 All right, so this is the video for lesson 8 continued. We just finished doing the homogeneous column 2D because it mixed 2D. So you should have watched that first before you start this one, because that one has a lot of background information that I provided. And on top of that, we made the mistake of missing that keyword zone in specified permeability so hopefully that helped you remember. This is very important. And then you have, I guess, that's the value of making mistakes from my side. And then you'll see how things are fixed and all that. OK, so here we are going to, in this one, I'm going to talk about how to do the one zone case. And again, we are doing what we are specifying all the different keyword blocks starting from specifying the domain, and then flow, and then transport, and then the reaction, then the initial condition, boundary condition, all that, so we'll be following that order. First, let's also start with discretization. And again, we're using 25 by 100 grid blocks, 2,500 grid blocks. So essentially, you would have the same discretization, for example, just like what we did before for the homogeneous case. Distance, units, and you would have millimeters. And then you have x zones, 25, and spacing 1.0 millimeter. Y zones, you have 100, again 1.0 millimeter as a spacing. And then you are going to specify your domain. But now we cannot specify velocity directly because there's average process, but there's also processing different zones as they are different. The middle zone is the magnetic side. The outside zone is the quartz, and they have different velocity. So we are not going to specify fixed velocity. So here we are going to just do maybe velocity update, whatever it is. And then we do need to specify the minerals because different minerals are in different parts of the column. So you actually will need a magnet side. You also need quartz. And then you will be specifying different minerals in different parts of the column. So let's do flow first, just like what we did before, because you do need to calculate is the flow units are all everything you need to calculate the flow field. So again, we are doing time units being seconds. And then you have distance units being meters of calculate flow. So then you will be specifying permeability. So when you specify permeability, when you do default, you do need to really specify your zone. So I'm going to specify for everything to be 8.74 E minus 30, which is the permeability of the quartz zone first. So when I do default, that means the whole domain has this permeability. Why do I do that? Because then I don't need to specify separately. Later I will overwrite the magnet side part and then overwrite that. So this is the permeability of you kind of specify for the whole domain default. You don't specify zones. But then I write later on permeability x for the magnet side zone is we calculate that before doing this simulation. It's for the middle zone. So you have 1 centimeter width of magnet side zone in the middle. And then 0.75, 0.75 to the two other side. So in terms of grid blocks, you would have 8 to 18. Actually, it should be 9 to 18. It is the middle magnet side zone. 13 points. So that's for the magnet side. This will be y. So that's the specify the magnet side zone. OK, so by doing that, first of all here, I specify everywhere it has this value. Now later I specify in these zones you would have these values. So this part of the zone will be overwritten by these values. And the region one that is not specified is going to remain the same. So you still have cross zone have this value. But the middle magnet side is going to be overwritten by these values. And then again, we are going to specify permeability x, like the no flow boundaries. And you would have zone 0, 0, 2, 6, 2, 6. So these are the ghost cells from 0 to 0, 1 to 100, 1, 1, permeability x, 0. And then again, this zone is very important, 2, 8, 6, 2, 6. Actually, I might made a mistake in the previous mixture. It should be really the ghost cell outside of the grid block 1 for x, grid block 25 for x, because these are the no flow boundary. Again, this would be no flow. So if I made a mistake, make sure you know that there was a mistake. No flow boundary. All right, that's permeability. And then we need to specify pressure. Let's see, again, we put the value 0.1 everywhere. This doesn't really matter. As a code, we essentially use Darcy's law given the heterogeneity distribution of permeability and then do the calculation. So whatever initial value is going to be erased, but we don't want to leave it undefined. Pressure in that will be 3, 8, 9, 0. We did the calculation before we do the submission. So again, specify zone will be in the 1, 2, 25, in the ghost cell, just before you have grid block 1. 1, fix. And then your pressure 0 again. Zone 1, 2, 25, that's x. And then y is 101, 101, fix. OK, so that's a flow. So you are supposed to have everything you need to calculate the flow field. Let's look at transport. Transport will be very similar to what we had before, that we need all these dispersing diffusion related distance units. Again, it will be centimeters, time units, seconds. I'm going to do the same fixed diffusion as what we did in the previous one, 6.342 e minus 6. And then you have cementation, exponent, cementation, dispersivity. Dispersivity, again, the first one for x and 0, 1 is for y. So according to the number in the table, 0.004, 0.07 centimeters for the two dispersivity. So that's for the transport. And then we need to specify specific care of the column. Now, in here, you have two different zones. One is the rectum, one is the cross zone, the other is the magnetized zone. So we actually specify the two minerals. First of all, we need to specify the primary species. Now, I talked about before, this is a tracer test, so we definitely need bromide. But also, I mentioned, as long as you put different minerals, you need all the elements, building blocks for that mineral. So for magnetized, you