited a wider spread in median pore size, and a larger maximum observed pore size compared to the Marly samples (Fig. 2). The greater proportion of microporosity in Vuggy limestones contributed to the much lower permeabilities (0.009 to 0.03 mD) measured in these samples compared to the Marly dolostones. Macropores (including vugs and fractures in these cores, in addition to larger pores) comprised roughly 10–20% of total porosity, but were disconnected at XCMT resolution. In samples V-1 and V-2, macropores were uniformly distributed throughout each core, while small fractures were more prevalent in samples V-3 and V-0.5 and may have contributed to higher connectivity within those cores. Calcite specific surface areas in the Vuggy samples were quite high (10–13 times greater than in the Marly samples), with dolomite specific surface areas similar to Marly values for the case of V-0.5 and up to 4 times greater than Marly measurements in the remaining Vuggy cores (Table 4).

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Fig. 3. Representative images of Marly dolostone cores at (a) full core scale (XCMT image), and (b) pore scale (SEM image). Decreasing phase density is represented by darker gray-scale values (e.g., pore space appears as black).

Fig. 4. XCMT images and profiles of calcite, dolomite, and pore space versus z location before and after reaction, for Marly samples reacted at pCO2 (a) 3; (b) 2; (c) 1; and (d) 0.5 MPa. Pore space both prior to and post-reaction is shown in gray in XCMT images. Macroporosity is presented as a fraction of total pore space in plots. Note that plot z-axes have been truncated to better represent the regions of interest near the fluid inlet (reactive flow from left to right).

All Vuggy limestone cores were tightly cemented by calcite with varying amounts of dolomite. We identified four distinct ‘‘matrix’’ regions through gray-scale analysis and calibration of the tomography data with high-resolution electron images (Fig. 5; Table 5). We hypothesize that the distribution of these matrices contributed to the creation and maintenance of distinct chemical microenvironments where net dissolution depended on differences in effective surface areas and mineral reaction rates as well as local permeabilities. Matrices 1–3 can be distinguished

largely by their calcite abundances and effective surface areas, which increase from 21% to 70% with corresponding increases in specific surface areas from 10,000 to 36,000 cm1. Dolomite abundance decreased from matrix 1 to 3 while porosity remained similar within these matrices. Matrix 1 regions contained the most connected micro- and macropore space (apparent in SEM images, Fig. 5). In contrast, matrix 4 consisted of densely packed calcite with the highest specific surface area (>70,000 cm1), no dolomite, and a significantly lower total porosity of only 4% (Table 5).

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Fig. 4 (continued)

periods of roughly 5–6 days (with the exception of the 3 MPa case), dissolution within the Vuggy limestones remained localized in well-defined channels or ‘‘wormholes’’ (e.g., [34]) spanning the length of each core (Fig. 6, images), in contrast to the more stable fronts observed in the Marly samples. Concentric circular patterns shown at the inlet of some samples in Fig. 6 result from the radially counter-bored pattern of the endcap (see Section 2.3). Although the broad range of observed pore sizes and exclusively submicron porosity between macropores likely generated an extensive range of local fluid velocities prior to the introduction of CO2, final tomography images showed that only one dominant wormhole carried the majority of fluid by the end of each experiment. Comparison of porosity and mineral abundances between the pre-reaction volume that dissolved to form each wormhole and the pre-reaction total core average (Fig. 6, accompanying plots) showed that wormholes formed and connected regions with higher porosity and lower calcite (primarily matrix 1 but also 2, 3), as well as utilizing fractures and vugs where present (e.g., samples V-3 and V-0.5). Fig. 5. Representative XCMT image of Vuggy limestone core, with inset SEM images depicting identified gray-scale matrices. Decreasing phase density is represented by darker gray-scale values (e.g., pore space appears as black).

The duration of each Vuggy experiment (with the exception of the V-3 case) was defined as a roughly 2t increase beyond t, the length of time required for the initial pressure differential measured across each core to decrease to below 5 psi. Pressure breakthrough time increased from 24 h during reaction with 3 MPa pCO2 brine up to 55 h for 0.5 MPa pCO2 brine reaction. After reaction

3.2. Solution chemistry 3.2.1. Marly geochemistry Over a shorter time frame compared to Vuggy experiments, output solutions from the Marly cores achieved saturation with respect to carbonate minerals and showed clear correlation with pCO2. As soon as CO2-equilibrated brine was introduced to each sample, calcium concentrations increased rapidly and monotonically in all four experiments (Fig. 7(a)). These calcium concentrations leveled off to steady-state values which increased in

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Fig. 6. XCMT images and profiles of calcite, dolomite, and pore space versus z location both over the entire core (dashed lines) and within the regions which later formed wormholes (solid lines), for Vuggy samples reacted with pCO2 (a) 3; (b) 2; (c) 1; and (d) 0.5 MPa. Macroporosity is presented as fraction of bulk or wormhole volume. Pore space has been filtered to show only newly produced porosity as gray in XCMT images (reactive flow from left to right).

