 Hello, everyone. Welcome to NPTEL, Rural Water Resource Management course, week five lecture three. In this week, we are looking at groundwater hydrological components and properties that can be augmented or can be modified for better rural water resource management. The stress is on groundwater management in these couple of lectures because it is the most complex water resource to manage. And to understand how much water is available, it is very important to understand these properties from which we could estimate or understand the groundwater potential for the region. With a small intro, let's get into today's topic permeability. Before permeability, we did discuss hydraulic conductivity very tertially in the previous week, but in this current week we looked at specific yield and porosity. The other more related parameter is permeability. As the name suggests, how do you define permeability? Permeability is the measure of the soil's ability to permit. So from permeability, you can take permit, water to flow through its pores or voids. So either way, the first objective is to understand where to get the water. And for that, you need pores and voids. And then you have the permit of water into these voids and so like spaces, right? So that is the soil's ability to permit is called permeability. So let's look at this diagram, the first diagram. Water comes in and it goes through all the pores, the groundwater. It can get stored, it can fill up the void, it can drive out the air and thereby replace the air with water. This is a loose soil wherein the soil particles are not touching each other so the water can easily flow. I just want to make a very important point here. So sometimes we look at books and they say rocks and then soil. So do not differentiate it for groundwater because groundwater occurs in the soil profile and also the rock profile. So the same parameters would exist in both phases. For example, porosity in the rocks or porosity in soil, permeability in the rocks and permeability in the soil. Our goal is to understand the groundwater's potential for which the terms do occupy the same meaning in both the soil and the rocks. And please understand if you want to go even further, the rocks is what disintegrates, weathers and then forms soil. So it's not that we're discussing something different, but it is just the depth at which we are. We are at a shallow depth, it is a soil profile. If you go further down, it is a rock profile. So let's discuss the first image which is the loose soil, which means the particles are loosely bound to each other. There is a lot of void space and the void may have air or water. Now water is flowing. So groundwater comes in and it finds a void space. So water can easily flow in and out. Why should it flow in and out so that it can occupy the void spaces. Once it fills, it will flow to the next void space available. So easy to flow, it is high permeability. So because the soil is permitting, it has high permeability. Then we have a dense soil, which means more density of soil particles. It is close to each other. And it is showing that water can go through in and out, but with some tortuous parts or very, very selective parts. So here water can go in two parts or even multiple parts here because it is loosely bound. But here water would first hit the surface and then see that this is much easier to flow so it will come around the rock. It doesn't matter if it has to traverse long. So the distance is not a question here. Water would flow through the least resistant path. Even if it takes a longer distance, it is not smart. It doesn't think that I can push and get myself quickly to the other end by going through this path. No, it only flows through the least resistant path. So water is coming. It hits here. It has high resistance whereas here it has low resistance so it comes here relatively. So it comes down and then flows through this cracks. So the dense soil has a very high amount of particles which are connected to each other, the solid particles. And by that it has very less space. And more sorted, I would say, right? So sorted and some wide space are there. Low permeability. So the soil is not permitting water to enter that easily. So these are two different examples of high permeable soil and low permeable soil. It is not just the density of the soil that is the key factor here. Some soils can be hydrophobic, which means it repels water. So then there is no permeability there. So some soils, for example, would repel water so it naturally would not permit water to flow through its system. So that is one thing. The other thing is, is it just the soils property? No, because if you have the same soil, let's say I'm taking a sandy soil in both the cases. The size matters, the size of the grain matters one and also the land use pattern matters. So if you have a forested ecosystem where roots are there and the roots died, the roots die, decompose, etc. What happens to the root parts? It becomes void and those could be making the soil a high permeable system. So the soil matters on the dense soil, maybe it's a barren soil, maybe it is a compacted soil, people walk grazing, those kinds of soil. So it is having a high density. The density could be a soil property or the land use land problem property. Moving on, note that Q, which is a unit of velocity is not actually a fluid velocity. So what is Q? Q is any velocity we are trying to estimate the distance over time. So actual fluid velocity is defined as V. So if you have a container and you put soil in it and you pass through, so let's say one meter container, and