Rock Mech Rock Eng (2013) 46:455–464 DOI 10.1007/s00603-012-0336-9

ORIGINAL PAPER

Permeability of Wellbore-Cement Fractures Following Degradation by Carbonated Brine Stuart D. C. Walsh • Wyatt L. Du Frane Harris E. Mason • Susan A. Carroll

•

Received: 7 November 2012 / Accepted: 12 November 2012 / Published online: 7 December 2012 Ó Springer-Verlag Wien 2012

Abstract Fractures in wellbore cement and along wellbore-cement/host-rock interfaces have been identified as potential leakage pathways from long-term carbon sequestration sites. When exposed to carbon-dioxide-rich brines, the alkaline cement undergoes a series of reactions that form distinctive fronts adjacent to the cement surface. However, quantifying the effect of these reactions on fracture permeability is not solely a question of geochemistry, as the reaction zones also change the cement’s mechanical properties, modifying the fracture geometry as a result.This paper describes how these geochemical and geomechanical processes affect fracture permeability in wellbore cement. These competing influences are discussed in light of data from a core-flood experiment conducted under carbon sequestration conditions: reaction chemistry, fracture permeability evolution over time, and comparative analysis of X-ray tomography of unreacted and reacted cement samples. These results are also compared to predictions by a complementary numerical study that couples geochemical, geomechanical and hydrodynamic simulations to model the formation of reaction fronts within the cement and their effect on fracture permeability. Keywords Carbon sequestration  Wellbore integrity  Fracture flow and transport  Chemo-mechanical coupling

Prepared by LLNL under Contract DE-AC52-07NA27344. S. D. C. Walsh (&)  W. L. Du Frane  H. E. Mason  S. A. Carroll Lawrence Livermore National Laboratory, 7000 East Av., Livermore, CA, USA e-mail: [email protected]

1 Introduction Long-term sequestration of carbon dioxide is intimately linked to wellbore integrity, as wellbores present an obvious vertical conduit for subsurface transmission of carbon dioxide and carbonated brines (Carey et al. 2007; Metz et al. 2005; Pawar et al. 2009). Understanding the movement of these fluids along cement fractures and interfaces is of particular importance, as these pathways offer potential escape routes around seals and out of the wellbore environment (Duguid et al. 2005; Carey et al. 2007; Lewis et al. 2012). Alkaline wellbore cement degrades in the presence of acidic carbonated brines—causing distinctive layers of reacted material to form adjacent to the cement surface (Duguid et al. 2005; Carey et al. 2007, 2009; Kutchko et al. 2007; Wigand et al. 2009; Duguid and Scherer 2010; Agbasimalo and Radonjic 2012). The lower-pH brine leaches calcium from the cement, creating a Portlanditedepleted (CH-depleted) layer in contact with the unaltered cement. Next the dissolved calcium reacts with the CO2rich brine precipitating a layer of calcium-carbonate minerals. Finally, the dissolution of the calcium-carbonate layer produces an amorphous-silicate region adjacent to the brine. It has been speculated that precipitation or dissolution as a result of these regions may either trigger an increase in fracture permeability or fracture sealing. However, the effect on fracture transmissivity is complicated by changes to the cement composition that affect material strength and, as a byproduct, fracture geometry. This paper describes how these chemical and mechanical processes influence fracture growth and sealing within wellbore cement under conditions relevant to long-term carbon-dioxide storage. An ongoing series of core-flood reaction experiments are outlined that were conducted on

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mated cement and host-rock samples in a core-flood reactor at temperature and pressures typical of carbon sequestration. Data obtained from the experiments—X-Ray Computed Tomography (XRCT), mineral identification within the fractures, pressure and solution composition—provided input and constraints for the numerical model. The model itself combines geochemical, hydrodynamic and geomechanical modules to simulate the cement-brine-host rock system. Here, we describe in detail the method used to model the reaction front penetration and present results from one of the tests to illustrate the processes involved. The experimental and modeling results highlight the need to consider the effects of coupling between the chemical and mechanical alteration on the fracture permeability.

