CHUCK NEWELL: We've been talking about dilution as a attenuation process some times, but today we're going to sort of follow up on the last lecture, which we talked about sort of different groundwater issues. But today review one of the most important 10 things in the entire groundwater field and that is Darcy velocity versus seepage velocity. DAVE ADAMSON: Well, that's a pretty strong statement. Why is this one of the 10 most important things in groundwater water? What about the error function in the advection dispersion equation? CHUCK NEWELL: Well, the error function is important, but really I'm going to introduce this paper-- a really great paper by Dr. Don Siegel at University of Syracuse-- and it's called Reductionist hydrogeology, 10 fundamental principles. So this is the top 10 list of anybody in the groundwater field that he says that people should know. DAVE ADAMSON: Well, what compelled him to write this paper? CHUCK NEWELL: Well, let's go into the paper a little bit. And so he goes in there and he's a college professor and he says, "I write this essay to present my 'top 10' list of what students and practicing hydrogeologists fundamentally need to know to be successful-- the 10 points that I want my students to remember even 10 years after they graduate." DAVE ADAMSON: Well, those are some pretty lofty goals. I think if I remember back to my college days, I remember that you retain knowledge and then it sort of decays on a first order curve. So I don't want to spoil your punch line, but I'm guessing Darcy velocity versus seepage velocity is one of the 10 most important things that shows up here on Don Siegel's list. CHUCK NEWELL: You've got it, Dr. Adamson, and here it is. He's talking about number 2 here and he talks about, with respect to Darcy's Law, the difference between seepage and Darcy velocity needs to be so well known that it becomes second nature-- the former calculates how fast groundwater moves and the latter is how much it moves across a cross-sectional area. DAVE ADAMSON: OK, well that's one of the 10 most important things. Do you remember any of the other nine? CHUCK NEWELL: Yeah, there were a couple. One was don't push your data farther than it can stretch. Contour with your head, not by your computer, the piezometric surface is different than the water table, groundwater chemistry is greatly under-appreciated, contaminant plumes should be considered narrow and no wider than a few times the width of the source at their heads. DAVE ADAMSON: Well, these 10 powerful proclamations-- is he standing on top of a mountain when he's giving these? CHUCK NEWELL: No, I imagine his thoughts were collected after teaching a lot of students at Syracuse and he was probably just sitting around his chair, drinking coffee and talking to his grad students. OK, well let's go through it and so here's our slide from last time-- this is the Darcy's experiment. So if you look at this, we've got these different tanks and flows going through there. q over a is this Darcy velocity, but the key thing is porosity in this thing. DAVE ADAMSON: No porosity in Darcy's Law. CHUCK NEWELL: So then, here we're going to break out the two equations-- I'll do the one on the leff-- there's Darcy velocity, sometimes called specific discharge and it's just this v sub d is equal to k times i-- hydraulic conductivity times the gradient. DAVE ADAMSON: In contrast to the seepage velocity, which is also known as the interstitial velocity, but this is a velocity v sub s in this case, where you're taking that Darcy velocity then dividing it by the porosity. And porosity is unit-less in this case, so again, you get a velocity term and length for time. CHUCK NEWELL: Awesome, OK. Well, let's look at when you use which one for different conditions. We've got some things here, this Darcy velocity-- that's really when you're talking about flow, you need things in liters per minute or liters per day. You're thinking about how much actual flow is going across a cross-sectional area. DAVE ADAMSON: And then on the right, the seepage velocity. This is basically whenever you need a velocity information. So for example, you wanted to know how many meters were traveled per year for ground water contaminate or something like that. CHUCK NEWELL: OK, and this reminds me sort of this whole world of groundwater hydraulics equations. We've got the Theis equation on the left there. This describes how a capture zone builds as you're pumping water from a well-- you see porosity in there. It's basically got some transmissivity in there, which is this Darcy velocity times the aquifer thickness. Then we have the Thiem equation. Does it have a porosity? DAVE ADAMSON: Again, no porosity in there. CHUCK NEWELL: So, the general rule is if you're dealing with flow and you're trying to get gallons per minute, liters per day, Darcy