Okay, well today we're going to be talking about time and in particular remediation time. And in other words, how long you have to wait. How long you have to go until our critical space is cleaned. So I'm sort of remember there's this a great term from Rod Serling or sort of 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. Okay? 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, okay? So in some ways it describes a problem of estimating remediation time 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. >> That's quite an introduction. [LAUGH] I guess, we can go ahead and get started. I assume we don't have anymore Twilight Zone references throughout here, but there are Twilight Zone episodes. Lots of different remediation timeframe models that we can work with. >> That's right. So let's take a look at a couple. We've got some that are shown here. There's one called it's a SourceDK, that's sort of a clever name. You see how it's sort of spelled in there, right? >> Yeah, yeah, I know you like model names that are easy to decipher. >> 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, Mark Widdowson. But we sort of break these out into, how do they get the number? How do they get this remediation time frame? At the very top, there's one that's really talk about logarithmic extrapolation. And a lot of them deal with these box 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 the remediation timeframe. Okay, 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 Airforce that's out in here. >> Yeah, a little bit of a older version, I see that our old company name, Groundwater Service is on there. >> That's right, so new name GSI Environmental. But the equations are still correct, they're still good. And they have these different tiers, Tier 1, Tier 2, Tier 3 to do this. So, Dave, let's look at Tier 1. >> Tier 1's just concentration versus time data, right? >> So empirical data, and sort of this is the way it works, it's you can download this spreadsheet and then you have to do these three steps, and what are they? >> Okay, again, you've got concentration versus time data that you're entering up into this table up in there. You have to specify a clean-up level, so what you're trying to get to. And then basically your answer's going to come out of here. >> That's right, so you have to put the dates in, in a date format. You have your concentration, make sure 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 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 actually are 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 timeframe, collecting this particular model that's in there. Okay, let's go back to SourceDK and look a little bit about the box models again. And this type box models used in bio screen and a sort of more powerful version of this is used in the rem core model. But let's go through again some of the math at how this works. And we talked about this in the last lecture. But we're going to talk about mass bounces of these source zones to ask this question, how long do I have to wait to reach my clean up goal? So here is this idea this first order of decay. We've got this different masses in there. We've got a 10 kg in the source, which is 10,000 milligrams, right? And then we have a, what's flow going through the source? >> Well, we got 500 liters per day going through that source. >> And then 2 milligrams per liter, you just basically say take the mass divided by the mass discharge in which case how many years we gotta wait? >> We got a ten year estimate here for renetion time frame. >> That's right. But I think as we talk last time, you'd be careful this is not they way these models work but if you're going to sort of go through it which to illustrate this, we're sort of presenting this graphically right here. >> Yeah, and this looks pretty familiar. I think we wrote a paper on this, right? >> 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. >> 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. >> 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 understand the dynamics of that, that if you do this remediation in some cases, you do not get something like this. >> Right. >> You do not get this 70% reduction in the Remediation Timeframe. >> Yeah. >> And so, here's just how the math works. This RTF source depletion is in the top, the numerator RTF MNA's in here. And for this simple step function, you just hit this remaining fraction. And that's were the ratios of these two timeframes. Okay, but it's not like that in real life Dave. Why not? >> Well, no. Again and 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. Something more on the order of what you'd see on that right hand panel, where you've got that decayed occurring. Maybe a first order rate that you can describe with that ks term that's shown there. >> Okay, 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, [SOUND], it completely cleans up. It's this more slow decay, and you need models like this to sort of simulate this type of 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, and the x-axis is the mass discharge leading 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 affect the Remediation Timeframe? >> Well, you no longer get sort of that equivalent reduction in your mediation time frame, so you look on the x-axis of where that were you are going to get to without source depletion, 130 years. With source depletion removing 70 % of the mass, it still takes you 103 years to get to that concentration goal. >> So the key point is don't think remediation is going to give you this complete benefit that is going to remove X percent of the mass, it reduces remediation timeframe by this, it is more complicated than that in these remediation time frame models can really help you understand that and see, see what the relative benefit of some of these remediations are. Ok so, if you actually put this into an equation here Dave, its the same idea, what's the ratio of remediation with source depletion on top, what's this where RTF remediation time frame for MNA, this is the reduction at the remediation time frame we get. If we do that active remediation, what are those expressions look like? >> Well, I mean we got a ratio that's based on the first source of the case and I got this natural log terms in it, but it's basically the ratio than 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. >> Okay, so it's remaining fractions. How much is left, how much you didn't get out >> Exactly. >> From that act of remediation. The concentration goal is the CG over CO, and then I can just use this button right here? To get the logarithm. >> Okay. >> And then, but wait, there's no mass term in here. Why is that? >> There's no mass term, the mass just sort of cancels out in this case when we're doing it. >> because in this case you're looking at the ratios of these two, so you're sort of free from having to try to do that dirty calculations with all that uncertainty, this 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 are sort of the graphics of the curve with three different things. We talked about the step function and the first order model, but let's just to go through example. Y-axis is percent reduction of the remediation timeframe. How much benefit you do get from active remediation compared to MNA? This is a Reduction of the Source Mass, so 1 minus this remaining fraction, gives us some example Dave. >> Well, I mean If you're looking at First Order Model, so that's that green line there, you can imagine that maybe you reduce the source mass by 80%, something like that. So where would you find yourself then on the source reduction curve? [CROSSTALK] >> Looks like your mediation timeframe is reduced by about what, 15%? >> Yeah, so maybe not that much. >> 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. That's difficult to remove. >> Yeah. >> Okay. Now just one last thing is that the REMChlor or 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? >> Well, that's gamma. That's written right there, so I can remember that. >> Okay. And you can turn that dial, so you get this sort of, instead of just the first order decay type thing. You get these different characteristics and sort of the idea that if you have a site that's really old there's not much naple there but you think it's dominated by matrix diffusion maybe turn that dial, so that maybe you get a gamma that's maybe closer to two and you can then get a better simulation of this. But REMFuel powerful tools to look at remediation time frame for MNA And you go in there and reach into the heart of that dragon, pull out some of the mass and then see what that change or mediation time frame is what benefit you get. Okay, well should we wrap up and I guess the key points there are several of remediation time frame models that are available. >> And then that time frame reduction's not going to necessarily be linear related to the amount of mass that you remove. >> A key important point that we try to bring out and if you don't believe it, run the models and you can sort of see how this works. And but one other note is there's considerable uncertainty in these remediation timeframe estimates. So you have to understand that going in.