A Tale of Perfect Goose Eggs: CO2 Plume Computer Modeling Options

A Tale of Perfect Goose Eggs: CO2 Plume Computer Modeling Options
Author: Paul Blackburn, Bold Alliance
Sept. 30, 2024

Introduction

This is the third of a four-part blog series about carbon dioxide (CO2) pipeline ruptures.  It describes the different types of computer modeling available to estimate the size of danger zones following CO2 pipeline ruptures.  The other blogs in this series cover:

• 1: Chasing a Wild Goose Egg: Understanding Computer Plume Modeling for Carbon Dioxide Pipeline Ruptures (The basics of CO2 pipeline ruptures and the need to know the danger zone following a rupture – Sept. 23, 2024)
• 2: Is Your Goose Cooked? The Potential Health Impacts of CO2 Pipeline Ruptures (Sept. 25, 2024)
• 3: A Tale of Perfect Goose Eggs: CO2 Plume Computer Modeling Options (The computer models available to predict the size of danger zones for CO2 pipeline ruptures – Sept. 30, 2024)
• 4: Good for the Goose, Good for the Gander: Who Should Have Access to Plume Modeling for CO2 Pipeline Ruptures? (Public access to CO2 pipeline rupture computer modeling and industry and government efforts to keep it secret – Oct. 2, 2024) 

The goal of this series is to help current and potential future neighbors of CO2 pipelines access technology that can help them understand whether or not they are at risk.  

What Tools Exist to Predict If You Are in a Danger Zone?

Now that we’ve reviewed the potential risks and health impacts of CO2 pipeline ruptures, how can you predict whether or not you, your family, and your animals might be exposed to high concentrations of CO2, putting you in the danger zone?  The primary tools available for determining CO2 pipeline danger zones are different types of computer models that predict how far dangerous concentrations of CO2 would extend from a rupture site.  

Imagine gently blowing out a candle and watching the smoke rise from the smoldering wick.  Inside without wind, the smoke might curl in twists above and around the candle.  The smoke would scent the air near the candle with the smell of burning wax.  Eventually, the smoke would dissipate throughout the room to the point that you can no longer see or smell it.  Outside in a breeze, the smoke and its scent might be blown immediately away.  You might see the smoke briefly and, if you were downwind, smell it for a moment.  But, what if you wanted to predict what happens to the smoke?  To predict where it would drift in the room and how fast it would dissipate?  That’s what computer plume models do.  

Would computer models be able to predict exactly how the smoke would curl in a still room?  No, but they could predict the approximate distance from the candle the smoke would be visible and smellable, depending on the amount of smoke produced, any air movements, the effects of physical obstacles, etc.  No computer plume model is perfect.  They are merely tools that provide estimates of how far the smoke will go.  It’s just that some computer models are better than others.  

There are different two types of computer models: dispersion models and computational fluid dynamic (CFD) models.  Each type has its strengths and limitations.  So, how does one shop for CO2 pipeline rupture plume modeling software?

Our starting point for computer model shopping is a peer reviewed scientific paper published on February 23, 2024, by Drs. John Abraham, Lijing Cheng, and John Gorman, entitled “CFD Simulation Models and Diffusion Models for Predicting Carbon Dioxide Plumes following Tank and Pipeline Ruptures—Laboratory Test and a Real-World Case Study.”  Yes, that’s a mouthful, so I’ll just call it the “Abraham Paper,” after its lead author.  If you scroll through this paper, you will see that CO2 plume modeling is complex, but please read on because the following attempts to describe this modeling in understandable terms.  

Many factors affect the movement, size, and concentrations of a CO2 plume following a pipeline rupture, including the diameter of the pipeline, the length of pipe vented, whether isolation valves work properly, the density of the CO2 at the time of the rupture, how the pipe physically ruptures, wind speed and direction, atmospheric turbulence, air temperature, topography/landscape, and even the type of vegetation near a rupture site.  The computer programs used to model CO2 pipeline ruptures integrate multiple mathematical formulas to estimate how some or all of these factors impact plume movement and concentration.  The more factors modeled and the more sophisticated the math, the better the model should work.  

