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, H_{2}S, etc.

Using typical electrochemical and mass transfer
parameters^{8} (including 5x10^{-10} m^{2}/s for sulfate
diffusivity in biofilms) at 25^{o}C and a biofilm aggressiveness of -2
(on a log_{10} scale), simulation results can be obtained to demonstrate
many interesting phenomena. For simplicity in this work, non-acidic pH and
absence of CO_{2} are assumed and the effect of H_{2}S corrosion
is also ignored due to low H_{2}S 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 (E_{corr})
decreases over time. E_{corr} impacts the corrosion driving force |E_{corr}
- E_{eq}|, 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 H_{2}S generation.
This may lead to the formation of protective FeS films that can slow down
corrosion^{15}. 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 this^{8}. 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.

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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.

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**

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/(m^{3}s).
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.