REGENESIS Technical Perspectives – Part 2 – Using Modelling to Explore Hidden Processes
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Jeremy, a question here is, can I get a copy of the PlumeForce software?
I knew that would come up. That was the first question last time as well. At the present time, the PlumeForce software is Regenesis internal only, but we do provide free support with it on Regenesis projects.
So the next question here is, the modeling you showed was impressive, but how do you know that it is accurate?
That is a good question, and it’s perhaps the most frequent of FAQs I come across for modeling. I think the best way to answer it is to use the words of my favorite modeling mentor, English statistician George Box, and a statement that I think all modelers who might be on this call will be familiar with. All models are wrong but some models are useful. The point is that a model is only ever an approximation of reality. At best it’s only going to give us a trend line, it’s never going to give us a reproduction of site data or real-world data because that’s always going to be subject to noise. Lines and real-world data are a bump up and down. But that doesn’t stop it being helpful. If you consider other common models like universal gas law, PV equals nRT, that is only an approximation to reality. It’s never actually accurate. It’s always slightly wrong, but it is supremely useful and helps us understand how things behave.
So models can be wrong, but still useful because they can help us understand how things behave and multiple factors come together. What might driving the patterns we see and how sensitive the system may be to a given parameter. It helps our understanding. So what I’d really say to answer the question is that it’s not necessarily about accuracy but more about understanding. Modelling is better employed as a means of increasing understanding rather than a tool for placing bets. But so saying that, it is possible to calibrate model to cite data. And once it’s calibrated, the predictions that it makes are going to be a lot closer to what we might then expect further on. And as we get more calibrated fits with more modeling experience, then the default parameters that we might put in for a given scenario might be that much more representative. And so the next model fits will be closer and closer to what we might say accurate. But chasing accuracy with a model is not always the most useful way to use a model.
I was interested by what you said about kinetic equilibria and that they are widespread in remediation. Can you give some more examples?
Okay, so from a modeling perspective, kinetic equilibria occur whenever you’ve got an input and an output and when at least one of those rates is concentration-specific, nonlinear. So in plain English, it means that we get a kinetic equilibrium whenever there’s one process that will reduce the concentration co-occurring with another process that increases the concentration. We used biodegradation in the example in the webinar, but a number of other examples could have been the case. Many of them that I come across are based on back diffusion as one of the inputs pushing the concentrations up again and this can feature in a number of ways. Bank diffusion rate is concentration sensitive also so it fulfills one of the criteria.
The steeper the concentration gradient we create the faster the bank diffusion so it’s a bit like the harder we push down on an iceberg the more the iceberg pushes back up. So we might have bank diffusion as an input, the output might be degradation again or it might simply be dilution from incoming clean water post remediation. In fact, in the next webinar, I’m going to actually come up with some examples of that where we’ve got clean water coming out of a barrier, meeting mass that’s back diffusing out of the formation downgrade into the barrier and what that will do to our results and how we can monitor it. So that’s kind of a segue to our next webinar with respect to PFAS treatments.
Hello and welcome, everyone. My name is Dane Menke. I am the Digital Marketing Manager here at Regenesis and LandScience. Before we get started today, I have just a few administrative items to cover. Since we’re trying to keep this under an hour, today’s presentation will be conducted with the audience audio settings on mute. This will minimize unwanted background noise from the large number of participants joining us today. If the webinar or audio quality degrades, please try refreshing your browser. If that does not fix the issue, please disconnect and repeat original login steps to rejoin the webcast.
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Today’s presentation is the second in our Regenesis Technical Perspectives webinar series on the application of advanced modeling for in-situ groundwater treatment using colloidal activated carbon. This module in the series shows how modeling can provide a window into hidden processes and shows why the mechanisms behind what we see may not be as they first appear. With that, I’d like to introduce our presenter for the series.
We’re pleased to have with us Dr. Jeremy Birnstingl, vice president of environmental technology at Regenesis. Dr. Birnstingl serves as a senior Regenesis technical resource on key remediation projects involving advanced institute technologies worldwide. He is the author of the PlumeForce software used for design and modeling of the Regenesis activated carbon-based technologies. Dr. Birnstingl received a bachelor’s of science in environmental biology from the University of Essex and a PhD in environmental chemistry from the University of Lancaster. He is a fellow of the Royal Society of Chemistry in the United Kingdom and a chartered environmentalist. He has over 30 years’ experience in the commercial and academic environmental sectors, including 20 years with Regenesis. His creative and scientific insight have been recognized through three commercial patents.
All right, that concludes our introduction, so now I will hand things over to Dr. Jeremy Birnstingl to get us started.
Great. Well, thank you, Dane, and welcome everybody to this webinar series on practical use of modelling in the design and management of Plumestop projects. Just to be clear, this is not a training course in modelling itself, but it’s rather an exploratory tour of what modelling can contribute to assisting our engineering activities and understandings when we’re delivering efficient and successful projects. So this is module two of three. And in it, we are going to explore how modeling can expose hidden processes that lie behind the limited data that is available to us through groundwater samples from monitoring wells.
