 All right, let's start lesson 6, which is 1D foreign transport in homogeneous system. And so what I'm going through here is example 6.1. You probably noticed that this lesson is very different from the previous ones. In the previous ones, we always talk about batch reactors. And it's a well-mixed system, only reactions. We have talked about equiscomplexation, mineral dissolution precipitation, surface complexation, and exchange so far. And we skip lesson 5, which is on redox reaction abiotic. I realize that in this cloud, I don't think there is a lot of interest in abiotic redox reaction. So I think we'll skip that. Now this is starting a new unit, which is on physical processes. And we are doing only physical process for this unit. So we start with flow and transport with homogeneous system, 1D, which is simplest you can get. We talk about several different processes. One is advection, which is essentially you kind of think about, let's say you are swimming, and you kind of go with the flow. You don't do much. Very relaxing, you just go. So it's like a solid is go together with the flow at the same speed as a flow. And it doesn't do much by itself. So the advective flux, essentially, is the concentration, time, the velocity, and all these things. You can go back and review these equations. And then we also talk about diffusion, which is driven by concentration gradient. One example I always like to use about diffusion is imagine you have a cup of clean water. You're putting one drop of food dye, and you can see that that drop become bigger, and eventually become homogenized in the water. And so that's driven, even you are not doing anything. So this is driven by the differences in concentration in different parts of the system. That's diffusion. And then there is also dispersion process. Now dispersion process is somewhat similar like diffusion, but it's different course. Because usually we are thinking about post-media. And in post-media, you have all these post-structure that are not uniform everywhere. So you could have started to go through some long paths, some slow paths, and these tortuous paths. Essentially, it kind of leads to spatial variation in different parts of post-media. And actually, that's the overall effect. It's almost like diffusion from a larger scale when you look at the system. So essentially, what we are thinking about is, so typically what's being done is we lump the diffusion and dispersion process, mechanical dispersion and diffusion, combine them to become hydrodynamic dispersion, which have two terms. One is diffusion, the other is dispersion. And so this is just a quick recap of what's discussed in this lesson. And here in what I'm going to talk about is having the example set up. And so let's go through the question first and think about it a little bit. Here we are, so this example, we're talking about 1D column, 10 centimeters long. And we're injecting a tracer into a system as a concentration of 1.2 times 10 to the minus 4 more per liter. And you're given permeability, which is 1.75 times 10 to the minus 13 meters squared. You have also a porosity. It's giving you the dasey flow velocity of 4.2 times 10 to the minus 6, which is actually a meter cube per meter squared, per meter per second. And then you also have the molecular diffusion coefficient in water, which is 1.8 times 10 to the minus 9. You have a cementation exponent. You have a dispersivity alpha, all these values. Now by now, if you have already read the text carefully, you should know what are the use of all these numbers. Now before we do the simulation and setting up system, we do need to do some quick calculation in terms of what's going on, and what are the numbers that are coming through. So here, before the numerical experiment, I'm asking you to do, first of all, take the pressure gradient for the dasey flow velocity. We talk about, for the flow, the calculation will follow dasey's law. And the driving force, essentially, is the pressure gradient. So you need to put in the input file some kind of a pressure gradient. How much difference in pressure in the two ends of a column in order to get this dasey flow velocity that I give to you. And then the second one will be calculating the effective diffusion coefficient, dE. Mechanical diffusion coefficient, dM, which all have expressions in the text material. And then the hydrodynamic dispersion coefficient, dH. And I'm asking, what dominates the dH? So this is about the diffusion dispersion process. The first question about the flow velocity. And then the third one is calculate the characteristic time for a direction which is residence time. The residence time, essentially, kind of calculates. For example, let's say you have a lot of different solute particles, thinking about all these trees that go into a system, a lot of different particles. So it's the average time scale that one particle stays in the column. Some flow is the same, but the diffusion process, so there's some side to go out of system faster than others because of the diffusion dispersion process. So residence time, essentially, kind of quantifies the average time. And then I also ask you to calculate pE number. And based on pE number, predict which term will dominate during the transfer process. And then at last, it's setting up the crunch flow with 100 group blocks and run the simulation. So supposedly, I'm just going to give you some hint. I don't want to give you the answer. There's answer in the text, online text, that you can get, actually, by clicking on it after you go through this video. But I kind of want you to try your first by yourself because it's always better to try yourself first, try your best. And then you compare your answer with the solution. That's the way you get practice. And then if your answer is wrong, you kind of