CHUCK NEWELL: Today we're going to continue our talk about matrix diffusion and give a little more historical background about the changing role of two key contaminant transport processes. First, dispersion sort of versus diffusion. DAVE ADAMSON: I think the key point here is for many years groundwater models and modelers, they sort of focused on dispersion as the key process that really controls and drives how plumes develop. Now we're going to talk more about this emerging view, a real shift in our thinking, that says that we can explain contaminant transport a lot better by focusing on dispersion processes as opposed to-- sorry, diffusion processes rather than dispersion. CHUCK NEWELL: Exactly, Dave. And so this is sort of this new idea. It's sort of catching on, but hasn't. It is not completely accepted right now. But let's start with what we call this process of mechanical dispersion. And it's the idea that if you have this porous media, these sand grains that are out there, that there are different flow velocity's going through these different channels as you see in this image here. There are different paths that these different contaminants or solute takes as they sort of go through here, sort of like a pachinko system, these little steel ball bearings are going down. DAVE ADAMSON: Price is right reference. CHUCK NEWELL: Exactly. And then all that causes this plume to spread, and this idea of matrix diffusion. The key points that we make in this is that it's the grain size scale, these different paths that make these plumes spread. But there's no real theoretical basis for this large scale dispersion. In some ways it's been used as a fudge factor for computer modeling. DAVE ADAMSON: OK, well that's dispersion, maybe then we take a look at diffusion. So diffusion is a different process, we're describing the spread of particles to random motion from regions of higher concentration to lower concentration. In this case, diffusion is one of those things that's been studied by a lot of real scientific giants, some of those are mentioned here, you have Fourier and Fick, we've got a nice picture here of Fick, and Einstein, and Smoluchowski as well. CHUCK NEWELL: I don't know if you remember, we were in Denmark, and sort talking about matrix diffusion and we said that, well Einstein, who was the second greatest physicist in the world was involved in this diffusion process. DAVE ADAMSON: And then I think the Danes, they said, well Chuck, who is the greatest physicist then, involved in this field? CHUCK NEWELL: And I said, well, of course, the greatest physicist in the world is Niels Bohr, the great Danish physicist. And we got project, right? DAVE ADAMSON: Yeah, exactly. It worked out. CHUCK NEWELL: So let's talk about Fick's law a bit more, here's this picture. What's going on with the picture here? DAVE ADAMSON: Yeah, again, we're talking about the situation where things are moving in this case from left to right, from high concentration they're moving into a lower concentration and there's an example listed here. CHUCK NEWELL: I started talking about the Motel 6 example, that if you go into a motel room, people have been smoking a lot of cigars up there. Maybe that air has completely been exchanged, but you can still smell that smoke from those cigars or cigarettes. It's diffused into the curtains, it's diffused into the carpet, and it's coming back out. And so that's one of these ideas on diffusion. DAVE ADAMSON: OK. CHUCK NEWELL: But how do you describe this mathematically, Dave? DAVE ADAMSON: Well yeah, we're usually talking then in terms of some sort of a diffusive flux. So that's in this equation, this J term, and that's going to be equal to a diffusion coefficient, something that's a compound specific type term that describes that rate of flow via diffusion. And then you've got this change in concentration over change in distance terms, that's your concentration gradient term, dC over dx. CHUCK NEWELL: Great, OK. Well now let's go to a more groundwater specific example. Here's a great paper from 1985 done by Sudicki and colleagues at the University of Waterloo. So what we've got is a sand tank here, you can see that the sand is that white bar on the top left panel, sort of a silt on either side. And they ran this thing, they ran solutes through this sand. And they talked about the effects of this redistribution, of their tracer, across the strata by transverse molecular diffusion. So here's what happened when they ran it. Dave, what's on the axes of this graph? DAVE ADAMSON: All right, well we're looking at on the y-axis, the relative concentration, so think about 100% is at the top. And then we're simulating days, so time, in this case, on the x-axis. CHUCK NEWELL: And so the red line, here, is what they said if you're doing advection dispersion by itself, that thing sort of gets through real quick, it breaks through real early. And then you would see everything happen within basically eight days to flow across there. But what really happened was this blue line and it just took longer to get there because some of this contaminant's was diffusing up and below and you have this sort of much more muted response that you're looking at. In some ways like this capacitor you described in week 1. DAVE ADAMSON: And so that's 30 years ago, that paper came out in 1985. CHUCK NEWELL: So now let's go to another paper, this is in the 1990s from John Cherry. It's another paper about pump and treat, Mackay and Cherry, 1989. And they are sort of theoretically describing why groundwater pump and treat cleanup systems-- remediation systems aren't cleaning up as fast as they can. So one their conclusions was, they have this drawing here, but what do they say here? DAVE ADAMSON: Basically, as plumes are spreading through these aquifers, the dissolved contaminants move quickly through those permeable zones and then they slowly invade-- I like that, very slowly invade the less permeable ones by flow or diffusion. CHUCK NEWELL: Some good writing, here, in this paper. Then they talk about what are the implications that over years and decades, this invasion, as you talked about, can cause the plume to occupy large volumes of low permeability material here. To obtain clean water from wells it's necessary for the lower permeability parts of the aquifer system to get cleaned up as well and to clean up those high