5.4 Setting up in CrunchFlow Example 5.1

Microbe Mediated Reactions

Li Li: So let's get started. This is lesson 5, so we'll be talking about microbe-mediated reactions. I put in the reading materials the importance of microbe-mediated reactions-- how ubiquitous they are in natural environment. And we also talked about the biogeochemical redox ladder in the reading material. So things happen in sequence.

And then we have this example of-- we're talking about soils, so I grabbed some soil in the back yard, putting it in a water bottle in the kitchen. So this is the cup, I would say. So that's the system we have. In that example, we put some soil there. Let's close it. We have some water there. So we have some soil. Let's just put these as grains.

And the water originally has some oxygen in it. And I told you that the soil that I have we just recently fertilized. That means you will have nitrate in the system. So essentially, in the system, you have oxygen and nitrate as electron acceptors. And typically, for example, the soil usually have bacteria already there. Microbes is everywhere. They do a lot of work.

And also, usually, you would expect the soil carbon have-- the soil have some organic material. So essentially, it also have organic carbon, which we use acetate to represent that. So essentially, we're talking about a system that has water in it. It's well mixed. It has bacteria in it. So let's use that to represent bacteria. And it has two electron receptors, oxygen and nitrate. Perfect.

We have a system. We know it's going to have something going on, right? And again, this is well mixed. We are not talking about the advective transport, dispersion-diffusion yet. So this is a well-mixed system, meaning there's no concentration gradient in the system.

Now, then, the other system you have-- so you have microbes We use microbes The formula for bacteria is C₅ H₇ ON. Something like that. And it depends on what type of bacteria it is. If it's using oxygen, then we put oxygen on the side, just to indicate this is oxygen-reducing bacteria. If it's nitrate-reducing bacteria, we put nitrate there, just to distinguish between the two different bacteria. So essentially, you have two types of bacteria there in the system.

That's the system you have. And what's there? All the players, right? Now, we think about the reactions, what are the reactions? So first of all, we talk about, in the biogeochemical redox ladder, oxygen is the one that is going to be used first, because usually it has fast reaction rate. The microbes also get more energy out of it. So that means it has growth advantage, because it can grow more with the same amount of organic carbon they have. So the first one we call aerobic oxidation, meaning you have the transformation from CH₃-- we use acetate to represent organic carbon. I'm not putting all these numbers into stoichiometrics. But essentially, just writing what are the major products.

So organic carbon will become oxidized to become bicarbonate or other forms of carbon. If it's relatively acidic condition, you might have CO₂ gas coming out. And you have water or hydrogen under whatever condition it allows. And then you would grow bacteria.

So bacteria is also one of the products that we talk about. It'll has N. And then producing the oxygen. It's oxygen-reducing or aerobic bacteria or microbes. So that's the oxygen related reaction.

So we talk about, OK, that reaction will happen first. And remember, this is a closed system, meaning we have a certain amount of oxygen dissolved at first, and then it's going to be depleted over time because of reaction. So the microbes will be using this up. And then, the next steps, the next reaction that's going to happen will be denitrification.

So You will have, again-- that's assuming we will have plenty of organic carbon there. So then you will have nitrate. Again, there will be inorganic carbon become produced. It's the same process, If you think about it, as the human system. We breathe oxygen. We eat food, like grains, bread, rice, different type of, essentially, organic carbon. And then we breathe out CO₂, which essentially is another form of bicarbonate, right? And then the water. Let's not write that.

And then you have another type of bacteria coming-- microbe coming out, which will be the denitrification microbe. So these are the two drivers of the system. But then, typically, you would also have-- I'm just writing at the side-- there should be a somewhat fast reaction compared to these microbe-mediated reaction. Would be the transition between CO₂ aq, bicarbonate, and carbon. These are the inorganic carbon species that we know is going to happen. We talk about that in aqueous speciation or aqueous complexation reactions that we discussed before. So these are very fast reactions. So the major drivers are really these. And if we have other species, for example, calcium or magnesium, if there's plenty of them, there might be precipitation come, because these reactions will produce a lot of bicarbonate. And bicarbonate can-- when the condition allows, it could precipitate calcite, for example.

We're not going to focus on these. Our major goal right here, right now, is talking about these drivers. And if there's applications that you will need to consider these as something that would be specific about particular applications.