As Dane mentioned, the series is about expanding our understanding of activated carbon remediation projects using modeling to help. And modeling is essentially a means offering a window into the governing processes behind the limited snapshots that we can get from monitoring wells. Once we have that information built into the model, we can leverage it and use it to improve design, we can use it for performance tracking and projection, and we can use it to support engineering management and control. So in this series, the previous webinar introduced plume stop and modeling and the connection between the two and provided illustrations of how designs can be explored and optimized with the assistance of a model, in other words the use of modeling to design better.
This second module will go deeper and show how modeling can provide that window as I mentioned and also illustrate why some of the mechanisms behind what we see may not be as they first appear, in other words using modeling to better. And then the next webinar module after this is going to explore how modeling can be used as a support tool throughout a project, helping with communication, data interpretation, and performance optimization. In other words, modeling to understand better. So without further ado, let’s move on directly.
First quick recap of webinar one, which was a week ago, and perhaps some of us on this call have not watched that. It will be available as a recording, so by all means use it to catch up. In a slide what we covered in the first webinar is what is plume stop. Plume stop is tiny particles of activated carbon in liquid and carrier polymers that can paint the subsurface. It provides a means of slowing plume eviction by two to three orders of magnitude, a hundred to a thousand times or thereabouts. What is a model? A model could be thought of as being rather like flight simulator. It gives us a means of desktop performance prediction of different remediation or treatment scenarios. How do we use them together?
Well, plume stock performance can be explored with any model to some extent and the last webinar went into this as you can tell from this slide, but sophisticated models can be used to optimize reagent selection and dosing. So was all covered in the last webinar. This present webinar is more about the spooky stuff, the hidden processes and how we can use modelling to see a lot deeper, in other words how modelling can provide us a degree of x-ray vision into things that would normally be beyond a mere mortal’s sight. What we’re going to cover in this are the principles of emergent phenomena, in other words processes in combination versus processes in isolation, patterns and behaviors that can emerge when multiple smaller parts come together. We’re gonna look at the principle of kinetic equilibria, where two or more opposing dynamic processes find a balancing point.
For example, when a system may appear to have stalled, when in fact, quite the opposite is true. And we will shine a light onto the impact that hidden mass can have on what we observe. The contaminant mass that is not in the dissolved phase in groundwater, and therefore visible to us in monitoring well samples, but that will interact with the groundwater and influence the course of the project, the hidden mass. How do we account for and manage that? We have our window into the hidden dynamics of all the above, so that they can be understood and accommodated in the project design and delivery.
Let’s start by introducing PlumeForce, which is the model that we’re going to be using in these exercises. PlumeForce is modeling software for in-situ groundwater remediation. It was developed by Regenesis and we use it to support our clients’ projects. It was designed by me, starting in about 2016, when it became clear that existing off-the-shelf fate and transport models were limited in their ability to accommodate activated carbon and other remediation products in their calculations. Plume force is a multi-phase finite difference model it accommodates dynamic sorption, desorption, destruction, formation and competitive interactions between target and non-target species and what the software does is that essentially it predicts groundwater concentrations at any point in space and time in the model domain.
This has valuable uses to us at different stages of a project. At the conceptual site model stage when we’re really working at what’s happening on a site before we do anything to it, it helps identify information gaps and the drivers of what we see. We can use it for design optimization, selection of agents, experimentation with different doses, and helping understand expectations of what a different remediation scenario might actually achieve at this point in time, that point in time, another point in time, and so on. We can also use it as a performance yardstick for tracking a project and managing it. That we’ll get onto more in the third webinar of these three.
From the first version in 2016, PlumeForce has progressively been refined and extended as we’ve been able to compare the model predictions from it with actual field performance and therefore use this circular process to hone the software as a working tool. The present functionality at this point in time, spring 2023, is that it can handle the complexities of multiple reagents, the spatial arrangements of their placing, different overlaps, etc. The different timing of additions, the consumption of the reagents, and their longevity. It will consider the interplay of multiple competing species. Contaminant mixtures, parent-daughter cascades, natural and hidden competitors that might not be contaminants of concern, or even in our analytical suite, but will nevertheless compete with our target species for sorption sites on the plume stop activated carbon.
So we touched a little bit on that in the previous webinar. It will also consider the interplay of multiple phases or compartments. The importance of multiple phase consideration is because in many cases relatively little contaminant mass is in the groundwater, yet this is what generally measure. Like an iceberg, most of the mass is hidden and we’ll look more deeply into this in the present webinar. So let’s get on with it. Let’s apply the tool and see what we can learn. The theme of this particular webinar then is what lies behind what we see. Appearances can be deceptive. Something appearing innocent might be hiding something more challenging and likewise something that appears broken might actually be functioning perfectly. Something that appears to be stopped might be cruising.