permeability systems. So, here, in 1989, they're talking about matrix diffusion. What's ironic is this paper, they also talk about DNAPL. And the whole industry really focused on that piece of the paper. And only much more recently we've realized that these folks were onto it a long time ago. DAVE ADAMSON: Yeah, exactly. CHUCK NEWELL: OK. So let's now go to 2008. A great book by Fred Payne, Remediation Hydraulics, it really goes into this whole thing, dispersion versus diffusion. And they start talking about heterogeneity's and the scale of these heterogeneity's. So here's some pictures. And if you look at the one on the top right, you can see that you have these very abrupt interfaces between high permeability material, on the left 10 to the minus 2 centimeters per second and 10 to the minus 6th material, just off to the right. Just on a matter of centimeters there, Dave. And so most of the flow on that top panel's going, really, through that highway at the very top. And then you can see at the bottom, the contaminants are distributed well. So the subsurface is like this big reactor with billions and billions of tiny baffles that prevent this mixing that's going on there. So what do they talk about though, in terms of heterogeneity and what homogeneous sites look like? What's that saying? DAVE ADAMSON: Well yeah, I mean they're talking-- looking at that top panel of sites that are archetypically homogeneous, have 1,000 to 10,000 fold variation in hydraulic conductivity at very small scales, scales of 1 to 10 centimeters. CHUCK NEWELL: Almost like you can't see it. So you're not going to see this potentially in a log and they say it's at the fine-- in micro scales. It's often below this detection limit that you have of conventional characterization techniques like taking that core and plunking it on the table and look at it, you may not see this. And so it's really difficult to map and interpret when you have that variability that's really high. So here's this potential paradigm shift, this ITRC training that's coming out, the DNAPL characterization. Great work from the ITRC DNAPL team there. This talks about sort of a new paradigm, a new thinking about transport that's sort of based on this. And the first is heterogeneity really replaces homogeneity. Almost all these systems we deal with out there in nature have a lot of heterogeneity to it, so that's the first one. DAVE ADAMSON: Yeah, and then also, this idea that you can't describe these things with sort of the classical Gaussian way. You have to move to more sort of the lognormal ways of thinking about how things are being transported. So look-- think about those longer tails. CHUCK NEWELL: Exactly. The diffusion causes this contaminant storage is a key point. DAVE ADAMSON: And then that storage may be considered an attenuation mechanism. And that's what we talked about and the last thing that we'll continue to talk about throughout this week. CHUCK NEWELL: Your capacitor idea, and that basically there's this one idea, this paradigm, that says we should replace dispersion with diffusion, and that's this key point. And so all of these are really important, because you sort of put all these together. And originally, I'm a chemical engineer, was thinking that all we have to do is just get these chemicals into this reactor, which are these sand beds and that's all you had to worry about. But there's a lot more. The stratigraphy, the geology becomes lot more important. And in some ways, we get to the point now, where I'm saying that in terms of our field, it's-- what do we see? DAVE ADAMSON: Ah, the revenge of the geologists. Here's a geologist looking happy that people are finally listening to him after all these years of him telling about these sorts of processes. CHUCK NEWELL: These are important. These are all the chemical engineers trying to learn about this, becoming a very important part of our remediation story that this whole diffusion piece is all about the stratigraphy, about the geology. So geology becomes much more important here. OK. Dispersion out, diffusion in, there's this emerging argument. And so there's this idea that based on our increasing knowledge and controlling role of geologic heterogeneity and-- I'll let you pronounce this one, Dave. I can't do it. DAVE ADAMSON: Anisotrophy. CHUCK NEWELL: You're so cool, you're good. In the subsurface, these are controlling the subsurface containment fate and transport. So let's go to two panels in the old idea, the classical view, is all about dispersion. And what's going on here? DAVE ADAMSON: Yeah, so if you look at this dispersivity model that's shown in this panel, it's sort of classically looking as things transport down. If you were to go at any particular point, you would see these nice symmetrical curves and sort of easily predictable ways of describing where the contaminants are. CHUCK NEWELL: Just beautiful symmetrical cloud in some ways that goes out. But now this new idea, if you have to account for this stratigraphy, this geology, it looks something like this. You have these transports occurring in these poor space channels, this mobile zone that's in there. And it's surrounded by these lower permeability zones that may occupy most of the aquifer. And it will store stuff and then they will release it slowly. So that's this key idea-- maybe we should be thinking about our sites more like the panel on the right. And even change some of our models and think about our whole set up. So this idea of this paradigm shift, still not completely accepted by everybody, sort of an emerging idea, right? DAVE ADAMSON: Yeah, I think more people are still probably more towards the left than to the right. CHUCK NEWELL: OK. But wanted to bring up some new thinking that's going on, particularly in this idea of dispersion versus diffusion. Well let's wrap up, there's this new conceptualization of contaminant transport that abandons dispersion as a basis for accounting for local hydrogeneities and aquifers and as an explanation for dilute concentration in wells. DAVE ADAMSON: And then at the same time, sort of embracing diffusion and slow advection as a fundamental governing processes at a lot of contaminated sites. CHUCK NEWELL: And just to wrap up that diffusion and dispersions really important to understand how this natural attenuation works, how transport works, but a big deal for M&A.
