Now that we've discussed the types of minerals that are out there and what type of contaminant degradation reactions they might promote, it's time to turn our attention to the kinetics of these different reactions. So, as you know, I got my undergraduate degree in chemical engineering, so this is something that really, really gets me excited. So, I'm ready to go. >> No, that's good to hear. Do you want to take this entire lecture then? >> No, let's do the tag team. Go ahead. So, the key point is, we want to understand these rates because being able to estimate these rates is really this key factor in demonstrating the viability of monitored natural attenuation. As we've discussed previously, you need to be able to estimate how fast the attenuation is occurring, and that's how long it might take to clean up a site or to control a plume. >> Yeah, that's right, and if our primary concern at these sites is to eliminate any potential risks to receptors, the reaction rate has really big implications in terms of how a plume will either shrink or expand. >> So, really thinking about how are these kinetics or abiotic reactions. So, a key question is, how are they different? How is abiotic different than biotic? >> Well, let's take a look at this in terms of sort of the individual steps that are involved. Remember that we've got a biogeochemical process, and so we've got a biological, geochemical as well as chemical reactions, and we break those down in terms of the kinetic associated with each one of these. So, this is part of a graphic that was borrowed from a Navy paper that came out. You'd think that the first one, the biotic step, the formation of basically the reduced iron and the reduced sulphites. We're talking about rates on the order of days, and then we move into the precipitation of the minerals. So, that formation, for example, of iron sulfide that takes place basically instantaneously. So the reaction kinetics are really favorable in this case. But then we move in to the actual abiotic degradation of the containment itself and so here's an example of PCE being degraded by an iron sulfide and we're talking about half flies in this case under sort of an ideal conditions on the order of 30 days. >> And okay so several steps three steps here that are involved >> That maybe the key point is that it's that last one in this one, that abiotic reaction itself, the degradation of the contaminant that's really the rate-limiting step. This one says 30 days but I think that's under idealized conditions, right Dave, in the field. >> Sure, it's going to be longer? >> Yeah, yeah, definitely could range out into the years. >> Okay, let's go to the reaction models. >> Okay, so there's a lot of different ways that you can describe this kinetics and we'll deal with some of this first order and normalized first order or second order. There's also zero order, which we're not necessarily going to deal with within this particular lecture. >> So, zero on the zero for this lecture. >> Zero on the zero order, exactly. >> Let’s go to first order >> So first order, this is a sort of kinetic formula that should be familiar to most people. But again, we're talking about change in concentration overtime, being first order with respect to the contaminant concentration, then there's some first order rate coefficient, and we're going to call this k in this case. That's really defining your rate. So, the solution of this reaction is in exponential form. Looking at C at any particular time being equal to C not, exponential rate to this minus kt, and that t is the time in this case. >> So, if you want to visualize this, in terms of a graph, we've got a graph up here. The y axis is really this natural log of this normalized concentration. The concentration at any time, divided by that starting concentration, that's on the y-axis. On the x-axis, you just have time. And this can be from a lab study or in the field, but it's just the number of days or years or whatever you have on that x axis And then you got the slope of this thing, and that slope is this rate, is that right too? >> Yeah, and this is a what is essentially a pseudo first-order rate coefficient, since the influence that the mineral has on, and it's sort of built-in into that rate coefficient. And some people like dealing with rate coefficients, other people like dealing with half-lives, I know you're a half-life sort of a guy, so the conversion for that is pretty straightforward and shown there. And you get this rate coefficient and this half life, you can compare it to other attenuation rates just with the idea that it may be different especially if you're dealing with field data to differentiate between the abiotic component and the biotic component. >> Just a couple quick points if you have a k and you want to think about it in terms of a half life use that formula on the right. Side there t 1/2 = 0.693 / k. If you have a tough life, you want to convert it to a k, it’s the same formula but, where did the 0.693 come from? >> That if I remember correctly, it’s the natural log of 2 so >> Did I get that right. >> You're a brilliant guy that sounds right. >> Thanks. We then now just going to look at this as normalized first-order reaction. So the initial form of the reaction is the same where again, looking at the changing concentration over time in this case we've got a KN which is essentially a second-order rate coefficient where we've got our rate expression having this S term in it. So it's a reactive mineral. Either concentration or surface area something like that that we're actually building into our rate reaction. So the solution of it is then shown here. it's got a similar formula. But we're then using the k value, the first order rate coefficient, and we can divide by that reactive mineral concentration or surface area, that S term. So here's the graph again. The same graph, the log of this normalized concentration on that Y-axis, and then time on the x-axis. But at the very end, you have this slope and then you modify it with either, say, an area or a concentration. Right? >> Yeah. And that's summarized then here in these points. So again, first-order with respect to contaminant concentration and reactive mineral concentration. We're sort of assuming that the reactive mineral concentration in this case is constant with time. So, that's why we're able to then sort of normalize at the end and divide by it. If in this case, the concentration or Surface area of the reactive mineral was to increase, obviously you'd increase the rate of contaminant attenuation that you'd see. And again, this is pretty useful because it accounts for the amount of mineral that you have, the caveat is that it may be actually sort of difficult to establish what that concentration or that surface area of that mineral is. >> So it's said, be careful reading some of these papers, or maybe this rate, and if it's divided by the surface area of the mineral >> And you want to apply it to your site, you're going to have to somehow estimate how much surface area you have, and that can be difficult. >> Yeah, and if you're looking for rate information, there's at least two main ways of getting this sort of data. You can either go to lab studies that have already been completed and use their rate coefficient that they've already established, or you can go to field data and try to get your own rate coefficients. So we'll talk about both of these. >> Cool. Lab studies have a lot of benefits basically we're talking about fairly controlled conditions that we're setting these things happen so you can determine the amount of contaminant, you can readily see it go away. And actually then Then get a true