correlation with input brine pCO2. Final magnesium concentrations also scaled with initial pCO2 levels but were small in comparison to calcium shifts (roughly an order of magnitude less) despite greater dolomite specific surface areas, reflecting the faster kinetics and higher solubility of calcite relative to dolomite (Fig. 7(b); Table 4). TIC levels also displayed steady-state behavior at values consistent with those predicted by geochemical speciation modeling, with the exception of the 3 MPa experiment, which was terminated early, and the 0.5 MPa experiment, which was slightly lower than expected. Modeled in situ solution pH levels (Fig. 7(d)) leveled off at values at least 0.8 pH units higher than input CO2/brine pH values, indicating that solutions were buffered to a similar extent over core transit times. As expected, chloride and sulfate chemistry (not shown) did not vary in these experiments, reflecting the lack of chloride-containing minerals or anhydrite in these cores.

Over the duration of CO2/brine reactive flow, solution chemistries from all four Marly experiments resulted in tightly clustered carbonate mineral saturation indices (see Fig. 8), despite differences in initial pCO2 and resulting pH values. We interpret this clustering as evidence that brine solutions achieved saturation with the carbonate constituents of the Marly cores, indicating that the equilibrium reaction length scale in these experiments was much smaller than the average flow paths within each core. We use these results to define the extent of calcite and dolomite steady-state saturation in the following discussion as 0.25 ± 0.2 and 0.30 ± 0.3 log Qi/Ki units for calcite and sedimentary/disordered dolomite, respectively, where the ratio of Q, ion activity product, and K, equilibrium constant, signifying chemical saturation index with regard to the mineral of interest. Q/K indicates the saturation index with respect to a given mineral, i, defined as the ratio of the

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Fig. 6 (continued)

ion activity product (Q) to the solubility constant (K) at relevant temperature and pressure. Disordered dolomite was preferred to ordered (hydrothermal) dolomite to describe this mineral because Weyburn formations were originally deposited in a sedimentary environment. The M-3 chemistry values were not included in the calculation of steady-state saturation due to the abbreviated timescale of this experiment, but most later-time solution samples also fall within the defined extent of saturation. 3.2.2. Vuggy geochemistry Calcium concentrations responded quickly to the introduction of CO2 in the Vuggy experiments, with fairly rapid (<1 day) increases to peak levels, followed by decays to lower steady-state values after pressure breakthrough times (Fig. 9(a)). This behavior was most obvious in the 2 and 1 MPa experiments, but two final and independently collected samples from the 3 MPa test also con-

firmed a decrease to similar calcium levels. The pCO2 = 0.5 MPa experiment, however, showed only a slight decrease in calcium levels after pressure breakthrough. Magnesium concentrations increased significantly above input brine levels for the 3 and 0.5-MPa experiments, but remained largely unchanged for the 2 and 1-MPa cores. Similar to the results of Marly experiments, neither chloride nor sulfate levels varied during these experiments (data not shown). Measured TIC data showed steady-state behavior at levels consistent with input brine concentrations, excepting the 0.5-MPa case, as was observed during the Marly experiment with same initial pCO2. The discrepancy between experimental measurements and predicted calculations may reflect difficulties in adequately controlling very low pCO2 conditions in our systems, or uncertainties in the thermodynamic data. With the exception of the 0.5-MPa case, modeled solution pH at the end of each experiment was very close if not identical to the input CO2/brine solution values

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Fig. 7. Solution chemistry: (a) calcium; (b) magnesium; (c) total inorganic carbon, TIC; (d) modeled pH versus time for Marly dolostone samples reacted with pCO2 0.5–3 MPa brines. Horizontal lines in (d) indicate the pH of corresponding input (unreacted) brine/CO2 solutions.

Fig. 8. (a) Calcite and (b) dolomite saturation indices versus time for Marly dolostone experiments. Black lines indicate the range of average saturation indices calculated from 2, 1, and 0.5 MPa results at times t > 0.9 days.

