Dynamic Evolution of Cement Composition and Transport Properties

Article pubs.acs.org/EF

Dynamic Evolution of Cement Composition and Transport Properties under Conditions Relevant to Geological Carbon Sequestration Jean-Patrick Leopold Brunet,†,‡ Li Li,*,†,‡,§,∥ Zuleima T. Karpyn,†,‡,∥ Barbara G. Kutchko,⊥ Brian Strazisar,⊥ and Grant Bromhal# †

John and Willie Leone Family Department of Energy and Mineral Engineering, ‡Earth and Mineral Sciences (EMS) Energy Institute, Earth and Environmental Systems Institute, Pennsylvania State University, University Park, Pennsylvania 16802, United States ∥ National Energy Technology Laboratory-Regional University Alliance (NETL-RUA) ⊥ National Energy and Technology Laboratory (NETL), United States Department of Energy, Pittsburgh, Pennsylvania 15236, United States # National Energy and Technology Laboratory (NETL), United States Department of Energy, Morgantown, West Virginia 26507-0880, United States §

ABSTRACT: Assessing the possibility of CO2 leakage is one of the major challenges for geological carbon sequestration. Injected CO2 can react with wellbore cement, which can potentially change cement composition and transport properties. In this work, we develop a reactive transport model based on experimental observations to understand and predict the property evolution of cement in direct contact with CO2-saturated brine under diffusion-controlled conditions. The model reproduced the observed zones of portlandite depletion and calcite formation. Cement alteration is initially fast and slows down at later times. This work also quantified the role of initial cement properties, in particular the ratio of the initial portlandite content to porosity (defined here as φ), in determining the evolution of cement properties. Portlandite-rich cement with large φ values results in a localized “sharp” reactive diffusive front characterized by calcite precipitation, leading to significant porosity reduction, which eventually clogs the pore space and prevents further acid penetration. Severe degradation occurs at the cement−brine interface with large φ values. This alteration increases effective permeability by orders of magnitude for fluids that preferentially flow through the degraded zone. The significant porosity decrease in the calcite zone also leads to orders of magnitude decrease in effective permeability, where fluids flow through the low-permeability calcite zone. The developed reactive transport model provides a valuable tool to link cement−CO2 reactions with the evolution of porosity and permeability. It can be used to quantify and predict long-term wellbore cement behavior and can facilitate the risk assessment associated with geological CO2 sequestration.

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INTRODUCTION Carbon capture and sequestration (CCS) is considered a promising option for the mitigation of CO2 emissions.1,2 One major concern about CCS is the possibility and impacts of CO2 leakage over an extended period of time.3−5 Injected CO2 leads to a pressure increase in the deep subsurface, potentially resulting in leakage through interfaces, fractures, or faults in the deep subsurface.6,7 Abandoned wells have been considered as a major potential leakage pathway because of their common occurrence,8 reactive nature,9 and potential defects that are susceptible to mechanical and chemical degradation. 9,10 Reactions between cement and acidic CO2-saturated brine can change cement structural integrity, alter its transport properties, and therefore, change leakage likelihoods and rates. Modeling and experimental studies have shown that leakage of CO2 under certain circumstances can result in groundwater acidification,11,12 heavy metal mobilization,13,14 and accelerated dissolution of minerals,15 all of which can have significant environmental impacts. It is important to understand and quantify CO2−brine−cement interactions and predict the longterm evolution of cement properties.16 Substantial experimental work has been performed to understand cement CO2 interactions in recent years. After © XXXX American Chemical Society

exposure to CO2-saturated brine, distinct zones have been observed to develop, including a degraded (porous and decalcified) zone, a calcium carbonate zone, and a portlandite depletion zone, beyond which was unaltered cement.17−21 Mechanical strength of the degraded zone has been reported to decrease to less than half of the original value.17 The precipitated calcite also led to a significant decrease in porosity and change in mechanical properties.22 Along with the compositional alteration, the flow and transport properties have also been found to change significantly, typically with 1−3 orders of magnitude change in effective permeability and diffusivity.18,23−25 Along with experimental work, field studies have aimed to assess long-term wellbore integrity.9,26 These studies confirmed experimental observations on compositional alteration, while the assessment of long-term effects remained indefinite. Reactive transport models have been developed to understand Special Issue: Accelerating Fossil Energy Technology Development through Integrated Computation and Experiment Received: December 9, 2012 Revised: May 1, 2013

A

dx.doi.org/10.1021/ef302023v | Energy Fuels XXXX, XXX, XXX−XXX

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Table 1. Reaction Network for CO2−Cement Interactions, Reaction Thermodynamics, and Kinetics43,47 number 1

+

Ca(OH)2 (s) + 2H ⇔ Ca

2

2+

+

log k (mol m−2 s−1)a

A (m2/g)43

αa

+ 2H 2O

21.05

−6.20

16.50

0.18

2+

32.60

−10.10

45.00

0.33

−8.11

−6.10

1.00

0.08

−10.00

1.00

0.00

C−S−H(s) + 3.6H ⇔ 1.8Ca

3

CaCO3(s) ⇔ Ca

4

SiO2 (am) ⇔ SiO2 (aq)

number 5

2+

+ CO3

+ 7.0H 2O + SiO2 (am)

2−

−2.54

aqueous instantaneous reactions (thermodynamics controlled)

log Keq47 −13.30

H 2O ⇔ H+ + OH− +

−6.09

HCO3−

6

CO2 (aq) + H 2O ⇔ H +

7

HCO3−

8

CaCO3(aq) ⇔ Ca 2 + + CO32 −

9

CaCl+ ⇔ Ca 2 + + Cl−

0.60

10

CaCl 2(aq) ⇔ Ca 2 + + 2Cl−

0.59

11

CaHCO3+ ⇔ Ca 2 + + HCO3−

−1.11

12

CaOH+ ⇔ Ca 2 + + OH−

−0.45

13 14 a

log Keq47

solid-phase precipitation and dissolution reactions (kinetics controlled)