look at differences and you become understand what went wrong in your category. So you know which part you don't understand, which part you need to pay attention to. So I don't want to give you this answer right now. So suppose we already know the answer. I'm going to tell you first one, your dasey flow velocity will be calculated from the dasey's law. And pay attention to the two different flow velocity we talked about in the textual material. One is dasey flow velocity. The other is linear flow velocity. And the reason there are two different flow velocity is that we have post-media. And post-media has post-space. It's not everywhere water can go through. So the water only goes through the post-space. So the linear flow velocity is essentially the real flow velocity that the water goes through in the system. So dasey flow velocity is what we see after we get out and we were assuming everything is all available, the flow velocity we see. So you can think about dasey differ by a factor of velocity. And I can tell you that the linear flow velocity is faster than dasey flow velocity by a factor of 1 over a velocity. It's too complicated to explain. So you should go back and review the equation and all that. In any case, let's look at the example. So setting up a crunch for example will be the way I see it in a 1D system. We'll be thinking about, first of all, you do these calculations about flow, pressure gradient, and the different parameters that you need to put in the input file. And then you go through several steps. Setting up a domain. You need to tell the system how long is your column and how much resolution you want to give it to it. Do you want to do 100 grid blocks? Or do you want to give it to only 10 grid blocks? And what is your initial and boundary condition? And how fast your flow is going? And how fast what are the transport parameters? So setting up a domain. And then setting up flow, setting up transport. And also, you want to tell the system in the output keyword grid block how you are going to output the modding results. We'll be talking a little bit later after we talk about these first three items. All right, so this is our question. So let's go to our folder. Which I'm using the blank that, as you guys suggested, I started using all this with blank. Let's do the, I prefer using the notepad instead of word. So we have the, because this should be lesson 6. OK, so the first thing we need to do is look at the question Let me make this in the side, input fire to the other side. OK, so we have a 10 centimeter. Well, we need to tell the system the code. How much do we have in terms of the size of a domain, right? And we always need to, you had some discretization before. It's always for batch rupture. So you have only one grid block and the overall volume of the system. We always need to tell them the distance first, right? So the distance units would be, let's say I'm using, because this time I'm going to use millimeters. We've used meters before, centimeters before. So let's do millimeters. And you have a 10 centimeter column. So essentially you, which is 100 millimeters, right? And we want to divide that into 100 grid blocks. That's what does the question tell you, 100 grid blocks. So that means you have 100 grid blocks, and each of them is 1 millimeter, right? So you have x zone is, and each of them is 1. That's your domain, that's the length of your domain. But also you kind of need to tell what is your system, what is your chemical system. Now, since you only have chaser going through the system, you would, the species, the primary species, what do you have? We talk about this bromide. We don't have any other chemicals. So this would be bromide, right? And we have bromide in the database. So you have bromide. You don't have a second species. So you don't put in any second species. You don't have gas. You don't have anything. So because it's a column and we are kind of injecting something, flushing something into the column, so you will have inlet, right? Your condition, your inlet condition is essentially whether you're injecting. And then if it's a sand column, let's say we call it a sand zone, or just sand, whatever we call it. Here I'm calling that sand zone, right? So in the inlet, we are saying that the contrition is 1.2 times 10 to the minus 4, more per liter, or more per kilogram water. So let's do this. We will be putting the primary species. The inlet would be, let's again, we need to specify units, right? So the code doesn't take more per liter. So this is, again, relative clean water. So you can do more per kilogram water. And then you have, again, we specify temperature just to be explicit. But if you don't specify the code, it will use 25 degree as default. So being both inlet and the sand zone in the column, you need to specify the primary species. And we said that is 1.2 times 10 to the minus 4, more per kilogram water. We don't really need to specify pH or anything because it's just bromide. Now what about in the sand zone? Sand zone, actually, we probably can copy this, but we will have different temperature initially, I'm sorry, different contrition initially. So I'm dragging into contrition. Okay, it didn't specify what is initial concentration within the column. Let me just add a little bit of thing here. So it's more explicit. I'm dragging into the contrition, a tracer bromide is dragging into the column. With the contrition of this, as they originally says, no bromide initially to be consistent. So that means your bromide ratio will be zero or whatever I use typically is a very low contrition. That's your condition for where you have, what you have injecting into a system and what you have initially in the column. We also kind of need to tell the system what is the property of the column. So we do need a porosity