(Fig. 9(d)), indicating little to no buffering during later-time transport through the established wormholes visible in XCMT images of those samples. Periods of peak calcium concentrations occurred prior to pressure breakthrough for each core (Fig. 9(a)), and the majority of calculated saturation indices also indicated carbonate saturation during this time (Fig. 10(a)). These observations indicate that prior to pressure breakthrough, reactive brine percolated through low porosity regions between larger vugs or macropores, dissolving available calcite (and/or dolomite). Newly generated pore space in turn channeled more reactive fluid through these discrete regions, creating localized flowpaths of increasing porosity. During this time period calcite saturation was achieved over the reactive path length. We note, however, that the V-3 experiment exposed to the highest pCO2 brine remained undersaturated with respect to calcite during the pressure breakthrough period, indicating that the new effective path length in this fluid/rock system was now

shorter than the equilibrium reaction length scale. Lower calcium concentrations and more acidic pH values observed after pressure breakthrough for the 3, 2, and 1 MPa experiments demonstrated less calcite dissolution and buffering of the solution, because advective transport through new low-resistance open channels reduced the effective residence time of the flowing brine. In contrast, the 0.5 MPa experiment maintained both calcite and dolomite saturation for several days after wormhole breakthrough, perhaps indicating that the effective reactive path through this core’s dissolution feature was still long enough to allow steady-state chemical conditions to develop at such a low pCO2 level. 3.3. Dimensionless number analysis of heterogeneous samples Previous studies in the field of engineered carbonate dissolution have utilized dimensionless ratios (e.g., Péclet, Pe, and Damköhler, Da, numbers) as a means to compare and describe results from a

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Fig. 9. Solution chemistry: (a) calcium; (b) magnesium; (c) total inorganic carbon, TIC; (d) modeled pH versus time for Vuggy limestone samples reacted with pCO2 0.5–3 MPa brines. Horizontal lines in (d) indicate the pH of corresponding input (unreacted) brine/CO2 solutions.

Fig. 10. (a) Calcite and (b) dolomite saturation indices versus time for Vuggy limestone experiments. Black lines indicate the range of average saturation indices derived from Marly experiments.

range of experiments utilizing various sample materials, dimensions, flow rates, and reactive conditions. However, as noted by Daccord et al. [3], the choice of a meaningful lengthscale (a necessary parameter for both Pe and Da estimation) is challenging in evolving reactive systems such as these. In this discussion we consider both the core lengthscale to capture averaged transport properties for each experiment, and also the median micropore throat diameter to capture processes at a smaller scale. The Péclet number, Pe, is used to relate diffusive and advective mass transport, and is defined as:

Pe ¼

mL D

ð1Þ

where L is a characteristic length scale (L), D⁄ is a coefficient of effective molecular diffusion (L2 T1), and v is an average linear velocity (L T1) defined here as v = q//, with specific flux per

cross-sectional area q (L T1) and porosity /. The kinetic number, Nk, compares the relative importance of diffusion versus reaction; we utilize the form for Nk given by Steefel and Maher [35] with the addition of a mineral heterogeneity weighting factor, w, related to calcite abundance: 2

Nk ¼

AkL ¼ /D C eq

     Acal kcal Adol kdol L2 wþ ð1  wÞ  C eq;cal C eq;dol /  D

ð2Þ

where L is again defined as some characteristic length scale, k is a kinetic rate constant (M L2 T1) describing calcite or dolomite reaction, A is the mineral-specific reactive surface area (L1), and Ceq is taken here to be the observed steady-state concentrations of the indicator species (calcium, magnesium) for each carbonate mineral (M L3). Note that Nk is equal to the product of Pe and Da, the Damköhler number, which is a comparison of advective versus reactive timescales:

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Da ¼ Nk  Pe1 ¼

AkL /mC eq

ð3Þ

Table 6 provides parameter values used in dimensionless number estimation, in addition to sample-specific porosity and surface area values found in Tables 3 and 4. Analysis at the smaller length scale (pore throat dimensions from Fig. 2) provides very small values of Nk and Da (106–103; Table 7) suggesting that fluids remained well-mixed at the pore scale for all samples, because physical mass transfer was fast compared with calcite and dolomite reaction rates. At the core length scale, however, both Marly and Vuggy samples yield the high Pe and Da values characteristic of mass transfer-limited (‘‘mass transfer-controlled’’) conditions associated with unstable wormhole patterns, e.g., [35], despite very different responses to CO2-induced dissolution in the two sample types. The resulting variations among dimensionless numbers calculated at either length scale are approximately only an order of magnitude (Table 7), and indicate the relative insensitivity of these values to the wide range of observed dissolution features, from inlet-centered dissolution (most Marly cases), to incipient channel formation (M-1 case), to dominant dissolution features with variable degrees of branching (Vuggy cases). The porosity contrast number, D, is another parameter that describes the relative importance of dissolution instabilities in steadily propagating reactions fronts versus instantaneously arising preferential pathways [37]. Developed from linear stability analysis, D illustrates the effects of porosity (and thus permeability) variations on the development of mineral dissolution fronts and is defined as:

D¼

  /f 1 /i

ð4Þ

where /i and /f indicate porosities ahead of (initial, or downstream) and behind (final, or upstream) the dissolution front, respectively. Values of D for the Marly samples are generally close to 2, while all Vuggy cases produce D values much greater than 5 (Table 7), in keeping with Szymczak and Ladd’s [37] prediction of channel/ instability growth from the inlet for higher values of D. A reasonable extension of such linear stability analysis may be examination of the spatial distribution of pore space using fine-scale character-