So we have these reactions. These are the processes we focus on. And then we'll be thinking about the species. What other species are there? So, for sure, we would have all the electron acceptors there, which is oxygen-- it dissolved oxygen. You have nitrate. You have its CH₃ COO. These are the variables that we are solving for in these equations.

And then we also have-- let's put bicarbonate. But we know this is going to be also carbonate, CO₂ aq, or H₂ CO₃. These three are almost like equivalent with each other. Hydrogen ion, for sure, and then it goes with OH-. Electron acceptor, electron donor, products. Nitrogen is-- did I write? OK. Here, I should add another, which is the product of denitrification. One product of denitrification will be N₂. There could be a lot of-- a few other intermediate reaction products, like NO₂-. People have seen that. Or ammonia, even. This could happen too. We're just using this as an example. So N₂. So these are the major species.

But also, when we solve for these, when we are writing these four reactions in terms of these reactions. Microbe as products. We also should have C₅ H₇ ON₀ O₂. And then C₅. These are the two major products too. It's not just the abiotic species. We would consider the microbes are the products of this reaction too. So these are the species that you are solving.

So we are not talking about other complexation reactions. So really, we're focusing on these species. And you probably quickly know, by this time, these are the-- these could be the second species, second species, second species. These are the things that we consider. And then the primary species would be oxygen, nitrate, this, this, hydrogen, N₂, N₂, and this. These are the primary species. Let me just write as primary to indicate the color. So that's what you have in terms of variables that we are solving for. Now, again, we are talking about the well-mixed system. So when we think about the reactions, the equations, it would be really the reaction in terms-- for example, for oxygen, you have something like this. It would be dc dt for oxygen, for example.

Oxygen is being consumed. So the volume-- so it's really volume of the bottle, the mass, and then times this dc dt. But then you also have, essentially, the mu. The mu-- let's call this mu as the stoichiometric coefficient. Fish It's consuming. It's in the left-hand side of the reaction, meaning it's being consumed. So this is stoichiometric. If, for example, this is 0.5, this value will be 0.5. And then we will be-- we think about the consumption. The rate of this will follow Monod, dual Monod kinetics. So you would have this mu max for oxygen term. And then we have this-- how much bacteria there. So it'll be the C₅ H₇ O₂ N.

I should have an O₂ here. That's why I feel something is missing. It's weird. O₂. It should all have O₂ there. All right. So you have these species, O₂, and this is oxygen-reducing bacteria. So $\mu$ max, concentration of biomass, and then you should have two Monod terms. One is for concentration of oxygen, and then the Km oxygen plus concentration of O₂. That's an electron acceptor. And then you have the C-- . Sorry, I am writing a bit of-- so this would time, right? So Km, and then the plus C acetate. CH₃. I can't write anymore, but you know what I mean. So this is electron. Donor term electron. Acceptor term biomass. Maximum reaction rates. So that's for oxygen.

Similarly, you would write this for V dc. It's also being consumed. So essentially you would have the same, but you will have mu of CH₃ COO- and the same expression. Right? It's the same reaction. We just consume different chemical species in different proportions. And you would write again, also, for bicarbonate. That's one of the products. So you really should have positive sign before this. So you have to write V dc dt. This would be like total carbon. And then $\mu$ of bicarbonate. So all this goes on. So you will be writing for all these.

Now, when you are write for-- so if you only have oxygen, you would have oxygen, this acetate, bicarbonate, and other species. That's good enough. But if you have nitrogen, then your equation for nitrogen would be a little bit different, in the sense that you would have the would same. But they would be replaced by nitrate acetate. But you will have the inhibition term by oxygen, because oxygen would act as inhibitor for denitrification to occur. When you have plenty of oxygen in the system, denitrification is not going to happen. Only after this concentration of oxygen has been decreased to levels that this term is more or less much higher than this, then this value would be close to 1. Then denitrification really kicks in. So that's for nitrate. Also notice, when you have both electron acceptors, this reaction will be happening at the same time just, at first, oxygen what will be the dominant one, because this term will have very small value, will inhibit denitrification to happen. But then this, the rate of this will become smaller and smaller because oxygen becomes smaller concentrations, this term becomes bigger and bigger. So there's a switch between different electron acceptors. The other thing is when you have multiple electron acceptors, when you write these acetate equations or when you write these for the produced inorganic carbon, you need multiple terms too, because the denitrification process also contributes to the consumption of acetate and production of bicarbonate. These are common products or common reactants. So you have multiple terms if you have the nitrate-related term.