This talk is going to explore the hidden stitching at the back of the tapestry so that we can better understand the picture that we see, and it will draw on modelling of the insights and illustration. So let’s take a look at this. Much of the confusion can be because of emergent phenomena. In other words, simple parts coming together into something new that could be a lot more complex. A lot of simple parts can become a complex whole. So simple parts can come together in surprising complexity and what emerges is not always obvious. We might be familiar with the individual voices performing the orchestra that we might be listening to. All of them might be simple in their own right, but the symphony that comes together when they’re all functioning at once is something else again.
If we want to try and put this together in our heads, it is not an easy task and will take an awful lot of thought and skill to really weigh up all of the dynamics and their interactions. There are a lot of moving parts and processes coming together to form the picture that finally emerges. In our contaminated groundwater symphony, the individual voices might be advection, transformation, matrix diffusion, sorption, desorption, competition, different treatment reagents, etc. All may be simple in and of themselves, but what emerges might be complex and counterintuitive. The modelling allows the full symphony to therefore be explored, and it’s the modeling that puts it all together.
By way of example, I’m going to draw on two analogies in this talk, icebergs and waterfalls. So let’s start with icebergs. The iceberg provides our first equilibrium analogy. Icebergs are helpful because they provide an example of equilibration between a visible and a hidden, an invisible compartment, and this occurs widely in the field of remediation as we’ll see. In this case it’s frozen, a static equilibrium. The ice we see is the ice we’ve got, there is no flux. So in this remediation example, let’s say that we’ve got to get iceberg under the regulatory threshold of a bridge. That bridge isn’t moving and the iceberg has to go underneath it. This requirement, icebergs and bridges, might not be quite as abstract as you think. This is the same bridge from another angle, and yep, we’ve got icebergs.
This is Jökulsson in Iceland in spring, so perhaps at about this time of year, this is what it looks like. Let’s then take a look at the task. We’ll presume we’ve got bridge clearance of about 50 feet, I think that would be. Let’s say that one of these big icebergs in the background isn’t going to come through and it has an elevation of 70 feet. So we’ve got to get it under the bridge otherwise it’s going to smash the bridge. So 70 foot iceberg, 50 foot bridge, let’s say we remove 30 feet of ice, right? The new iceberg elevation is going to be 40 feet, right? Nope. The new elevation of the iceberg is going to be 67 feet because an awful lot of the iceberg was underwater. Most of the mass is hidden but all of the mass is in dialogue. So if we change any part of it the rest is going to adjust and everything will adjust to that.
Iceberg above water was in equilibrium with the ice below water. 10% was visible, 90% was emerged and invisible to us. And it’s invisible even though it’s the greater part. So bringing this back a bit closer to our remediation scenario, it’s not actually that different from what we might get from groundwater samples. If we’re looking at PCE, for example, and some not unusual groundwater parameters, we would indeed have about 10% of the PCE in solution and about 90% of the PCE sorbed to the soil. So if we take three micrograms per liter of sorb concentration, it’s not going to go down by 3%. It’s going to go down by 0.3% because of re-equilibration with the hidden mass. And that was under a normal system.
If we’re using something that is going to increase the KD, increase the sorption by two to three orders of magnitude, like plume stop, then suddenly pretty much all the mass is going to be invisible to us. Rather than 10% visible, maybe about 0.001% might be detectable in groundwater because we’ve changed the equilibrium so much by adding the plume stop. So if we want to monitor and try and measure what’s happening with that, we’re going to need some other tools to into that. Let’s take an example of a site in the Midwest USA. This one is an industrial site. It has high concentrations of contaminants and high flux and there is only a narrow accessible area for treatment located in the roadway between the buildings and the property boundary. Let’s take a closer look.
We’ve got chlorinated solvents TCE and DCE measuring about 16 milligrams per liter. Ground water’s moving in this direction. On this project, we threw pretty much everything we had at it. We’d call it a kitchen sink project. Plume stop, electron donors, inoculum, S-micro, ZVI, another regenerative remediation project. And all of this was applied in the roadway here between the shed and the boundary fence. The idea was that the plume stop would increase the contaminant residence time in the reagent zone that we would have a greater efficiency of treatment, increasing reaction time and therefore efficiency in keeping the treatment zone footprint particularly small. And this was valuable given the high concentrations, the high velocity and the limited space that we have with the boundary.
The data that we have from an in barrier well. And to get an idea of what’s happening with this with so much the mass on the plume stock is how modeling is going to basically give us X-ray vision tool. So let’s see how this comes in. Here are some of the actual data from the site and what we can see is a rapid reduction in dissolved VOC and the appearance of ethane and ethene which are plotted on the secondary axis that’s the green and the blue lines and this is consistent with the sorption that we got and the bio and ISCA reductions. But how much reduction did we actually get? We can see some is going on, but the concentrations are far, far from stoichiometric. So what is actually happening by way of reduction?
