Corrosion Rate Calculations – Details

Calculated Corrosion Rates (CRs) are displayed on the Corr Rates IF tab of the Calculation Summary.

The following CRs are calculated in IMS:

On CML level:

• Long CR, using the first and last thickness readings.
• Short CR, using the previous and last thickness readings.
• Linear Regression CR, using all non-ignored data.
• Historical CR.
• Dynamic Linear Model (IDAP) CR (based on Bayesian statistical methodology).

On Circuit level:

• Average Long and Average Short CR.
• Suggested CR, user specified CR.
• Extreme Value Analysis (EVA) for Heat Exchanger tube (HX) (only if enabled).

Note: The maximum of Long CR, Short CR, Linear Regression CR, and Suggested CR will be used to calculate RL (and NID).

Long Corrosion Rate Calculations per CML

The Long CR calculation (Long CR) is a good indicator of what is happening to the wall thickness over the total life of the Equipment. Fluctuations in thickness readings due to inaccurate UT and RT readings are minimized over a longer period of time (other NDE methods might be used to gather NDE data).

The assumption here is that the CR is more or less constant over time.

Example

The following table shows the following thickness readings for a CML:

Then for metric:

For US Customary units:

This Long CR is calculated for every CML/MP. The Maximum Long CR is then shown on the Corr Rates IF tab of the Calc Summary (see Tab: Corr Rates IF). The driving CML/MP is also shown.

The Max Long CR is shown on the Corr Rates IF tab of the Calc Summary.

 

Short Corrosion Rate Calculations per CML

The Short CR calculation is a good indicator of what is happening to the Equipment during the most recent period of Equipment operation. Sometimes the Equipment's operating conditions (i.e. flow rates, temperatures, fluid composition) change, which can result in changes to the CR.

The Short CR can be significantly affected by inaccurate UT/RT measurements. The shorter the interval between thickness readings, the greater the impact of inaccurate thickness readings. Careful identification of CMLs and examination points are necessary to enhance the accuracy and repeatability of the data.

Example

The below table shows the following thickness readings for a CML:

Then for metric:

For US Customary units:

Linear Regression Corrosion Rate Calculations per CML

Linear Regression is a mathematical algorithm (least squares) and is therefore a “Basis” of a CR and does not actually depict a real time CR. However, a Next Inspection Date (NID) will be derived. Linear Regression was developed as a method to consistently determine/plot the relationship between separate data-points of any kind and is used in many industries. In the case of IMS, it is used to show a relationship between separate thickness measurements for a CML.

Formulas used to calculate linear regression are:

For 2 points:

Straight line intercept w/ y axis):

Linear Regression formula:

To compute the associated CR based on linear regression for a CML, a "best fit" line is calculated by IMS and plotted on the CR graph for the Calculation Summary. This line represents the basis for determining a linear trend/relationship with the measurements (including the Nominal), in order for linear regression to predict a CR and NID. The CR is determined from the slope of the line at the current thickness and the time interval at which the line intersects the remnant thickness. The NID is determined from the time interval multiplied by the Total Interval Factor (TIF).

Note: Time Error and Growth Error readings are used in linear regression calculations. See Data Quality (Identifying Anomalies). Only measurements that are marked “Ignored” in the measurement table are not used. For IMS to calculate linear regression, the CML must have at least two (2) measurements. For renewed CMLs there must be at least two pre-renewal measurements.

For linear regression, a correlation Coefficient is calculated. This is an important value to review. You will find it on the CML Calc Results tab of the Calc Summary (see Tab: CML Calc Results). The coefficient value can vary between –1 and 1. A value of “1” or “–1” indicates a perfect linear relationship between CR and time, which is an indication of consistent thickness data. Values closer to 0 indicate a les linear relationship, which can indicate inconsistent thickness data. In this case, a review of the measurements may point out measurement(s) that need to be marked “Ignored”.

The linear Regression Correlation Coefficient.