2 Core-Flood Experiments Core-flood experiments were performed on cylindrical samples comprising mated cement and caprock half-cores (Fig. 1a) to investigate the effect of carbonated brine on cement fracture permeability. The mated cores were fabricated by first griding flat surfaces in separate cement and caprock slabs. These surfaces were joined together in a vice and cores were taken along the seam to create complementary cylinder halves. The cement half-cores consisted of Class G Portland cement cured in a hydrothermal vessel at pressure, temperature, and duration in accordance with ASTM Test Method C114. The resulting cylindrical samples were 15 mm in diameter and between 30 and 37 mm long. The caprock halves consisted of fully dense quartz-sandstone cemented with calcite, which were sourced from an oil wellbore in Kern County, California at a depth of 13,927 ft. The samples were provided thanks to Larry Knauer of Chevron and the California Well Sample Repository. Without additional treatment the flat interface between the mated half-cores would be virtually impregnable to flow. Hence, a bead-blasting and masking approach was employed to generate an aperture between the mated halfcores (Fig. 2). This approach was adopted (1) to ensure a degree of reproducibility in creating the samples, (2) to guarantee sufficient interface apertures for XRCT imaging,

and (3) to regulate the initial pressure/flow conditions for the samples. The cement surface of the sample was initially masked with a metal grid of regular circular openings and abraded with a pressurized spray of glass beads to create isolated pockets 50–100 microns deep. The grid was then displaced relative to the original position and the cement half-core bead-blasted a second time to create a new set of 20–40-micron-deep pockets. The process resulted in an interconnected network of circular apertures in a hexagonal pattern. While the fracture geometry created for these tests was relatively simple, the same masking and bead-blasting approach is also capable of generating more complex flow path geometries. Core-flooding experiments are conducted on the rejoined samples with CO2-rich brines. The composition and preparation of the brine used in this study was designed to be in or near chemical equilibrium with calcite and dolomite at 60 °C and to match conditions observed in the field (Smith et al. 2012). Reagent grade inorganic salts (NaCl:1.01 mol/L, Na2SO4:3.69e-2 mol/L, MgCl2:1.59e-2 mol/L, CaCl2: 3.53e-2 mol/L, and NaHCO3:7.92e-3 mol/L) were dissolved into millipure filtered water. After full dissolution, the brine was purged with N2(g) to remove dissolved O2, heated to 60 °C, and pressurized with CO2 inside a separate mixer vessel for over 12 h. Carbonated brine solutions were injected at constant flow rates for 8 days, during which time the sample and the mixer vessels were maintained at a constant temperature of 60 °C. A detailed description of the experimental setup of the core-flooding apparatus can be found in the supplementary material for Smith et al. (2012). In this paper, we concentrate on results from one of the tests with a pCO2 of 3 MPa and a constant flow rate of 0.1 cc/min. Flow conditions were selected to be in approximate agreement with previous studies of fracture flow in wellbore cement by Carey et al. (2009) and prior core flood experiments by Smith et al. (2012). Nevertheless, we anticipate that the flow rates are greater than would be experienced under typical downhole conditions. A confining pressure of 24.8 MPa was applied to the cores and the outlet pore pressure was held fixed at 12.4 MPa. The ratio of pore-pressure to confining pressure was determined by safety factors in the experimental design (Smith et al. 2012). While this ratio is less than would be

Fig. 1 Experiments described in this paper were conducted on mated cement and caprock halfcore samples. Tomographic cross-sections are shown of a unreacted and b reacted samples, with c a magnified view of the reacted zones at the cement-caprock interface

(a)

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(b)

(c)

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Fig. 2 A masking technique, illustrated on the left, was used to create artificial fracture surfaces in the cement halfcores. A test sample generated with this method (which was not used in the experiments due to the large fracture across the center) is shown on the right

expected in the injection phase of a carbon sequestration project, it is anticipated that the effective pressure (i.e. the difference in confining pressure and fluid pressure) to be more influential on the system response rather than the absolute value of the pressure. The inlet pressure was adjusted automatically to maintain the correct flow rate, and monitored in real-time to record changes in the permeability of the sample. Samples of the outlet brine solution were taken at regular intervals for later chemical analysis.