velocity, if you're drilling with speed, you're going to use seepage velocity. DAVE ADAMSON: All right, well, maybe we take a look at this then in a flow cross-section. CHUCK NEWELL: And so here's something we did for the ITRC training that we use. We got a lot of questions at the mass flux training where people seemed to have trouble with this concept. Every training we get, people would ask us about it. Basically we're trying to say that if you're thinking about flow, this is how these two different pictures look. I'll just look at the diagram there-- that Darcy velocity is sort of averaged over the entire transect area, this width times this height. And if you're trying to calculate flow-- you see the formulas down there-- you're going to take this hydraulic conductivity times the times the gradient-- that's this Darcy velocity-- and then you're going to multiply it by width and the height there. And you're going to get those guys and you're going to get a flow. On the right hand side, you can do the same thing if you start with seepage velocity, but you have to count the seepage velocity as just the flow through the open pore space itself. And so then you have to put this correction factor in-- and just look at the equations. You end up at the same place, but it's really two different things that are used for two different ideas. So that's the key idea about Darcy velocity versus seepage velocity. DAVE ADAMSON: That's a good overview of the fundamentals of groundwater transport, but things have been established for about 100 years. Maybe we transition to some newer developments. CHUCK NEWELL: And so, there's this idea of using effective porosity. There are some new concepts with this and so we'll describe this a little bit. So I want to start out with, on the left, is actually a manual that I wrote, the BIOSCREEN manual. It says if we're thinking about effective porosity, in this BIOSCREEN model it says, here's some different values that you can use, but you typically estimate it. And a commonly used one for sand and silt is an effect of porosity of 0.25, so that's this one sort of conceptual model for this. DAVE ADAMSON: OK so in this case, the effective porosity is a little bit smaller than the total porosity, but there's another way to think about effective porosity as well, right? CHUCK NEWELL: And this is coming from this book, Remediation Hydraulics, and we've talked about it before with Fred Payne, Joe Quinnan, and Scott Potter. And they're coming from a world doing a number of tracer tests or mediation projects and they tried to apply some of these concepts of effective porosity and they just said, no, it just doesn't work. So the table here is from their book and here's all the tracer tests they used. And they said, if I'm actually going to match how quickly that plume moved, what effective porosity would I need? And it was a lot lower than was, for example, in the BIOSCREEN manual. So they said, hey, we should be using the concept that they call mobile porosity and maybe that's a better way to sort of think about all this stuff. So let's compare and contrast here on this slide. On the left, Dave, what do we have? DAVE ADAMSON: Basically that's the effective porosity base on BIOSCREEN, where you're saying a value of something on the order of 0.25 might be an effective porosity. CHUCK NEWELL: That's right. And on the right hand side, there's this new concept of mobile porosity. And they say in their text here that for the purpose of assessing plume migration rates, assume a mobile porosity. Maybe the numbers are more like 0.02 to 0.1. Maybe it's 5 to 10 times lower than that. It would be more appropriate than using the more common 0.25 value. So, some interesting discussions about how this mobile porosity more or less works. DAVE ADAMSON: And that's pretty interesting. I think it's worth emphasizing that these are fairly new concepts, maybe not universally accepted, but sort of a new take on how you'd estimate what the seepage velocity might be. CHUCK NEWELL: That's right. And thinking about changing from scale where you're pumping to supply water for a city, you're really thinking about now remediation scale-- I'm trying to clean up the site. Well let's wrap up and so some more key points are two different types of groundwater velocities. And number 1 is use the Darcy velocity, also called specific discharge, to get flow information as this term is the groundwater flow per area. DAVE ADAMSON: And then on the other hand, you'd use the seepage velocity, also the interstitial velocity, to get the rate of plume migration. CHUCK NEWELL: And then there's this third emerging concept that's out there. Use smaller effective porosities when calculating seepage velocity. If you're thinking about scales of the remediation site and they call this the mobile porosity.
