The Influence of Rock Mineralogy on Reactive Fracture Evolution in Carbonate-rich Caprocks

Transcription

1 The Influence of Rock Mineralogy on Reactive Fracture Evolution in Carbonate-rich Caprocks Kasparas Spokas 1, Catherine A. Peters 1 *, Laura Pyrak-Nolte 2,3,4 1 Department of Civil & Environmental Engineering, Princeton University, Princeton, New Jersey, Department of Physics and Astronomy, Purdue University, West Lafayette, Indiana, Lyle School of Civil Engineering, Purdue University, West Lafayette, Indiana, Department of Earth, Atmospheric and Planetary, Purdue University, West Lafayette, Indiana, *Corresponding author: Dr. Catherine A. Peters (cap@princeton.edu), E417A Engineering Quad, Department of Civil & Environmental Engineering, Princeton University, Princeton, New Jersey, Table of Contents Introduction 2 X-ray fluorescence map of the Eagle Ford shale 2 Pressure Dissolution 2 Table of Modeling Parameters 5 Permeability vs. Transmissivity 6 Original Asperity Map 8 Contact Area Evolution 8 List of Figures Figure S1. a) Optical image and b) X-ray fluorescence map of the Eagle Ford shale. Figure S2. Aperture Change Map of the simulation of the all-calcite fracture with pressure dissolution at 50 MPa. Figure S3. Differences in apertures between the simulation with pressure dissolution and their transmissivity evolutions. Figure S4. Transmissivity (red) and permeability (blue) evolution in the a) Amherstburg limestone and b) Eagle Ford shale simulations. Figure S5. Contact area [%] evolution for the 10, 30, and 50 MPa all-calcite simulations versus time [hrs]. List of Tables Table S1. Modeling parameters used. Equilibrium parameters, molar volume of calcite and the gas constant are from the PHREECQ database. Introduction S1

2 This supporting information provides the Eagle Ford shale x-ray fluorescence map used to create the Eagle Ford binary mineral map, methodology and results of including pressure dissolution in the model, and supplemental result figures. 1. X-ray fluorescence map of the Eagle Ford shale X-ray fluorescence (XRF) measurements were performed at the National Synchrotron Light Source (NSLS) at Brookhaven National Lab (Upton, NY USA) using the x-ray microprobes at beamlines X27A and X26A. X-ray fluorescence maps were collected by raster flyscanning the approximately 7 μm x 10 μm beam at kev over regions of interest within the samples, centered on the fracture surface. Elemental maps of Ca, Fe, and Sr were generated by gating their Kα emission lines and applying appropriate cutoffs to eliminate low count noise and spurious high counts. Figure S1 shows an (a) optical and a (b) XRF map of the eagle ford shale. Figure S1. a) Optical image and b) X-ray fluorescence map of the Eagle Ford shale. 2. Pressure Dissolution Pressure dissolution consists of two main processes: dissolution at mineral contact points under stress and diffusion of dissolved species toward the edge of the contact asperity and into the adjoining pore fluid. In this study, we utilized the stress-adjusted mineral activity derived by Taron & Elsworth, 2010 (58). For a cell i in which there is a contacting asperity, the activity of the solid is related to mechanical force on the asperity: S2