I'm not going to detail everything. But essentially, that's what you think would have. So solving these equations. Let's say you have all the species. You'll be writing how many independent equations for primary species. And you have three fast reactions that you can form algebraic relationship to solve these other secondary species. You solve everything as a function of time. So this is dt. This is not partial t. Now, in that case, what do you think will happen when we have these products? So I talk about we have some magic powder putting in the bottle will help us. We read our numbers. What do you think will be the trend of, for example, oxygen? And what's going to be the trend of temporal evolution of nitrate. Using nitrate for this one. How do you think they are going to look like in terms of curve? So that will be actually the output of the model. You can see about how it was going to happen. So aerobic oxidation going to happen. First, oxygen concentration is going to be consumed first, then decreased. So let's say it's maybe oxygen starts from here. You see a decreasing trend of oxygen. Let's say it's something like that.

And then, what about nitrate? So nitrate is-- at first, because it was in the presence of oxygen, you wouldn't see much of nitrate decreasing. So it probably, at the beginning, it's going to, let's say, start from somewhere here. It'll be relatively flat. But it also, when the nitrogen-- I'm sorry. When the oxygen starts to decrease, it just start to show a sign of-- it depends on rates. How fast, how long it'll take. It depends. So when it's like almost completely depleted, then you would have nitrate kind of going full swing. And then it's going to decrease really fast. But then, when you think about the products, this produced N₂. So N₂, let's say, at the beginning, it's not much. It's almost zero. Now, when nitrate starts to be denitrified, then N₂ starts to increase. Increase. It's almost like in the mid-- it almost mirrors nitrate. So this would be N₂. That's the product of denitrification. Oxygen decrease, followed by nitrate decrease, and oxygen increasing.

What if you also have sulfate? Let's use another color. Let's use blue again. What if you have nitrate? So let's assume there's no ion there. So when you have sulfate-- so there's another electron acceptor, which is sulfate, which is also pretty active in subsurface environment. Probably not in very shallow soil, but in bit of deeper, when you don't have a lot of oxygen, you tend to have sulfate.

So sulfate would be probably, let's say, something like-- let's start here. It would start to become decreased when this denitrification happen. Then the concentration decreases. Then it will also follow maybe one-- depends on how much electron donors you have and acceptors. This is representing sulfate. And the product of that is sulfides. So sulfides probably would be small at the beginning. But then it'd be increasing over time. Something like that. Call it HS-. This is like randomly ending. Another electron, except it's not easy equation. But if you need to write for sulfate too, then you would have three major microbe-mediated reactions. And in addition to that, you would also have an equation related to sulfate and sulfide production. And notice, also, sulfate reduction will be inhibited by both oxygen and nitrates. So you have two inhibition terms. So in that case, only when oxygen and nitrate is depleted to pretty small amount, then the sulfate reduction can start occurring. So these inhibition terms really would ensure the biogeochemical redox ladder in the system.

OK. So that's what we have for this unit, for this lesson. And you can use this. Will set up stage for you to do the homework. Think about different reactions that are going to happen in sequence in natural systems-- in soil, aquifers, and then how microbes evolve and the different concentrations involved with time.

Actually, we didn't talk much about microbes. But the microbial concentration will increase over time, following where the-- different types will be following their own electron acceptor. Electron acceptor evolution. Oxygen decrease and aerobic microbial will be increased. Things like that. OK. So let me stop here, and you are ready to do the homework. Thank you.

Li Li: OK. Let's look at this example 5.1, which we are going to set up control rounds for microbe-mediated reaction. So system is still a closed system with a bottle, which means we don't have flow comes in, flow comes out. We're really focused on the reaction itself.

And you imagine there's a bottle, 200 milliliter in volume. We have soil which contains some organic carbon. We also have nitrate and oxygen in the system.

And then we also have these magic powder, et cetera, which we're very excited about. Everything is ready to do this. Now, these two reactions that I put here, aerobic oxidation, denitrification reaction, these two reaction is already written as an outcome of a half reactions that we discussed earlier with these specified energy petitioning proficient in term how much goes into catabolic pathways, how much goes into the anabolic pathways. OK. So here we are looking at these two interaction, imagining that these are happening. Aerobic oxidation should occur first before denitrification. I also put the rate of kinetic parameters here.