unit, which is 0.40, as you can tell here. So it's 0.40. Actually, a column that is packed in lab, we found again and again the process, no matter how tight you pack it, it would typically run 0.38 to 0.42 or something. It's almost, for some reasons, always around these numbers. Okay, so that's your porosity. But also you need to tell the system how fast is your flow, how big is your permeability and all that. So we need a flow unit, which okay, which is a keyword block flow. In the flow, you can tell what condition you have that related the flow of the system. So if we do flow, again, the first thing we need to specify is distance. You can always specify different units in different keyword block. That could eventually translate anything together. But also here, we also need time units. Let's do this with second. And then we're going to tell the system, we're going to calculate. This is the keyword that you are going to use often later. Calculate flow. You're actually putting the tool of force. If, so there's several options to do, to calculate for. One is for example, this to calculate flow. The other is to just specify constant flow. Let me just search for calculate flow. So you actually, if you put that true, it's logical. If you put true, the system will base down the permeability and pressure gradient you give to the system and the calculate flow velocity. If there's another keyword, it's called constant flow. If you specify constant flow, then you specify directed x, y, z component of the dasey flux in the units of default will be meter cube meter square per year. Now, so different between these two. And usually we prefer calculate flow is that when you do a constant flow you will not be able to update the flow if, for example, the process for meter changes. So typically we do that for example, let's say you have a non-reactive column, the same column actually in our system, it's OK to do constant flow. If you just want to specify the flow velocity there, you can actually put constant flow and put a specific constant dasey flow velocity. When you do calculate flow, so let's say you have a reactive column, some mean or dissolving out or something precipitate that. So your process will keep on changing. Your point meter will keep on changing. And with calculate flow, the system actually can update the flow field over time. So that means if you have, let's say, post base open up, the flow velocity will become faster over time because of that. In constant flow, once you specify constant flow, you can, the flow is not going to change. It's always going to be that constant flow. So that's the advantage of doing calculate flow. Now, OK, so that's calculate flow. But in order to calculate flow, you need a few things, as I mentioned. We would need the parameters that you have for dasey flow. So here, I'm going to specify permeability, x, and in the question, I'll give you 1.75 times 10 to 1. So you already have meters there, so 1.75e minus 13. That's your permeability. You need to specify the permeability x or y or z. When it's y and z is not specified as a code nodes, you are not really interested in that direction. You only have one grid block in that direction. It's by default. So you specify that as your permeability. So this permeability should have a unit of 1.75e minus 13 meters squared because the distance unit is meters here. So your permeability, but you also need the pressure gradient. So you need to specify the pressure in the two boundaries. One is in the inlet end, the other is in the outlet end. So this is done by specifying pressure. And then you always kind of set it as everywhere pressure is 0 first, and this is by default. And then I'm going to say in one of the boundaries, so flow will be going from inlet to outlet. So it should be in the inlet, you have higher pressure. So here we do. This is the number that we calculated in the previous step from question 1 to 3. So you can go and look into the solution to see what is the number. So this is a pressure gradient we calculated. So you specify the pressure in the inlet end, and you will need to specify where you have this pressure. And you will need to say 0, 0, and 1, 1. So this is specified, we call it ghost cell. So the code has 100 grid blocks in the column. And then we call the ones that just before grid block 1, we call that 0. So you specify that grid block, the pressure is 2, 1, 3, 0 Pascal. And we fix it. We put the keyword fix, meaning it's fixed. And then you will specify the other side. Our latter side is pressure will be 0 again. But then you also need to specify what is the zone. And here we should have zone. And it's in the ghost cell that is our side of the hunch. So it's right after the 100 grid block. So here, there, you will specify it's 1, 0, 1, and then 1, 1. This is because this is one dimension. Later on, you will realize what you are going to do for two dimensions. So now you have the pressure in the inlet zone, 0, 0, is 2, 1, 3, 0. And then pressure in the outlet 1, 0, 1 is grid block 1, 0, 1 is 0. So essentially, if you imagine you have the boundary because in numerical simulation you need boundary condition, you need another kind of break bar just before each boundary. So essentially, you have 100 plus the 0 grid block and 101 grid block. So you essentially have 102 grid blocks. So that's the flow part to specify. Now with that, you should be able to calculate what is the flow velocity that is specified here because this pressure gradient is calculated based on this dusty flow velocity. And so that's flow, that's velocity. You will also need, that's flow, that's for the other active part. We also need to do specify the transport part. OK, let's just try it around it once so that we know there's nothing, no error in the system just to make sure. If we do, then we try to