you're passing through water in one side. And then you are timing how long the water takes to transverse through the tube. Right here, for example, Q through a block or a tube of soil and it comes out. So you have the time by which it came out and the distance. So you can calculate the velocity Q. So even though it has a unit of velocity, which is length over time, one meter over number of time, let's say it took 10 minutes. So one by 10 minutes in the units will be meters per minute or meters per meter, yeah, meters per minute, right. It's not actually a fluid velocity because water doesn't go through a straight path. So the actual fluid velocity is defined to be V, which is average linear velocity or pore velocity because the pore is what allows the water to go through. So it can also be called as a pore velocity. So water is coming in. It doesn't flow like a cube just goes in and comes out like a tunnel where you have a car coming in and going out on the other side because it is empty, right. The tunnel is empty. It's not going to hit anyone. It just goes out. But water moves across and finds the way where it has to go. So look at how up and down it has to go through a path. By this, what I mean is the distance might be the same from A to B, but the path it takes would make the distance longer and thereby the time longer. So the average linear velocity which is V is given as Q by N E, where N E is the effective porosity. In the previous slide in the yesterday's class, you would have noticed N is SR plus SY, which is specific retention plus specific yield here. Even though the porosity is there, there is an effective porosity because not all pore space conducts water allows water to flow. And that is called N E effective porosity, the fraction of connected pore space in the medium. So as long as it's connected, so you can have spaces, but if it's not connected is as good as for water to flow is as good as saying no connection, no wide space for water. Okay, so the effective porosity is actually the fraction which is connected between the pore space in the medium. When we say medium, it could be soil medium, rock medium. Okay. So this defined hydraulic conductivity for permeability, we will have another lecture, just focus on hydraulic conductivity, which is a very, very important factor for groundwater hydrology. But here what we'll do is we will look into just one component in the hydraulic conductivity equation. K is a hydraulic conductivity is a function of both matrix and fluid properties matrix is the soil matrix rock matrix, the medium. So these terms, if you start reading the books that we have prescribed, you would understand that matrix medium system, all these words will be interchanged for the soil profile and also profile or rock profile fluid is the water that goes in so you can also know water properties, but water can be mixed with other things so it's okay to call it as fluid. So K is your hydraulic conductivity, which is a function of small k which is intrinsic permeability. Okay, the topic of today's lecture and row which is your fluid density. Here it is water. So you can have water density. Gravity is your gravitational acceleration or accession due to gravity G and mu which is fluid viscosity. Okay, here we can use water terms. So if you know you're going to do groundwater, then the row and mu can be replaced by water's values. So let's look at the equation K equals to small k by in times rho G by mu. Now rearranging you get small k on this side. Okay, and big K times mu by rho G. Since now you know what are the constants mu, rho G are all known constants. Okay, so K is nothing but a function of these constants and hydraulic conductivity. Okay, so let's look at this is how you would define permeability or estimate permeability by knowing K. So if you know in groundwater hydrology some parameters, you could back calculate the other parameters because all of them are a function of the solid space, which is your soil and the pore space. Also it is a function of the liquid. Moving on, is it one dimensional? Is permeability one dimensional? Pure sand particles are easier for water movement. For example, you are moving from right of your screen to the left. So water is moving in this direction. And all the images that we have seen in the lectures, we see one dimension. So water is moving and it is finding the less resistance path or the effective porosity which has made that the pores are connected. It is finding that connection and flowing through it. It finds all these sand particles very distantly separated and it flows through the sand particles. Then you have another medium, another example where sand clay mixture retards movement of water into small pore sites. The same material, if you see the sand is sand, but now if you're mixing clay to it, because loam is sand, silt and clay, here we're taking a sample which has sand and clay. Clay is much smaller in size, the grain size, which is the dark brown component. And then you have your gray component, which is your sand particle. So what happens is your brown particle starts to oppose the movement of water or not permanent. So it is not increasing your permeability but decreasing your permeability. For example, let's take here the water which was coming through. Water which was coming through is now blocked because of clay. I hope you remember about clay. The property, as I said, it has a very small specific yield. So it is very hard to drain water out of it. And it has high surface retention, specific retention, which means it will hold on to the water. Once it falls onto