New experimental techniques, including time-lapse photography, micro-indentation, and nuclear magnetic resonance (NMR), have provided improved measurements both of the kinetics of corrosion of cement and resulting changes in mechanical and transport properties. The results are being used to verify numerical models and to test the effects of reservoir conditions (e.g., pH, CO2 concentration) on the rate of corrosion.

 

Measurement of corrosion kinetics

Graduate student Ed Matteo has used time-lapse photography to measure the rate of corrosion of cement by acidic brine with greatly enhanced precision (Figure 8).

Figure 8. Plot of corrosion depth vs. square‐root of time for flow‐through experiments ranging from pH = 0 to pH =3.7 and for both the 1 bar CO2 case and for the “No CO2” case (acid in equilibrium with the atmospheric level of CO2).

The results show several new features: (1) at a given pH, the rate of attack is faster when CO2 is dissolved in the water (as predicted by modelling work described below); (2) the corroded layers contract (that is, the residual silica gel occupies less volume than the cement from which it formed), which will enhance the leakage rate; (3) the accumulation of debris from the corrosion reactions retards the attack.

The kinetics of attack in these experiments are clearly diffusion-controlled, as the depth of the corroded layer increases strictly in proportion to the square root of time. By performing these studies over a range of temperature, T, and pH, it has been possible to establish a predictive relationship for the rate of advance of the corrosion front, S :

As shown in Figure 9, this expression accurately predicts the corrosion rates found in a set of studies from the literature as well as the group’s own measurements. These results will permit extrapolation to less aggressive conditions, which are more typical of field conditions, but where the rate of attack is too slow for laboratory study.

Figure 9. Rate of advance of corrosion front (“Slope”) versus pH calculated from eq. (1) agrees within a factor of 2 with other data from the literature.

Accumulation of debris from the reaction reduces the attack rate by about a factor of 3, as shown in Figure 10a. Nevertheless, the relationship between the amount of calcium extracted and the depth of the attack is unchanged, as indicated in Figure 10b. Thus, there is no indication of a change in the phases that dissolve or precipitate; the debris simply constitutes a physical barrier to diffusion that retards the corrosion. Thus the rate of leakage may be strongly influenced by factors, such as the angle of the well and the rate of flow, that affect the removal of debris.

A simple analytical model for flow of carbonated brine in an annular gap around the cement in an abandoned well shows that the acid would be quickly consumed as it rises through the gap. For example, if the width of the gap is 10 microns, then it would take centuries for the corrosion to extend upward by a meter. Therefore, there should be little risk of small leaks expanding into serious ones as a result of corrosion by acidified brine. There might be a greater risk of damage by two-phase flow (brine + CO2) in the annulus, but that situation must be analyzed using dynaflow.

Figure 10. (a) Amount of calcium extracted from cement paste as a function of time for samples held upright (so that debris accumulates) or inverted (so that debris falls away from surface); (b) correlation of calcium extracted with depth of corrosion.

Analysis of the pore structure by nitrogen sorption and electron microscopy indicate that the silica gel produced by the corrosion of the cement paste is not significantly influenced by the pH of the solution. Therefore, properties measured on gels created under the relatively aggressive conditions of these lab experiments can be assumed to represent the corrosion layers that would be formed under field conditions.

Diffusivity of water within the pores of the corrosion layer is being measured by NMR, in collaboration with Dr. Leo Pel at the Technical University in Eindhoven. Preliminary results yield values that agree well with the diffusivity found by fitting corrosion data to model results. More precise measurements are now underway.

 

Indentation experiments

Apparatus, shown in Figure 11, has been constructed that permits indentation measurements on cement paste before and after corrosion to determine the change in modulus, hardness, and permeability. Using the spherical tip, the permeability of a synthetic silica gel was found to agree very well with values obtained independently; measurements on corroded pastes are underway.

Figure 11. Photo of micro‐indentation instrument (left) with accompanying schematic describing individual components (right).

Young’s modulus has been measured using this system by indenting the cement surface with a 1.5 mm diameter spherical indenter. A load cell measures the force, while displacement is measured with a linear variable differential transformer (LVDT). The loading is imposed by a stepper motor that can be programmed to move the indenter tip at a constant speed, on the order of microns per second. Figure 12 shows a plot of load versus displacement for a typical indentation experiment, which can be used to calculate Young’s modulus, E, via a method widely employed in the literature.

Figure 12. Load vs. displacement data from a typical indentation experiment

Values of E in the range of 20 GPa have been measured for Class H cement samples. The current experimental plan includes characterizing the samples corroded under various boundary conditions by measuring Young’s modulus and hardness as a function of depth through the degradation zone.

 

Reactive transport modeling

In collaboration with Bruno Huet (now at Schlumberger), the group has published an analysis of the kinetics of corrosion of cement paste by a carbonated brine, using a reactive transport module within dynaflow (see “Simulation of CO2 injection” below). The transport and geochemical modules are coupled in a sequential iterative approach to model: (1) mineral dissolution/ precipitation, (2) aqueous phase speciation, and (3) porosity-dependent transport properties. Simulation results reproduce qualitatively the dissolution of cement hydrates (calcium hydroxide, calcium-silicate-hydrate, and sulfate phases) and intermediate products (CaCO3) that have been observed experimentally.

Originally, to obtain agreement between simulations and observations, it was necessary to adjust the diffusivity arbitrarily. This issue is being addressed experimentally by using NMR to measure the diffusivity directly on corroded paste; preliminary data indicate that the value obtained previously by fitting is close to the true value. Experiments were designed in collaboration with Bruno to evaluate how the boundary conditions (pH, and concentrations of CO2 and Ca2+ ions) control cement reactivity. The results are consistent with the predictions of the model, indicating that the model can be trusted to simulate corrosion during leakage.