This being said, all CO2 plume models provide an estimate of how far dangerous concentrations of CO2 may travel.  No model is perfect.  Modeling cannot predict exactly where CO2 from an actual rupture will go, because that depends to a large degree on the wind and other factors at the time of a rupture that may change from hour-to-hour or even minute-to-minute.  

Model sophistication is important.  More sophisticated models can take into account many factors using complex mathematics and provide more accurate predictions in diverse circumstances.  However, collecting and inputting required data and assumptions is time consuming, as is running multiple scenarios for different weather conditions and rupture types.  In contrast, less sophisticated models do not take all factors into account and their mathematics are simpler, such that less expertise and time are required to use these models.  However, this simplicity means that less sophisticated computer models are generally less accurate and less able to handle unusual situations.  

Due to the time it takes to run a more sophisticated model, they are best used in pre-rupture route and emergency planning efforts when there is time to collect data, evaluate assumptions, and integrate a model’s predictions into routing and emergency planning decisions.  Pre-rupture model runs should generally consider worst-case circumstances, because citizens and emergency responders need to know and plan for the worst.  Worst-case modeling assumes the largest possible release, weather conditions conducive to spreading high concentrations of CO2 the farthest distance, and rupture locations and times that might have the greatest impact on the largest number of citizens.   

Less sophisticated models are best used in response to an actual rupture when speed is more important than accuracy, so that emergency responders and citizens have at least a quick and dirty estimate of the danger zone.  Simpler models can benefit from knowing the site, size, weather, and other factors at the time of a rupture, but they cannot take into account all important factors.  As a consequence, they may underestimate the extent of dangerous CO2 concentrations.  The usefulness of a less sophisticated model to citizens and first responders depends on how soon after the rupture it is run, the accuracy of the data and assumptions, the accuracy of the prediction, and how quickly its prediction is provided to first responders and citizens.  An underestimation of a danger zone could be fatal, so less sophisticated models should be used conservatively. 

Model accuracy also depends to a significant degree on the quality of the data and assumptions input into the model.  There is an old saying: trash in trash out.  The predictions of a model should be understood in light of the quality of the data and assumptions input into it.  Modeling for which inputs are not disclosed should be viewed skeptically.  

It is entirely reasonable to use sophisticated models for planning purposes, and then use quick and dirty models in responses to actual ruptures.  Moreover, it would be reasonable to use both sophisticated and unsophisticated modeling during emergency response planning, because doing so would allow emergency responders to understand the limitations of less sophisticated modeling.  

Since all computer models are based on mathematical formulas that estimate CO2 movement, all models should be calibrated against experimental data and real-world rupture information.  When plume computer models were first developed, they were calibrated using data from wind tunnel and small-scale outdoor experiments.  Over the past decade, a number of scientists have conducted larger scale CO2 pipeline rupture tests (e.g., here and here) that provide additional understanding of how CO2 plumes move in reality.  This being said, even these larger-scale experimental ruptures are much smaller than would be expected from large-diameter long-distance pipelines.  Therefore, plume models should also be calibrated by comparing their output to the observed impacts of actual large-volume ruptures, such as the Satartia rupture.

What Types of Computer Models Exist?

The Abraham Paper says that there are two basic types of plume models: dispersion modeling and computational fluid dynamic (“CFD”) modeling.  As a general observation, dispersion modeling is less mathematically sophisticated, and CFD modeling is more mathematically sophisticated.  The strengths and limitations of each of these model types are discussed below.  