fix it. So this will be example. OK, I really should call it 6.1, which I'll change that. 1 blank number of, OK, no suffix and maxim block calling, error in opening database file. Let's see what happened with the database file. OK, so the database file I specify here is data.com.dbs. And what I have here, I call it example 5.1. Let's change everything to 6.1 so it's consistent with the number there. Going to close this window. This should be deleted because we're not going to use that anyway. And change this to 6.1. So in order to have consistent between the name of database I provided here with that database in this folder, I should have example 6.1 as a database file. Because essentially, this line is telling the code to look for this file, data.com.dbs. And then the code will be looking in this folder for that database. And then it couldn't find it. So then it gave us an error. So the database name should be consistent in here. Let's try it again. This example, make sure everything is 6.1 blank. OK, so databases do not. Oh, OK, because I'm changing the name and then I'm changing it here. And this name is still 5.1. So I'm changing. So in 6.1, it's probably still that. OK, so this should be changed to example. Just copy it and paste. OK, save it. And then I'm doing here again. Example 6.1 blank. OK, let's see. Looks like there's something. Either you didn't like the format, or let's look at the blank one. OK, did it go through DBS? Specific. OK, speciation of geocamp conditions. So at least it doesn't give us error. Prosthetic for this chemical condition. OK, inlet. Inlet doesn't have positive media, so it should be 1. And then sun zone, prosthetic for this chemical condition. It should be 0.4. Oh, yeah, OK. I know what it is now. Because I changed it to 6.1 using the previous version of the input file. OK, so I'm going to delete this one. Just make sure I have everything in whatever put this to there. So what happened is that we call this 6.1, but I used the previous version that was not saved. So the code essentially to have an empty one. So now I'm calling that 6.1. You name it to 6.1. OK, it has everything there. All right, so let's do it again. Example 6.1 blank.in. OK, no initial conditions. So because we haven't put it in yet. About in one, that's fine. So that's the right stage we should be in. OK, so open it again, and we'll continue on this. I just want to check in the middle of when I'm doing this. Make sure if I have some errors, I'm going to fix not wait until everything until last minute. Because the more you put in this larger chance, you could get mistakes. And I kind of don't want to wait everything until at the end. Just make sure that in the intermediate time, I check, and there's nothing wrong there. OK, so here we have this inlet sand zone. Our next step would be actually proceed. I should probably use not just drag. I should use keyword fixprocity, 0.4, because this is the column. That's the same column. So you're not going to change the process. So it's fixprocity, so it's also updateprocity2 that you can actually update the prosody. You will know, we'll learn more about this later. So specify the prosody here, which is 0.4. OK, and then we look at the transport unit. So we already, OK, let's look at the conditions. What we are going to set as inlet condition, what we are going to set as sandstone. So for the initial conditions, we are going to say the sandstone will be given to Gribach 1 to 100. So what this mean is that in Gribach 1 to 100, it all has a condition of the sandstone which we specified here. So the name of here, it should be the same as the name here. So that's your initial condition within the column. And then in the boundary, we are injecting. So because this is a system that 1D, and you actually have two boundaries, right? One is the inlet boundary and the outlet boundary. So you are going to say x big game, which is inlet. You'll be using inlet boundary. And then you'll be using flux. The reason we specify flux, that means the flow will be just coming in. It's not a fixed boundary. It's not something that we put it at constant. So x big game will be specified as the inlet boundary. And then you have x and we specify as outlet. And outlet should be the same as the sandstone because its flow just coming out of the sandstone, right? At the grid block 101, go sell. You will have the same condition just as if you are getting at sandstone. Again, here we use a flux to make sure everything is smoothly coming out without jump and everything. OK, so that's your initial condition and boundary condition is specified there. And then we can specify the transport properties. And we talk about transport property. We have several transport properties. Diffusion, dispersion. And for diffusion, you have diffusion coefficient. You also have cementation factor and all that. But first of all, let's specify, again, distance, right? You always specify distance units, which is, let me call it this time, maybe centimeter. It's really specified with the convenience of whatever. That's with the numbers. Distance units, you have centimeters. And let's also do time units, which is seconds. Because usually diffusion is given in units, either centimeter square per second or meter square per second. So I'm going to do a second there. And then I'm going to use fixed. I only have one species, it shouldn't really matter. But sometime, if you have multiple species, you can put in the diffusion coefficient of specific species. If you want to explore on that, go into the menu and look up information. So let's say you have, for example, if you have seven or five different species in your system, if you want to specify the specific diffusion coefficient for hydrogen ion, for calcium, for OH minus, all these different species, you can set your funding for