The Linear Regression CR is determined by fitting the best straight line through the data. The calculation tries to minimize the distance between the fitted line and all of the data points. Ordinary Least Squares (OLS) regression is used to minimizes the sum of the squared residuals. Linear regression is not used in calculation method #2 (refer to calculation method selection for details).

In general, a model fits the data well if the differences between the observed values and the model's predicted values are small and unbiased.

Example

The table below shows the following thickness readings for a CML:

Thickness measurements versus time and linear regression calculation.

The slope of the line is the CR, in this example it is 0.10 mm/y.

Linear regression also calculates the R² values. R² is a statistical measure of how close the data are to the fitted regression line. R² is defined as the percentage of the response variable variation that is explained by a linear model:

R² is always between 0 and 100%:

• 0% indicates that the model explains none of the variability of the response data around its mean.
• 100% indicates that the model explains all the variability of the response data around its mean.

In general, the higher the R², the better the model fits your data.

Historical Corrosion Rate Calculations per CML

When a CML is renewed, the previous readings are marked with an “H”. This indicates that they are Historical Readings. Also, the previous CR is used to calculate the Next Inspection Date (NID) and the Remaining Life (RL) for this renewed CML. This is called the “Historical Corrosion Rate”. In the TrendPlot which you can find on the Circuit Details Page, the black dots represent the Historical data.

The TrendPlot showing historical data (black dots).

As soon as a second reading is added to the renewed CML, the Historical rate is no longer considered in the calculations.

For more information see PEI Trending and Corrosion Analysis.

Dynamic Linear Model (IDAP) Corrosion Rate Calculations per CML

Wall loss through corrosion by nature is a time dependent process. However, since the environmental and process conditions are usually varying over time, it is seldom a strictly linear process. Dynamic Linear Models (DLMs) reflect this (stochastic) behavior of the model parameters. Moreover, events may take place that have such a large impact on the wall thickness and/or the CR that explicit modelling is required.

Trending is an application of a so-called multi-process DLM where several models are updated simultaneously. Posterior probabilities are used to decide which model applies at a certain moment in time and a weighted average of the models is used for prediction. Trending does the following for each feature considered, given wall thickness measurements over time:

• It predicts the wall thickness at future moments in time.
• It predicts the CR.
• It estimates the Remnant Life (RL).
• It indicates anomalies in measurements and in corrosion behavior.

By looking at actual wall thickness readings over several years, it becomes clear that often:

• The experimental variation (scatter) is quite large.
• There are often many “outliers”.
• The CR is in general not constant over time.
• The number of measurements in a series is often limited.

This makes this type of data less suitable for forecasting using simple regression techniques. Therefore, we use a so-called Multi-process Dynamic Linear Model (DLM). This is a special case of Bayesian* forecasting and has several advantages:

• It is more flexible, i.e. model parameters (CR and wall thickness level) may vary over time.
• Subjective knowledge, e.g. prior estimates, bounds on parameters, changes in the process, etc. can be incorporated.
• It is fully recurrent, i.e. at any point in time all past information is condensed into the posterior probability distributions.

*Note: Bayesian refers to methods in probability and statistics named after Thomas Bayes (c. 1702–61), in particular methods related to statistical inference: Bayesian probability or degree-of-belief interpretation of probability, as opposed to frequency or proportion or propensity interpretations.

In the Data Analysis Module four models have been implemented (that is why it is called a multi process model). In the main model (Model 1) the parameters of the model, the level and the slope, are allowed to vary slowly in time (linear). The other 3 models have been implemented to cope with discontinuities in the data trend:

• Model 2 representing a wrong measurement (outlier);
• Model 3 representing a sudden change in level. This could happen e.g. when a piece of Equipment is changed, without notification in the database; and
• Model 4 representing a sudden change in CR (change in slope). This could happen e.g. when operating conditions are changed at some point in time.

The four models are illustrated below.