3 Numerical Model Real-time permeability measurements provided a measure of the integrated response of the samples over the course of the experiment. In addition, X-ray tomography (discussed in Sect. 4) revealed changes to the samples at the beginning and conclusion of the experiments. Unfortunately, however, our current experimental setup does not permit in situ XRCT imaging while maintaining the appropriate pressure and temperature conditions. Instead, numerical modeling is used to gain additional insight into the sample behavior at the pressure and temperature conditions of our experiments. A suite of separate numerical models was used to represent the interaction between the fluid flow, transport of dissolved species, mechanical deformation and the propagation of the reaction fronts. The coupling between the various numerical models is illustrated in Fig. 3. These modules are combined in an open-source computational framework, GEOS, under development at Lawrence Livermore National Laboratory (Settgast et al. 2012). GEOS is designed for multi-scale multi-physics simulations with a focus on the geosciences. Although this paper concentrates primarily on the reaction front model, the other modules are outlined briefly below. Deformation of the cement and host rock is modeled using an implicit Lagrange discrete finite element solver. The deformation solver is coupled to the flow solver via the

Fluid Solver (FVM) Mechanics

Solid Solver (FDEM)

Flow rate

Fracture aperture

Dissolution

Transport Solver (FVM) Aqueous chemistry

Reaction Front Model

Fig. 3 Flow-chart illustrating the numerical models employed to simulate fracture growth and healing and the processes by which they are coupled

fluid pressure applied to the fracture surface. In addition, the fracture aperture is controlled by the relative positions of the deformed surfaces of the solid body. This provides the ability to simulate the effects of confining pressures on the flow characteristics of a sample, as well as simulating the effect of the fluid pressure on the aperture. Flow and transport within the fractured regions are modeled with a cell-centered finite difference approach, in which the fracture is represented as a set of two-dimensional finite volume elements embedded in a three-dimensional volume. A similar approach, used to simulate fluid flow for hydraulic fracturing simulations, is described in Johnson and Morris (2009). The fracture width is determined by an aperture thickness ascribed to each element in the two dimensional surface. As dissolution is slow relative to the flow rate, we adopt a quasi-static approximation in the simulations. At each timestep in the simulation, the steadystate flow is found based on the distribution of apertures in the fracture. From the steady-state flow solution, we then solve for the transport of the reacting species. The updated concentration distribution is then supplied to the reaction front module which calculates the rate of reaction, and updates the fracture apertures and solid material properties in response to changes in the reaction front positions. To model the reaction front growth, we adopt a method similar to that employed by Ulm and co-workers (e.g. Mainguy and Ulm 2001; Ulm et al. 2003) to simulate calcium leaching from cementitious materials in water. In Ulm’s original approach, the system is represented as a set

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of coupled moving boundary problems. Transport between fronts is governed by the advection-diffusion equation:   o o½Ca2þ  o o½Ca2þ  ð/½Ca2þ Þ þ ux ¼ Deff ; ð1Þ ot ox ox ox where [Ca2?] is the calcium concentration, ux is the Darcy velocity, / is the pore volume fraction, and Deff ¼ /D s is the effective diffusivity (with D the diffusivity and s the tortuosity). Front movement is controlled by jump conditions in the form:   dxI o½Ca2þ  2þ ½½q2þ ¼ M ð1  /Þ D ; ð2Þ eff Ca Ca ox dt where ½½A ¼ Ajxþ  Ajx denotes the jump in a quantity A across the front, [[q2? Ca (1 - /)]] is the change in calcium density, xI is the interface location, and MCa2þ is the molar mass of calcium. We have extended Ulm’s model to account for diffusive transport of multiple chemical species and changes to chemical equilibrium. When the diffusive length-scale is large relative to the reaction front width, the concentration distribution is well approximated by the steady-state solution. Similar assumptions have been adopted in modeling carbonate dissolution in karst formations (Buhmann and Dreybrodt 1985a, b; Dreybrodt et al. 2005). In this event, the steady-state condition can be found implicitly, by solving a set of coupled equations, describing the chemical equilibrium and mass transport across the entire set of reaction fronts. Chemical equilibrium at each of the reaction fronts is accounted for by mass-balance equations for aqueous species, coupled with additional equations describing the reaction front chemistry, and charge-balance equations to obtain the pH at each of the reaction fronts. To describe the reaction fronts in the model, we begin by expressing the chemical reaction equations for aqueous speciation and solid dissolution in the form N X

m0ji Aj !