the table once. You have all different diffusion coefficients. You can do that by listing all the different species and then putting these numbers. So for fixed for bromide, I'm going to say, as what is said in the question, diffusion coefficient is 1.8 times 10 to the minus 9 meter square per second, which is here, we have centimeter square. So it's 1.8 times minus 5 centimeter square per second. That was in meter square per second in 10 to the minus 9. So this is centimeter square, that would be 1.8 times 10 to the minus 5. And you also need fixed diffusion. You also need cementation exponent. Now, this cementation exponent is that value m. Like we talked about, the Kegel and effective diffusion coefficient in prismedia is phi m times d0, which is in the diffusion coefficient in water. So this cementation effect m is the cementation exponent. This is 1.0 here. Yeah, m is 1.0. So that takes care of the diffusion part. But then we also need to have the dispersivity, which is 0.07, as we specified in the question. Now, so we don't really need to expressly calculate mechanical dispersion and hydrodynamic dispersion here. The code we actually be using that expression and based on the number here, to calculate all the dynamic dispersion term. So that's the transport unit. Now, we also need to tell the code how often we want to see the snapshots of the column. I talked about before that. Now, here you have both time dimension and space dimension. So we can actually output both the breakthrough curves, which is at the end of columns, the concentration coming up and how the change in function time. But also, you can get snapshots of what happened within the domain at different times. So this will be specified in output. So let's do time units. And I'm going to specify in days. When I did the calculation for the present time, it was around, present time was about 0.1 days. So I specified days. Now, and I'm putting time series. And I'm called the breakthrough curves dot out. That's the name of the breakthrough. Every time we call a breakthrough, it's a contusion. Actually, it's not necessary to be the last grid block. It just here I'm specifying this is the last grid block. But if you want to look at the time evolution of a particular grid block. For example, let's say I'm trying to do this I call the breakthrough curves 100. If I want to have another time series for another grid block, let's say I'm trying to look at the middle of the column and see how this contusion changes the middle column and how that's different from the effort. You are going to do this. So this is the grid block you are looking. And this is the grid block you are looking at the end of column, the middle column. And you call them different names. So at the output, you have both of these breakthrough curves. And if you draw them together, you will see how different these are. And you think about what's the process. So that's the time series for a particular location for the whole running time. And then we are going to say I'm going to get some spatial profiles, which is a concentration, for example, in the whole system at different times. These are snapshots. So I'm starting from very close to the initial time. And then I'm going to look at 0.05, which is almost, because the resin time is about 0.1, if I remember correctly. This is about half of the resin time. And then 0.11 is about the resin time. And I 0.11 days. And I also want to look at 0.22, which is maybe I will call it 0.16, which is 1.5 resin time. And this is 2 resin time. And I will do 3 resin times. So that's the time. So this is very close to the initial time. Half resin time, 1 resin time, 1.5, 2, and then 3 resin time. So this is essentially a game. So you should have, for example, all different concentration, or total concentration, you should have 1, 2, 3, 4, 5, 6. You should have 6 files for each type of kind of choosing output. Now, I think we're ready to run. I believe let's just go and see. Example 6.1, so it's running. OK, so now you have all these. So there's no mistakes. Surprising. OK, let's go. Let's look at the two breakthrough curves. This is for the breakthrough curve for grid block 50. And this is the breakthrough for grid block 100. I always try to name the files very explicitly. So once you look at it, you know what is it for. So this is because it doesn't make it easier for you. So this is a long file from very early on to very like the end of the time for 3.3 days. If you don't want it to be that frequent output, you actually can change screen output. So you can change the screen output to make it output less frequently. Let's say if I put every 30. So this is how many time steps, how many frequently in time steps. So this is output in the breakthrough every 30 time steps, before it was every 10 time steps. If you rerun again, you are going to get a shorter. You're going to get a smaller breakthrough curve. Not that it matters that much, but I just want to show you that. If you are kind of thinking, OK, I did say too much. All right, let's look at it again. So you do have, if you notice, it does have a shorter file compared to what I had before. So it has the breakthrough. This is time series at gray cell 51.1. And then the concentration. And then it's a log concentration. We talked about that in the art profile. The resin time is about 0.1 days. So half resin at the resin time, it should, more or less, if you look at the text for the files at resin time, should give you about half of the inlet concentration if the code is running, doing everything correct. And the inlet concentration is 1.2 times 10 to minus 4. So at about 0.1 days, let's look for this. You should get about half of the 1.2. OK, either we did something calculation wrong or whatever. At a residence time, one residence time, you shouldn't have the