degradation rate something that's not influenced by maybe dispersion or things like that, that are more difficult to control for in the field. You can construct this sorts of reactors with actual site materials so you can sort of recreate the conditions that you're dealing with in the field. And then, there's lots of literature data that's out there. So, there is a resource for sort of getting your own rate using information other people have done to your benefit in these cases. >> An example graph here. Here's the concentration of cis-DCE in micrograms per liter on the y-axis. It's a semi-log scale. We got time of incubation and days in the x-axis. You see these two curves. The slopy one, it's the one that's the live one, that's actually happened with these abiotic reactions, and then the other one is a reaction, a straight line, that's the controls, and you can compare these, get these slopes and get some of these rates. >> Yeah, in this case it was magnetite that was responsible for the reaction. So, again, as we mentioned before, there's a lot of information out there. One of the best resources is this paper by Hean, Wilson, et. al, just published on groundwater monitor mediation where they compiled rates from all the different lab studies that they could find out there. And they found Got this great tables within this paper that sort of go through various chlorinated solvents in this case, various minerals that are responsible for these reactions. Then they put forward what the rate coefficients are, in this case they're talking about 75 different rate coefficients they're able to To include within this paper. >> Quite a bit of these normalized ones with some sort of weight per meter squared of surface area of mineral, is that right? >> Yeah, that absolutely right. >> And then what are the ranges of these raise? >> They are Well, a lot of times. Again, they could be within days when you're talking about lab conditions. When you've started extending these into field conditions, I think that based on. You do a lab study, you may have a lot reactive minerals. In this case, we will promote a fast reaction. Field studies were more thinking generally in terms of years. Another thing that this paper does which is sort of nice is that it then does sort of a comparative in terms of which particular chlorinated solvent in these case would be expected to be degraded faster. It's sort of a reaction chain in this case. And some of the citations are shown here and you can see looking at different chlorinated solvents maybe cis DCE not as readily degradable. TCE may be more degradable in these cases but it can give you an idea maybe which ones might be expecting to see faster rates for. >> And this paper, some ways it's one of these Standing On The Shoulders Of Giants and they really talk about all this different literature and they put it in one place, really a great paper, something that if you really want to know more about the subject. Get this it all paper from ground water monitor remediation. >> We've talked about some of the benefits. We do also need to acknowledge some of the challenges of using lab data. These are sort of you're looking at this is an individual lab study and may not necessarily be comparable to other lab studies. You use different procedures. You might get different results. Is depending on. How that goes and you can see that in some of the data that are out there. Again whether these are representative or not of field conditions that's a big question all the time and again we've talked about this reaction as relying on biological and geochemical reactions. Those aren't always as easy to recreate in the lab as they are in the field. And then there is always this idea of whether. You actually know enough about the systems that you're dealing with in order to extrapolate rates in the lab where you know a lot about what's going on to the field where you may only have a slight understand to what's happening. >> And I thought of one more benefit from lab studies that you didn't mention was, certainly keeps a lot of grads students employed. And so something we want to keep going. So lab studies can provide good information. And keep those grad students going towards their degrees. >> Okay, yeah, definite benefit there. Let's switch then to field studies. So the benefits here is that a lot of times you've got monitoring data that you can actually use to help you determine a rate coefficient that might be in that case more applicable to the conditions at the particular site that you're working on. And then, again we don't need to worry so much about recreating all those individual reactions, we know we probably have the minerals in place or we know we probably have the, we either do or we don't have the biological reactions that you need to have happen. So, the system is actually working as you'd want it to work. And here's just another graph again, y axis this naut log of the normalized concentrations, but in this case in the field, we're looking at sort of this time as you leave the source and so This is travel time that you put in there, or you just do log concentration versus time. And you take that slope and divide it by that seepage velocity, to get that point. So you have to sort of account for the travel time of that plume that goes in there. And then just this note, there are these two different types of rates. There's apples and oranges. A point attenuation rate is a concentration vs. time at a particular point or monitoring well, And then concentration versus distance is at one snapshot in time. And it talks about how that abiotic degradation is degrading that packet of water as it flows down gradient. >> Exactly. >> Challenges, field studies, there's not been a lot of these sorts of comprehensive evaluations of what the rate coefficients are so you may not have as big of a sort of >> Database that drawn in terms that if you're trying to compare get rates from other field studies and use them for your own particular site. And then there's idea that maybe actually difficult that it field site to separate out what's happening in terms of abiotic processes versus the other process that can happen as groundwater is moving through And so knowing what that true abiotic degradation rate might be hard from field data, it might include the contribution of dispersion, diffusion, absorption or even source decay in these cases. So it's shown then here at the bottom right on here the rate coefficient that you might get from that field, from the log normalize concentration versus time or travel time. Might be actually a bulk rate coefficient. >> A combination of multiple processes that occur. >> Exactly, exactly. So where does that leave you? Basically, if you're looking to establish abiotic degradation rates or an idea of the level of abiotic degradation that's happening, you're probably going to need to rely on a combination of things. You might want to use Your own field data, you might want to take a look at the lab data for re-coefficiencies already out there and use a combination of those to help you out. >> Okay, let's wrap up. >> Mm-hm. >> So, basically the things that we discussed today are abiotic reaction rates and how they're expressed when you typically use first-order type reactions or normalized first-order rate constants that account for the mineral concentration of mineral surface area, okay. And segment key points is you get this rate constants from either this lab data or field data. >> And then there's all this literature data that's out there use it, you should definitely try to use that if you can. These are abiotic rate constants that you can use to help you out at your site.