3 a CaCO3,i = exp (( σ π(δx/2 ) c) V m 2 f i RT ) (S1) where V m is the molar volume of calcite, R is the gas constant, T is the temperature of the system, and σ c is the critical stress (see Table 1). Therefore, instead of assuming a mineral activity of unity, as is done in equation 3, a stress-adjusted activity of the mineral is included in the Transition State Theory rate equation R PD = b i π( Δx V i 2 )2 k(a s,i ) exp ((σ a σ c ) V (a m ) (1 Ca2+) (a i CO2 2 ) i RT K sp exp((σ a σ c ) V m )). RT For cells in which there is a contacting asperity, R PD is added to the solution-driven dissolution calculated at the column surfaces perpendicular to flow and converted into a column height change in cell i. Whether this leads to the elimination of the contact point depends on whether the support for the normal stress of the fracture is taken up elsewhere. The second component of pressure dissolution is the diffusion of dissolved species through the contact fluid interlayer. For contacting asperities, the advection term of Equation (1) effectively goes to zero, and the diffusion along the fluid interlayer to the adjoining pore fluid, where the solute concentration is generally lower, proceeds according to Fick s Law (bc s ) t (S2) = 0 + (ωd m C s ) + R SD + R PD (S3) where ω is the thickness of the fluid interlayer. The interlayer thickness ω remains very uncertain, with no estimations by either theoretical or empirical methods. A value of 4 nm was used as in previous modeling studies (Table S1) (58). In this model application, pressure dissolution is calculated concurrently with solution dissolution and the dissolved solutes are distributed to surrounding cells. Immediate precipitation of minerals on the adjoining pore wall was not considered. Rather, dissolved species that are transported along the interlayer are added to adjacent grid cells, where they are subjected to stress-free thermodynamic equations where precipitation can occur. Simulations of the all-calcite fracture were performed with and without pressure dissolution at 10, 30 and 50 MPa normal stresses. Results show that dissolution driven by the reactive flow still dominates the overall fracture alteration, as is evidenced by the development of a channel with large apertures and surrounding regions containing the contacting asperities (Figure S2). The effects of pressure dissolution were not significant for the normal stresses of 10 and 30 MPa scenarios, but there was an effect for the 50 MPa case, which is discussed below. S3

4 Figure S2. Map of change in aperture ( b) of the simulation of the all-calcite fracture with pressure dissolution at 50 MPa after 36 hours. Although one might expect the mechanism of pressure dissolution to reduce transmissivity overall, as has been reported (26, 55, 59), our simulation results indicate that the addition of pressure dissolution leads to a slight enhancement in transmissivity (Figure S3) for the 50 MPa case. This enhancement is caused by the relative changes in the channel and surrounding areas. Pressure dissolution results in an aperture reduction that is relatively constant across the entire fracture. Some areas around the channel have smaller apertures relative to the channel, the aperture reduction caused by pressure dissolution is proportionally large in these areas. In the channel area, the aperture reduction due to pressure dissolution is proportionally small. As a result, the decrease in local transmissivity, which is proportional to b 3 (72), is relatively larger in cells outside of the channel. This enhances the delivery of reactive fluid to the channel and strengthens the feedback associate with channelization. Therefore, while pressure dissolution results in aperture reductions across the entire fracture, enhanced channelization leads to greater apertures when simulating pressure dissolution. This is clearly observed when comparing aperture maps between the simulations with and without pressure dissolution. The map in Figure S3 shows this difference, where red and blue indicate areas where apertures are smaller and larger for the simulation with pressure dissolution, respectively. Outside the channel, the dominant effect is a decrease in apertures due to pressure dissolution. Inside the channel, apertures are larger reflecting the enhanced channelization caused by the addition of pressure dissolution. S4

5 Figure S3. a) Difference in aperture between the simulation with pressure dissolution (PD) and without, at 50MPa normal stress, after 48 hours. Red regions indicates areas where apertures are smaller with pressure dissolution and blue regions indicates areas where apertures are larger. b) Transmissivity evolution with and without pressure dissolution. The finding that pressure dissolution enhances channelization is counter to what is the often-described effect of pressure dissolution. That said, the effects of pressure dissolution at the pressure and temperatures relevant for CCS and displayed in Figure 5 remain relatively small. Given pressure dissolution s relatively small effect, it was omitted in the interest of computational efficiency in the simulations presented in the next section. 3. Table of modeling parameters Table S1. Modeling parameters used. Equilibrium parameters, molar volume of calcite and the gas constant are from the PHREECQ database. Parameter Value Source D m 10-9 m 2 /s Oelkers & Helgeson, 1988 k 1, k 2, k , 1.1x10-4, 1.5x10-5 mol/m 2 s Deng et al., 2015 (27) K sp PHREEQC Database E 72 GPa Lin, 2013 S5

