Skip to content
Calculating Probabilistic Corrosion Depth Versus Growth Rate

During the 19th Pipeline & Technology Conference (PTC) held in Berlin on April 8 – 11, 2024, the OneBridge Solutions team was proud to present “Analytic Derivation and Validation of Probabilistic Corrosion Growth Model.” This paper discusses a method of providing estimations of metal loss depths at future times without relying on calculating a corrosion growth rate. This probabilistic model makes use of all historical inline inspection (ILI) provided depths and accounts for ILI sizing accuracy i.e. tolerance and certainty, without the use of Monte Carlo (MC) simulations.  

Impetus (Why) 

Many corrosion models employed by the industry currently ignore uncertainties in ILI depth measurements. However best practices and US regulations require that uncertainties be accounted for in reported ILI results per §192.937(c), §192.712(e), and §195.416(c). 

Additionally, the common two-point model for calculating a corrosion growth rate (CGR) by using just two data points may penalize operators by yielding more uncertain results or requiring operators to choose specific ILI results and discarding the rest of the available information. 

Final Product (What) 

An efficient analytical probabilistic model that utilizes ILI depth, sizing accuracy, and time elapsed between inline inspections as inputs was developed, which generates a probability distribution of both true corrosion depth and growth.  

Calculation of corrosion growth rates is typically an intermediate step towards predicting future depths used in models like ASME B31G to determine repair conditions. The probabilistic model outputs depth distributions directly and offers a simple way to assign depth uncertainty.  

Derivation (How) 

Inline inspection data from 1,294 assessable pipeline segments across 4 major pipeline operators were analyzed, specifically targeting those pipelines that had three (3) or more ILI runs. Anomalies were automatically matched between the data sets using our Cognitive Integrity Management (CIM) platform. These matched anomalies are referred to as chains: single chain are one-to-one matched anomalies and multi-matching chains are when many-to-one or many-to-many anomalies are matched. Anomalies used to derive the probabilistic model needed to be:  

  • Matched anomalies 
  • Over 3 ILI runs 
  • Where the final matched anomaly is linked to a field repair in CIM  


These requirements provided 966 single chains and 847 multi-matched anomalies for a total of 1,813 anomaly chains to work with.    

The model derivation relied on the assumption of normally distributed depth errors and statistical independence of successive ILI measurements. Extending the Pipeline Research Council International (PRCI) PR-331 model, which used two-point inputs and MC simulations, an analytical solution applicable to any number of ILI depth inputs was created. This approach has the advantage of utilizing all available data coherently, specifically advantageous to operators who perform ILIs as their primary method of assessing integrity.  

Please consult the paper for a more detailed discussion on the model derivation.

Common Deterministic CGRs 

The simplest corrosion growth rate is the two-point model, commonly used for deterministic CGR calculation per anomaly. This model can yield overestimated or negative CGRs, limiting its applicability and necessitating corrections.  

The weighted all-point model emerges as a superior choice when more accurate but less conservative estimates are desired. We employ these two models for comparison with the analytical probabilistic model we developed. The all-point model uses a weighted linear regression where the least-squares minimization assigns weights to measurements based on the reciprocal of their errors. 

Comparison with Deterministic CGRs 

Deterministic CGR uses ILI depths, sometimes from only the two most recent ILIs to determine future depth. The probabilistic depth model uses all ILI depths and their uncertainties. Additionally, ASME B31G calculations often add the latest ILI tolerance to the ILI depth, leading to increased conservatism. The key advantage of the probabilistic approach lies in the model's output—the depth distribution calculated at any future time. With this distribution, operators can easily identify the most probable future depth and customize the level of uncertainty by selecting desired percentiles from the distribution. 

Comparison with actual CGR 

Future depths were calculated using the two deterministic corrosion growth rates as well as the probabilistic depth model and were compared to the field-measured, sometimes referred to as “actual” values, on a unity plot. The comparison can be seen in the figure below, which demonstrates that the probabilistic model predictions exhibit a trend line closest to the unity line, while the two-point model deviates the most. 

Unity Plot

Figure 1: Unity Plot for all Models


Use Cases

When calculating the remaining life or confirming the pipeline reinspection interval, for example, – instead of using future depth provided from a deterministic CGR, one can use the most probable depth when calculating the burst pressure at a future time for increased accuracy.

Additionally, using the maximum allowable operating pressure in addition to the pipe diameter, wall thickness, and SMYS, the burst curve can be calculated for all depths between zero and the wall thickness using the ASME modified B31G model. In this scenario, flaw length and future depth are treated as continuous probability distributions according to the tolerances specified by the ILI service provider. Given the depth probability distribution output from the probabilistic model, one can use it as a direct input to a Probability of Exceedance calculation.


Probabilistic determination of depth may provide a better solution for estimating future metal loss depth by considering data from all ILI runs as well as ILI sizing accuracy.

This probabilistic corrosion depth model was validated using MC simulations to produce identical results up to the precision of MC. Additionally comparisons of estimated “future” depth with field measurements provided additional validation.

Operators can use the future depth probability distribution from the model as a direct input to other calculations to make decisions regarding their integrity management programs. Finally, explicit probability distributions can provide operators with a practical way to assign realistic uncertainty on the future depth value.

Overall, the model provides:

  • Depth probability distribution at any future time, to be used directly (without relying on CGR).
  • CGR probability distribution at the time of the latest ILI, if needed
  • A rigorous way to assign errors on future depth and to calculate probability of certain depth values
  • A straightforward way to plug-in the results into other calculations where probabilistic inputs are required.


Learn more about how OneBridge Solutions can correlate and analyze thousands of inline inspection data sets here.

Comments or questions? We’d love to hear from you.