+

⇔ H + CO3

+

−9.62

2−

−2.54

−

0.73

NaCl(aq) ⇔ Na + Cl +

NaHCO3(aq) ⇔ Na +

HCO3−

0.024

Values of log k and pH dependency α were obtained by fitting the BSE image data. All other parameters were from cited references.

the experimental and field observations and predict long-term behavior.24,27−32 Carey and Lichtner simulated cement−CO2− brine interactions during two-phase flow,29 with a major focus on the alteration at the cement−rock interface under flowthrough conditions. Huet et al.33,34 modeled the cement carbonation in a CO 2 -rich environment to reproduce observations by Duguid et al.21 Jacquemet et al. simulated a diffusion-controlled system, where cement interacted with both H2S and CO2.27 Most work has focused on understanding the compositional evolution of cement without relating to transport and flow properties, such as porosity and permeability, in the long term. As such, their applications to risk assessment of leakage are limited. Experimental studies have shown that the magnitude of cement alteration depends upon various factors, including, for example, temperature, pressure,19,35−37 CO2 concentration, pH, flow and transport conditions (diffusion versus advection controlled),37 and the composition of surrounding rock materials.21 Under the same exposure conditions, cement embedded in carbonate host rock showed no alteration, while those embedded in sandstones demonstrated more significant alteration.20,21 For neat cement without host rocks, alteration depths have been found to be less than 1 mm within a year of exposure to CO2-saturated brine in closed systems under diffusion-controlled conditions. In contrast, in open systems, where the advection process dominates, a few millimeters of alteration depth have been observed within several months.19,36,37 Studies have also found that the initial cement properties, including porosity and portlandite content, are important in determining the extent of alteration during CO2− cement−brine interactions. Cement samples that went through different curing procedures showed varying degrees of alteration under the same CO2 exposure conditions.19 Cement alteration has also been found to change with the amendment of cement with additives,35,38 because different chemical components can lead to different reactions.39

With many variables that can contribute to the extent and time scales of cement alteration, it is critically important to develop models to provide a mechanistic and quantitative understanding on the coupled reactive transport processes and to identify key parameters controlling long-term wellbore integrity. Such models will enable the prediction of long-term property evolution and will facilitate risk assessment calculations associated with geological carbon sequestration. In this context, the objective of this work is 3-fold. One is to develop a reactive transport model that couples reaction thermodynamics and kinetics with transport processes using constraints from experimental observation under diffusion-controlled conditions.19,36 The second objective is to use the model to systematically understand and quantify the role of initial cement properties (in particular, initial porosity and portlandite content) in determining the rates and extent of cement compositional alteration. The third goal is to link the cement compositional alteration to long-term flow and transport properties. Here, we focus on diffusion-controlled conditions because flow velocities are typically very slow under deep subsurface conditions.40

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METHODOLOGY

Cement is a complex material produced by hydrating a mixture of tricalcium silicate (Ca3SiO5), dicalcium silicate (Ca2SiO4), tricalcium aluminate (Ca3Al2O6), tetracalcium aluminoferrite (Ca4Al2Fe2O10), and additives.41 Wellbore cements are usually classified into classes A− H. Among these, classes H and G are the most commonly used. The major components of the hydrated class H cement are calcium− silicate−hydrate (commonly abbreviated as C−S−H in the cement community) and portlandite [Ca(OH)2].41 C−S−H is an amorphous solid phase with varying calcium/silicate ratios. Cement properties are challenging to characterize, primarily because of the sensitivity of the hydration process to the curing conditions, including temperature, pressure, and abundance of amorphous material.19 Different curing processes have been reported to lead to major differences in cement properties and its capacity to withstand the effects of CO2−brine exposure.19 The porosity of class H cement has been reported to vary B


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from 10 to 50%.41 The abundance of portlandite has been reported to vary between 10 and 45% of weight, while the C−S−H component has been reported to vary from 65 to 80%.19,41 In this work, scanning electron microscopy (SEM) images and longterm alteration data from Kutchko et al. were used as constraints in the base case scenario to develop a reactive transport model to characterize the cement−CO2−brine interaction and diffusion processes.19,36 In the experiment, a class H cement core was exposed to CO2-saturated brine for 9 days. The SEM analysis and images revealed three distinct zones: a degraded zone I at the brine−cement interface, a calcite zone II, and an unaltered cement zone III with a subtle portlandite-depleted zone sitting right next to zone II, as will be discussed later. Given the large uncertainty related to the cement property and composition, the developed model was then used to predict the extent of cement property alteration with an array of initial porosity and portlandite values. The porosity values were varied from 10 to 50% with an interval of 5%, while the initial portlandite content values were varied from 5 to 45% with an interval of 5%. A total of 81 cases were simulated in this work. To examine the combined impact of initial portlandite and porosity, we define φ as the ratio of portlandite volume percentage to porosity.