Table 6 Parameters used in dimensionless number calculations. Parameter [units]

Values

Linear Darcy flux kcalcite (neutral mechanism, 60 °C) kdolomite (neutral mechanism, 60 °C) Ceq,calcite

4.72  106 m s1 105.38 mol m2 s1 [34]

Ceq,dolomite D⁄, 60 °C

ization data to establish a permeability contrast indicator of the unreacted rock as a predictive tool for the overall form of the dissolution front. Recent two-dimensional numerical simulations performed to examine competing parameter effects in reactive systems found that the initial porosity correlation length (i.e., spatial variability of pore space), rather than the variance of permeability or the form of the porosity/permeability relationship, most strongly influenced the development of complex flow patterns, with mineralogic variability playing a secondary role [38]. The role of these factors on reactive transport are all further explored in three dimensions in our companion work [16]. 3.4. Effective carbonate mass transfer rates Estimates of the impact of dissolution on the evolution of porosity and permeability in carbonate reservoirs rely on quantification of mineral reactivity. Calcite and dolomite kinetic expressions that tie dissolution rate to mineral/fluid saturation using Arrhenius-type expressions have been developed from well-controlled experiments in systems with pCO2 < 0.1 MPa ([39], and references therein). However, it is not known if these expressions can be extended to the higher pCO2 levels associated with geologic carbon storage (up to 10 MPa). Pokrovsky et al. [40] attempted to resolve this issue by measuring calcite, dolomite, and magnesite dissolution rates at 25 to 150 °C and pCO2 from 0.1 to 5.5 MPa under far-from-equilibrium conditions. Although these measurements represent a significant advance, it is still uncertain if these rates can be extended to the near-equilibrium conditions that quickly develop even under the high pCO2 concentrations found in geologic storage environments. We first analyze the chemical data from these experiments, and then compare these data to available kinetic dissolution formulations to evaluate their suitability for use in reactive transport simulations (e.g., [16]). In our experiments, we measured mass transfer rates from changes in solution chemistry sampled at the core outlet, reflecting the influence of both mass transport as well as mineral reactivity. Effective (or bulk) carbonate mass transfer rates, Rmass, (M T1), were derived from simple increases in output elemental concentrations, C, normalized to the constant volumetric flow rate, Qvol, (L3 T1) as:

Rmass;dol ¼ ðC Mg;outlet  C Mg;input Þ  Q v ol

ð5Þ



Rmass; cal ¼ C Ca; outlet  C Mg; outlet  C Mg; input  C Ca; input  Q v ol

ð6Þ

where dissolved magnesium was used to first estimate dolomite dissolution and to adjust dissolved calcium to estimate calcite contributions. To derive these effective mass transfer rates (which include the effects of physical transport and so should not be confused with true net rates), we assume that calcite is chemically pure (i.e., CaCO3); dolomite possesses an ideal molar formula (CaMg(CO3)2); and calcium and magnesium dissolve in stoichiometric proportions. Errors shown with rate values (Figs. 11 and 12) represent the range of possible rates calculated from variations in Cinput terms (obtained via sampling of influent brine, both before and after each experiment).

106.57 mol m2 s1 [34] 0.053; 0.049; 0.047; 0.044 mol L1 (for 3; 2; 1; 0.5 MPa, this work) 0.019; 0.018; 0.017; 0.0164 mol L1 (for 3; 2; 1; 0.5 MPa, this work) 2  109 m2 s1 [36]

Table 7 Dimensionless number results for sample types over various length scales. Length scale

Core ID

Pe

Nk

Nk/Pe  Da

D

Pore-scale (L = d50, Fig. 2)

M-3, -2, -0.5 M-1 V-3, -2, -1, -0.5 M-3, M-2, M-0.5 M-1 V-3, -2, -1, -0.5

(1.4)  102 (1.5)  102 (2)  103 (2)  102 (2)  102 (5)  102

(6)  105 (1)  104 (5)  106 (1.3)  104 (2)  104 (5)  105

(4)  103 (6)  103 (3)  103 (6)  101 (9)  101 (1)  103

1.9 2.2 5.8 1.9 2.2 5.8

Core-scale (L = 3 cm)

