*4.1. Injection of the CO2-Reactive Solution with Di*ff*erent Injection Pressures*

The 1 <sup>×</sup> <sup>10</sup>−<sup>12</sup> m2 permeability scenario is selected to model initial leakage and subsequent leakage remediation. Upward CO2 leakage through the microannulus was simulated for half a year before leakage remediation was applied. To remediate leakage, a CO2-reactive solution (composition given in Table 4) was injected into the CO2 containing microannulus. The solution is injected at a depth of 3048 m, which is 8 m below the top of the caprock. The CO2-reactive, lime-saturated solution is injected in order to react with dissolved CO2 to form calcite (CaO + CO2- > CaCO3). To inject the CO2-reactive solution in the model, we used a fixed pressure cell adjacent to the microannulus to allow for pressure-controlled injection, instead of defining a fixed injection rate. The sensitivity of leakage remediation to flow rates was asessed by variying the pressure of injection with 1, 5 and 10 bar overpressure for the microannulus pressure of 324 bar.

For all three injection pressures, the injection of the CO2-reactive solution leads to an initial increase followed by an interruption of the upward CO2 flow in the microannulus, but flow recovers (after *t* = 0 in Figure 5, showing the results of 5 bar overpressure injection). Calcite starts to precipitate in the microannulus at the level where the CO2-reactive solution is injected. Gradually the permeability of the microannulus reduces with a corresponding decrease of the CO2 and water flow rate (Figure 5). The rate of solution injection reduces as well, since the permeability decreases and the pressure is fixed. Figure 6a shows the initial higher injection rate with a higher overpressure and the decrease of injection rate with time. The moment of complete flow impairment occurs at the time when the microannulus adjacent to the injection cell is nearly filled with calcite, reducing the permeability to zero (Figure 5). All overpressures yield complete calcite clogging (Figure 6b), but with differences in the development of calcite precipitation due to the differences in the balance of calcium and CO2 supply. Within 10 days, all injection pressure scenarios predict clogging the microannulus with calcite precipitation, preventing further leakage of the CO2.

**Figure 5.** The development of CO2 and water flow rate (left axis, logaritmic) and the permeability (right axis, logaritmic) in the microannulus at the level of injection of the CO2-reactive solution. Results are from the 5 bar overpressure scenario. Data is plotted with time for the period around leakage remediation.

**Figure 6.** (**a**) The injection rate of the reactive solution for the three different injection pressures at the onset of the remediation procedure. (**b**) The evolution of calcite precipitation showing full clogging for all scenarios within the 10 days of leakage remediation.

#### *4.2. Sensitivity to Porosity-Permeability Relation Input Parameters*

The clogging process and specfically the calculation of the permeability based on the porosity development depends on highly uncertain porosity-permeability parameters [30]. A sensitivity study is performed reflecting the range in values for the critical porosity (ϕc) and power law (*n*) component as probed by Verma and Pruess [31] (1 ≤ *n* ≤ 6, 0.8ϕ ≤ ϕ<sup>c</sup> ≤ 0.9ϕ) and Xu et al. [35] (4 ≤ *n* ≤ 13, 0.88ϕ ≤ ϕ<sup>c</sup> ≤ 0.94ϕ). The initial leakage and subsequent remediation simulations (with a 1 <sup>×</sup> <sup>10</sup>−<sup>12</sup> <sup>m</sup><sup>2</sup> permeability) were repeated for six combinations of 2 critical porosity values of 0.8 and 0.88 (80 and 88% reduction of the original porosity) with three different power law components of 2, 6 and 10.

The calcite plug formed using the different porosity-permeability relation input parameters is very similar (Figure 7). A peak of calcite precipitation is observed next to the cell from which the reactive solution is injected. Above this interval, the microannulus is only partially clogged due to calcite precipitation. The relative insensitivity of the characteristics of the calcite plug to the porosity-permeability relationship can be explained by the nature of the remediation process. The process is designed to inject the reactive solution up to full clogging, meaning that with all parameters a full permeability reduction will be simulated. There is a small difference in the calcite formed in the upper part of the plug, with the 0.88ϕc–2*n* model yielding the most precipitation and a combinitation of 0.8ϕ<sup>c</sup> and 10*n* the least. The used porosity-permeability parameters do have a large impact on the predicted time that is required to achieve full clogging. The time it takes to perform the remediation method ranges from 7 to 113 days (Table 5). This indicates the importance of the porosity-permeability parameters for the prediction of the duration of the remediation procedure and for the asessment of the related costs and overall feasibility.