φ=

initial portlandite content (vol %) initial porosity (vol %)

database47 and thermoddem.43 The rate constants k and pH dependency α were obtained by fitting the Kutchko SEM− backscattered electron (BSE) imaging data19 and their long-term cement degradation data.36 The rate constants obtained for the best fit were similar to those reported in the literature.43 The initial specific reactive surface areas for each solid phase were from Marty et al. based on the work by others.43−45 The surface area is updated according to the change in mineral volume fraction and porosity, as will be discussed later. Extended Debye−Huckel equations were used to take into account the salinity effects. Reactive Transport Modeling. The reactive transport code CrunchFlow48 was used to simulate the geochemical reactions and transport process during cement degradation. Reactive transport codes solve mass, energy, and momentum conservation equations. CrunchFlow has been previously used in applications that involve flow, transport, and complicated reaction networks.48−53 In this work, we focus on systems with no advective flow, so that the only transport process is diffusion. Typical reactive transport formulation partitions the chemical species into primary and secondary species, where the primary species define the chemistry of the system and the secondary species are written in terms of the primary species through the equilibrium constant expression of fast, instantaneous reactions.54,55 This reduces the number of equations to equal the number of primary species rather than the number of all involved species. A representative equation for the total concentration of primary species Ca(II) is as follows:

(1)

This parameter is a quantitative measure of the initial volume “density” of portlandite per unit pore volume percentage. Reaction Network and Rate Laws. The reaction network includes mineral dissolution and precipitation as well as aqueous complexation reactions. The former includes the dissolution and precipitation of C−S−H, portlandite, and calcite. In comparison to the aqueous reactions, these reactions occur at much slower rates and are therefore considered kinetically controlled. The aqueous complexation reactions include CO2 dissolution into the brine and the formation of carbonate-containing species. These reactions typically occur within the time frame of milliseconds and, therefore, are considered thermodynamically controlled.42 The dissolution of CO2 lowers the pH and introduces acidity. Here, we simplify the chemistry of the cement into primarily C−S−H and portlandite, because other components in class H cement are minor. C−S−H was assumed to have a common 1.8:1.0 Ca/Si mole ratio. Under low pH conditions, both C−S−H and portlandite dissolve and leach Ca(II), which leads to the formation of calcite, typically known as carbonation. In addition, the dissolution consumes H+ and increases pH. The dissolution rates for C−S−H are typically slower than portlandite by a factor of 2 to as much as 4 orders of magnitude.43−45 As such, in early times, portlandite preferentially leaches Ca(II) and is the major Ca(II) source, while the dissolution of C−S−H catches up in later times.17,29 The dissolution of C−S−H leads to the formation of silica gel (amorphous silica) that is commonly observed in aged cement. Table 1 lists 14 reactions and their thermodynamics and kinetics parameters used in this work. A classical transition-state-theory-based rate law was used to represent the mineral reaction kinetics46

⎛ IAP ⎞⎟ R = Ak(a H+)α ⎜⎜1 − Keq ⎟⎠ ⎝

∂(ϕCCa(II)) ∂t

= ∇(ϕDe,Ca(II)∇CCa(II)) + R Ca(OH)2 + R C−S−H + R CaCO3

(3)

Here, the left side is the mass accumulation rate of Ca(II), and the terms on the right side take into account all processes that lead to the mass change of Ca(II). The first term is for diffusion. The R terms take into account the mass change as a result of various kinetic reactions that involve Ca(II), including reactions of portlandite, C−S−H, and calcite, respectively, as outlined in Table 1. The effective diffusion coefficient in porous media for Ca(II), De,Ca(II), along with the corresponding diffusion coefficients of other species, will be discussed in the next section in Table 2. Similar equations were solved for all

Table 2. Diffusion Coefficients for Chemical Species at 50 °C and 30 MPa57,58 Dw (m2/s)

species +

H Ca2+ OH− Cl− HCO3− CO32‑ CO2(aq) SiO2(aq) Na+ all other species

1.59 1.36 9.01 3.47 2.02 1.63 3.21 1.86 2.27 1.00

× × × × × × × × × ×

10−8 10−9 10−9 10−9 10−9 10−9 10−9 10−9 10−9 10−9

(2)

where R is the rate (mol/s), A is the reactive surface area (m2), k is the rate constant (mol m−2 s−1), aH+ is the activity of H+ (with no units), essentially the product of the activity coefficient and concentration of H+, α is the parameter that characterizes the rate dependency upon aH+, Keq is the equilibrium constant, and IAP is the ion activity product. The term 1 − (IAP/Keq) is an indicator of the degree of saturation with respect to the mineral. When IAP is smaller than Keq, the R term is positive, indicating that the mineral dissolves. In contrast, if IAP is larger than Keq, the mineral is oversaturated and precipitation occurs. The thermodynamic parameters for all reactions were interpolated for a temperature of 50 °C using data from the EQ3/6

other primary species listed in Table 3. The solution gives the temporal and spatial distribution of both aqueous species and solidphase composition. Quantification of Cement Property Evolution at Local and Core Scales. Local-Scale Porosity. During the cement−CO2−brine interaction, porosity evolves as a result of the reactions. The reactive transport model uses mass conservation principles to calculate the loss or gain in mass and volume for each mineral phase through dissolution and precipitation reactions. The porosity at time t in each grid block i, ϕi,t, can then be calculated on the basis of the following equation: C


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consistent with observations and quantification for porosity− permeability evolution induced by chemical reactions.60−64 The typical n values are between 3 and 75, with most values between 9 and 20. The ratio gives the relative change in permeability values of the cement.59 Effective Permeability at the Core Scale. The porosity and permeability values were updated for each grid block at each time step. The effective permeability can be calculated at the core scale for the entire sample by explicitly using the local permeability values. Here, we define two types of effective permeability. One is the “effective parallel permeability” or perme,P. As shown in Figure 1A, diffusion of CO2-

Table 3. Initial Concentrations of Primary Species in Cement Core and CO2-Saturated Brine aqueous species CO2(aq) (mol/L) Ca2+ (mol/L) Cl− (mol/L) Na+ (mol/L) SiO2(aq) (mol/L) pH mineral portlandite (vol %) calcite (vol %) C−S−H (vol %) SiO2(am) (vol %) porosity

brine

cement core

0.50 0.00 0.17 0.17 0.00 2.90

0.00 0.00 0.17 0.95 0.00 13.00

0.0 0.00 0.00 0.00 100.0

13.0 0.00 72.0 0.00 15.0

mtot

ϕi , t = 1 −

∑ ϕj , i , t j=1

(4)