j¼1

N X

m00ji Aj ;

ð3Þ

j¼1

where mji is the stoichiometric coefficient of the ‘‘jth’’ species with chemical symbol Aj. The equilibrium constants, Ki, for these equations is given by Ki ¼

N Y 00 0 fAj gmji mji ;

ð4Þ

j

where {Ai} indicates the species activity. The activities are related to species concentrations, [Ai], by fAi g ¼ ci ½Ai ;

ð5Þ

where ci is the ion activity coefficient (IAC). Charge balance is enforced by

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X

½Ai zi ¼ 0;

ð6Þ

i

and, at the brine boundary, equations are introduced to conserve the net dissolved concentration of the constituent elements (hydrogen and oxygen excluded): X ½Ei  ¼ Nij ½Aj ; ð7Þ j

where Nij is the number of atoms of element Ei in species Aj. The concentrations [Ei] are obtained from the parallelplate flow and transport simulation for the fracture. These equations yield a non-linear system describing the brine equilibrium: xi  eyi loge ðci Þ ¼ 0

for i 2 1; . . .; n;

ð8Þ

Nx ¼ b;

ð9Þ

My ¼ k;

ð10Þ

where n is the number of chemical species; xi = [Ai] for i 2 1; . . .; n; and xn?1 = l; yi = loge {Ai} for i 2 1; . . .; n; Mij ¼ m00ji  m0ji ; ki ¼ loge Ki ; and N and b are constructed from the equations describing the ionic strength l, charge balance and dissolved element concentrations. The nonlinear system is solved using a NewtonRaphson method in which the unknown variables are the components of the vectors x and y which include the aqueous species concentrations, the ionic strength, and the natural logarithm of the species activities. The equations for the aqueous equilibrium are not sufficient to solve the reaction front system under the quasi steady-state assumption—extra conditions in the form of Eq. (4) are required to describe the equilibrium with the solid fronts, as well as species transport between the fronts. Consequently, in the event that two or more elements are produced or consumed at the reaction front, constraints are introduced to balance the molar flux of elements based on the reaction front stoichiometry. For example at reaction fronts involving the precipitation of calcium carbonate, we enforce a balance between the production of net calcium and carbon, with the following jump condition:     o½Ca o½C Deff  Deff ¼ 0; ð11Þ ox ox i.e. net carbon produced (or consumed) at the boundary is equal to the net calcium produced (or consumed). In addition, elements unaffected by the surface reactions occurring at a given front are balanced by assuming the molar flux is constant across the surface. For example,   o½Si Deff ¼ 0: ð12Þ ox

Permeability of Wellbore-Cement Fractures

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These gradients are determined from the concentrations at the reaction fronts, and their immediate neighbors, based on the steady-state solution to the diffusive transport equation. In the event that the Darcy flow normal to the front is negligible (i.e. ux = 0) the quasi steady-state distribution is simply a linear interpolation of the dissolved element concentrations at the reaction fronts. In this case, jump condition terms of the sort found in Eqs. (11) and (12) can be expressed as,  Deff

o½Ei  ox

   Dþ Deff Dþ D fþ fo eff eff eff ½E  þ    ½Ei f  ½E i i lþ l lþ l X Dþ ¼ Nij þeff ½Aj f þ l j     Deff Dþ D fo f eff eff  þ ½Aj    ½Aj  þ l l l   X fþ f þ  þ Dij ½Aj  þ Dij  Dij ½Aj fo  D ¼ ij ½Aj  ;



