CHUCK NEWELL: OK, well today we're going to talk about time and in particular, remediation time, in other words, how long you have to wait, how long you have to go until our critical space is clean. So I'm sort of-- remember, there was this great term for Rod Serling or sort of the phrase. He talks about there's this fifth dimension beyond which that is known to man, a dimension as vast as space and timeless as infinity. It's the middle ground between light and shadow, between science and superstition, and it lies between the pit of a man's fears and the summit of his knowledge. And that's the dimension of imagination. So in some ways, it describes a problem of estimating remediation frame. There's a lot of uncertainty, but we keep asking the question. It's a tough problem, a fearful problem, but we want, in some way, to estimate this beyond relying solely on our imagination and make up a number. DAVID ADAMSON: That's quite an introduction. I guess we can go ahead and get started. I assume we don't have any more Twilight Zone references throughout here, but there are Twilight Zone episodes, you know, lots of different remediation frame models that we can work with, right? CHUCK NEWELL: That's right, so let's take a look at a couple. We've got some that are shown here. There's one called SourceDK that's sort of a clever name. You see how it's sort of spelled in there. DAVID ADAMSON: Yeah, yeah. I know you like model names that are easy to decipher. CHUCK NEWELL: Yeah. And then there's the BIOSCREEN, BIOCHLORS, and then there's the REMChlor model, REMFuel, Matrix Diffusion Toolkit, the NAS software, specially developed natural attenuation software developed by Frank Chappelle and Mark Widdowson. But we sort of break these out and how do they get the number? How do they get this remediation time frame? At the very top, there is one that really talks about logarithmic extrapolation and a lot of them deal with these boxed models, right? So we're going to really focus on those type of sort of expressions to sort of tell you a little bit about the fundamental options you have to go out there to estimate this remediation time frame. OK, well let's go to the model with maybe the best name out there, the SourceDK. And so you can download this thing from the GSI website. It was developed for the US Air Force that's out in here. DAVID ADAMSON: Yeah, a little bit of an older version. I see that our old company name, Groundwater Service, is on there, so. CHUCK NEWELL: That's right, so new name, GSI Environmental, but, you know, the equations are still correct. They're still good. And they have these different tiers-- tier one, tier two, tier three to do this. So let's look at, Dave, let's look at tier one. DAVID ADAMSON: Tier one's just concentration versus time data, right? CHUCK NEWELL: Some empirical data and sort of this is the way it works is you can download this spreadsheet and then you have to do these three steps, and what are they? DAVID ADAMSON: OK, well again, you've got concentration versus time data that you're entering up into this table up in there. You have to specify a cleanup level, so what you're trying to get to, and then basically, your answer is going to come out of here. CHUCK NEWELL: That's right. So we have to put the dates in a date format. You have your concentration mixture. You've got your duplicates and your non-detects fixed up. But you put them in there and then it draws this line and it's a logarithmic extrapolation, a first order decay-type model. In this case, they had these data and it says that you're going to reach this clean up sort of goal in about four years, with the data we're showing here. It also shows you the 95% limits on this. So if you have a lot of scatter in your data, that range may really increase. But this first method, just these extrapolations is the simplest way if you have a lot of data. And we're actually going to talk a lot more about this in some of the other lectures, that this is how you can do this in terms of estimating remediation time frame, collecting this particular model that's in there. OK let's go back to SourceDK and look a little bit about the box models again. And this type box model's used in BIOSCREEN and a sort of a more powerful version of this is used in the REMChlor model, but let's go through again some of the math and how this works. So we talked about this in the last lecture, but we're going to talk about mass balances with these source zones to ask this question, how long do I have to wait to reach my cleanup goal? So here is-- this idea here is this first order decay. We've got this different mass that's in there. We've got 10 kilograms in the source, which is 10,000 milligrams, right? And what's the flow going through the source? DAVID ADAMSON: Well, we got 500 liters per day going through that source. CHUCK NEWELL: And then two milligrams per liter. You just basically say, take the mass divided by the mass discharge, in which case, how many years do you have to wait? DAVID ADAMSON: Got a 10 year estimate here for the remediation time frame. CHUCK NEWELL: That's right. But I think as we talked last time, be careful. This is not the way these models work, but if you're going to sort of go through it, to sort of illustrate this, we've sort of presenting this graphically right here. DAVID ADAMSON: Yeah, and this looks pretty familiar. I think we wrote a paper on this, right? CHUCK NEWELL: That's right. So sort of planning level models for source attenuation and MNA, but here's this example. I've got a certain source. If I'm just not going to do any remediation to that source, then it's going to be out there 40 years. But then if I removed 70% of the mass so that the RF, the remaining fraction, is 0.3. DAVID ADAMSON: Yeah, well, I mean, we've assumed a step function, so that changing that mass by 70% would change your remediation time frame by 70%. You go from 40 years to 12 years, that red line. CHUCK NEWELL: So we sort of wrote this paper with this idea that people are, in many cases, trying to compare monitored natural attenuation. Will it clean things up soon enough versus remediation? And we want to really make people sure to understand the dynamics of that, that if you do this remediation, in some cases, you do not get something like