Well, let’s have a look at what we can unwrap with this. This is the same chart that we saw before, but now I’ve put the contaminants on a common axis. So we can see the cis-DCE and the TCE going down rapidly to pretty much non-detect. And then we can see a tiny little blep of ethene at about a hundred days. Those are the measured data on the left. These are the modeled data on the right. The slopes are different due to data point spacing, but in both we can see the same story. Pre-treatment dissolved phase concentration drops to a trace and a transient detection of ethene forms peaking after the decline in the parents, not during the decline in the parents. The concentration changes are far from stoichiometric as I mentioned. We can see the sorption and destruction occurring at how much of each.
The challenge of course is that most of the mass isn’t in the water that we can sample and so we can’t follow the usual parent-daughter transformations and concentration changes to track the destruction. All we can see is the tip of the iceberg. So the image on the right is a groundwater concentration window out of the plume force software. Other windows that we have within the software look at total mass in the system, and so this is how we can get insight into what’s happening. And what I’m looking at here is the concentrations prior to applications. So on the right, we’ve got the familiar dissolved phase graph of concentration versus time in the monitoring well, and on the left we’ve got a block diagram for one of the compounds in the mix, TCE. We can see the TCE mass in the groundwater, but we can also see the model compartments. The vertical axis that we have here is milligrams of contaminant per litre of aquifer material, not per litre of water.
So specifically what we’re looking at in blue here is the mass of TCE in the water, the groundwater phase that we can model, the high fluxing water, the high care units. In brown, we’ve got the TCE mass that is sorbed to the FOC that would correspond with that. And in grey, we’ve got what we’ll call stored mass in the low care units, the mass that has into the lower flux, the lower conductivity matrix, the area from which back diffusion might come from. In this scenario there’s no treatment, just a slow ambient bio-attenuation. All the species are degrading slowly. TCE is dropping but DCE and vinyl chloride are at a steady state where formation and destruction rates balance. There’s no treatment.
Now we add the reagents, plume stop, electron donor, and s micro zvi. The plume stop is another compartment to the block diagram. It immediately sobs the mass that was in the aqueous phase and the destruction of the TCE by the s micro zvi is so fast where the reagent contact occurs that it’s almost immediate and the only mass left here is in the middle of the barrier is the mass that’s in the low k units where the reagents have not penetrated and meanwhile the equilibrium has changed so that the low k unit mass begins to back diffuse out and the stored mass is reduced but as soon as this happens and it becomes accessible it’s either sawed by the plume stop or knocked out by the treatment reagents. The mass in the groundwater the mobile high k units we sample that drive the risk just remains negligible at this time you can see hardly any blue here at all.
From the groundwater sample on the right, we can’t really tell if it’s been sorbed or destroyed. But with the modelling, we can see a little bit more of that. Let’s move on to some of the other species. This is DCE. And in this case, we can see that the dissolved phase mass disappears almost immediately. The blue mass disappears, it’s sorbed onto the carbon. But this time, the overall destruction of DCE is far slower because DCE is much less reactive with the ZVI. So we see the mass from the groundwater and the FOC partitioning onto the carbon and then some of the mass from the lower K unit back to fusing a little and again, getting caught on the carbon.
So none of it really shows up in the groundwater. All of the action is now starting to take place in the salt phase. Where it starts to get more interesting is with daughter products further down the line. So here we’ve got some more striking changes. The DCE mass balance may have been broadly static, but with the vinyl chloride we can see that the total mass actually increases quite substantially for a period, even though none of it’s showing in groundwater. What is formed through the destruction, the bio-destruction of the DCE has itself been captured on the carbon, so none of it is actually in water or driving a risk. So this is essentially the familiar daughter product man that we might see in groundwater.
But here, of course, it’s remaining close to zero because it’s been captured on the carbon. And then when we move to ethane, we see a big jump up in the ethane from the beginning once we’ve added our reagents. It goes up by about an order of magnitude. And this is at last where the iceberg peaks out of the water. And we can see a little bit of the ethane appearing in the dissolved phase here, which corresponds to what we can see the groundwater right over here. That detection is actually very helpful for us because it gives us something that we can start to get a quasi-calibration to. It gives us a qualitative and also a semi-quantitative indication of what might be happening. And because ethene is the last of the species in the degradation process from isca or biodegradation, if our modelling is predicting about the right quantity and timing of ethene, then we can presume that a number of the other points are broadly in the right place.
Biodegradation of ethene is relatively fast, so the peak soon drops, but it does reach a plateau for a period with respect to the total mass in the system, which we can see here, while the formation and destruction rate balance. So this is another one of the kinetic equilibria. We’ll have more of this shortly. Overall then, what we’re really looking at in this modelled image is a tiny bit of the iceberg mass appearing in the groundwater sample. The majority of the action is hidden to us, but now with the modelling we can get insight into what’s going on in hidden compartments which are out of sight. And with this model we can infer back through the other compounds for which nothing is showing in our groundwater samples and gain similar insight.
So now we’ve got the model built and providing reasonable correspondence with measured data, we can begin to interrogate it. We can explore some what-if scenarios to see how the system might behave if we adjusted or removed any components. What happens if we take out one of the reagents? Do we really need to plume stop, for example, if we have bio and ZVI? Now this might not be helpful for the current project because it’s already in the ground, but now we’ve got a calibrated system that’s behaving about right, we can get to understand a lot more about the what-ifs that would then help us with another project down the track. So what does happen if we take out the plume stop? Well, we get something like this.