¼

j

ð13Þ where l? and l- are the widths of the reaction zones on either side of the front; D? eff and Deff are the corresponding fo effective diffusivities; [Ei] and [Ai]fo are the

concentrations of constituent elements and aqueous species at the front; and [Ei]f-, [Ei]f?, [Ai]f- and [Ai]fare the concentrations of constituent elements and aqueous species at the fronts on either side of the reference front. Thus, the effect of the flux conditions of the sort given in Eqs. (11) and (12) is to couple the equations at the reaction fronts. The solution to the resulting system of non-linear equations (summarized below) yields the equilibrium state at all of the reaction fronts. 2 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 4

xfi1  cfi1 expðyfi1 Þ Nxf1 Myf1 D1 xf1

3

ðD1  D1þ Þxf2 xfi2  cfi2 expðyfi2 Þ Myf2 Mf 2 yf 2 D2 xf2

D1þ xf3

ðD2  D2þ Þxf3 xfi3  cfi3 expðyfi3 Þ Myf3 Mf3 yf3 D3 xf3

2 3 0 7 6 b 7 7 6 7 7 6 k 7 7 6 7 7 6 0 7 7 6 7 7 6 0 7 7 6 7 7 6 7 7 6 k 7 7 6 f2 7 7 6k 7 7 6 7 D2þ xf4 7 ¼ 6 0 7: 7 6 7 7 6 0 7 7 6 7 7 6 k 7 7 6 f3 7 7 6k 7 7 6 7 3 f4 7 6 0 7 D xj 7 6 7 f4 f4 f4 7 xi  ci expðyi Þ 7 6 0 7 f4 5 4 k 5 My kf 4 Mf4 yf4

ð14Þ The method is readily extended to include an arbitrary number of fronts and species beyond those considered here. Once the system has been solved, the dissolution rate at each of the fronts can be determined using the same method as in Eq. (2). The updated front locations, along with changes in brine chemistry due to transport along the fracture, provide new input conditions that are used to find the quasi steady-state at the following timestep. The new front positions are also used to update the material properties employed in the solid deformation model.

(a) 4 Results

(b)

(c) Fig. 4 Tomographic cross-sections of reacted sample: a X–Y crosssection, b X–Z cross-section; c Y–Z cross-section for a sample reacted with a carbonated brine with 3 MPa p CO2 at a flow rate of 0.1 cc/min and temperature of 60 °C

Three-dimensional X-Ray Computed Tomography (XRCT) images were taken of the cement-caprock samples prior to and following the core-flood experiments at the 8.3.2 beamline, ALS, Berkeley, California. The XRCT measurements were collected at voxel resolutions of 4.44 lm along all three spatial dimensions. Each scan produced a CT image in the x–y plane of size 4,008 9 4,008 pixels (17.6 mm 9 17.6 mm). The total number of scans along the z-axis was approximately 8,000 per core, with the precise number depending on the core length. XRCT of the unreacted cement sample revealed the existence of a few narrow (*4 lm) fractures in the unreacted cement and caprock half-cores. These appear to have had little effect on either the main fracture flow or the extent of the reaction fronts: the main reaction fronts do not preferentially follow or avoid these secondary fractures; and there is little or no deviation in the extent of the

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Fig. 5 Distribution of pore-space within the reaction zones from the sample shown in Fig. 4. Gray lines denote approximate front locations

1 brine SiO2−CaCO3 CaCO3−csh csh−ch

0.9 0.8

Unreacted

Distance (mm)

0.7 0.6 CH depleted 0.5 0.4 CaCO 0.3

3

0.2 amSiO 0.1

2

0 0

0.02

0.04

0.06

0.08

0.1

Flow rate (cc/min)

Fig. 6 Simulated reaction-front locations as a function of flow rate. Plots give reaction-front positions after 1 day. Fracture aperture dimensions: 1 cm 9 1 cm 9 0.1 mm (color figure online)

reaction fronts on either side of the fractures—although there is evidence of precipitation (likely calcium carbonate) within these secondary cement fractures. The individual reaction fronts are clearly visible in the post-experiment XRCT images (Fig. 4). The overall depth of penetration for the reaction fronts is relatively uniform along the length of the sample, but varies across its width due to local variations in the flow. The porosity increases in all of the reaction fronts, except the region of calcium carbonate precipitation (Fig. 5). In particular, the porosity is high in the amorphous silicate region adjacent to the fracture, and the calcium carbonate precipitation does not appear to counteract the increased porosity due to cement dissolution. The post-experimental XRCT images also reveal significant fractures in the amorphous silicate region directly adjacent to the fracture. These fractures were observed to form at the conclusion of the experiment as a result of