Dispersion Models

Dispersion modeling assumes that a chemical upon release will disperse into the atmosphere based on a number of factors including wind direction and speed, atmospheric turbulence, temperature, and other factors.  However, the math used in these models assumes that plumes spread symmetrically and are circular in cross-section, which is not what happens in the real-world.  Instead, many complex factors influence how CO2 spreads.  For example, CO2 movement is influenced by hills and valleys (topography), changes in wind speed and direction over time, vegetation, and other factors.  The practical result of the simplistic math used in dispersion modeling is that these models lay symmetrical goose egg-shaped plumes.  Dispersion models would predict that the smoke from a candle would take the shape of an egg, perhaps almost round or long and skinny, but the math in the model produces a symmetrical plume.  The relative simplicity of dispersion models may result in CO2 plume predictions that are wildly inaccurate, because in the real world, plumes are rarely, if ever, egg-shaped.  Although dispersion models claim to be calibrated, historically their calibration is based on data from wind tunnel experiments and controlled small-scale outdoor releases of small amounts of CO2.  Such experimental data may bear little resemblance to the movement of CO2 following a full-bore rupture of a large-diameter miles-long pipeline in complex terrain and weather conditions.  Common dispersion modeling software include PHAST, ALOHA, CANARY, SLAB, HEGADAS, DEGADIS, and FRED software.  PHAST is frequently used by the oil, chemical, and pipeline industries to predict danger zones for their emergency planning purposes.   ALOHA and CANARY are typically used by emergency response agencies to predict chemical movements following actual ruptures, because they can quickly provide a rough estimate of danger zones.  

The Abraham Paper found that PHAST™, which is owned by DNV, a European standard setting and consulting group that provides services to the U.S. pipeline industry, produced very large errors during early experiments, and in more recent studies continued to significantly under-predict CO2 concentrations.  DNV regularly issues updated versions of its PHAST software, so it is possible that it has recalibrated PHAST based on new data, for example from the Satartia rupture.  Unfortunately, the validation process of PHAST is kept confidential by DNV so is not subject to public review.  

Below is an example of the output from a PHAST model run for a full-bore rupture of a 24-inch outside diameter pipeline with a segment length of 10-miles.  The rupture site is to the left and the plume moves to the right under the influence of an assumed wind speed of 2.24 miles per hour, the slowest speed that PHAST could model.  

In comparison, according to the PHMSA Failure Investigation Report, the Denbury pipeline that ruptured near Satartia had an outside diameter of 24 inches and a segment length of 9.55 miles. The wind speed at the time of the Satartia rupture was also very low.  Thus, the assumptions for this PHAST modeling are very similar to those that would have been assumed for the segment of Denbury pipeline that ruptured near Satartia.  It should be noted, however, that the volume modeled here was about 20 percent less that the actual volume released near Satartia, because Denbury failed to promptly close the Tinsley valve upstream from the rupture.  As a result, the Satartia rupture released at least 20 percent more CO2 than would have happened if Denbury had promptly closed the upstream valve and fully isolated the pipe segment.  

This modeling effort was commissioned in 2022 by the Pipeline Safety Trust.  The Bold Alliance shared in the cost, which totaled about $3,000.  The Pipeline Safety Trust selected the basic parameters (length, diameter, pressure, temperature, flow rate, wind speed, etc.) based in part on the announced specifications for the Summit project trunk lines.  Other than specifying the pipeline diameter, length, wind speed, and rupture type, neither the Pipeline Safety Trust nor the Bold Alliance attempted to control the modeling or sought changes to the model output.  

The plume produced by the PHAST model is symmetrical like an egg.  This symmetry is a function of the math at the heart of this model that simply stretches out the plume shape depending on a number of factors.  The “0.04 fraction” (4% CO2 concentration) footprint for a 2.24 mile per hour wind speed (the blue line) extends about 3,050 feet (about six tenths of a mile) from the rupture site.  As a reminder,  4% CO2 concentration is considered “immediately dangerous to life or health” or IDLH, which is a workplace safety standard set at the level at which a person might not be able to self-rescue due to disorientation or intoxication.  At a 4% concentration, CO2 typically causes headaches, dizziness, and breathlessness, but not unconsciousness, depending on the exposure duration, except perhaps in individuals with pre-existing health conditions. 

As mentioned, this PHAST model run indicates that the plume from the Satartia rupture would extend at a 4% concentration only about six tenths of a mile, meaning it predicts that CO2 concentrations would be well below this level in Satartia, even assuming that a somewhat greater volume of CO2 was released.  If the PHAST model is correct, then the Satartia rupture at most would be expected to cause the citizens of Satarita to have headaches and perhaps some breathlessness, but probably not unconsciousness or rapid, severe intoxication.  Moreover, this PHAST model run does not predict that the three closest victims (about six-tenths of a mile from the rupture site) would pass out within a couple of minutes or that their car would stall due to a lack of oxygen.  