**Figure 7.** The calcite content fora1m section of the microannulus after leakage remediation, showing a peak adjacent to the level of reactive solution injection. The results are shown for six scenarios of different porosity-permeability relation input parameters.

**Table 5.** The predicted time of remediation up to full clogging of the microannulus.


#### *4.3. Stability of the Plug in Time*

After the remediation procedure, the reactive transport simulation is continued for 1 year to assess the stability of the calcite plug with time. This allows for equilibration of the system and continuation of diffusion and possibly flow. To assess the stability of the plug and the chemical evolution within the microannulus, two porosity-permeability scenarios were selected representing the most (0.88ϕ<sup>c</sup> – 2*n*) and least calcite precipitation (0.80ϕ<sup>c</sup> – 10*n*).

Throughout the microannulus, the pH remains around 4.6 in the post-remediation phase, indicating the wellbore environment is still acidic and is not buffered by the cement within the year after leakage remediation that was simulated. The caprock minerals show no significant reactions in this time period. The main observed process is the increase in calcite volume fraction throughout the microannulus (Figure 8a), the thin original plug is plotted for comparison. After the remediation method stops CO2 leakage, the process of natural sealing becomes dominant throughout the micoannulus adjacent to caprock due to the absence of flow. This results in clogging by mainly calcite precipitation and minor amorphous silica precipitation. After one year of reactions following the remediation procedure, the 0.80ϕc–10*n* scenario yields full clogging of the microannulus (Figure 8a,b). The 0.88ϕc–2*n* scenario does have two sections of partial clogging, but full clogging of the rest of the microannulus (Figure 8b). The partial clogging above the original plug is due to absence of CO2 which has been completely consumed, yielding a zero gas saturation (Figure 8c). The gas saturation is highest just below the plug and just above the CO2 reservoir. The zero permeability of the plug continues to block the CO2 flow and causes the gas saturation above the clogged level to decrease with time as CO2 migrates and is consumed by reactions. The permeability impairment forms a pressure block, with the microannulus below the plug approaching the CO2 reservoir pressure and the microannulus above the plug retaining hydrostatic pressure.

The two porosity-permeability scenarios both yield sigificant natural sealing after clogging by injection of the remediation fluid. This indicates that reduction of leakage due to the remediation procedure enhances the natural capability of the wellbore system to seal and form a barrier against future leakage.

**Figure 8.** The development of the microannulus within 1 year after remediation. Results are shown for (**a**) calcite around the original plug, (**b**) permeability of the microannulus, and (**c**) gas saturation of the microannulus adjacent to the caprock.

#### **5. Discussion and Conclusions**

Despite the function of annular cement as a seal preventing oil, natural gas or stored CO2 to migrate to aquifers or to the surface, wells are known to leak due to microannuli formed by processes such as cement shrinkage or pressure and temperature fluctuations [2,5]. The width of a microannulus formed tends to increase for larger temperature differences between the produced or injected fluid and the rock formation, which is especially relevant for cold CO2 injection [36]. The higher risk of microannulus formation during CO2 injection combined with high abandonment pressures asks for an assessment of CO2 microannulus leakage and methods for leakage remediation. Due to the high reactivity of cement with carbonated brine, the chemical processes are key. A field-scale wellbore model was developed which successfully incorporates CO2 migration by two-phase flow through a microannulus and diffusion of dissolved CO2 into the adjacent caprock and cement. This enables the simulation of the complex reactive transport processes of a storage system, including a storage reservoir, wellbore cement with a continuous microannulus from reservoir to caprock, and caprock overburden. Despite the large scale of the model, it was successful in predicting the well-known small-scale reaction characteristics as found in experimental and (small scale) modelling studies [6,8–12].