A lot more of the daughter products would be visible, particularly the cyst DCE. The TCE is taken out pretty rapidly, but the species, less so because zerovalent iron has a much slower impact on DCE, vinyl chloride and the others. DCE vanishes but basically from a design standpoint we can see that Plume Stop takes the theatre of operation out of the groundwater and onto the sorb phase, so with remediation engineers, which would we prefer? Do we want all of that mass in groundwater fluxing out of our treatment zone or do we want to keep it in place where the reagents can do their thing and where the mass that comes out of the treatment zone is negligible?
Remember here we’re looking at mobile mass and so we don’t want that fluxing down gradient particularly on this site where ground water is fast and the site boundary is close. And this is not mass that’s breaking through, this is mass that was already in the system that we’ve been treating so extending the barrier or the barrier won’t actually make a difference in this case. Okay, that was an example of a static equilibrium. The ice was frozen. What about dynamic systems, ones which are in a permanent state of flux? Well, this takes us from icebergs to waterfalls and perhaps a pleasant shift in climate and temperature. So let’s talk about waterfalls.
This particular waterfall, as a interest interlude the Iguazu Falls complex bordering Argentina and Brazil. They are the largest waterfall complex in the world. This is a shot I took a number of years ago. I only managed to get a few good photos of this from a distance because so much spray blows out from the falls that hits you as a very welcome cooling wind in the tropical heat. My camera lens was soon covered in droplets which really spoiled any attempt at further pictures and it was way too steamy and humid for any of those droplets to dry. The falls were just awesome. They were like looking at the white cliffs of Dover in thunderous motion. Really, it was a life experience.
But anyway, back to cleaning up groundwater. The waterfall analogy is about static patterns in non-static systems. The way the analogy works is that water in the waterfall is always changing, but the shape of the waterfall stays the same. What we’ve got here is a kinetic equilibrium, literally a moving balance, a system in a state of flux, but in which the inputs and the outputs balance. So kinetic equilibria crop up in remediation again and again. They are an emergent phenomena. An example that we’ll explore occurs with contaminant transformations and specifically the cascade of parent to daughter biotransformation’s when we’re doing, say, a biotreatment of the chlorinated ethenes. It’s interesting that we, in fact, use the word cascade to look at the transformations of parents to daughter solvent biotransformation’s.
We’re almost referring to it as a waterfall already, but this is the cascade, I mean, PCE to TCE to CYS-DC to vinyl chloride to ethene. So in this graph, for example, we’re looking at concentration versus distance in the direction of groundwater flow. PCE is flowing in at about a milligram per litre, it hits a biozone at about the 10 foot point, an electron down a barrier say, and we then see the sequential appearance and disappearance of the biotransformation projects. When the input is ongoing, concentrations at any point along this wave can appear static as degradation proceeds. In other words, we’ve got a standing wave, a waterfall.
The system is fluxing all the time, the actual molecules are changing all the time, but the pattern and the concentrations that we see at any point along this wave remain broadly the same. That’s our waterfall, that’s our fixed cascade. To emphasize this even more, here is a waterfall cascade. The parent VC is flowing in continuously and getting transformed continuously all the way to ethene, but at any point in the flow we see different stages of the transformation process. It appears static, but it’s not like a waterfall. The water might be flowing through, but the waterfall stays put. So waterfalls are an analogy for kinetic equilibria. The water is always there, it shapes constant, the water changes from one moment to a next. When a pattern is fixed, it does not mean its constituents are. It’s just that the input and the output rates balance.
Let’s look at that graphically. The phenomenon might look something like the blue line is an output, destructive, maybe it’s isca, maybe it’s bio, doesn’t really matter. The kinetics are first order. In other words, the rate has an exponential function. It’s not equal to one. It changes as concentration changes. On the horizontal axis, we have contaminant concentrations in groundwater. This end is high and this end is low. The is dropping left to right. On the vertical axis we have the instantaneous rate of change, in other words the gradient or derivative of the concentration versus time plot dc by dt. But there is an equilibratory input too.
We’ll use back diffusion as this example. The system was broadly stable before we started any treatment but as soon as the contamination destruction takes place then we upset the equilibrium. And as we destroy mass in the accessible transport components, the higher K zones we can inject reagents to, we set up a concentration gradient with the storage compartments where back diffusion comes from, the lower K units or porous, but lower permeability deposits. And then diffusion follows the gradient. The more our remediation chases down the concentration in the treatment zone, then as the concentration changes from high to low on a horizontal axis, then the steeper the gradient becomes. And as the gradient gets steeper, diffusion gets faster, and we can see this with the curve.