The PHMSA Failure Investigation Report stated that Denbury conducted a PHAST analysis in 2011 to determine which communities along its pipeline would be at risk.  It predicted that Satartia would not be at risk.  PHMSA found in its Consent Agreement for the Satartia rupture that the 2011 PHAST model run conducted by Denbury was “wrong” – a goose egg.  The PHAST modeling investigated by the Pipeline Safety Trust helps us understand why the PHAST model output relied on by Denbury was “wrong.”  It lacked the sophistication needed to predict the danger zone for that pipeline at that location in those circumstances.  It was the wrong tool for that job.  

The Abraham Paper describes dispersion models as being inherently limited and “crude” due to the relative simplicity of their mathematics.  But, it also recognizes that dispersion models have a role in response to actual ruptures where time is of the essence.  Ultimately, it may be possible to improve and re-calibrate dispersion models enough to ensure their accuracy when used in response to actual ruptures, but for now they should be used conservatively.  Where time is not of the essence, such as when selecting a pipeline route or preparing an emergency response plan, dispersion models should not be used because they are not the best tool for these tasks.  

Computational Fluid Dynamic (CFD) Models 

CFD models are based on an entirely different scientific and mathematical approach to predicting the extent and concentration of a CO2 plume.  Essentially, CFD modeling creates a three-dimensional virtual space that takes into account the shape of the land and breaks the atmosphere above it into millions of different sized three-dimensional cells, and then predicts the movement of CO2 in each of these cells based on mathematical formulas.  Many different factors can be modeled, including but not limited to the momentum of the plume, changes in wind speed and direction, gravity, turbulence, the shape of the land, the presence of buildings, type of vegetation, etc.  The model then combines these cell-level predictions into an overall prediction showing the movement of the entire plume.  CFD models do not assume a circular plume cross section or symmetrical expansion.  Their mathematics are far more complex than dispersion models.  CFD modeling requires far more setup effort, data input, computing power, and time than dispersion modeling.

The Abraham Paper describes a CFD model constructed by Dr. Abraham tested against both experimental CO2 release data and health reports from the Satartia rupture to see if the model predicted the observed health impacts.  

The following are two cross sectional images of the “computational mesh” (individual cells) created by the Abraham CFD model.  The top image shows the cells for the overall landscape near Satartia and the bottom is a closeup of the rupture site.  The horizontal cells at the bottom are the land and the cells above are in the atmosphere.  The model contains more cells near the rupture site to more accurately predict CO2 plume motion as it jetted from the pipeline.  The cells generally ranged in size from 1 to 20 meters/yards across, but near the rupture site they were about 10 centimeters (4 inches) across.  In total, the model calculated the movement of CO2 in about 36 million individual cells.  

When compared to small scale experimental plume data, the Abraham CFD model significantly outperformed historical PHAST models in predicting CO2 levels.  Moreover, the Abraham CFD model’s predictions were based entirely on physical principles without calibration or other modifications to improve accuracy.  Put another way, the CFD model was reasonably accurate without any tweaking.  

The Abraham Paper also modeled the Satartia rupture to determine if the CFD model would have predicted that the people of Satartia were at risk.  The CFD model produced the following CO2 plume for the Satartia rupture.  This is a top view with the rupture site in the lower right and the general area of the Satartia shaded in the top center.  The red area is predicted to have an average of 10% CO2 concentration and the dark blue essentially normal levels.  

This model output is dramatically different from the PHAST output provided above.  It is not egg-shaped.  Instead, it shows two distinct plumes of CO2 with between 5% and 8% concentration in and near Satartia, the center of which was approximately 1 mile from the rupture site.  The CFD model predicted that the CO2 would settle to both the east and west of the ridgeline and Highway 433, and then flow downhill toward Satartia on both sides of this ridge.  It also shows that up to about one-half mile from the rupture site, CO2 concentrations were at least 10% – high enough to rapidly render victims unconscious and stall a car engine.  It should be noted that the concentrations shown are time averaged.  Short-term concentrations may have significantly exceeded these averages, especially nearer the rupture site.  If this CFD model had been used by Denbury prior to its rupture, it would have predicted that the people of Satartia were at risk.  Moreover, the predicted CO2 concentrations are in accordance with observed health impacts by the Satartia rupture.  