Previous simulations showed an initial critical CO2 leakage velocity of 0.1 <sup>×</sup> <sup>10</sup>−<sup>5</sup> <sup>m</sup>/s below which calcium released from dissolving cement minerals can diffuse towards the microannulus where calcite forms which clogs the microannulus and prevents further flow [18]. For our models, a low enough leakage rate to facilitate natural sealing was achieved with an initial microannulus permeability of 1 <sup>×</sup> 10−<sup>13</sup> m2. The possibility for natural microannulus clogging at low leakage rates is similar to the self-sealing potential of fractures in cement as demonstrated by e.g., Huerta et al. [16]. They discussed the critical residence time for the CO2 fluid to be present in a cement sample for a fracture to close. However, natural sealing is not solely dependent on the flow rate as determined by the systems permeability. Nonuniformity of the microannulus geometry can lead to local changes in flow velocity affecting the sealing process [19]. The specific chemistry of the cement and rock formations has a large impact, with, for example, a high potential for calcite forming in the microannulus when the host rock is a carbonate [17]. Previous modelling showed anhydrite clogging of the microannulus related to relatively high sulphate concentration in the formation water of the caprock [18], whereas the chemical characteristics of the cement and surrounding formation water in our model led to dominant calcite clogging. The thermodynamics and kinetics of the cement phases still pose uncertainty in the chemical processes in the microannulus [17]. Our kinetic parameters for CSH and silica may be considered conservative, yielding only minor amorphous silica in the microannulus. In addition, the uncertainty and variability in the reactive surface area of cement phases may further affect the predicted leaching of cement and natural sealing process. A dedicated uncertainty assessment with varying parameters for dissolution/precipitation kinetics and mineral reactive surface areas was out of the scope of this study but would be needed to assess the sensitivity to natural sealing of the microannulus.

For high leakage rates when natural sealing is not predicted to occur, the process of microannulus clogging can be induced by adding calcium to the system [22–24]. We injected a calcium-rich brine to react with the dissolved CO2 in the microannulus, yielding a full permeability decrease due to calcite precipitation, as graphically represented in Figure 9. There are large uncertainties in the clogging process regarding the porosity-permeability relation of mineral precipitation in a microannulus. As discussed by Ito et al. [23] and Druhan et al. [24], the porosity-permeability relation is of utmost importance for predicting effective leakage remediation. However, compared to our previous numerical modelling study [22] in which we injected the CO2-reactive solution in an aquifer above a caprock leak, leakage remediation in the microannulus was predicted to be more successful and far less sensitive to the porosity-permeability relation. This is due to the confined nature of a microannulus and the more difficult placement of a plug above a caprock leak path. In our study, the uncertainty of the porosity-permeability relation was primarily expressed in the time it takes for remediation and not in the success of remediation. A longer remediation time is related to the larger amount of mineral precipitation and porosity reduction that is required to achieve full permeability reduction when using a more conservative porosity-permeability relationship. Hence, accurate design of the remediation procedure requires additional data on the porosity-permeability behaviour of a microannulus. The previous study [22], indicated the significance of the leakage rate on the success of leakage remediation. The design of the remediation procedure would require knowledge on the actual leakage rate or a numerical sensitivity study on the possible range in initial microannulus permeability and resulting

leakage rate. With a higher initial leakage rate, injection of the reactive solution might require a higher injection pressure.

Permanent leakage remediation, considering long-term CO2 storage, requires a chemically stable plug in the leak path. Our model results indicate that the formed calcite plug does not only remain stable, but that cessation of flow enables natural sealing in the microannulus at the level below the plug. The increase in sealing of the microannulus enhances the potential for intentional clogging as a remediation method. Future work could focus on the sensitivity of the intentional and subsequent natural clogging process to the chemistry of the CO2 reactive solution and the cement and formation rock chemistry. The chemical nature of the plug is of less importance when subsequent natural sealing can take over the barrier function, even if a placed plug would degrade in time.

**Figure 9.** Graphical representation of the CO2 leakage and CO2-reactive remediation.

**Author Contributions:** Conceptualization, L.W. and M.K.; methodology, L.W. and M.K.; software, L.W. and M.K.; validation, L.W.; formal analysis, L.W.; investigation, L.W.; resources, L.W.; data curation, L.W.; writing—original draft preparation, L.W.; writing—review and editing, L.W. and M.K.; visualization, L.W.; supervision, L.W.; project administration, L.W.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