Where ϕi,t is the porosity in the grid block i at time t, mtot is the total number of solid phases, and ϕj,i,t is the volume fraction of each solid phase in grid block i at time t. Average porosity of the whole domain, ϕaverage, can be calculated by arithmetically averaging over all grid blocks in the cement. Local-Scale Surface Area. During the cement−CO2−brine interaction, the reactive surface area was updated at each time step according to the change in overall porosity and mineral volume fraction using the following equation:

Ai , j , t

2/3 ⎛ ϕ ⎞⎛ ϕ ⎞ i ,t ⎜ i ,j,t ⎟ ⎟ ⎜ = Ai , j ,0⎜ ⎟⎜ ⎟ ⎝ ϕi ,0 ⎠⎝ ϕi , j ,0 ⎠

Figure 1. Illustration for the two types of effective permeability. (Left) Conceptual figure showing diffusion of CO2-saturated brine and that the induced reactions can alter cement properties from both the side and the bottom of the cement in a wellbore. (Right) (A) Effective parallel permeability and (B) effective transverse permeability.

(5)

where Ai,j,t and Ai,j,0 are the surface areas of mineral j in grid block i at time t and time 0, respectively, ϕi,t and ϕi,0 are the porosities at grid block i at time t and time 0, respectively, and ϕi,j,t and ϕi,j,0 are the volume fractions of mineral j at time t and time 0, respectively. This equation states that the surface area of individual minerals evolves with porosity and the corresponding mineral volume fraction. Local-Scale Diffusion Coefficient. The values of De evolve as a function of porosity. Effective diffusion coefficients in individual blocks typically follow Archie’s law with the following form:

De, i , t = ϕi , t mDw

saturated brine can occur from both the side and the bottom of the cement plug, leading to zonation and cement property alteration in different directions. If leakage occurs, the fluid flow will be typically from the deep subsurface to the ground surface through a cement core. Dependent upon the relative direction of the diffusion and the main leaking flow, the zonation and altering properties could result in different effective permeability values at the core scale. If diffusion was from the side, as shown in Figure 1A, the altered cement core consists of a series of zones with distinct permeability values in the direction vertical to the flow. The flow can preferentially go through the local high-permeability zones, such as the degraded zone, and bypass zones with low-permeability values, such as those with calcite formation. Therefore, the value of perme,P is controlled by the largest permeability values in the domain. This is what is called “parallel beds” in the literature and can be calculated as follows:65

(6)

where De,i,t is the effective diffusion coefficient in the grid block i at time t (m2/s), Dw is the diffusion coefficient in water (m2/s), and m is the cementation factor. This cementation factor accounts for the tortuosity of porous media and its effect on diffusion.48 Values of Dw at 25 °C were from Li and Gregory56 and were adjusted to the target temperature and pressure in this work using the Stoke−Einstein equation and data from Kestin et al. for viscosity.57,58 A cementation factor of 4.8 was obtained by fitting to the experimental data. This is consistent with the observations by Huet et al. that porosity reduction during cement degradation leads to large changes in diffusivity values.34 Local-Scale Permeability. With the evolution of porosity, the local permeability in individual grid blocks was calculated using a power law form as follows:59

permi , t permi ,0

⎛ ϕ ⎞n i,t ⎟ = ⎜⎜ ⎟ ϕ ⎝ i ,0 ⎠

n

perm e,P, t =

∑i =tot1 permi , t li Ltotal

(8)

where perme,P,t is the core-scale effective parallel permeability at time t, li is the size of the grid block i, ntot is the total number of grid blocks, and Ltotal is the total length of the domain. The “effective transverse permeability” or perme,T, as shown in Figure 1B, was defined assuming that the diffusion and, therefore, the cement−brine contact, is at the bottom of the cement core. Therefore, the leaking fluid flows will be in the same direction as the diffusion. In this case, the cement core consists of a series of zones with distinct permeability values varying in the same direction as the flow. The fluid will need to flow through each zone. As a result, the effective permeability is typically controlled by the lowest permeability value in the domain. The effective transverse permeability at time t can be calculated using the classical formulation of series beds65

(7)

where permi,t is the permeability value in the grid block i at time t, permi,0 is the initial permeability, ϕi,0 is the initial porosity, and n is the exponent. We chose the value of n to be 11 based on a transient test on a cement sample by Ghabezloo et al.59 The large value of n is D


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Figure 2. Laboratory observation and simulation output on day 9 of exposure to CO2-saturated brine at 50 °C and 30.3 MPa, with the cement−brine interface at 0 mm. (A) BSE−SEM image of cement19 and (B−F) predicted spatial profiles of (B) porosity, calcite, and portlandite volume fractions, (C) pH, (D) TIC (left axis) and Ca(II) (right axis), (E) calcite rate, and (F) portlandite rate. For panels E and F, negative values are for dissolution rates and positive values are for precipitation rates, with zero rates meaning at equilibrium with the solid phase. Note that calcite precipitation rates in panel E mirror portlandite dissolution rates in panel F. Note that zone II is the most reactive zone, characterized by simultaneous calcite dissolution and reprecipitation, portlandite dissolution, and sharp gradients in pH, TIC, and Ca(II) values.