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Effective mass transfer rates for calcite and dolomite from the Marly dolostone and Vuggy limestone experiments are shown in Figs. 11 and 12. Data from the Marly samples show that carbonate mass transfer rates increased monotonically, with calcite achieving steady-state levels more quickly than dolomite. Final measured calcite mass transfer rates were roughly two to three times faster than dolomite rates despite greater dolomite abundance and higher surface areas (see Tables 3 and 4). In contrast to the stable dissolution behavior and mass transfer rates observed in Marly experiments, mass transfer rates measured in Vuggy experiments were much more variable. Effective calcite mass transfer rates increased to levels similar to those noted in Marly systems during pre-pressure breakthrough times but then steadily declined to levels of 40–60% of the peak values after dominant wormholes were established. Bulk dolomite mass transfer rates were generally much lower (even fluctuating around zero) in most Vuggy experiments compared to Marly ones, in agreement with tomographic data showing lesser dolomite abundances in Vuggy cores. Negative dolomite mass transfer values theoretically indicate possible precipitation, but none was noted by XCMT analysis within any reacted core, in keeping with the observation that dolomite precipitation proceeds extremely slowly if at all [41]. These effective mineral-specific (indicated by subscript ‘‘min’’) mass transfer rates, Rmass, incorporate the effects of advective, diffusive/dispersive, and reactive processes:

@C min @t   @C min @ 2 C min Q min ¼ v / þ D / þ A k 1  min lump; min @x @x2 K min

Fig. 12. Effective (a) calcite and (b) dolomite mass transfer rates versus time for Vuggy limestone experiments.

Rmass ¼ /

ð7Þ

where Amin (L2 L3) represents reactive mineral surface area; D⁄ (L2 T1) represents the effective diffusion coefficient for aqueous species; and dissolution can be described using a lumped mineral-specific kinetic rate constant, klump,min (M L2 T1), and a reaction affinity term involving that mineral’s saturation index Q/K (see Section 3.2.1 for definition). The klump term represents a functional expression associated with some particular rate mecha-

nism, which may or may not include an additional dependence upon another chemical species (e.g., activity of hydrogen ion or fugacity of CO2 as is common in many carbonate dissolution expressions). Kinetic rate constants cannot be directly derived from effective mass transfer rates from differing experiments due to differences in physical transport caused by variations in porosity, local fluid velocities, and/or effective path lengths among these samples. However, by considering only periods of steady-state behavior where @C=@t = 0, we obtain:

m/

  @C min @ 2 C min Q ¼ D / þ Amin klump; min 1  min 2 @x @x K min

ð8Þ

which can be further reduced to:

m/

  @C min Q  Amin klump; min 1  min @x K min

ð9Þ

because diffusive transport is less dominant than either advective or reactive transport over the length of the core (the scale of available geochemical observations) as indicated by Péclet and kinetic number values 1 for both the Marly and Vuggy cores (Table 7). A ratio of each resulting expression for calcite to dolomite (C:D) mass transfer (Eq. (10)) then yields, by algebra, a linear equation in which the variable velocity and porosity in a given experiment cancel, and the relative amounts of dissolved calcite and dolomite, DCC/DCD, are dependent on ratios of calcite and dolomite lumped rate constants, surface areas, and reaction affinity terms as shown in Eqs. (11) and (12) for mass transfer evaluated over the entire sample length. The reaction affinity terms are referenced to the far-from-equilibrium chemical driving force imposed at the inlet and are maintained at a constant value (1 for all experiments except those at the lowest 0.5 MPa pCO2 conditions).

@C C =@x DC C  @C D =@x DC D  Fig. 11. Effective (a) calcite and (b) dolomite mass transfer rates versus time for Marly dolostone experiments.

  1     klump;C DC C ð1  Q C =K C Þ AC   ¼ ð1  Q D =K D Þ DC D AD klump;D

ð10Þ

ð11Þ

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Fig. 13 shows measured calcite and dolomite surface area ratios plotted versus averaged effective steady-state mass transfer ratios, as well as trends predicted by independent calcite and dissolution experiments (see Table 8), where the slope is equal to a ratio of calcite:dolomite lumped rate constants. The resulting linear trend for seven of the eight experiments suggests that rate constants for calcite dissolution were about 17 times higher than those for dolomite at the conditions of our experiments. The V-0.5 experiment had large uncertainties in calcium and magnesium Cinput terms, and thus we excluded this data point from consideration here. Our results fall within the bounds predicted by many independent calcite and dolomite rate equations, with the best agreement shown by the so-called ‘‘neutral’’ or pH-independent rate mechanism compiled and proposed by Palandri and Kharaka [39]. The strong linear correlation in Fig. 13 suggests that the effect of pH resulting from varying brine pCO2 (4.25 6 pH 6 5.75) was averaged over the length scale of the core as solutions evolved towards carbonate saturation. However, it is important to recognize that this treatment averages the effects of changing solution composition over time, and does not consider changes to accessible surface area or pathlength over time. This comparison does suggest, nevertheless, that currently available empirical rate laws provide reasonable initial bounds for estimating carbonate reactivity in CO2 storage reservoirs in the absence of more detailed calibration experiments. We further calibrate carbonate reactivity parameters in our companion paper in this issue [16]. 3.5. Estimates of porosity change Quantitative comparison of pre- and post-reaction XCMT images provides a measure of new pore space generated by carbonate dissolution, if (as in these experiments) the newly created void space is large compared to the XCMT resolution. In addition, the bulk mass transfer rates shown in Figs. 11 and 12 can also be integrated over time and manipulated by mineral molar volumes (36.9 and 64.4 cm3/mole for calcite CaCO3, and dolomite CaMg(CO3)2, respectively) to obtain rough estimates of the volumes of minerals removed via dissolution. Solution chemistry data from pre-CO2 flow periods were not included in these estimations because no significant changes in differential pressure/permeability were noted during these times. Table 9 provides final porosity estimates, as well as percentages of new pore space attributed to calcite dissolution, calculated using XCMT data versus solution chemistry. For the Vuggy limestone