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dehydration of the sample. They extend only through the amorphous silicate region and do not influence the formation of the reaction fronts. The penetration depths of the reaction fronts observed in these experiments are greater than those from related experiments by Carey et al. (2009) and Kutchko et al. (2007, 2008). The reaction fronts in Fig. 4 penetrated to a depth of approximately 2 mm after 8 days in the core-flood reaction, compared to less than 500 microns after 9 days for reaction fronts observed by Kutchko and co-workers, and 50–150 microns after 16.6 days (400 h) in experiments by Carey et al. (2009). The experiments were conducted at different temperatures (40 °C for Carey et al. (2009), 50 °C for Kutchko et al. (2007, 2008) and 60 °C in this study), however, our modeling suggests that changes in temperature over this range should have little effect on the overall reaction front penetration or the relative widths of the fronts. Differences between published experimental results may be partially attributed to differences in brine chemistry and flow rate. The experiments by Carey et al. (2009) involved a mixture of supercritical CO2 and brine rather than dissolved CO2. Moreover, in Carey et al. (2009), the brine was simultaneously reacted with an exposed steel bar to mimic the effect of CO2 on a wellbore’s steel casing. In Kutchko et al. (2007, 2008), the cement sample was placed in a static CO2/brine bath, rather than a flow-through experiment as done here. Other experiments conducted with flow through conditions observe substantially higher rates of degradation (Duguid et al. 2005), and our simulations indicate that the reaction front widths decrease sharply at low flow rates (Fig. 6). At lower flow rates, the reaction-front model also predicts thicker calcium carbonate layers (relative to the other reaction fronts), a finding that is also supported by the experimental results. In our experiments, the width of the calcite region is relatively thin compared to the other fronts, whereas in Kutchko et al. (2007, 2008), the precipitated calcite layer is comparable in size to the other regions. Microstructural differences between the cements may also have influenced the reaction front formation. The reaction front simulations indicate that growth of the different regions is strongly influenced by their tortuosity and the relative volume fractions of calcite and precipitated calcium carbonate (Fig. 7). At large times and with fixed brine chemistry, the reaction front growth predicted by the model approximates Fickian diffusion. Under these circumstances the volume fractions of calcite and precipitated calcium carbonate largely determine the relative speeds of the leading edge of the depleted region and the calcium carbonate layer (though not their absolute speeds), while the tortuosities influence the overall rate of propagation of the layers. If scaled by the same factor the tortuosities alter the steady state growth of the reaction fronts in proportion

Permeability of Wellbore-Cement Fractures

brine SiO2−CaCO3 CaCO3−csh csh−ch

Distance (mm)

0.5

Unreacted

0.4 CH depleted 0.3 CaCO3

0.2 0.1

amSiO2

0 0

1

2

3

(a)

4

5

6

7

8

6

7

8

Time (days) 2 brine SiO2−CaCO3 CaCO3−csh csh−ch

1.8 1.6

Distance (mm)

Fig. 7 Front positions predicted by the reaction front model are sensitive to the tortuosity of the reaction regions and relative volume fractions of CaCO3 and Ca(OH)2. a Simulations with higher tortuosity, and Ca(OH)2 volume fractions yield reaction regions widths similar to those seen in Kutchko et al. (2007, 2008). b While lower tortuosities, and relative Ca(OH)2 volume fractions produce reaction regions closer to those observed in these experiments. c Comparison between experimental reaction fronts (background and dashed lines), and the results of the numerical model (solid lines) (color figure online)

461

Unreacted

1.4 1.2

CH depleted

1 0.8

CaCO3

0.6 0.4 amSiO2

0.2 0 0

1

(b)

2

3

−13

−14

2

Permeability (m )

10

−15

10

−16

10

−17

0

50

100

5

Time (days)

10

10

4

150

200

Time (hours)

Fig. 8 a Total permeability of half-caprock, half-cement core over time while flowing brine for the sample shown in Fig. 4. Confining pressure maintained at 24.8 MPa and pore pressure maintained at 12.4 MPa

to its inverse square root. A thicker (relative to the other layers), more competent calcite band would slow transport across the fronts, reducing the rate of degradation.