the water, it swells because of the water's volume also clay mixes and swells. Once it swells, it will stop the water from going in. So that is why you could see all the groundwater issues in clay soils pretty pretty drastic. You don't see recharge, but still farmers are using the water because they see the water, but it doesn't recharge as frequently as the other activists. So coming back, let's take this path, path one and path three. Path one, you could see that the clay is just stopping right in the front. And even if it can go through this lot of clay. And then here you see small, small clays on this path, which actually totally blocked your way through the tunnel. So there is no forest space that is connected, and we'll have to stop. So what do what it will do, it will flow through the less resistant path or least resistant path, it will then jump into here and come slowly through this material. Notice what has happened, your velocity has decreased, and thereby your water movement hydraulic conductivity has decreased, thereby your recharge has decreased. So this is how a solid material the soils properties rocks properties can impede your groundwater recharge. Come back to this slide where permeability is there, your game might be the same, but now if you increase your density or fluid because of the density of your particles mixing with water, understand that water can also take soluble nutrients and soluble salts from your soil material. What happens if row changes if row increases your permeability decreases. Same way, your hydraulic conductivity decreases your permeability decreases. So it is a very, very direct relationship with hydraulic conductivity and an indirect relationship with your density. Moving on. Is it one dimensional. No, you have three dimensional movement of groundwater thing we've touched a little bit basics on this water can move in the z plane, which is vertical and also in the XY plane, which is horizontal lateral. So both these things is the XY plane and then your z plane, water can move up and down up due to capillary rise down due to gravity, and then in the XY plane which is driven by a slope XY plane is also because of your gravity and some part of capillary, but mostly on this way so it is your gravity acting. Also when you have plant and other species which are trying to pull the water water moves you have a pump water moves right so that is your XY plane moment. So what are you seeing here, you are seeing that it is not one dimensional, the water can move multiple dimensions right so it is also important to understand the differences in these properties in a 3D plane, not 1D plane. So you do have models groundwater models and other models which are 1D, and it is only used for specific purpose, you cannot generalize the results into a 3D plane, because the 3D version would have different forces acting on just not just gravity acting on it. Let's move forward. Let's look at some ranges for permeability. So as I said I'm now using different sources to interact with you on the values that you could use and most widely used values are from the Fries and Cherry book on groundwater 1979. So you could see here that you have a range for the values and the range is because of the size and also the management of the land, which means gravel doesn't have one size there are multiple sizes for gravel and depending on the size you have different values for permeability and hydraulic conductivity. Let's look at the permeability of silty sand as an example for today, silty sand which has sand in it and a little bit of silt in it, not clay, we are not mixing clay here, but sand, so you have clean sand, silty sand, silky losses, which has some play on it, but let's take silty sand. And what do you see here is the range, the range for K, the small K is permeability while bigger K is hydraulic conductivity and look at K's units, it is centimeter square, whereas hydraulic conductivity is like a velocity, this length per time. So the multiple units K Darcy or K gallons per day per feet square. Okay, and you could bring it back here because gallons is volume feet square is area you can calculate, you can remove the dimensions to come at length per time, all these are length per time, whereas these are. Yes, length square or area. So coming back, silty sand has a K centimeters, let's use SINS, K centimeter square is anywhere from here, 10 power minus 10 to here, 10 power minus six. So think about it, 10 power minus four is the range right so from 10 power minus 10 it can go anywhere to 10 power minus six. So this is a big range for silty sand. I'm going to take the average almost the center. Okay, the center is around 10 power minus nine K, and for hydraulic conductivity is 10 power minus four. So which means 0.0001 for hydraulic conductivity, and for a centimeter square unit permeability it is 0.0008 zeros and one. So think about eight decimals and a one spaces decimal spaces nine but eight zeros and one which is such a small number for permeability. You cannot say it's negligible. If it comes in the denominator because it can pull down your values, the range I'm saying it's not negligible. So you need to be very careful in finding the accurate permeability value. So your results, your results can suffer by four orders magnitude minus four, right, 10 power minus four difference anywhere from as I said, Cindy sand is anywhere from minus 10 to minus six. So you have 10 power minus four as a difference and it means so many units orders of magnitude can be impacted. Also in the other words, you can also understand the permeability can be