But since the destruction rate slows as remediation proceeds and the concentration drops, the lines invariably cross. So between these two processes, an in process and an out process, both concentration-dependent, we will invariably get a kinetic equilibrium and this results in a stable concentration where the input rates and output rates balance. It doesn’t really matter what the concentrations were to start with, the rate will always gravitate towards that equilibrium. It’s as if the water is flowing into the bath as fast as it’s flowing out. We have a waterfall, it looks fixed but the mass is changing all the time.
So a kinetic Equilibrium will emerge as an emergent phenomenon when input rates and output rates balance. A system will naturally settle at a stable equilibrium concentration when three parameters are satisfied. There needs to be an input and an output. At least one of these has to have a concentration dependent rate and the rates are identical. In other words, they cross and the crossing point is where the sum of the two rates becomes zero. Scenarios where this occurs as emergent phenomena are very widespread and they can be easily overlooked and confused. Something that is stable over a period of time looks fixed or stalled and we’re tempted at that point as remediation engineers to intervene but the system may be far from stalled with destruction roaring away but at a point of stability and so rather than intervene sometimes it’s better for us to simply understand, confirm that these processes are on and then monitor them to ensure they continue to go on.
They occur when input rate equals output rates and input examples are the ones I’ve listed on the left. Effective flux, degradation, desorption, back diffusion, DNAPL solution and output examples can also be the vector flux, maybe pump and treat, biodegradation, sorption onto the FOC, forward diffusion, isco, iscr. There are plenty of examples. Most of these exhibit nonlinear kinetics, typically first order or quasi first order. And so in most of these cases, kinetic equilibria will naturally arise. The system will gravitate to the equilibrium and then exhibit apparent stasis like a waterfall. Let’s simulate an example in plume force.
Here is a plot of a migrating attenuating plume. Plot is concentration against distance, so we’re looking at how the VOC species transform over about 500 feet in this case. It’s entirely hypothetical, we’re just exploring rate patterns. We can see PCE, TCE, DCE all degrading nicely, but the vinyl chloride concentration there in red at the bottom appears static. So why is this stalled? Is it a microbial deficiency? End point inhibition, maybe the redox isn’t optimal. Well, in reality, in this case, these are the degradation rates that I’ve put in there. The vinyl chloride has a half-life of 20 days. It’s 10 to 25 times faster than its parent degradation, so it looks like a stall, but it is not a stall. As we’ve seen, the vinyl chloride flatline is a kinetic equilibrium. It’s moving fast.
If I use the model to turn off the degradation rate of DCE, I’ve put the half-life for a million days, we can see what the stall really looks like. It’s not a flat line at all. It’s where the input is continuous but the output has dropped right down and so the concentrations start to climb right up. That’s what a stall looks like. What gets interesting though, and the reason we can see how stable kinetic equilibria can be is that here in the model I’ve increased the vinyl chloride concentration to a thousand micrograms per litre. It was originally just 50 micrograms per litre so I pushed it right up, but the kinetic equilibrium that it reaches is almost exactly the same as we had to begin with. That’s because the equilibria that we get are largely driven by rates rather than the starting points.
The equilibrium is something system moves to and then stabilizes at. Who’d have thunk it? What would be the natural interpretation of this graph? It would look like the vinyl chloride degradation was fine up here but then suddenly it stalled and started to slow down and we might want to run in as engineers and intervene whereas really the degradation is moving fast. So appearances can be deceptive, things are not always they seem, and strange phenomena can emerge from this interplay of simple processes. We’ve got time for one more example. This is from another real site in Europe. It’s an example of standing wave confusion. We’re looking at a pilot study, a reactive zone bio barrier. We’re in fractured limestone. It’s deep.
The treatment is going down to a depth of about 200 feet below grade. We’ve got fast groundwater. It’s reported as about 1200 feet per year. I’m not sure if it’s quite as fast as that, but we’ll work with that for the case of the analysis. And it’s hot. The incoming TCE is about 50 ,000 micrograms per litre, or double this at the peak. The graph that you can see on the left is in micromoles per litre. 300 micromoles per litre here is about 40 ,000 micrograms per litre, 40 ppm of TCE, and we’ve got about seven years of performance data on this pilot project. The treatment was a Regenesis reagent, 3D micro emulsion, a slow release electron donor, and the treatment was actually just a single application. The data of the first well downgrade into the reagent application looks very different from what’s coming in up gradient. The TCE concentration has reduced by about 95%, and we can see the molar ratios of daughter content, this is micromolts per liter, the molar ratios of daughters pretty much add up to the TCE that we had going in.
So there’s clearly some biodegradation coming on as we’d expect from an electron donor addition. The longevity is remarkable from one application, we could speculate the reasons, but that’s not really present for the necessary analysis. Suffice to say that the donor is long lived and the donor dose that we put in was very high. The relevant point for this analysis is that we still have high concentrations of daughter products even seven years after electron donor application and the vinyl chloride and ethane concentrations are higher now than they were in the first two years or so, the first 750 days.