So we have $\mu$ max, Km, which are half saturation constants, and inhibition coefficient, which is Ki for denitrification reaction because it's going to be inhibited by the presence of oxygen. OK. And then we are charged to answer the question, which reaction would occur first, which I already told you. But we are going to look at what is the magic powder, of course. We are going to look at just the evolution of the concentrations for different species. How does acetate concentration, which is organic carbon, evolve over time? In addition, we are looking at oxygen nitrate, totally organic carbon, biomass, et cetera.

So let's look at our folder. Now here when you look at this there are several reactions. I'm sorry. There are several files. The same one is the Input file. There's one Database file, which is Old Rifle Database. That one is a regular database that you have seen before similar to like the database datcom .dbs, which has a lot of fraction equivalent constants, reaction stoichiometry, and primary species, second species, and all that. That's the same.

One major thing that is different is now here you have two more database file, which is AqueousMicrobe and SolidMicrobe. AqueousMicrobe list all the microbe-mediated reaction stoichiometry that occur in aqueous phase. For example, for this example 5.1, you have aerobic oxidation. You have nitrate. You have denitrification. All these reaction happen in the aqueous phase. So this file is for aqueous phase microbe-mediated reactions. There is another file which is SolidMicrobe, which has catabolic pathways for reactions that occur that involve solid phase. For example, if you have reduction of iron oxides, these reaction stoichiometry would appear in this file instead of the previous aqueous file. So in this particular example, we actually don't use this SolidMicrobe.

This is putting here just for those of you who will be running microbe-mediated reaction involving solid phase. It's going to be handy for you later when you need these reaction's stoichiometry. So what's in this aqueous microbe?

The reaction's stoichiometry is actually more complicated from you just see in the example file. So it actual written as these two half reactions. One is catabolic.

So it's a catabolic. What catabolic mean is breaking down things. So essentially, it's the oxidation of acetate here becoming inorganic carbon, which is bicarbonate. So essentially, you have these reactions that happen, right? You think about this keq value. This should be capital K. This keq value is more like a dummy number. It's big, which means it's not going to functioning as limiting the reactions.

The reaction almost always new dox reactions. Reaction almost occur always in the direction from left to right, meaning acetate become bicarbonate as long as you have the reactants that are still there. So that's catabolic. But you also notice there's another anabolic reaction which includes, for example, the build up of bacteria. So you have C₅H₇O₂ Anabolic mean building up things.

So essentially, this reaction is indicating using the ammonium and acetate to build up microbial material C₅H₇P₂. The bacteria is using oxygen. So this is how you figure, OK, this actually is for the oxygen reducing bacteria or micro-organism. So you have these two. And in the online material, we talk about how much the energy produced from the reduction of oxygen goes to the catabolic pathway and anabolic pathway. And this is fs and fe values, essentially, for these purposes.

So if you look back in these, so here we're saying fs and fe is the number for aerobic. And it's different for denitrification, which is determined by reaction thermodynamics. OK. So you will be looking at this. And so what's in the Input file? Let me open it. And the Input file, so I mentioned the key difference is you have these two additional database. Essentially, in this case, it would be really one additional database. So everything else would be very similar. You have this runtime. You're reading database. You have output keyword spatial_profile. Putting these different times, times the areas.

And you also have these, for example, discretization which you only have one grid. You should have the total volume of 200 milliliter, which is 200 centimeter cubed, which is same as 200 milliliter. You don't have boundary condition, because it's closed system. You have initial conditions. So let's look at aqueous kinetics. So if we think about aqueous kinetics, right, you have this anaerobic oxidation. And you're essentially picking up the name.

This block is different in the sense, OK, you will need to specify aerobic oxidation reaction-- the pathway you have for aerobic oxidation half. So this name is there to be the same as this name, which is the catabolic pathway. So once it recognizes the name, it recognizes this reaction stoichiometry. And then also in the Input file you have another the pathway which is with this name. Which the code will be picking up this pathway, looking and picking up this name and process. OK. So here, you have aqueous kinetics block.