this. You do not get the 70% reduction in the remediation time frame. And so here is just how the math works. This RTF source depletion is in the top, the numerator. RTF MNA is in here. And for this simple step function, it's this remaining fraction and that's what the ratios of these two frames. But it's not like that in real life, Dave. why not? DAVID ADAMSON: Well, no, and again, we talked about this in a previous lecture, that you would expect to see more of a sort of a decay in that source term over time, not a steep drop off. So something more on the order of what you'd see on that right hand panel, where you got that decay occurring at maybe a first order rate that you can describe with that ks term that's showing there. CHUCK NEWELL: OK, so more complicated, but more realistic because it's sort of-- this is what we see out there in real life. We don't see plumes that are clean, that are dirty for years and years and then it gets to be a Wednesday, then on Thursday, pshh, it completely cleans up. It's this more slow decay and you need models like this to sort of simulate this type stuff. Now if you're doing this type of equation, here's that same curve. It's mass discharge on the y-axis, time in years in the x-axis. This is the mass discharge leaving that source. We've got the two curves. It's the same idea. If I remove 70% of the mass, I get the red curve, but how does that effect the remediation time frame? DAVID ADAMSON: You no longer get sort of that equivalent reduction in your remediation time frame, so you look on the x-axis of where you're going to get to-- without source depletion, 130 years, with source depletion moving 70% of mass, it'd still take you 103 years to get that concentration goal. CHUCK NEWELL: So the key point is, don't think that remediation is going to give you this complete benefit that if you move x percent of the mass, it reduces remediation time frame by this. It's more complicated than that and these remediation time frame models can really help you understand that and see what the relative benefit of some of these remediations are. OK so if you actually put this into an equation here, Dave, it's the same idea. What's the ratio of the remediation with source depletion on top? What's this RTF, remediation time frame for MNA? This is the reduction in the remediation time frame you get. If you do that active remediation, what do those expressions look like? DAVID ADAMSON: Well I mean we've got a ratio that's based on a first order decay, so they've got these natural log terms in them, but it's basically the ratio then of the concentration goal over the original concentration on the top there divided by the remaining fraction, and then you've got a denominator that has sort of the natural log of the goal over the original concentration. CHUCK NEWELL: OK, so it's the remaining fraction is how much is left, how much you didn't get out from that active remediation. The concentration goal is a CG over CO and then I can just use this button right here to get the logarithm-- DAVID ADAMSON: OK. CHUCK NEWELL: --and then, but wait-- there's no mass term in here. Why's that? DAVID ADAMSON: There's no mass term. The mass just sort of cancels out in this case when you're doing it. CHUCK NEWELL: Because in this case, you're looking at the ratios of these two. So you're sort of free from trying to do that dirty calculations with all that uncertainty. This just says if you got this first order decay-type process and you remove that much of the mass and this is the remaining fraction and this is how far you had to go, hey, there's that ratio that's in there. I think we've actually got this as a curve, right? So here is sort of the graphics of the curve with three different things. We talked about the step function in the first order model, but let's just-- to go through example. Y-axis is percent reduction of the remediation time frame, how much benefit you do get from active remediation compared to MNA. This is the reduction in the source mass, so one minus this remaining fraction. Give us an example, Dave. DAVID ADAMSON: Well I mean if you're looking at first order model, so that's that green line there, you could imagine that maybe you reduce the source mass by 80%, something like that. So where would you find yourself then on the percent reduction curve and time frame? CHUCK NEWELL: Looks like your mediation time frame is reduced by about, what, 15%? DAVID ADAMSON: Yeah, so maybe not that much really. CHUCK NEWELL: From 100 years to 85 years. But this is partly dependent on the C goal to the C original. This says, in this case, you have four orders of magnitude to go. This sort of tells you how much of that tail on the end you have to deal with, but that's difficult to remove. Now just one last thing is that the REMChlor model, the REMFuel model have the same sort of box model, but they got an extra dial in here that we talked about in the last lecture. Remember what the name of that variable is? DAVID ADAMSON: Well it's gamma, and it's written right there, so I can remember that. CHUCK NEWELL: OK. And you can turn that dial so you get these sort of instead of just a first order decay-type thing, you can get these different characteristics. And so there's these idea that if you have a site that's really old, there's not much NAPL there, but you think it's dominated by matrix diffusion, maybe turn that dial so you got a gamma that's maybe closer to two and you can then get a better simulation of this. But REMChlor, REMFuel, powerful tools to look at remediation time frame for MNA and then you go in there and reach into the heart of that dragon, pull out some of the mass, and then see what that change in remediation time frame is, what benefit you get. OK, well shall we wrap up? And I guess the key points, there are several of these remediation time frame models that are available. DAVID ADAMSON: And then that time frame reduction's not going to necessarily be linear related to the amount of mass that you removed. CHUCK NEWELL: And a key important point that we've tried to bring out and if you don't believe it, run the models and you can sort of see how this works. But one other note is there's considerable uncertainty in these remediation time frame estimates, so have to understand that going in.