whole breakthrough. This looks like you already have a breakthrough. OK, so at one time, or maybe I didn't remember the resin time, correct? But in any case, at this time, at the end, you would reach to the inlet concentration. And early on, for the half of that time, you should have a half of the inlet concentration. Let's say 0.5 or something, 0.6, you would have half of the concentration from inlet. So in any case, you can check later. I don't remember exact number. But we can check number if the calculation is not correct. You can do it. You can change numbers and everything. OK, so that's the breakthrough curve. And then you have the concentration in early times. So that's very close to the initial time, right? Almost everything is in log 10, more per kilogram. Almost everything is in order of 10 to minus 10, right? So it's very close to the initial condition. Except probably the first several gray blocks, right? So you have 100 gray blocks, right? So this is about 10% of gray blocks. You start to have a concentration coming. All right, so this is 0.5 of the residence time. So essentially, you have 6 file in each and the total concentration of every file you have set. Now check the flow velocity. This flow velocity is in the units of meter cubed per meter squared plus meter per year. And actually, when you do the calculation, you want to check this flow velocity file. This should be in different units. But you want to check the concentration of this. I'm sorry, it's the flow velocity of this with the velocity that I give to you in the question to make sure they are essentially the same. If not, then you will need to adjust your pressure gradient to get the number in the question that I give to you. Because otherwise, then it's not consistent. You get what I mean. All right, so that's the velocity. Speciations, these are not really because you only have one bromide, so it doesn't really matter. Pressure, just make sure your pressure is OK. So that gives you the pressure gradient. Pascals, 2, 1, 1, this is what are we inputting essentially for the whole system, right? 2 z, this is 10. Every grid block, you have 2,000, 2, 1, 3, 0 or something. So each grid block have about 20 or something. So this is your pressure distribution essentially based on Darcy's law. That's the anything else that I need to go through. I think that's it. So if you apply that bromide, a contribution will see a breakthrough. And then in the homework file, I'm just quickly go through homework. OK, let's skip that. Let's not look at that. In the homework file, what is interesting is I'm asking you to do another tracer test. The tracer test we just did was, we did it for, like, we always have one starting from time 0. We always have tracer running. Here, we are going to have the tracer. We injected tracer for just 1 tenth of the resin time. So it's only, like, a pulse, essentially. And I'm going to ask you to plot that, which I think is interesting because you get to see the whole process of how things will be evolving. I think the first question will be very interesting because I hope you visually see the process. So let's say you inject a pulse of that. And you plot a spatial profile of the tracer at 1 tenth of resin time, 2 tenths of resin time, 4 tenths of resin, 8 tenths of resin time. And I ask you to plot all the spatial plot in one figure. So you will have maybe a different color for each time. And you will see the evolution of the concentration profile change at different time. And it would be an interesting trend. And think about the trend and why it looked like that. And then the second question is, if you change the alpha when you have different flow velocities, this really should be 6.1. If you change the dispersivity, how you will see the change in this evolution of the concentration profile? That's the first question. So it's essentially everything the same as in the example. But then we are just having a pulse 1 tenths of the injection. And you will be using the keyword block, the keyword restart. So you will be setting up, look for the information about restart in menu. So you essentially will be inject, have this inlet concentration for 10% of the resin time. And then the rest, you'll be injecting water. OK, let me make that more explicit. Clean water into the column. OK, and then the question is the second question. I'm asking you to change a lot of parameter like flow velocity, dispersivity, molecular diffusion. You do a series of calculation. And then answering questions about how things are going to change at different time, at different flow velocity. And then I'm also asking to calculate packing number, DE, DM, DH, and all these things. And make a table and look at how things are different at different conditions. This will give you some interest compression. It's a lot of repetitive work. But it will, at the end, give you some interesting insights about how the PE values would affect these transport processes. I might make this, maybe I'll just mix it if you have the energy to do it, do it. Otherwise, I think it's fine if you understand the first question well. Or maybe you just do the first question. Or maybe you'd pick to do maybe one question, one parameter for each. So one point, the middle one is always the same as what you already run in the example. So it's actually two more summation for each of these questions. It's for two for this, two for this, two for this, and two for this. And then you essentially change kind of summarizing a table. OK, anyway, so I think we're done for this unit. So you can explore a lot of things in the homework. And if there's any kind of big thing that you think you don't understand, make sure you take notes. And we'll cover these in the discussion. Let me know what is your biggest concerns and everything. All right, have fun.