And this aerobic oxidation H₅ is defined as false aerobic oxidation reaction. we actually don't need this hw5. This is really not necessary. Actually, all the code is looking for is this name and the other name here. So this is for the catabolic pathways. This is for the anabolic pathways that build up, so C₅H₇O₂ which is oxygen reducing microbe. So if you go back into, for example, the aqueous microbe, the corresponding name is here. So it would take up for catabolic you would have this reaction stoichiometrically or reducing by the code. And when it sees this, it will have this set of reaction's stoichiometry reading. Now, we also talk about those $f$_s and $f$_e values, right? So in the Input file, you are actually putting the 0.4 the fs and fe value here and here. So this is essentially the $f$_e values, 0.4 and 0.6.

So this is are how you specify these $f$_s, $f$_e values. So essentially, the code is already programmed to reading these half reactions and then use these $f$_s and $f$_d values to come up with overall reaction as we indicated here. So you don't need to worry about changes, like this detailed calculation. As long as you have the $f$_s and $f$_e values, you're able to construct that. And then this rate is a $\mu$ max. So actually in this increase microbe, you also have-- so the top part is the reaction stoichiometry. And there's aqueous kinetics in the bottom part.

And so the bottom part, essentially, is telling you the reaction to the form-- OK, rate expressions. So form of the rate law-- or actually, it says this term needs-- if you have H₅ here-- hw5 is what I'm talking about. This name needs to be the same name as what you have here. So if the database says have this dash or underscore h homework five, then you do need it here then to be consistent as a kinetic block. Anyway, so look at this. We talk about all the reaction for microbial kinetics. So this rate, essentially $\mu$ max, is the same as the Input file.

And then you have monod_term. Which mean it depends on total acetate aqueous oxygen concentration. These value are the key m value for acetate. This is a key m value for oxygen, which is the same as what you have here. So all these reaction kinetics terms are essentially in the later part of the bottom part in the database aqueous microbe.

Same for denitrification reaction, which I'm not going to detail. So essentially what you have here is, OK, aerobic oxidation H₅. The coder will be looking for both reaction's stoichiometry of the two half reaction, build up the reaction, and then look for other kinetic information-- same for nitrate reduction inhibition homework five. So you use corresponding rocks for this reaction and also for catabolic and anabolic. Notice that here your $f$_s and $f$_e numbers of different now, right? This would be the $f$_e actually. This is $f$_s. So they're different, because of the reactions I've done for microbe-mediated reactions.

So these are the aqueous kinetics. And pay attention that with all these reactions when you look at the reaction in the database, it's important as you put these-- for example, primary species acetate, ammonium, nitrate, oxygen-- in the primary species. Bicarbonate, for example. The other things that are really important is that if you think about how we will present the biomass-- right, so biomass a lot time once they are coming out of the consumption of organic carbon, they can either stay in the water phase or a lot of times they attach to a solid phase and form biofilm. And it's not as mobile as in the water phase.

And actually a lot of literature has been showing that this is a big tendency, forming biomass or biofilms. They are not very mobile. So essentially, what we do in the code-- if you look at these reaction stoichiometry, they are really producing aqueous microbe, right? These are aqueous faces. But then we are saying once they have produced, they will quickly become solid phase attach on the surface. So we're actually using a kind of precipitation reaction to approximate that process. So there is a reaction related to this. And there's a solid phase call a mineral. Mean Yeah. So there's a solid phase species. So you have this C₅H₇O₂NO₂, C₅H₇O₂NNO₃, right? So these are O₂NO₃.

These are the species that actually goes into representing the biofilm. So we put a relatively small kind of-- it still follow this, still follows TST rate law as an approximation. But you can put smaller keq or larger keq values to control how much the biomass can be in aqueous phase. Is The majority of them usually come into the solid phase or biofilm phase quickly. And use these reaction rates to represent how fast they become biofilm. If you put these very small values, like 10 to minus 8, 10 to the minus 10, then a lot of biomass will be flushing out. Because the resin time is fast. The resin time is short compared to the precipitation reaction to happen. So you want to put these rates relatively high if you want to see a lot of biomass actually go through solid phase.

And quartz is representing the majority of the soil here to say, OK, essentially soil, like soil is a majority. A lot of them are quartz. That's why it's here. But it's actually not necessary to be here. Because it's not involving any other reactions. Let me see. So primary species, secondary species-- these are all necessary reaction. And then you have these conditions, right? So initial condition you want to be consistent with the example.