(c)

Likewise, variations between the reaction fronts may also be driven by changes in brine chemistry—brines undersaturated with respect to calcite would enhance dissolution of the calcium carbonate layer. Although, our experimental results and the reactionfront-model simulations show an increase in overall porosity within the fracture region, the total permeability decreases steadily over the course of the experiments. This is illustrated in Fig. 8, which shows results from an experiment that experienced an almost 100-fold decrease in the fracture permeability over a period of 8 days. The reduction in the sample permeability may be partially a result of swelling in the amorphous silicate layers. Amorphous silicate has higher molecular volume than the calcium silica hydrates in the unreacted cement, and expansion of the amorphous silicate zones would clog the fracture aperture, preventing flow (Fig. 9c). However, a higher molecular volume in itself does not guarantee an overall increase in the cement volume, as portlandite has also been removed from the amorphous silicate region and thus swelling might only result in a reduction of local porosity. Indeed if anything, experimental results by Duguid et al. (2005) and Duguid and Scherer (2010) appear

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(a)

(b)

(c)

(d)

Fig. 9 Cartoon illustrating two potential contributing factors to the decrease in permeability observed in the experiments. a The initial fracture apertures (white regions) are held open by cement asperities that act as pillars; b over time the intact cement is eroded by the reaction fronts. c A reduction in permeability could be caused by

swelling of the amorphous silicate region resulting in a reduction of the fracture apertures; d alternatively (or in conjunction with c) weakening of the pillars could result in collapse of the pillars, reducing the fracture aperture and decreasing the permeability

Table 1 Young’s moduli obtained from nano-indentation of the reacted layers

these cement ‘pillars’. Nano-indentation conducted after the completion of the core-flooding experiments (Table 1) shows softening of the material within the reacted layers. Compression of the pillars as a result would cause an overall decrease in the hydraulic aperture (Fig. 9d). Additional simulations were conducted to investigate how fracture permeability is influenced by the bulk modulus of the cement (Fig. 10). The bulk modulus must be decreased to less than 1 GPa to reduce the fracture permeability by an amount comparable to that seen in experiment. This is smaller than would be expected from measurements of the elastic moduli of calcium depleted cement (Constantinides and Ulm 2004) where the elastic modulus was observed to decrease to approximately 14 % of the value in the unreacted cement, and smaller than would be expected from our nano-indentation measurements. Thus it seems likely that if the reduction in fracture permeability is mechanical in nature, it should be accompanied by some plastic deformation. Evidence of plastic deformation can be found through comparative analysis of the pre- and post-experiment tomography (Fig. 11). Employing techniques from Particle Image Velocimetry (PIV) (Raffel et al. 1998; Adrian 2005) that have been adapted to the three-dimensional XRCT images, the relative displacements of correlated points in the unreacted and reacted samples are determined. In traditional PIV methods the cross-correlation is found by comparing two dimensional windows, whereas in the XRCT-PIV method applied here, three-dimensional volumes are compared. The extra dimension of the XRCT-PIV correlation windows makes the analysis more robust in the presence of instrument noise and reaction of the material. The resolution and accuracy of the method is further increased by using a multiple-pass approach in which the result of the initial PIV analysis is used to improve the analysis in subsequent passes, equivalent to the multiresolution approach with discrete window offset employed in traditional PIV methods (Scarano and Riethmuller 1999). Changes in local strain are obtained from the sample by

Layer

Young’s modulus (GPa)

Unreacted cement

28 ± 7

CH-depleted

21 ± 6

CaCO3

18 ± 3

am-SiO2

9.6 ± 1.0

Moduli, in particular that of the am-SiO2 layer, should be regarded as approximate due to drying of the sample (Smith et al. 1995) −13

Permeability (m2)

