And a value of one assumes that the source concentration false of a time but

it's an exponential decay.

>> Got it. >> And

if the value is greater than one, then that results in a long

tales that are representative of matrix diffusion processes.

>> Cool, so we've used this model a lot and

it really is a way to represent this matrix diffusion with these long tales.

Any source zones that are being caused by the matrix diffusion.

Now, right now the model only has the matrix fusion and

the source term with the gamma.

But Dr. Folta's working on this new model called REMChlor MD.

Though have matrix fusion both the source and in the plume and so,

that I think that's going to be pretty important to them.

So now let's go to another model,

it's a relatively simple equation that's a sort of base on an on and off concept.

You want to explain how that works?

>> Yeah, how this works is that you have a source with the defined learning period,

that's the on period that extends over a certain

period of time The source is then turned off, and

you switch to a release period where the concentration in the transmissive zone

that originates from non-bag diffusion sources is instantly switched off.

At many sites, the on period is typically in the 1960s or 1970s.

And the off is when the source weakens so

much that most of the plume is being sustained by matrix diffusion.

Or when the source has been remediated.

>> Okay, so on the picture here, maybe 40, 50 years of loading on the top panel.

And then the model assumes to get cleaned up in one day, basically, and

have this back diffusion that's occurring.

You know the math behind this, let's take a look at that.

What's going on here?

>> So, it's a very simple equation and we call it the square root model.

Why do we call it that?

>> because it's got a square root.

>> Square root.

>> Is that right?

Okay.

So if different parameters are in there.

Number one, what do you need to run this model?

Pretty simple.

You need to know the porosity of those clays or silts.

>> And you also need to know the affected fusion coefficient of the low

permeable units.

>> And that handles the torchousity, right?

Retardation factor.

Is there any organics in there that's going to absorb contaminants in that

sub-surface?

>> And you need the time loading started.

That's the years before the simulation time.

>> Okay, like it started in 1960 and then it got cleaned up in 1990 or

something like that.

And then you need the concentration that was loading into the interface and

finally, you need to know what pi is, right?

>> What pi is, yeah.

>> There is a pi there, so maybe that's the tough one.

So, that's this example of this particular model.

Let's go to an example of how this was applied,

this is some work we did at this EMW site, near the San Francisco Bay area.

What's on the Y axis there?

>> So we have the TCE mass discharge rate in grams per day index on the Y axis.

>> And then we got actual times when this is a pumping treat system that was running

in 1998 to 2013.

Each of the golden squares there, as an actual data point that they measure

the mass flux or mass deterrence coming out of the wells.

If you're using a conventional flushing model,

it would say, hey, I would be cleaned up by the year 2000.

But in real life, it just cleaned up a lot slower because of this matrix diffusion

and when we apply that square root model, you think it matches pretty good?

>> It matches pretty good.

>> Okay, so that's, this analytical model, the square root model.

We another one that's a little more complicated.

Let's talk about this and we call this the Dandy-Sale model.

>> So why you call it the Dandy-Sale model?

>> Well, it's just the author.

It's Tom Sale, Julio Resembron, Dave Dandy.

Julio some how got left out of the lurch here.

But conventionally, all the people call it the Dandy-Sale model

in terms of analytical, journal of contaminant hydrology.

And it's got this different source zone, instead of a horizontal plane source.

What does that source look like?

>> We have a vertical source zone in the Dandy-Sale model.

>> Okay, so something like this and the concentration goes through an makes this.

>> Right, and

you also have higher concentrations near the bottom rather than the top.

>> That's right, so more complicated, as you can see, I think right in here.

Shahla, what's going on in this particular graph here?

>> Well, it's a pretty complicated double integral.

And it's the dude integral, because it ends in dude.

>> At the very bottom right there, you're right, the dude.

>> The dude.

>> Okay, a little bit big Lebowski going on here.

And also fortunately for me, the only thing I understand here is the pi.

We've got some of that going on.

But this model's more powerful.

It sort of handles more of the physics and

chemistry of this back diffusion a little bit better.

But how do people access these models?

>> Well, they've been incorporated into the ESTCP matrix diffusion toolkit.

>> And who wrote that?

>> Well, we and GSI in collaboration with Tom Sale at CSU.

>> But you're the lead author, right?

Mm-hm. >> Yes.

>> So what's in this matrix diffusion toolkit, and where do they get it?

>> So, it's a free tool, first of all.

And so it was developed for ESTCP, as we just mentioned.

And you can obtain it by Googling ESTCP matrix diffusion toolkit.

And it incorporates both the square root and Dandy-Sale models.

And can you help you estimate mass and concentration,

and mass discharge in both the transmissive and low key zones.

And it's a free, easy to use and Excel-based spreadsheet.

>> Got it, okay.

What did you spend the most time on the square root model or the other one?

>> Yeah, the dude model.

>> Okay, the dude model. Lot of math in that, but

you get the more power with that particular one.

>> Yes.

>> Okay, let's talk a little bit about modeling matrix diffusion.

I think maybe we wrap up.

And maybe our first point is this numerical modeling requires much higher

resolution than commonly practiced.

And it's maybe these layers that are a couple of centimeters thick that you

have to use.

>> The SERDP project ER-1740 type sites

provide key insights on behavior of plumes affected by matrix diffusion.

>> That's right and then, analytical models can model matrix diffusion, but

they require the simplification, on and off is one example of that.

>> And the ESTCP matrix diffusion toolkit is a key tool for

matrix diffusion modeling right now.

>> Got it.