will need mg2 plus. And then because it's mgCO3, so you also need CO2AQ. You need carbon species. For quartz, you will need the aqueous species SiO2AQ. But also, it is in water, so let's just put H plus there. Just in case some of the magnetized is written into H plus. And then second species, then you will need OH-minors. This species doesn't really matter in the tracer test, but it will be important later. But since we are going to specify different mineral zones in the even where only for the physical process, we do need all the chemical building blocks. So SiO2AQ, then you need bicarbonate species. And then, OK, so these are primary species. And then you need to specify your inlet. Let's just copy all the primary species there, because we know we need inlet. Just like what we had before. Units still do molar. Just to be consistent, let's still do molar temperature. Inlet divided by bromide concentration of 1.210e minus 4 magnesium, we know we consider it's clean water. So let's just put very low concentration there. Here we also put very low concentration SiO2, very low concentration, because these doesn't really matter at this point. And maybe we put pH of 7.0. Shouldn't really matter, because it's not going to do calculus that much anyway. So for the condition, in the column we have quash zone, and we have magnetized zone. But so essentially, we will need both of these. And then primary species, so this will be an initial in the quash parts that you still do by low concentration bromide. But here, not these are specific in the equest phase. Now we are also going to specify the solid phase. And for quash zone, we talk about the positive quash zone is 0.38. So I mean the solid phase is 0.62. So you would have quash is essentially volume fraction of 0.682, and you put a magnetized there, because you don't have magnetized there. You are going to put very low. So essentially, that will give you the code will calculate, OK, you have this much solids. With a total solid phase of 0.62, then it will calculate positive being 0.38. Just I'm just making notes here. OK, so for magnetized zone, we will be still having the whole thing, but except the solid phase is different. Because for magnetized, you still have initial condition, not much of these species. But now your quads will be very small number. And then your magnetized, remember, your magnetized property is 0.54. So your magnetized volume fraction will be 0.46. So that's adding up to be 1. So you have the different conditions just to avoid confusion. So that's the three condition inlet quads magnetized. Now let's specify for the initial conditions, you would have at first, let's specify the whole domain. So there are more quads, let's specify the whole domain being quads. So you put in like 1 to 25, and then 1 to 100, 1, 1 for quads. So that's the thing, OK, everywhere you have quads. But then I'm going to overwrite that the middle part, which is 9 to 18, will be the magnetized, or taking the magnetized initial condition. So that's what it gives you, especially the initial condition. Then we need the boundary condition. Where's the boundary condition? OK, for the boundary condition, it will be very similar, x beginning, y beginning, x will be inlet. You have flux, x, and you will do quads. It doesn't matter much, it's inlet that is important. And y begin. So again, it will take whatever that is coming out of a column. It shouldn't really matter, boundary condition. And then you have output. Again, you need to specify how frequently you want things to. How long do you want to run? How frequently you want output? Where do you want output? Spatial profiles, specify. Let's do it the same as what we had before, 0.01, 0.15, 0.2. So run the same time as the previous one. And then let's do the time series output for maybe also for the middle. But if you want to look at every outlet block, you're welcome to do that. You don't have to have only one. For example, you can specify 25 different time series for all the alternate block. Let's say I'm just doing another one time series. Breakthrough, let's say I'm looking at 20. And then you'll be specified 20, 101. So now you have two different groups. You're looking at a certain square block in the outlet cross-section, and then turn this group in the outlet. And then you will be output since this is a tracer test. So all it matters to us is bromide. And then we have time series interval should be whatever, 4, 10, or whatever it works. All right, so that seems all we have just kind of quickly looking through. I usually try to be clear about what I put in and what I keywords and not making too crowded. So I'm going to separate that because a lot of time it's easier to see. Line up, boundary condition, transport, velocity, discretization, minerals. For minerals, it's important you realize that for the name of minerals, you need the capital in the first letter. Otherwise, the code doesn't recognize it. And then flow, and then you define all the character flow, permittive value, permittive value. Make sure I have all the zones there when I define a specific zone for certain numbers. Zone, zone, OK. All right, primary species, second species, initial condition, quartz, magnetite, that's consistent with, let me see, initial condition. Actually, yeah, it's consistent with permittive setup. Condition inlet, condition inlet, you're putting high concentration bromide. And then condition quartz, machine magnetite, you're putting specific volume fraction quartz and various fraction of magnetite for them to be adding up to be one with porosity. All right, so it looks like all right. OK, so it looks like it's taking in. And we didn't make mistake again this time, which is good. OK, so first time step is speeded out. And I want to point you to the velocity. So the reason there's velocity and velocity evolve is because I'm putting porosity update. So the code will try to update a porosity, although there's no reaction going on or anything. That's fine. And then you