10

−14

10

−15

10

−16

10

2

4

6

8

10

Bulk Modulus (GPa) Fig. 10 Simulated total permeability of half-caprock, half-cement core as a function of cement bulk modulus

to show a slight reduction in the cement volume following reaction. That said, even these results may be inconclusive as desiccation of the sample would result in contraction of the amorphous silica layer. Alternatively, the permeability decrease might be a consequence of the degradation in the cement’s mechanical properties. The aperture is maintained by a few asperities on the cement half-core that act as pillars propping open the fracture. By the end of the experiment, the reacted layers have extended throughout

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Permeability of Wellbore-Cement Fractures Fig. 11 XRCT-PIV analysis images from the sample shown in Fig. 4: a tomographic crosssection from the reacted sample; b the displacement field obtained from the XRCT-PIV analysis (number of displacement vectors reduced by a factor of 10 along each dimension, background color indicates magnitude of displacement normal to the fracture surface); c Volumetric strains, v ¼ xx þ yy þ zz ; and d strain normal to the fracture, n ¼ ij ni nj : Darker regions in c and d denote regions of compression while lighter regions indicate areas of expansion. Note the large compressive strains (darker regions) in the amorphous silicate and in the portlanditedepleted regions adjacent to the cement-caprock interface. The analysis also reveals the closure of a thin vertical fracture (dark line in c). White regions, indicating strong dilation, correspond to desiccation cracks in the amorphous region or, in a few cases, the result of falsecorrelations in regions of calcite precipitation

463

(a)

(b)

(c)

(d)

determining the appropriate displacement field gradients. As the initial and final tomography is conducted at atmospheric pressure, the calculated strain is an indication of inelastic changes in the sample. This analysis shows evidence of deformation in the amorphous silicate regions and regions depleted of portlandite adjacent to the fracture. Nevertheless, some caution should be exercised before extrapolating these results to the larger wellbore environment. The decrease in permeability observed in these experiments is dependent on the scale of the sample cores. The reaction regions in the experimental samples extend across the diameter of the samples, and thus the internal ‘‘pillars’’ of reacted cement provide the only support to hold the fracture open. In contrast, larger natural fractures are likely to experience more channelized flow than observed in these experiments. Thus natural-fracture flow pathways may be less prone to collapse due to additional support outside the reaction regions. This may explain why, for example, experimental studies have observed decreasing permeability in cement fractures with CO2 exposure, however, in the field-samples obtained by Carey et al. (2007) there was evidence of extended reaction at the cement-rock interface, several meters from the base of the well.

5 Conclusion Flow of carbonated brine through well-bore cement fractures results in the creation of distinct reaction zones adjacent to the cement-brine interface. These reaction zones increase the porosity of the cement immediately adjacent to the fracture. However, the effect of exposure to carbonated brine on the overall fracture permeability is complicated by the fact that the reaction zones also alter the mechanical properties of the cement fracture. The impact of wellbore fractures on the long-term viability of carbon sequestration sites is a product of coupled chemical, hydrological and mechanical processes acting on the fracture interface. In these experiments, the reactions between the carbonated brine and the cement actually reduce the fracture permeability—despite the increase in cement porosity. This appears most likely a result of the reaction fronts weakening the asperities that maintain the fracture opening. This conclusion is supported by geomechanical testing conducted during the experiment, numerical modeling, and post-experimental XRCT analysis. Swelling of the amorphous silicate layer may also contribute to the reduction in fracture permeability, but the degree is difficult to ascertain due to sample desiccation. The results of

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this work highlight the need to consider coupled chemical, hydrodynamic and geomechanical influences on the fracture surface to understand the effect on permeability. Acknowledgments We gratefully support for this work under the DOE National Energy Technology Laboratory, Project AA3030100. We would like to thank Larry Knauer and the California Well Sample Repository for the caprock samples used in our experiments. The Advanced Light Source is supported by the Director, Office of Basic Energy Sciences of the US Department of Energy under Contract N. DE-AC0-2-05CH11231. We thank Yelena Scholokhova for collecting and processing the tomography data and Alastair MacDowell and Dula Parkinson for their assistance at the beamline. We are also grateful to M. Smith for her assistance with the experiments, as well as D. Ruddle and S. Torres for their assistance in the preparation of sample cores. This manuscript was approved for release by LLNL with release number LLNL-JRNL-598999. 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 make 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.

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