There are the different chemical species. The condition doesn't give you this. We usually put this for small numbers. Bacteria would build up that quickly. And let me see. So these conditions and then others-- so you do need to put a soil microbe to represent the biomass. And we do put in some volume fraction here to represent initial amount of these biomass here. A lot of time, they are like volume fraction essentially. If you put very small numbers, the system will need to take a long time to build up enough biomass. So you'll see concentrate decrease at some point. So if you put small numbers, there will be a lag phase in terms of how much biomass need to grow first before they actually functioning to allow you to see changes in concentrations.

So this is for the Input file. For a solid microbe, actually there's a set up in the system that you only have reactions stoichiometric there. So reaction kinetics, that actually is doing the Old Rifle Database. Because these reactions, original was already there. So aqueous microbe was added later on. So it's a bit different there. But anyway, in one of these or two of these file, we find the reaction's stoichiometry and reaction kinetics. So let's run this.

So everything is put in there. Let's run this. And we can kind of quickly walk through the Output file. So if we look at Output file, each of these have four time, 1, 2, 3, 4. And that's because in this file, we have put in a spatial profile. We have 1, 10, 20, 30-- four time points. Really for the batch reactor it sees spatial profile, not necessarily you can comment them out. If you would like to do that, then we can actually-- let me just do this, so you Output file is a bit cleaner.

You really don't need that other file. So I'm deleting all this. And I'm going to change-- I just comment out, so then it wouldn't have spatial profile coming out. And let's rerun it. Oh. OK. Sorry. So I do need that. Because I do need this spatial profile to give the time points, when it's going to end. So let's put 30, which means it's going to be end in a month. So you do need this. This is necessary for a way to look at a time evolution. You can just put one, so you would only have one spatial profile coming out. Let's rerun it. OK. Now, you have all this. And you notice every one of these species only have one, right? Because I only give one time point for the code to spit out a spatial profile.

But what we are really looking at should be time series. Which, essentially, it's kind of-- later one, when we introduce column expander. It's kind of like bricks through curves. And the grid block is the grid block number. We have one grid block number. This will give the time evolution of these chemical species in this particular a grid block. So let's look at this first. So this will be the file that it will rely on to plot out the concentration of different species.

See, OK. It's here. OK. So you can look at time, pH, oxygen, NO₃, N₂, acetate, bicarbonate. And this is a bit harder to see. But the easiest way would be you expose them either in Excel or read them in MATLAB, and then directly plot. And actually so let me just close this. So output in for this example is really this. So we have already plotted out You can see this. So Reaction I, of course, would occur first. And you can look at the concentration as a function of time. And organic carbon, right? So what this tell you is this is based that carbon chemical output, right?

So we talk about oxygen will be consumed first. So O₂ is coming down and not coming back again, because it's being consumed. And then at first, nitrate is still remain like its flat, meaning it's not much reduced. But then it wasn't reduced right after oxygen is consumed. The reason why-- if you look at the Input file, you realize that nitrate have a relatively small concentration at the beginning. So that's what I'm talking about. First of all, it has lower rate than aerobic. For example, mu max is much smaller. And also initially, doesn't have as much biomass there. So essentially, the denitrification biomass need to build up over some time. So that's why you see very flat even after oxygen is consumed, remain flat for a certain period of time, about 10 days, and then start to get down. Because at that time, there's enough bacteria to do that.

And it's actually you can see that in this bacteria biomass figure, right? Biomass is a function of time. And you have the nitrate reducing bacteria build up. Early on, it's relatively small. It takes some time to build up, right? Take a bit of time to build up. And then the oxygen reducing bacteria increase quickly, because it has faster rates. And once they get to the point about beyond five, it remain constant. Because it does not grow anymore. Oxygen is all gone.

Now, correspondingly, you see for acetate, so both reaction consume acetate. And they are producing DIC, which is bicarbonate. So acetate is being reduced.

Why you see this kind of changing almost like in slope here? Because x oxygen reduction is much faster just as this is same slope right here. And then this one is almost mirror the nitrate concentration. So essentially, this is corresponding to the consumption of acetate by nitrate. And these two essentially mirror each other with this almost symmetric reactions stoichiometry, right? So DIC increase quickly first, but then slow down until denitrification with certain rates that are higher. So these are things that you can actually look at and think about. So is this one, you do see the redox later. Oxygen occur first, nitrate occur second. But it doesn't occur right away after oxygen, because it has a bit of lag time.

Well, this is example 5.1. And homework have some extension questions that are related. But there's also another reaction that I asked you to look at, which was sulfate. You will be looking at the different files and the sulfate related reactions.