Fig. 13. Effective calcite:dolomite mass transfer ratios (derived from averaged steady-state fluid samples) versus surface area calcite:dolomite ratios (derived from XCMT/SEM analysis), plotted according to Eq. (12). Filled symbols represent data from Marly dolostone experiments; open symbols represent Vuggy limestone data. Also shown are highlighted regions and a dashed line indicating appropriate ranges of published kinetic rate constant ratios [39,40] calculated at similar pH and pCO2 conditions (see Table 8 for further details).

15

samples, the two techniques yielded fairly similar magnitudes for produced pore space, with the exception of the V-0.5 MPa case (for which errors in geochemically derived porosity estimates are far larger due to uncertainty in Cinput values). Consistently larger and more systematic discrepancies, however, are noted in the ratios of calcite to dolomite contributions to new porosity. Calcite is determined to have contributed far more to pore space generation (i.e., greater volumes dissolved) than dolomite from solution chemistry data compared to XCMT analysis (70–81% versus 39–49% for Marly cores; 90–101% versus 35–62% for Vuggy cores). Post-experiment tomography revealed that substantial volumes identified as dolomite-rich in pre-experimental tomography gray-scale data disappeared completely after wormhole formation and could no longer be identified in the post-experiment Vuggy datasets, while chemistry data predicted much less dolomite dissolution. This discrepancy may be attributed to uncertainties associated with gray-scale calibration of the XCMT data. A second explanation is that rapid dissolution of calcite cement (e.g., as noted in matrix types 1 and 2) left behind a weak skeleton of large dolomite crystals that did not contribute to fluid chemistry by virtue of lower specific surface areas or their slower reaction rate. These remaining dolomite crystals may have been flushed out of the cores and removed from chemistry samples by filtration (no filters were saved to validate this hypothesis), or expelled from the cores during post-experiment nitrogen gas flushing. A similar physical removal of less-reactive anhydrite grains was noted in a previous experiment conducted on a different Weyburn formation sample [25]. A final and less likely explanation is the impact of the assumption of chemically pure carbonates. Variations in actual calcium and magnesium quantities in each mineral would affect derived estimates but would require high levels of impurities in order to fully account for observed differences. 3.6. Pressure and Wormhole evolution (Vuggy limestones) We discuss pressure evolution from the Vuggy experiments only, as the Marly experiments did not show measurable changes in differential pressure. Development of preferential flow paths in the Vuggy samples was accompanied by large increases in bulk permeability signified by drops in fluid differential pressure which began almost immediately after the introduction of CO2-rich brine to each Vuggy sample (Fig. 14). We define the amount of time necessary for the differential pressure to decrease to essentially zero as ‘‘pressure breakthrough,’’ and correlate this time with the amount of CO2-brine exposure necessary to establish near-infinite permeability as a result of mineral dissolution. The fastest breakthrough time was observed for the 3 MPa experiment (24 h), while experiments at pCO2 = 2 and 1 MPa required slightly longer (37 h) and the experiment at pCO2 = 0.5 MPa experiment required 55 h to achieve a similar loss of differential pressure. The inverse correlation of pressure breakthrough time with brine pCO2 levels is related to the influence of CO2-induced reaction and variable macropore and fracture distributions with regard to fast pathway development. The relative contributions of reaction kinetics and effective permeability are examined in reactivetransport simulations discussed in our companion paper [16]. We are unable to directly relate pressure fluctuations to specific variations in core porosity and mineral distributions because XCMT images were not acquired at intervals during each experiment. However, pressure data are still useful in qualitative evaluations of wormhole evolution. Assessment of unreacted V-3 images led us to interpret the lack of inflections in the pressure–time data (Fig. 14) as the result of several small preexisting fractures, which likely provided preferred connections between some of the largest pores. The pressure responses for the other Vuggy samples were more complex, involving repeating sequences of linear and

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M.M. Smith et al. / Advances in Water Resources xxx (2013) xxx–xxx