This was interpreted by a third party reviewer as perhaps resulting from a stalling of the concentrations and an end to the bio and they felt that what was necessary was to switch to an aggressive ischium recirculation on the basis that there was vinyl chloroids still stalling and that they would be very happy to put in 200 feet depths in fractured limestone that was not going to be a cheap system to put in. But it also suggests that some confusion could have been underway as to what the actually reveal. So can modeling help us with this? Let’s take a look.
These are the field data plotted and in this case we’re looking at concentration coming in but we’ve got a number of wells. We’ve got an upgradient well here and downgradient wells and a distant well and this is the story that they’re telling. Groundwater is flowing in this direction and here is the monitoring well that we were looking at just now. Positions of the other wells are shown. So this is starting to look like a familiar standing wave. Here are the model data. Note that the graphs match where the monitoring wells are situated. Plume force model shows a bit more going on here in the field data. We can’t see this because there’s no monitoring there. But we can see that the model suggests there’s a big spike in DCE between the first two wells. So we’ve kind of got a window into some of the hidden parts.
Great, but so what? Well, what’s interesting is that we can see how the changes in the inputs influence the data patterns that we see in the monitoring well. So let’s go take a look. Here’s the in-barrier well that we were looking at a moment ago. And here’s the third-party reviewer’s interpretation of what looks like a slowing of the vinyl chloride degradation. But now, however, we’ve got a model built that’s matching the site data reasonably well, and is calibrated to the observations that we’ve got. So now we can start to interrogate it. So what would we have to change in the model inputs for the observed pattern to shift over time as it does in this particular monitoring well?
Interestingly we find that only one parameter has to change to very quickly get a similar pattern and in this image we can see a model generated data set based on the calibrated model fit that we were at previously, but in this what we’re doing is changing one parameter, the DCE degradation rate, and exploring the relative concentrations of the solvent concentration this results in, in a fixed point in a standing wave, the monitoring well in other words. In the bottom graph, the DCE degradation rate is increased from left to right. The actual rates are not important in range. So it’s a bit like looking at how the pattern might have changed over time, like the top graph, if the DCE rate was actually increasing. And we can immediately see similarities between the two graphs. The DCE plot crosses the TCE and the VCE plot here and here.
It’s not an exact facsimile match, but it does not have to be. What we’re exploring here is what can the patterns we see. We would not expect DCE rates to change alone. The system will acclimate and the microbial community will mature over time and none of the rates will be static. But we can see that what might have appeared as a vinyl chloride slowing might equally have been a net rate increase in the degradation. In fact the modeling fit falls more easily into place if we slowly accelerate the rates impact. And this is sort of what we’d expect from a maturing system over time. Excellent work on that by the University of Sheffield by the way for long-term microbial community maturation and deep aquifer settings. So the graphs on the right show two stations on the way.
Here we’re essentially looking at the full standing wave profile again at concentrations versus difference. So here’s the monitoring well point on the standing wave and we can see the different ratios of VOC species in the graphs and the DCE rates these correspond to with here and here on the other image. What we’re actually looking at then with the data that we can see in the well is kind of like looking through a slot window you might say. So we can only see what’s happening in this one well if we’re looking at this this one point. We can’t see what’s actually happening on the rest of the graph but with modeling we can start to explore into that. We could have perhaps done the same by building a plume figure on a map.
It’s one way to explore the bigger picture, but this is time consuming. It’s also dead in that the relationship between the plotted points has no numerical causative logic. So we might miss significant content, like the DCE spike in the earlier graph, but more importantly, we can’t experiment with or interrogate the pattern we see in order that we can explore what’s driving it and hence improve our understanding. So, to make this a little clearer in the few minutes I’ve got left, let’s look at a full time series for the increasing DCE rate so we can see how it’s going to change the pattern in the one world that we were looking at. This is a system that we’ve got with a very low DCE degradation rate. This is our active bio-stimulation zone of influence of the electron donor. And the model DCE degradation is set very slow.
I’ve given us a speedometer in the top left corner here. Here’s our monitoring well position, and remember this is a fixed point. And so following the data in this fixed well is a bit like looking through a gap in the fence, a slit window. So here’s our slit window gap in the fence. The image is getting a bit crowded so I’m going to remove the green active biozone so we can see what’s actually going on a little bit better. So now we see our slot window a bit more clearly. The dashed line shows our monitoring well position and our slit window view. And all we can see in the slit window at this particular point is that the TCE is gone. The DCE is abundant and a very small amount of vinyl chloride is present showing that we’ve got some onward degradation of the DCE, but we can’t tell that the DCE rate is slow.
So let’s increase the degradation rate a little. DCE quantity is still high, degradation is a bit faster, but now we’ve got a little bit more vinyl chloride showing. So this is similar to the early stages of the pattern measured in the field. So this is a possible scenario we might be looking at. This would be, in general, semi-quantitative terms. So we’re looking for patterns, not facsimiles. The TCE is gone, we’ve got high DCE, low vinyl chloride and lower ethene. So it’s kind of like the early stages of the analysis that we ran. Let’s start increasing the rate a bit more but in smaller increments so that we can see how things change. So bit by bit we’re increasing the DCE degradation rate and as this happens we can start to see how the ratio of DCE and vinyl chloride in the monitoring world change as the DCE rate increases. The DCE goes down and the vinyl chloride goes up.