perm e,T, t =

Ltotal n

al. reported an initial portlandite content of 16.4 wt %. The porosity of the cement was not reported; therefore, a typical porosity of 15% was used.41 Values of the molar volume and molecular weight were from the EQ3/6 database.47 With an initial porosity of 15%, the initial portlandite content was calculated to be 13 vol %. The remaining 72% solid volume was represented by C−S−H. The brine used in the model was a 1.0% in weight NaCl solution, equivalent to a concentration of 0.17 mol/L. The concentration of the dissolved CO2 was 0.5 mol/L based on a calculation of CO2 solubility under the experimental conditions (50 °C and 30.3 MPa) using equations from Duan et al.66 This concentration leads to a pH value of 2.9 as reported by Kutchko et al.19 A typical initial pH of 13 was used in the cement pore space.67 Initial conditions for brine and cement core are listed in Table 3. The system is closed with no-flux boundary condition. The simulation was conducted in one dimension with an overall length of 10 mm. The domain consists of 1000 grid blocks with a resolution of 10 μm. Therefore, the first 6 mm of the domain was specified as the cement core to be consistent with the experimental setup, and the remaining 4 mm was specified as the CO2-saturated brine.

l

∑i =tot1 permi

i ,t

(9)

where perme,T,t is the core-scale effective transverse permeability at time t. All other symbols are the same as in eq 8. The change in effective permeability compared to its original permeability value perme,0 can be quantified using the following equation: ⎛ perm ⎞ e, t ⎟ log10(β) = log10⎜⎜ ⎟ perm ⎝ e,0 ⎠

(10)

The perme,t and perme,0 are perme (perme,P and perme,T) at an arbitrary time t and initial time 0, respectively. This value quantifies the orders of magnitude change in effective permeability of the entire cement core. For all simulation cases, we quantify changes in effective permeability as a result of the CO2−cement interaction to understand controls on the evolution of flow and transport properties. Alteration Depth. The alteration depth was calculated by adding the length of the zones I, II, and the portlandite depletion zone right next to zone II, as shown in Figure 2. It accounts for the overall length that was altered by the CO2−brine−cement interaction. This is a measure of CO2 penetration depths into the cement. Simulation Domain and Conditions. The class H cement was represented by C−S−H and portlandite, because they typically occupy over 90 wt % of the total cement paste.41 For the base case, Kutchko et

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RESULTS AND DISCUSSION Base Case Simulation for the Development of a Reactive Diffusion Model. The BSE image in Figure 2A shows that, after 9 days of exposure to CO2-saturated brine, three distinct zones formed, including a degraded zone I right E


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Figure 3. (A) Comparison of long-term alteration data (zone I + zone II) from Kutchko et al.36 and modeling prediction. Initial cement porosity is 12%, and portlandite content is 20% in volume. (B−J) Predicted spatial profiles on days 9, 50, 100, and 365 for (B) pH, (C) TIC, (D) calcite, (E) portlandite, (F) C−S−H, (G) porosity, (H) ratio of the local effective diffusion coefficient (De) over its initial value (De0), (I) local permeability over its initial value, and (J) evolution of the permeability ratio log10(β). The solid line is for effective parallel permeability. The dashed line is for the effective transverse permeability.

the unaltered cement with no visual change in structure and composition. To understand and predict the long-term behavior of cement during its interaction with CO2-saturated brine, the simulations were run for 365 days to reproduce the 2008 experiments of Kutchko et al.36 The cement core was different from the one with the imaging data and has an initial cement porosity of 12% and portlandite content of 20% in volume. The spatiotemporal evolution of porosity and the corresponding change in effective diffusion and permeability at days 9, 50, 100, and 365 are shown in Figure 3. Figure 3A shows the long-term evolution of the alteration depth with error bar and the simulation output. Both experimental data and modeling prediction show that the alteration depth increased fast in the first several days, followed by a much lower rate, and eventually reached a plateau. After that, no further penetration was observed. The aqueous geochemistry, including pH and TIC, is shown in panels B and C of Figure 3, with the brine−cement interface at the location 0 mm. These two figures show the advance of the sharp diffusion front of CO2-saturated brine with low pH and high TIC values. The TIC values remain farely constant, except at the very front of calcite dissolution (small peaks at the sharp edge in Figure 3C). The spatial and temporal evolution of solid phases are shown in panels D−F of Figure 3. A comparison of panels B and D of Figure 3 shows that calcite almost always precipitates right at the diffusion front, where portlandite dissolves and pH is high. The calcite zone remains a dynamic moving front. The diffusion of the acidic brine leads to low pH values and dissolves previously precipitated calcite. At the same time, a bit further in the cement core, acidic brine leads to the dissolution of portlandite, which increases the pH and results in calcite precipitation. The diffusive reactive front continues to move inward, with the calcite zone becoming narrower and denser with an increasingly higher volume fraction in progressively localized zones, as shown in Figure 3D. The degraded zone I at the left of the diffusion front expands over time with continued dissolution of portlandite and C−S− H. Portlandite dissolution is more significant in early times and

at the brine−cement interface, a calcite zone II, and an unaltered cement zone III with a subtle portlandite depletion next to zone II. The simulation results reproduced the observed zonation and quantified the amount of compositional changes in these zones, as shown in panels B−F of Figure 2. On day 9, zone I has been degraded significantly, with portlandite completely depleted almost half way into zone II. The porosity values increased from the initial 15% to as high as 35% at the brine−cement interface. Portlandite depletion occurred because of the closeness to the interface and the low pH maintained by CO2-saturated brine. The pH in Figure 2C shows that the acidic brine has diffused into the interface of zones II and III, where portlandite dissolves (Figure 2F), which leads to a pH increase. Calcite precipitated in almost exactly the same location because of the relatively high local pH values, as shown in Figure 2E by the positive calcite rates, leading to the decrease in total inorganic carbon (TIC) and Ca(II) (Figure 2D). The aqueous geochemistry, including pH and the Ca(II) concentration, does change slightly in the CO2-saturated brine as a result of the concentration gradient and the diffusion process. However, this is hardly visible in the panels because of the large range of pH and Ca(II) values represented in the y axis. The TIC values remain relatively constant in brine because the brine is in equilibrium with the CO2 gas phase in the head space, which continues to replenish CO2 consumed by the calcite precipitation. Previously precipitated calcite also dissolves between zones I and II, as shown in Figure 2E by the negative rates. The spatial profile of the calcite precipitation rate mirrors portlandite dissolution rates with exactly the same shape and comparable magnitude in each specific location, indicting the tight coupling between the two reactions. In zone II, calcite volume percentage reaches as high as 15%. The magnitude of the calcite increase is larger than that of the portlandite decrease, which leads to an overall porosity decrease of approximately 2% in zone II. Portlandite dissolution at the interface of zones II and III led to a small porosity increase over the original value. This corresponds to a subtle portlandite decrease zone reported by Kutchko et al.19 Zone III represents F