Table 8 Equivalent 60 °C kinetic rate constants and ratio values for calcite and dolomite, as shown in Fig. 13. Identifier Neutral Acid + neutral, pH 4.3 Acid + neutral, pH 4.9 Carbonate, 3 MPa, pH 4.3 Carbonate, 0.5 MPa, pH 4.9 pCO2-dependent, 3 MPa pCO2-dependent, 0.5 MPa (Data points) a b c

60 °C klump,Cb

Formulationa k = kneut k = (kacid⁄aH+n) + kneut k = (kacid⁄aH+n) + kneut k = (k + ⁄pCO2n) + (kacid  aH+n) + kneut k = (k + ⁄pCO2n) + (kacid  aH+n) + kneut k = A + (B⁄pCO2) + (C⁄pCO22) k = A + (B⁄pCO2) + (C⁄pCO22) N/a

60 °C klump,Db

6

7

4.19  10 5.04  105 1.58  105 4.40  102 7.34  103 4.51  104 1.73  104 N/a

2.70  10 2.14  105 1.08  105 2.06  104 8.62  105 2.90  105 5.36  106 N/a

kC/kD slope

Reference

15.6 2.36 1.46 213 85.2 15.5 32.3 17.3c

[39] [39] [39] [39] [39] [40] [40] (This study)

See references for complete descriptions and values of additional terms. mol m2 s1. Excludes V-0.5 datum.

Table 9 CO2-induced porosity changes estimated from XCMT and geochemical data. Sample ID

M-3

M-2

M-1

M-0.5

V-3

V-2

V-1

V-0.5

Initial porosity (XCMT, vol/vol) Total new pore volume (XCMT, cm3) Total new pore volume (chem, cm3)

0.359 0.0157

0.310 0.0158

0.314 0.105

0.349 0.0258

0.150 0.0487

0.164 0.129

0.133 0.0897

0.153 0.0541

0.027 (±0.003) 47%

0.052 (±0.003) 39%

0.067 (±0.011) 48%

0.057 (±0.004) 48%

0.057 (±0.003) 35%

0.118 (±0.020) 52%

0.097 (±0.009) 62%

0.207 (±0.104) 49%

78%

71%

81%

70%

90%

100%

96%

72%

Calcite % of new pore volume (XCMT) Calcite % of new pore volume (chem)

nonlinear pressure drops. Without temporally continuous imaging of wormhole propagation, it was not obvious when linear versus radial growth dominated. Periods of relatively rapid differential pressure decreases likely corresponded to wormhole propagation through highly porous regions or fractures with rapid extension of wormhole path length. Decreases in slope or plateaus may indicate lateral shifting of the wormhole, or flow proceeding through ‘‘tight’’ low-permeability mineral matrix regions.

One important consequence of wormhole evolution is the significant changes in permeability associated with localized dissolution. Comparison of pressure-derived bulk permeability changes with changes in relative porosity inferred from solution chemistry provides insight into the range of variability of this relationship among the Vuggy samples. If a power law-based porosity– permeability relationship of the form

 k ¼ k0 

/ /0

n ð12Þ

is assumed (a variation on an expression given by Verma and Pruess [42] assuming no critical porosity value, and further validated with experimental data by Civan [43]) where k here refers to bulk core permeability and / represents sample porosity. The value of the power n prior to wormhole breakthrough can be estimated from trends in Fig. 15. Using solution chemistry-derived porosity data and bulk permeability values from pre-breakthrough time, Vuggy experiments demonstrate an average dependence of permeability evolution on porosity change of n  10 (R2 0.81, spanning an actual range of 7 6 n 6 21). These derived values for n are only slightly

Fig. 14. Fluid differential pressures, (a) absolute and (b) normalized by pre-CO2 value, versus time for each Vuggy limestone sample.

Fig. 15. Log-transformed normalized permeability versus log-transformed normalized porosity for Vuggy limestone experiments at pre-breakthrough times.

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M.M. Smith et al. / Advances in Water Resources xxx (2013) xxx–xxx