They’re starting to reach a crossing point where they match and there it would be on the other chart. Faster, faster, faster. And so this is the maximum rate that we’re going to look at. The vinyl chloride has continued to climb. DCE has continued to drop and that’s kind of the qualitative pattern that we saw with the site data. So this is our fastest degradation rate. The whole standing wave we can see has marched backwards up gradient as the DCE degradation rate has increased, but what we’ve been able to see through this slit window has simply been an increasing in the vinyl chloride and a reduction in the DCE. So the take home that we have here is that things are not always as they seem.
What was interpreted as a slowing might instead have been an increase, this interpretation has the implications of an awful lot of dollars. It is worth mentioning that with respect to this exercise the modeling does not have to be a facsimile reproduction. Real-world data themselves are seldom stable so therefore chasing an exact fit is often a fool’s errand. What is important is that we can use modeling to expand the picture based on limited data and then quantitatively explore what might be driving the picture. So what this does then is help us form credible conceptualizations of what’s going on. And once we’ve got these, we can then seek to validate or corroborate them against further site data as those data might become available. So the model to explorations reveal in this case that increasing the degradation rates of some or all species compresses the standing wave and the overall wave marches up gradient.
So here we can see the modeled images with the slower rates on the left and slightly faster rates on the right. Here’s our monitoring well again and as we can see the ratio of species changes. Specifically the pattern shifts from DCE being greater than vinyl chloride in the early days to vinyl being greater than DCE in the later days. These are our site data plotted over the same distance. So these are actually measured. Here are our monitoring wells again. And once more, we can see how the patterns change. DCE greater than vinyl chloride in the early days and vinyl chloride greater than DCE in the later days. So without the modeling, we would be much more hard pushed to be able to interpolate the data between the points.
What we can see in the real site is consistent with the model scenario, or put the other way, the model scenario is consistent with what we see in the field. And the inference that we can therefore get from this is that the microbial community is actually maturing and performing better with time rather than stalling, as the interpretation at first suggested. So appearances can be misleading. Things may not be as they first seem. So to conclude, standing waves can form whenever transformations occur in a fluxing system, for example a reactive zone bio barrier. The standing waves are static patterns in non-static systems like a waterfall. Contaminants are degrading but the point concentrations might stay the same and the point concentrations might even increase over time as the degradation speeds up.
Standing waves are just one example of a kinetic equilibrium. These are widespread, especially during remediation, and they occur whenever system inputs and output rates balance. Modeling can help us unwrap the data. It can help us see underlying mechanisms behind the observed patterns that we might be looking at. It helps us also explore conceptual scenarios and test them and interrogate them to see how sensitive they are and whether they stack up and what we might want to look at to test them. Things may not be as they first appear.
So to conclude this webinar, emergent phenomena, simple processes can combine to become complex. Putting it all together in our heads is challenging. Things may not be as they first appear. We talked about icebergs considering the invisible mass. Groundwater typically only contains a of the total contaminant mass in the subsurface, but it’s all that a monitoring well will measure. The hidden body of mass in or on the soil may dominate the performance, and this will be even more the case if plume stock is present. We need to know what’s happening in the hidden compartments to understand how the whole compartment will behave. Waterfalls, static patterns in non-static systems. These were our kinetic equilibrium.
In a fluxing system, a monitoring well reports data from only one point on a standing wave and concentration trends in that well may resemble a stall or a slowing when in fact the opposite is true. So these kinetic equilibria will form in many cases and this occurs when system inputs and output rates find a balance and often the system will gravitate towards that balancing point and then stay there changing only slowly. There’ll be a little more of that in relation to PFAS remediation in the next webinar. Modeling can offer a window into the governing processes behind the limited data snapshots that we have. It can expose hidden processes. It allows us to interrogate conceptual scenarios. We can better understand what is going on. We can make better decisions and we can use it as a tool to facilitate communication.
As I like to put it, it helps us understand better, design better and communicate better. So in the previous webinar we looked at how modeling can support the design. This webinar has focused on how we can use modeling to deepen our understanding. In the next webinar we’re going to look more at the communication. So coming up next time, modeling beyond design. How we can use modeling as a tool to support communication and managing expectations. How we can use modeling as a tracking and management tool, setting PAR for the remediation course and determining whether our performance is a birdie on PAR or a bogey or hopefully an eagle or an albatross.
We can use modeling for mapping the jungle, bringing order out of chaos, bringing clarity to complex datasets and we’re going to look at how modeling can be used to keep remediation on track, how we can use it to help steer a project between the ditches. More formally, we’re going to look at it for communication, expectations, management, performance tracking, and optimization and maintenance. So I believe I have a few minutes left. Thank you for your attention through this webinar. My contact details are here, or please respond to the survey that will be put out by Dane shortly after this webinar. And at this point, I’d be very happy to shift to any questions that we might have coming in.