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Figure 4. Sensitivity analysis for (A and B) cementation factor, (C and D) calcite equilibrium constant, and (E and F) calcite rate constant. The panels are spatial profiles of pH and calcite volume fraction on day 9. The comparison indicates that the cementation factor is the most important parameter and the driving force of the system dynamics is the diffusion process.

parallel permeability, calculated over the whole cement core, increased by 8 orders of magnitude in this time period, as shown in Figure 3J. The rate of increase is faster early on and slower at later times, which resonates the temporal patterns of alteration depth. Notice that, although the acid cannot penetrate further into the inner cement core after about 100 days, the continued dissolution of C−S−H in zone I leads to the continued increase in effective parallel permeability. The effective transverse permeability decreased by 10 orders of magnitude. This is because perme,T is controlled by the calcite zone with lowest permeability values. Sensitivity to Parameters. To understand the critical parameters that control the dynamics of the cement−CO2 system, sensitivity analysis was performed for the kinetic parameters (rate constants and pH dependence) of portlandite, C−S−H, and calcite, as well as the cementation factor. Equilibrium constants of the three solid phases were also varied to quantify the sensitivity of the system to the thermodynamic limits. Figure 4 shows the spatial profile of pH and calcite volume fraction on day 9 with different values of cementation factor, equilibrium constant, and rate constant of calcite. The system is not very sensitive to the portlandite and C−S−H parameters, indicating that portlandite dissolution is not limiting.

is depleted quickly in the degraded zone. Over time, C−S−H also dissolves and contributes significantly to the porosity increase in zone I. On day 365, the degraded zone I is essentially C−S−H-free. The porosity of the degraded zone I does not reach 100% because amorphous silica is generated as a reaction product of C−S−H dissolution, which eventually becomes the only solid phase in the degraded zone I. Calcite precipitates right after the diffusion front and dissolves as the acidic brine diffuses into the inner cement core. The dissolved volume of C−S−H and portlandite is larger than the precipitated volume of calcite at the front, generating a high porosity zone right after the calcite zone, which is consistent with observations in several experiments.17,19 Correspondingly, the local diffusion coefficient and permeability evolve over time, following patterns similar to porosity. Panels H and I of Figure 3 show that the local diffusion coefficients increase by orders of magnitude in the degraded zone after 100 days. In the calcite zone, the diffusion coefficient decreases to essentially zero after about 100 days because of pore clogging. This eventually prevents the acid from diffusing into the inner cement zone and, therefore, further cement degradation. Similarly, local permeability values increase by 10 orders of magnitude in zone I, while they decrease by more than 10 orders of magnitude in the calcite zone, indicating a significant change in local transport properties. The effective G


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Figure 5. Model prediction of spatial profiles for two cases on days 9, 50, 100, and 200. Case 1 has an initial portlandite content of 30% volume and an initial porosity of 10% (top, φ = 3.00). Case 2 has an initial portlandite volume fraction of 5% and an initial porosity of 20% (bottom, φ = 0.25). (A−E) For case 1, spatial profiles of pH, portlandite, calcite, C−S−H, and porosity, respectively, and (F−J) for case 2, corresponding spatial profiles of pH, portlandite, calcite, C−S−H, and porosity, respectively. Case I shows localized sharp diffusion fronts, which lead to significant pore clogging and severe degradation in zone I. Case II shows shallow and wide fronts with less severe pore clogging and degradation than in zone I.

portlandite and C−S−H depletion front move into the cement core. Similar to the base case observations, the change is much faster in early times than in later times. However, the two cases show very different dynamics. In case 1, the calcite zone is much narrower and the porosity decreases from the original 10% to almost zero. The zonation progressed inward by approximately 1.8 mm in 200 days. In contrast, in case 2, much wider and shallower calcite zones formed, which is compensated by the dissolution of both portlandite and C− S−H. As a result, porosity did not decrease much. Within 200 days, the diffusion front advances more than 4.0 mm. The dissolution of both portlandite and C−S−H leads to a significant increase in cement porosity in the degraded zone. The observed pattern can be explained by the relative rates of reactions, calcite dissolution and precipitation, and diffusion. Portlandite dissolves faster than C−S−H and is the major Ca source in early times. In case 1, a higher portlandite content leaches more Ca at higher rates, which leads to a much more pronounced decrease in portlandite content in the degraded zone in early times, as shown in Figure 5A. The combination of more leached Ca(II) and smaller available pore space with smaller porosity in turn results in faster calcite precipitation, more localized calcite, and more pronounced relative porosity reduction. This eventually results in a “sharp” reactive diffusion front that prevents acidic brine from further diffusion into the cement core. With the formation of the sharp barrier, the acidic brine leads to continued dissolution of C−S−H in zone I over time without moving inward, therefore resulting in close to 90% porosity in the degraded zone on day 200. The remaining 10% is the produced silica gel (amorphous silica). In case 2, however, the opposite occurs. A lower portlandite content with a larger porosity means a smaller amount of dissolved Ca(II) in a larger pore space, which leads to less calcite precipitation in a wider and shallower calcite zone and, therefore, a “wide” front, as shown in panels F−J of Figure 5. Without porosity reduction, acidic brine continues to diffuse inward and the degraded zone I expands over time. However, the extent of

