Well, we've introduced some of the principles of CSIA last time, and now we're going to take a deeper dive in how the data can be interpreted. Right, Dave? >> Yeah, that's right. And I'd like to start by repeating this slide from the last lecture. Specifically the statement from the 2008 EPA guide on CSIA. And I'm sort of repeating this because it reminds us that, for MNA, the goal is to use this data to demonstrate contaminate degradation. >> Okay, and that's definitely important but I know that CSIA has a lot of other forensic uses. Like identifying the source of contamination or determining that there are multiple sources, for example. >> And we'll discuss that a little bit in the next lecture, the focus of this lecture will be on how to use CSIA for MNA applications, which really helps narrow down what can be sort of a complex and overwhelming topic at times. >> Okay, well sounds good, take it away. >> Okay, well let's focus on the carbon isotopes today, and look at how the carbon isotope signal within a parent compound containment, something like TCE, would shift if degradation incurred. So, we'll go through a typical way that isotopic data would plot it. So Chuck, what are the axes on this graph? >> Okay, it looks like we have a dell value for carbon isotopes on the y axis >> In time or distance on that x-axis. So we can plot the changes over time and distance due to this degradation. >> Yeah, so not that much different than like a typical c versus t sort of graph. So you can imagine that it's time or distance progresses from left to right on that x-axis, and on the y-axis, fractionation will cause the isotopic ratio to increase or get heavier. >> Okay, I'd like to say, get less negative >> So degradation causes the ratio to shift upwards, as shown by this blue arrow. >> Yeah, so you start off with some initial dell value, perhaps representing un-degraded parent compound. And if you are lucky enough to have samples of, that sort along the down gradient plume or even from the source as it degraded over time, you might see this increasing trend relative to that initial dell value. >> And so that's what each one of these little blue dots are showing. The isotopic ratio is increasing. The amount of the degradation reflected in the difference between this initial value, and that value that's measured at a particular point in time or space. >> Yeah so that's [INAUDIBLE] >> Really that simple. But an important thing to remember is that there is some uncertainty here. To really demonstrate that fractionation is occurring, you have to meet sort of a threshold that's based on the precision and accuracy of the isotopic analysis itself. So, the U.S. EPA guidance has suggested that this needs to be at least two per mil, you can be really confident that what you're seeing isn't just some sort of analytical norms. >> You mean like, the change has got to be at least two per mills. >> you, so like, on this graph here we're seeing from like a -30 to maybe a -15, so >> A pretty good evidence that that's actual degradation that's occurring. Okay, so that's the basic premise and a couple of key points are shown here. Namely that these patterns can be used to estimate the fraction degraded and the rate degraded, if you apply the Rayleigh Equation, which we'll show later. >> Okay and secondly, some people think that maybe these isotopic data in some cases may provide an even better estimate of rates than the standard concentration versus time time data. That may be speculative, but the basic idea is that these data are less subject to these non destructive processes like dispersion that can really influence the rates that you get from looking strictly at concentration versus time data. >> Right. Okay, so let's take a look at another important way that the isotopic data are used specifically to determine if daughter products are, or aren't actually degrading. So, we've got our same plot here with the isotopic ration on the y axis, and time or distance on that x axis. In addition to the values for the parent, we're also going to plot the data from the same set of wells or time series for a daughter product, say cis-DCE, and those are those lighter blue dots below there. So now, the thing to remember is that cis-DCE is being produced from the TCE that is degraded and that the bugs preferentially degrade the lightest TCE first. So the cis-DCE starts out very light below the values of the TCE in the source area. But then also remember, that DCE is subject to being degraded as it's being produced. So you might be expected to show a shift as well in DCE. So you want to know if that shift is due to degradation or if that shift is simply due to the fact that the remaining TCE is becoming lighter as well. So one way to evaluate this is to see if that dell value for the daughter product never exceeds that initial dell value for the parent. So if it never moves basically above that dotted blue line. So if it doesn't, that means there's basically no degradation, or no evidence of degradation of that daughter, and it would be expected. To It's expected to do accumulate. >> Okay, now I think the next slide shows the opposite case, right? >> Yeah, yeah, so this is a slide where you're basically saying no degradation of the daughter product. So here's what you'd expect to see then, if you saw a degradation of that daughter product. The isotopic ratio for the daughter eventually is exceeding that initial dell value for the parent, that dotted blue line, meaning that the remaining cis-DCE was heavier than the initial TCE that produced it. So in some cases, the dell value for the starter product could even exceed the dell value for the parent compound. So that those lighter blue dots would go above the darker blue dots. >> Okay. So that's a good example how to gather lines of evidence for daughter product degradation. I see how it could be useful for cases where DCE is going away, but you are not seeing a lot of other common degradation products. So why don't we look at a different application, this time focusing on rates? >> Okay. So we're basing this approach on the equations that we showed during the last lecture. But one way to think about it is sort of, this is a lot of times a first order approximation. So we're trying to calculate in this case a first order rate coefficient with either time or distance. >> Okay so, here's our basic equation, solve for the first order rate coefficient. We have our isotopic values at time 0 at any time t, along with our Enrichment factor which is labeled as a look up value. >> Yeah, in this case. You can actually calculate your own Enrichment factor, I think we mentioned this before, if you have enough data, because it's really just the slope on a fractionation graph. But for field applications, I think most people are sort of forced with using literature values, which we'll show an example of later on. >> Okay. And let's put some numbers in here to show how you might do this. So this is based on change over distance. So I've got a value of -31 at well MW-1, near the source, and I see this increasing ratio as I move down gradient. And by the time I reach well MW-8, located 400 meters down gradient. I'm measuring a value of -15. >> So if you're interested in the attenuation rate over that distance, you basically need to find an enrichment factor, and for this case we'll use -20 for TCE, which is fairly common for this compounding degraded through the reductive decoronation pathway. >> Okay. And then if we substitute this values into array equation. We sort of run the numbers and if we get this value, this rate of 0.01 per meter, and then we can multiply this by a seepage velocity. Let's just say at the side, it's 100 meters per year. So 0.01/m, times 100 meter per year, gives us an overall rate, a first order rate of coefficient of one per year. Pretty neat. >> Yeah, so there's other forms of the Rayleigh equation which you can also use to get sort of the same information. For example, if you're calculating the fraction of compound remaining based on the isotopic ratios, you could also plot those fractions versus distance or time, to get a rate coefficient. >> Okay, well, nice example. I suspect the class will see something like this in our homework, right? >> Don't spoil the surprise, yeah. Okay, so the final slide is just showing some of those enrichment factors that you could maybe chose from. These are based on a compilation of various studies. And this was included in the User's Guide for an ESTCP project on CSIA and reactive transport. We'll touch on this project in a future lecture. This was one that was done at University of Oklahoma. The University of Amsterdam and GSI worked on this project as well. But I like these graphs, because it shows a lot of data and it also reflects that there's quite a bit of variability in terms of what you might see based on these various studies, but a good resource. Okay, well let's wrap up by looking at some of the key points. The change in the isotopic ratio can be used to estimate the fraction of compound that has been degraded and the rate of degradation. >> Okay, and the isotopic ratio of a daughter product is initially lighter, it's more negative than the parent, but then, get's heavier or less negative as it degrades. >> And then finally, literature values of enrichment factors can aid in the interpretation of CSIA data.