higher than the values of 8–9 cited by Civan [43] from analysis of sandstones and other sedimentary formations. However, the poor fit to the data (especially the V-2 and V-0.5 MPa experiments) indicate that even prior to pressure breakthrough, the value of n may not be constant in time. These results suggest that porosity/permeability relationships in these carbonates are different than the traditional cubic-law form (n = 3) and may require a much higher exponent value to accurately capture the effects of fast pathway development (see [16] for extended discussion). Although the samples we utilized have relatively low bulk permeabilities, the observations and conclusions drawn from these experiments may be applicable to other geological media possessing a range of relative permeability contrasts. In addition, knowledge of the type of expected dissolution front should influence the type of porosity/permeability relationships best utilized in reactive-transport simulations (e.g., [44]). 4. Conclusions We experimentally investigated the role of pCO2, carbonate mineral dissolution, and mineral and pore space heterogeneity on the development of distinct reaction fronts in samples from a relevant enhanced oil recovery and geologic carbon storage site. Pre-reaction characterization of Vuggy and Marly cores via XCMT and SEM analysis revealed the complex mineral and pore structures within these rocks. Calcite and dolomite abundance, surface areas, and reactivity as well as pore morphology and the distribution of macroporosity within each sample intricately influenced the development of dissolution features, from uniform porosity increases to fast pathway (‘‘wormhole’’) development. This study demonstrates that the degree of pore space heterogeneity of these carbonate rocks exerted a first-degree influence on the type of dissolution fronts and the resulting relationship between porosity and permeability. More homogeneous pore space distributions (90% of pore sizes differing by only one order of magnitude) led to sustained steady-state carbonate mass transfer rates, resulting in stable, uniformly advancing dissolution fronts with porosity increases that resulted in only small changes in permeability. Greater pore space heterogeneity, with the median 90% or more of pore sizes spanning at least 3.5 orders of magnitude, amplified the variability in local fluid velocity, leading to more variable mass transfer rates, preferential calcite dissolution, and the formation of unstable dissolution fronts and dramatic permeability increases of several orders of magnitude. Carbonate dissolution behavior in both sample types displayed behavior consistent with standard rate expressions that tie dissolution to thermodynamics (e.g., rate = k  [1  Q/K]). Specifically, the net dissolution rate decreased to zero at values of log (Q/K) = 0.25 ± 0.2 for calcite and 0.3 ± 0.3 for (disordered) dolomite. Additionally, the relative magnitude of the calcite reaction rate constant was about 17 times greater than that of dolomite during reaction with variable pCO2 fluids according to a simplified assessment of mass transfer and surface area comparisons. This finding broadly supports the use of several available published rate laws for carbonate reactivity, and may also specifically suggest that for similar scenarios where pH variation is relatively small (e.g., the pH 4–6 conditions observed in our experiments and at the associated CO2 storage site [17–19]), a carbonate kinetic rate formulation that does not require additional dependence on either pH or pCO2 may be applicable. The localized dissolution and corresponding pressure decreases noted in the Vuggy limestone samples allowed us to estimate values for n, a parameter linking porosity changes to resulting permeability in a power-law relationship. The Vuggy limestones demonstrated n values over a range of 7–21, with an average value of n  10 prior to fast pathway ‘‘breakthrough,’’ although the

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results also suggest that n may not remain constant with time. For carbonates or other more heterogeneous materials, understanding of the effect of such heterogeneity and the likelihood of fast pathway development should influence the choice of n value or descriptive porosity/permeability relationship best utilized in reactive-transport simulations. This study was conducted to quantify the relationships among fluid flow, heterogeneity, and reaction relevant to carbon storage at the Weyburn–Midale field by integrating characterization imaging, pressure, and solution chemistry data. The impact of heterogeneity on permeability evolution has been demonstrated in these experiments, and should be incorporated into reactive transport models to better calibrate mineral reactions and predict effective carbon storage and management in carbonate systems. These topics are the subject of our companion paper [16]. 5. Disclaimer This document was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes. Acknowledgments This work performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC5207NA27344. Funding for this work was provided by the Petroleum Technology Research Centre (PTRC), IEA GHG Weyburn CO2 Monitoring and Storage Project, and by the United States Department of Energy, Office of Fossil Energy, Carbon Sequestration Program. The authors would like to thank Gavin Jensen and Richard Wood (Saskatchewan Geological Survey) for providing core samples. We also acknowledge the valuable expertise of LLNL personnel Victoria Diaz and Rachel Lindvall (ICP-MS analyses); Rick Kemptner (core-flood reactor fabrication); Dave Ruddle (sample preparation); and Sharon Torres (SEM data acquisition). Pre-reaction tomography data were collected on the ID-19 beamline at the European Synchotron Radiation Facility, Grenoble, France, and we thank Paul Tafforeau for his assistance. The Advanced Light Source is supported by the Director, Office of Basic Energy Sciences, of the U.S. Department of Energy under Contract N. DE-AC02-05CH11231, and we thank Dula Parkinson and Alastair MacDowell (ALS, LBNL) for their help with post-reaction data acquisition and reconstruction on the 8.3.2 beamline. LLNL-JRNL608696. References [1] Hoefner ML, Fogler HS. Pore evolution and channel formation during flow and reaction in porous media. AIChE J 1988;34:45–54. http://dx.doi.org/10.1002/ aic.690340107. [2] Daccord G, Lenormand R, Liétard O. Chemical dissolution of a porous medium by a reactive fluid. I. Model for the ‘‘wormholing’’ phenomenon. Chem Eng Sci 1993;48:169–78. http://dx.doi.org/10.1016/0009-2509(93)80293-Y.

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