CFD models can even predict the effect of buildings on plume shape and concentration.  The following image was produced by a CFD model used in a 2011 study by the Lawrence Berkeley National Laboratory for the rupture of a 6-inch diameter 1 kilometer (half mile) long CO2 pipeline installed as part of the ADM carbon capture project near Decatur, Illinois.  This image shows the extent of the plume 190 seconds after a rupture near the tanks on the lower left.  

The predicted plume is also not symmetrical. Due to the small diameter and short length of the modeled pipeline, the danger zone is relatively small.  The white area above and to the right of the tanks shows the 4% CO2 concentration (IDLH) region; the blue area inside the white is the 10% CO2 concentration; and the red spot just above the tanks shows the area that would reach 25 percent CO2 concentration.  Even a few minutes exposure to 25% CO2 could be fatal.  The model even shows how the plume is affected by buildings.  

These examples demonstrate that CFD modeling is far more refined and realistic than simple dispersion modeling.  Is it perfect?  No, but much more capable than dispersion modeling. 

The primary barriers to using CFD modeling include the time and expertise required to input data into a CFD model, the time and computer power needed to run the model, and the resulting higher cost.  At present, CFD modeling is more expensive than dispersion modeling.  However, the cost of CFD modeling is not significant relative to the hundreds of millions or even billions of dollars that major pipeline projects cost, or relative to the tens or hundreds of millions of dollars of annual operating costs for existing pipelines.  Pipeline companies can certainly afford CFD modeling.  Also, the time needed to conduct CFD modeling for route selection and emergency response planning can be integrated into route selection processes and ongoing emergency plan updates.  As CFD modeling becomes more automated and computing power increases, the cost and effort required for CFD modeling should decrease. Perhaps in the future it will be possible for first responders to use CFD modeling in real time.

The Right Tool for the Job

The Satartia rupture demonstrates the harm that can result from use of an inadequate plume model.  Based on its use of the PHAST model, Denbury determined that the people of Satartia were not at risk.  Denbury, therefore, failed to coordinate with local first response agencies, and also failed to warn the residents of Satartia that they were at risk.  As a result, neither the response agencies nor affected citizens were prepared to respond to that rupture.  

So, what computer modeling should those who live and work along existing and proposed CO2 pipeline routes demand?  Likely, families and business owners would prefer CFD modeling for a pipeline rupture near their homes and/or businesses.  However, it would be expensive and cumbersome to conduct CFD modeling in all locations along hundreds of miles of pipeline where a rupture could harm people.  Also, the fact that computer models provide estimates of plume size means that a single model run could provide a reasonable plume size estimate for many similarly situated locations.  For example, it is reasonable to assume that a CO2 plume would behave similarly in relatively flat agricultural fields, all other factors being the same.  Therefore, a set of CFD model runs for a flat landscape would likely provide a reasonable estimate of the danger zone for other similar locations.  In contrast, areas that have higher populations and more complex topography could be subjected to site-specific modeling.  

As more and more CFD modeling runs are completed and made public, it is possible that government agencies could use them to develop simplified but effective guidelines when establishing danger zones and setbacks for CO2 pipelines of different diameters and segment lengths.  For now, the CO2 pipeline industry should bite the bullet and conduct and make public its CFD modeling, because doing so would help avoid future mass casualty events and increase public safety.  The need for more sophisticated modeling should be seen as a cost of doing business that, like it or not, need be borne by the pioneers in this field.  They can afford it.  

If you found this blog useful, considering reading the last installment in this series about government failure to require and publicly disclose plume modeling, and the pipeline industry’s proposed legislation to keep plume modeling secret based on unfounded fears that terrorists might use the modeling.  If you want to pipeline companies and governments to do plume modeling for you and your community, you will need to fight for it.

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