The BCSR model system has been solved numerically to develop MIC prediction software. MICORP version 1 with windows graphic user interface is the most basic version. A free version (with restrictions on the number of user adjustable parameters) is available from the speaker for evaluation upon request.  Version 2 is currently under development. It considers effects such as temperature, contribution to corrosion from APB, H2S, etc.

Using typical electrochemical and mass transfer parameters8 (including 5x10-10 m2/s for sulfate diffusivity in biofilms) at 25oC and a biofilm aggressiveness of -2 (on a log10 scale), simulation results can be obtained to demonstrate many interesting phenomena. For simplicity in this work, non-acidic pH and absence of CO2 are assumed and the effect of H2S corrosion is also ignored due to low H2S concentration coupled with non-acidic pH. The consumption of sulfate by the bulk biofilm cells is also ignored. Figure 1 is a partial screen shot of the software. Figure 2 shows that mass transfer resistance becomes increasingly important. The resistance ratio at time zero is 0.37 (largely charge transfer control), and at day 365 it becomes 58 (mass transfer control). This fact is manifested in Figure 3 indicating that the corrosion rate decreases quickly initially because the biofilm thickness has increased significantly. The percentage increase of biofilm thickness slows down and thus the further reduction of corrosion rate is decelerated. Figure 3 also shows the pit depth increase over time. The pitting corrosion rate is more severe initially when mass transfer resistance is less important. As pit grows, the overall thickness of the SRB biofilm increases. For a deep pit, there is a major mass transfer barrier hampering the sulfate migration from the bulk fluid to the pit bottom. Eventually, the growth of all deep pits will be severely limited by this. It is easy for the model to demonstrate that the growth of all deep pits has mass transfer control because it is difficult for any corrosive chemical to reach the pit bottom regardless how aggressive biofilm is able to catalyze surface reactions.

Figure 4 shows that the corrosion potential (Ecorr) decreases over time. Ecorr impacts the corrosion driving force |Ecorr - Eeq|, but it is the current density at the intersection of anodic reaction curve and total cathodic reaction curve in the E vs. i diagram that determines the corrosion rate. As expected, the corrosion potential values are between the anodic and cathodic equilibrium potentials. Sulfate concentration is important in this model. Increased sulfate concentration in the bulk-fluid phase will make more sulfate available for cathodic reduction on the iron and biofilm interface leading to more corrosion. Figure 5 demonstrates this. The effect of sulfate on CR gradually levels off because charge transfer resistance kicks in when sulfate availability is not that limiting. In reality, if the sulfate concentration is too large, SRB metabolic activity will be hampered due to substrate inhibition. Figure 5 uses the same biofilm aggressiveness for different sulfate concentrations without considering their impact on biofilm aggressiveness. Another factor is that increased sulfate concentration will lead to more H2S generation. This may lead to the formation of protective FeS films that can slow down corrosion15. These advanced mechanisms and also possible galvanic effect are being incorporated into Version 2 of our software.

Figures 6 and 7 show the simulated potentiodynamic sweep profiles. The intersection point of the anodic and cathodic curves yields the corrosion potential and corrosion current density. In Figure 7, the intersection point is clearly in the almost vertical cathodic curve region on the right. This is known as concentration polarization or mass transfer control region in the electrochemical reaction theory.  If the sulfate consumption in the bulk SRB biofilm is not ignored, there will be less sulfate reaching the pit bottom surface for its cathodic reduction, thus reducing the corrosion rate, especially in the later period of time that is mass transfer resistance controled. This behavior is shown in Figure 8. Figure 9 shows the effect of sulfate concentration on pit growth. A biofilm aggressiveness of 4 was used in the simulation. Lab tests typically last for several weeks, during which the pit does not grow to a depth that will trigger mass transfer resistance limiting. This means the sulfate effect is not pronounced in lab tests. However, for long term deep pits, mass transfer resistance is limiting. Increased sulfate concentration will greatly increase pit growth. Typical seawater sulfate concentration is 28 mM, while Arabian sea can reach 44 mM. Some produced waters may even have higher concentrations.  Figure 10 shows prediction of long term SRB pitting using a 7-day pit lab data point for calibrating biofilm aggressiveness.

The dual biofilm model can also cope with SRB in a dead leg situation in which there may be a thick stagnant liquid layer with significant diffusion resistance. The resistance can be lumped into the top biofilm resistance, or replacing it if there is no top biofilm. In the latter case, aqueous sulfate diffusivity should be used for the layer. 




The model can be used to predict MIC pitting progression provided that the BCSR theory applies. If the presence of the biofilm is uncertain, the model can still be used to predict the worst-case scenario that is also quite useful. As demonstrated above, many effects on MIC can be studied through simulation. This 1-D model does not predict pit width. A 2-D model may be considered in a later version of our MIC software.

Future MIC prediction will likely be a three-prong approach. A mechanistic model is needed to calculate pitting progression assuming that a corrosive biofilm is present. This provides a worst-case scenario. A biofilm detection method is needed to detect biofilms and possibly to provide data for calibrating the model if lab tests are not performed as a replacement. A new biomarker method based on ultra-sensitive EPS (extracellular polymeric substances) fingerprinting has been proposed by us to address this8. The third tool is risk factor modeling to predict the likelihood of biofilm formation. This will always be a probability model. 



    A mechanistic MIC model has been developed for practical applications. The model considers charge transfer resistance and mass transfer resistance. It can be calibrated with just a single pitting data point (pit depth vs. time) to obtain the aggressiveness of a particular biofilm. This model points to the future directions of MIC research including lab tests and field data collections. The following important observations have been obtained from the model:

(1)   Pitting rate decreases with time due to increased mass transfer resistance over time,

(2)   charge transfer resistance is important initially when pit depth is small,

(3)   mass transfer becomes increasingly important when the pit grows deeper, and

(4)   for deep pits, mass transfer resistance is always a controlling factor unless your biofilm aggressiveness is very small.


Figure 1. Partial screen shot of MICORP Version 1.1



 FIGURE 2 Simulated corrosion resistance ratio.


 FIGURE 3 Simulated corrosion rate and pit depth profiles.



 FIGURE 4 Simulated corrosion potential profile.


FIGURE 6 Simulated potentiodynamic sweep profiles at time zero.


 FIGURE 7 Simulated potentiodynamic sweep profiles at day 365.



FIGURE 8 Effect of sulfate consumption by the bulk SRB biofilm.

(The two R=0 curves are the same as in Figure 3. The two R<0 curves are from simulation using the same data as in Figure 3 except R=−1x10-3 mol/(m3s). Pit is assumed to be filled with sessile SRB cells. If the pit is filled with liquid, the R<0 curves will be much closer to the R=0 curves because the amount of sessile SRB cells will be much less.)


FIGURE 9 Effect of sulfate concentration in the bulk fluid phase. 30 day pit depth curve is similar to lab test scenario that is usually short term.




FIGURE 10 Prediction of long term pit depth in Arabian seawater.