6 σ c 0.43 GPa Stephenson et al., 2012 T 323 K V m 31.2x10-6 m 3 /mol PHREEQC Database R J/Kmol PHREEQC Database ω 4 nm Taron & Elsworth, 2010 (63) Oelkers, E. H.; Helgeson, H. C. Calculation of the Thermodynamic and Transport-Properties of Aqueous Species at High-Pressures and Temperatures - Aqueous Tracer Diffusion- Coefficients of Ions to 1000-Degrees-C and 5-Kb. Geochim. Cosmochim. Acta 1988, 52 (1), Lin, C.-C. Elasticity of calcite: Thermal evolution (2013) Physics and Chemistry of Minerals, 40 (2), pp Stephenson, L.P., Plumley, W.J., Palciauskas, V.V. A model for sandstone compaction by grain interpenetration (1992) Journal of Sedimentary Petrology, 62 (1), pp Permeability vs Transmissivity Ultimately in the subsurface, the total leakage of a fluid through a fracture for a given fluid pressure gradient will be controlled by the transmissivity of the fracture (Equation 2). Yet, most experimental studies of reactive rock fractures often report permeability, rather than transmissivity, as the quantity that describes fracture hydraulic properties (18, 22, 26-2, 41). However, this removes the nuances of evolving fracture geometry. Transmissivity is related to permeability by a simple relation (73) T = ka. (S4) In this equation, changes in transmissivity can be separated into changes to the permeability of the fracture, k, which describes the ease of flow through the fracture, and the cross-sectional flow area, A. As reactive fluid flowing through a fracture results in rock dissolution and aperture enlargement, both the permeability and cross-sectional flow area of the fracture change and it is difficult to separate out the contribution of each quantity. Therefore, the transmissivity, which reflects changes to both quantities, should be used to describe changes to the flow properties of a fracture. However, experimental results of reactive transport in fractures are often interpreted using permeability, not transmissivity. To do this, the parallel plate model, otherwise known as the cubic-law, is assumed to be valid across the entire fracture and is used to infer the permeability in combination with Equation (2) using experimental measurements of the flow rate and pressure gradient: Q = wh3 P (S4) 12μ k = h2 12 where Q is the flow rate, w is the width of the fracture, h is the parallel plate model aperture, P is the pressure gradient, and is fluid viscosity. (S4) S6

7 The use of the parallel plate model across an entire fracture that undergoes complex aperture enlargement, such as channelization, should be avoided. To illustrate the distinction between permeability and transmissivity using two heterogenous rock mineralogies, we provide an example of how one measure of permeability and transmissivity of the Amherstburg limestone and Eagle Ford shale simulations at 50 MPa could be calculated. In this demonstration, we compute a permeability using k = T/A inlet. (S5) where A inlet is the cross-sectional area of the fracture inlet. For the simulation of the Amherstburg limestone, the formation of a continuous area of large apertures in the direction of flow leads to significant permeability increase, as it decreases the resistance to flow by providing a flow conduit. Because the crosssectional area also increases and the multiplicative relationship between permeability and flow cross-sectional area (Equation S4), this results in transmissivity increasing at a faster rate than permeability (Figure S4). For the Eagle Ford shale simulation, however, the evolution paths of permeability and transmissivity are very different. Although both permeability and transmissivity increase initially, permeability levels-off while transmissivity continues to increase later in the simulation. The leveling-off of permeability reflects increased flow tortuosity as fluid flows around the unreacted layers that act as flow bottle-necks. Yet, transmissivity continues to increase because the overall cross-sectional flow area increases. This finding highlights the importance of characterizing the evolution of fracture geometry both in simulation and experiments, the latter of which can be done with xct imaging. Figure S4. Transmissivity (red) and permeability (blue) evolution in the a) Amherstburg limestone and b) Eagle Ford shale simulations. S7

8 5. Original Asperity Map 6. Contact Area Evolution Figure S5. Location of asperities at 50 MPa at t=0. Figure S6. Contact area [%] evolution for the 10, 30, and 50 MPa all-calcite simulations versus time [hrs]. S8