The four models.

Each time a new measurement is available the likelihoods of all four models are updated and a new prediction, which is a weighted average of the individual forecasts, is generated. Based on the posterior probabilities (if the probability of (one of) the alternative models (model 2, 3 or 4) is high), a warning signal is generated in the “Anomaly” or “Anomaly Last 2” column on the Results tab in the Data Analysis Module.

If the probability for models 2/3/4 is high a warning is given in the Anomalies columns in the S-IDAP module.

 

Average Long and Short Corrosion Rate Calculation

The average CRs are used to determine the calculated Next Inspection Date (NID) for a specific Calculation Methods (see Last section below).

To determine the Circuit Average Long CR, IMS sums all the Long Metal Losses (adds together the loss for all the CMLs) and sums all the Long Time Periods for each CML.

Example

Thickness readings (metric - mm).

Thickness readings (U.S. Customary - inches):

Suggested Corrosion Rate Calculations

When creating a new circuit, a Suggested Corrosion Rate is specified by the user. If you forget to input a Suggested CR, IMS will assign a default Suggested CR. The default Suggested CR is based on the Equipment group and the Calculation Method (see below). Generally, the user should determine and input the Suggested CR for the Circuit, with help from the Corrosion Engineer.

The Suggested CR is most needed when there are only a few wall thickness readings for the Circuit. For example, when only base-line thickness readings have been entered, the Suggested CR is the only CR that can be used to determine Next Inspection Date (NID) and Remnant Life (RL) (there are no Short and Long Rates yet). Once the corrosion history is determined for the Circuit, generally the Suggested CR might not control the Circuit’s NID as the actual CR may be controlling the Circuit. IMS will use the higher of the actual or Suggested CR in the corrosion calculations for each CML. Once an appropriate corrosion history is determined, the Suggested CR can be adjusted with input from Corrosion Engineer, and using information gathered from Corrosion Reviews and RBI analysis.

The Suggested CR is also useful when the CRs are expected to increase because of a process change. For example, if the historical rate is 0.07 mm/y (3mpy), but a process change will increase the CR to 0.21 mm/y (9mpy), then you can just input 0.2032 mm/y (9mpy) as the new Suggested CR.

The user entered Suggested CR and the Default Suggested CR.

 

Extreme Value Analysis (EVA) for Heat Exchanger Tubes

EVA (Extreme Value Analysis) is a statistical methodology that can be used to calculate and predict the CR for HX (Heat Exchanger) bundles. EVA can only be enabled for Equipment group Bundle.

The Calculation Methods

The Calculation Method factors, selected for a Circuit, have significant impact on how the RL and NID calculations work. When creating a new Circuit, one of the required fields specifies the Calculation Method.

The Calculation Method field.

Based on the Equipment group of the Circuit’s associated Equipment, the Calculation Method is automatically selected. This can be changed if desired. Also, the default Suggested CR (as explained above) and default Circuit Interval Factor (IF) are based on the Equipment group (see table below).

Default Calculation Method, Suggested CR and IF based on Equipment group:

Corrosion Rate

So, if the Equipment group is Air-cooled, Bundle, Furnace, Incinerator & Pipe/System, then the CR used in the calculations is the maximum of Long-term CR, Short-term CR, Average Long-term CR, Average Short-term CR, Linear Regression, and Suggested CR.

For other Equipment groups, the CR used is only the maximum of the Long-term CR, Short term CR, Linear Regression, and Suggested CR.

Note 1: IMS always calculates and displays the Circuit Average Long and Short CRs. But they are only used by Cal Method 1 to calculate the RL and NID for each CML.

Note 2: The DLM (IDAP) CR is not used in these calculations.

Interval Factor

In addition to the CR calculation, the Total Interval Factor (TIF), also called the Governing IF, also differs, depending on the selected Calculation Method. For Calc Method 1 a DSCF IF is also used (see Tab: Corr Rates IF).