Of all of the parameters used in this work, the cementation factor is the single most important parameter that determines the system behavior. With other conditions being the same, a larger cementation factor means a smaller diffusion coefficient and, therefore, smaller diffusion rates. In this work, it means smaller advance rates of acidic brine, as indicated by the pH profile in Figure 4A. This also leads to a calcite zone at the diffusion front that is closer to the cement−brine interface. In addition, a larger cementation factor also result in a sharper diffusion front and, therefore, narrower calcite zone, as shown in Figure 4B. In comparison to the cementation factor, the effects of rate parameters of calcite are much smaller. Larger equilibrium constants of calcite imply high solubility and more Ca(II) in the brine, which leads to a smaller calcite zone (Figure 4D). This also leads to a slightly faster diffusion front because the “blocking” effect of the calcite zone is smaller with a thinner calcite zone (Figure 4C). With smaller Keq values, the opposite occurs. The rate constant of calcite dissolution and precipitation also has a relatively small effect compared to the cementation factor. The sensitivity analysis shows that the driving force of the system dynamics is the diffusion process, the rate of which is controlled by the reaction-induced porosity evolution and cementation factor. Comparison of Two Contrasting Cases. This subsection aims to understand the role of initial porosity and portlandite content in determining the alteration depth, the characteristics of the calcite zone, and the evolving cement properties. Here, we show the predicted porosity and calcite profiles of two contrasting examples on days 9, 50, 100, and 200 in Figure 5. The top panels are for a portlandite-rich case 1 with an initial portlandite volume fraction of 30% and an initial porosity of 10% (φ = 3.00), while the bottom panels are for case 2 with an initial 5% portlandite and 20% porosity (φ = 0.25). The simulations were carried out using the parameters obtained in the base case simulation. The model predicts the formation of zones in both cases, as previously described. Over time, the calcite-rich zone and the H


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portlandite content, the alteration depth is not sensitive to either initial portlandite content or porosity. This is because sharp and narrow calcite zones form with high portlandite content, which clogs pores and prevents further cement alteration, as shown in case 1 in Figure 5. This is consistent with a previous observation that high portlandite content reduces the alteration depth, while low portlandite content and high porosity lead to high alteration depth. The alteration depth on day 200 for all 81 cases is shown in Figure 7B. In general, the alteration depth reaches a maximum in the top left corner with the largest porosity and smallest portlandite abundance, where the shallow and wide calcite zone dominates, as shown in case 2 of Figure 5. The opposite occurs when the initial portlandite is abundant and larger than 25%. Figure 7C shows the alteration depth as a function of φ for all 81 cases. This panel further confirms the observation from panels A and B of Figure 7. For φ < 0.5, the alteration depth is much more pronounced and with a much larger range varying from 1.0 mm to more than 6 mm. The largest alteration depth occurs for the lowest φ value. For φ values larger than 1.0, the alteration depth is typically smaller than 2 mm after 200 days of exposure, except for a couple of extreme cases. To understand how the local-scale reaction-induced alteration affects core-scale flow properties, panels A and B of Figure 8 show log10(βP), the relative change of perme,P, as a function of the initial portlandite content and porosity (Figure 8A) and relative change in porosity (Figure 8B). The perme,P values in all cases increase by 2−10 orders of magnitude. The largest increase occurs in the bottom right corner of Figure 8A for cases with the highest φ values and the largest increase in relative porosity (Figure 8B). The portlandite-rich cement generates local sharp calcite zones that prevent CO2 diffusion into the cement core. This limits the continued degradation only in zone I close to the cement−brine interface, which generates a preferential path with orders of magnitude increase in permeability. The change in perme,T and dependence are shown for all 81 cases in panels C and D of Figure 8. In general, there is almost a diagonal division between cases with no change (dark color in left bottom half) and with a significant decrease (light color in top right half), essentially indicating the division between no clogging with low-portlandite and high-porosity conditions and clogging under high-portlandite and low-porosity conditions. The correlation between the extent of alteration in effective transverse permeability and the relative porosity change shows

degradation in zone I is less severe in this case. On day 200, the porosity in zone I increases to 75% in case II compared to 90% in case I. The difference in the two cases leads to the difference in the evolution of the effective permeability, as shown in Figure 6.

Figure 6. Evolution of the effective permeability for case 1 with an initial porosity of 10% and an initial portlandite content of 30% in volume (φ = 3.0) and for case 2 with an initial porosity of 20% and an initial portlandite content of 5% in volume (φ = 0.25). (A) Evolution of log10(βP) for effective parallel permeability and (B) evolution of log10(βT) for effective transverse permeability.

Case 1 has about 9 orders of magnitude increase in perme,P over a period of 200 days with 1.8 mm alteration depth. Case 2, however, has about 5 orders of magnitude increase, albeit with an approximately 4.0 mm alteration depth. This is because the degradation in zone I is much more severe in case 1 than that in case 2, and the highest local permeability value dominates perme,P. In contrast, perme,T is controlled by the lowest local permeability values. Because the porosity in the calcite zone decreases significantly in case 1, perme,T, decreases by about 6 orders of magnitude within 200 days. In case 2, however, perme,T remains fairly constant, because there is not much decrease in porosity in the calcite zone. Effects of Initial Porosity and Portlandite Content. Figure 7A presents the alteration depth on day 200 as a function of the initial portlandite content for three porosity values, 20, 30, and 40%. It shows that, in general, when the initial portlandite content is less than 25%, alteration depth is much larger and is much more sensitive to initial porosity values. With 10% initial portlandite content, the alteration depth reaches close to 6 mm with 40% initial porosity compared to 2.4 mm with 20% initial porosity. Above 25%

Figure 7. Predicted alteration depth after 200 days of exposure to CO2-saturated brine in all 81 cases. (A) Alteration depth as a function of the initial portlandite content for three initial porosity values (20, 30, and 40%). (B) Alteration depth as a function of the initial portlandite content and porosity. (C) Alteration depth as a function of φ. I


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Figure 8. Relative change in effective permeability perme,P (top) and perme,T (bottom) on day 200 as a function of (A and C) initial portlandite content and porosity and (B and D) relative porosity change, defined as the difference between averaged porosity on day 200 and initial time (ϕaverage − ϕinitial), normalized by the initial porosity value (ϕinitial).