have porosity. So let's look at velocity. You will realize the velocity is different for different zones, as you can see. And that's more or less because we have different permitting different zones. So for these 2D, you will need to either plot out the spatial profile in 2D, in like tech plot, or MATLAB, whatever software you use. Now, only plot, the x velocity is not very meaningful. So I would say you just plot the x, the y velocity, which is in the direction of the flow. And you realize, OK, y is 1.07, they all have same units. You can go back and check with the corresponding, for example, a meter per day or something. But in any case, this is 1.07. This is 1.68 because we just have 2 zones. And you can imagine this will be the one in the middle zone that may decide to have a little bit higher permeability. In any case, if you divide 1.68 to 1.07, you get about 1.6 or something. And you realize, you might realize, that when you put the input phi, the permitted value of the magnetized zone is about 1.6 times of the quad zone. So essentially, the flow is distributed according to the permitted values. And if your product is issued to come up with, for example, flow velocity distribution, somewhat like the figure 1 that we showed with different flow velocity and everything in different places. That seems very slow for some reason. It's to the 6.35 times 10 to minus 2. OK, still have a bit of time to go. Because we have more species, and even we don't really care about these species, we just have to put it in there. And the code will try to calculate everything, I'm sure. So it's slower than the homogeneous column. But in any case, the breakthrough, so for the velocity, and actually for them, let's look at total concentration. OK, so you have x and y, and then you have all different species. But all your case is bromide. So you will be looking at this third column. When you try to calculate the overall breakthrough, imagine, OK, you have the 2D. And then in each of the gray bargain outlets, you have, for example, let me just go back. It's probably easier to explain with a figure. Is this really should be x and y, not x and z? I will change that. But in any case, this is your x direction, and this is your y direction. So the outlet will come out flow velocity different when y equal to 100. This will be y equal to 1, y equal to 100, right? And this is x. So you will have different flow velocity coming out from each of the outlet grid box. You will also have different concentration coming out because of different point building. So what I'm asking you to do, for example, I specify a little bit. So condition average, imagine, OK, when we take sample, we'll actually only have one outlet, not like everywhere you have a sampling point. So is that one outlet essentially integrating all the condition and flow velocity out of it? So when you calculate average breakthrough, you actually use a weighted flow rate weighted average to do the calculation. So it will need to be like C i coming out from each of these times the V i and cross section i of each out of this. That way you get a flow velocity, flow rate times condition, which is mass per time for all the integrating summation of all 25 grid block and divided by the overall flow rate. That'll give you the kind of average breakthrough. So what do you need to do when you look at these? Would it be, let me just look at it, maybe it's here. You look at bromide, and you will be looking at y equal to 100. And you sample each, you get each value, the flow velocity. Cross section area is the area of the grid block time velocity, right? Velocity times that cross section area, time the condition is what you get for each grid block. And then you add them up divided by the overall flow rate. So that's what you are going to do when you do the breakthrough curve. And you are going to see a bit of difference in the mixed column and in the 2D column. I'm not going to tell you at this point, but in any case, this is what you are going to do. OK, now we are at 0.16. So we have a little bit, I think we specify to 0.2. So you still have a little bit of time to go. So that's total contribution. Let me just open. OK, the permeability will give you the distribution of the permeability in different parts of the grid block. These have the units of log 10 meters square. So these are in log units. Plasticity, right? You have x, y. And then you have plastic somewhere. OK, for the magnetization, you have 54% plasticity. And 38% is 38%. So these are the output fires. Let me see. Weight, we're not really interested in that. So it has velocity. If you do have sink dissolving out, it will be updating the plasticity, permeability, and everything according to the plastic permeability relation in the code. And that actually will give you different distribution present permeability from the initial values over time. OK, I think we're done. Everything is out. And all you need to do is pry things out and look at the difference in the breakthrough curve. Think about why they are different. And you will be interesting to think about how they are different, why they are different, and all that. And I think this is the one-zone example with heterogeneity. And you can specify all that. So there's another option. Let's see if you have random distribution of permeability. We can specify in another separate file and read in other codes to read permeability for irregular-shaped heterogeneity distribution. And this, we're not going to cover this a little bit too complicated for now. So I'm going to stop here. And I'm sure you'll have fun. It's a little bit more work, but it's also very interesting. And very useful when you think about the heterogeneity of system, how physical processes are different. And later on, there will be another session in Union 3. We'll be talking about 2D reactive. So this is really building the physical process for that unit to lay down for the reactive one. All right, I'm going to stop here. I think it's a bit too long.