Portlandite-rich cement with large φ values (larger than 1) lead to localized, narrow, and dense calcite zones that represent “sharp” reactive diffusion fronts, which eventually prevent further diffusion of acidic brine and result in penetration depths limited to less than 1 mm after 200 days. However, this also results in the continued, localized long-term dissolution of C− S−H close to the cement−brine interface. This generates a preferential flow path and orders of magnitude increase in effective permeability.69 In contrast, portlandite-poor, highporosity cement with small φ values results in a shallow calcite zone represented by a “wide” front without a significant porosity reduction. This eventually leads to larger alteration depths. However, in comparison to portlandite-rich cement, portlandite-poor cement experiences a much less severe degradation close to the cement−brine interface and less increase in effective parallel permeability. This has interesting applications in abandoned wells that have gone through tens of years of Ca leaching, which often results in low portlandite content.9 If no other reactions occur to prevent continued CO2 diffusion, these cases may lead to deep CO2 penetration into the cement core. This work also relates compositional changes in cement to their effective flow properties. Dependent upon the relative direction of the diffusion processes that alter the cement properties, the effective permeability can either increase (parallel permeability) or decrease (transverse permeability). From the point of view of risk assessment, the parallel permeability represents the worst case scenario, in which CO2− cement interactions generate preferential flow paths. In contrast, transverse permeability represents the best case scenario, in which reactions lead to “self-sealing” behavior, also addressed in the literature.23,25,38 In general, portlanditerich, low-porosity cement leads to a significant increase in

two extremes. One is the close to zero log10(βT) values in Figure 8D, indicating no change in effective transverse permeability with large relative porosity change (larger than 1). The other extreme is the log10(βT) values ranging from −10 to −40, indicating tens of order of magnitude decrease in perme,T, essentially clogging, over relatively low-porosity values (smaller than 1). The transition between the two extremes occurs around the relative porosity values of 1, which corresponds to the diagonal line in Figure 8C. Essentially, this means that, with portlandite-rich cement and low-porosity value, the formation of a dense calcite zone leads to clogging.

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CONCLUSION Although various reactive transport models have been developed before,24,27,29,68 the developed model in this work allows for a powerful and detailed understanding on dominating processes and parameters during the CO2−cement interactions under diffusion-controlled conditions, the dynamic evolution of cement compositional and transport properties, and the tight linkage between local-scale reaction-induced changes and core-scale transport properties. The developed model allows for the quantitative visualization of the dynamic reactive diffusion front represented by the calcite zone, the characteristics of which determine the long-term evolution of cement flow and transport properties. In addition, this study analyzes the critical compositional variables that can control the long-term dynamics of cement alteration. The insights gained here will provide valuable input for risk assessment of geological carbon sequestration. This work reveals the importance of the relative abundance of portlandite abundance over initial porosity, defined here as φ, in determining the alteration length and cement properties. J


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ACKNOWLEDGMENTS This project was funded by the National Energy Technology Laboratory (NETL), U.S. Department of Energy, an agency of the United States Government, through a support contract through Project RES1000026 with URS Energy and Construction, Inc.

effective parallel permeability and a significant decrease in effective transverse permeability. The magnitude of these values highly depends upon the relationship between porosity and permeability. Although we carefully choose the relationship between porosity and permeability in this study, such relations are highly process-dependent, are closely related the microscopic details of carbonation reactions, and are distinct from one system to another, as shown for porosity and permeability alteration of other materials.70−73 As such, caution should be taken in using the absolute values of log10(β) calculated from this work. In this work, we chose to focus on diffusion-controlled conditions. If advective flow does occur, the system might experience a much deeper alteration of the cement, as shown in some studies.37 We chose to examine the relatively simple, class H cement that contains primarily C−S−H and portlandite among the various types of cements that have been used for different purposes.41 It is important to study other variables that determine the extent of cement alteration. However, even with the relatively simple chemical representation of the cement, our model provides valuable insights that help explain experimental and field observations. For example, cements with fly ash additives are common in the oil industry and are characterized by low portlandite content and high porosity values. Both experimental and field observations show striking difference in alteration depth between neat and fly-ash-bearing cement.35,74 Kutchko et al. showed that cement with fly ash has a much larger penetration depth, however, a much less severe degradation, as compared to that of the neat class H cement under the same exposure conditions.35 Characterization of portlandite−fly ash cement samples from a 30 years old well indicated a carbonation process and an increase in porosity and permeability.74 The extent of degradation is relatively small, and the cement remains to be an effective barrier. These experimental and field observations are consistent with our conclusions that, for cement with low portlandite and high porosity, alteration depth is much larger; however, the severity of the degradation is much less significant. This indicates that the developed model can be a powerful tool for providing a mechanistic understanding, quantification, and prediction of long-term cement properties in the context of risk assessment.

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Disclaimer: Neither the United States Government nor any agency thereof, nor any of their employees, nor URS Energy and Construction, Inc., 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 any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. The authors declare no competing financial interest. K


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