very high or very low, just for one type of solid type. So it is as important to get the properties very very accurate. Let's get a small introduction to hydraulic conductivity we will talk about this more in the next class, because this is one of the key parameters the others we can assume and get away with it, but hydraulic conductivity assumption should be avoided. Most easily available through your lab. And once you have your hydraulic conductivity estimated, you can go back and estimate the other properties. For example, as I said, if you know your hydraulic conductivity, you can estimate K because you know row G and me. And if you know K, you can go back to your other equations to get other porosity and other values, right. So in fact, we can rearrange. I'm taking the equation from reason cherry, which is basically looking at the velocity over area. Okay, and getting at what is the speed kind of a speed for velocity estimate q volume passing through a unit area. And the difference between the H and the L is the gradient. So let's look at it. Rearranging equation appears equation we get coefficient K has dimensions of L by T, which is length over time, same units as velocity, and it can be called as hydraulic conductivity. It may be also referred as coefficient of permeability. Why is it called coefficient of permeability, because in this equation, what it tells you is K is related to or is in is an agreement relationship with mu and doji where the bigger K hydraulic conductivity is your coefficient of mission ship. And it is that is why it's called since it's a coefficient you can call this coefficient of permeability. Now measure how easy a fluid can pass through for us again, the previous permeability is the soils property of permitting the water to come in. Whereas hydraulic conductivity is similar, but it is how easy a fluid can pass through which is your velocity and of your velocity estimate. So how easy your water can pass through is hydraulic conductivity, and it also depends on your permeability. So you can use the same figure, I'm using the same figure here to discuss that but what you could see is in a loose soil water can easily pass through. Okay, and that and therefore, if the easy fluid passing property can give you a higher hydraulic conductivity. For dense soil it is difficult to pass and so your hydraulic conductivity is low so right now you can understand it as a velocity and a measure of how easily a fluid example water can pass through the forest. Moving on, you can have two approaches to look at it dastian versus microscopic approach, whereas the microscopic approach is a very small focused look at the soil profile you can see that the soil particles are all look. Whereas in a microscopic everything is put in a tube and you really look at the tube. You don't care about what is happening inside you pass q which is your water volume across an area of cross section water passes through and comes out. Okay, and water passes through average linear velocity so you have an average linear velocity q passes through and comes out. Whereas in a microscopic behavior, you can look at variable velocities it's not one velocity, for example, water can pass through this path very fast, whereas water can pass through here very very slow. So this is the difference between macroscopic which is dastian dastian experiments are done using a macroscopic approach. So this is the true which is the real exact world or the complex sample reality is a microscopic view. You cannot actually do it. Yes, you have to understand that there are a lot of velocities that can be here in this diagram variable velocities can be high, but can you actually model each and every velocity know. What Darcy has done is he has taken a very macroscopic approach where all these velocities kind of cancel each other, or it actually averages and smooth as up. Darcy found experiment Darcy is a scientist for groundwater but he was initially an engineer who worked on pipes for fountains to in France to make the fountains beautiful etc and he was finding that how to you know monitor and measure the water flow through these pipes, and then he became kind of the groundwater scientist because he got these equations in the lab. So Darcy found experimentally that the discharge q, which is this one, how much water you apply is proportional to the difference is the height of the water. The hydraulic head, which is a high potential to low potential water for some high potential to low potential so you have a difference in head between the ends from a to b and inversely proportional to the flow length this length. So you come back in, in a setup for hydraulic conductivity to explain it further. All you need to know in this slide, while we are finishing off today's lecture is that all the experiments, we are done with a macroscopic view, even though the microscopic true reality could be different. Okay, so if someone says are you assuming all this no it's not assuming but we're kind of averaging the effects into a macroscopic view, you cannot go in detail for each and everything, you can if you want to focus on a specific but for groundwater hydrology the macroscopic view is used, not the microscopic you cannot say how many pathways are for example I don't care how many pathways are there, but how much volume is passing through my soil profile is more important. Moving on, as hydraulic conductivity is also given in the freeze and cherry book, you would see multiple values very similar to permeability you will have multiple values multiple rates. Now, it is a function between each other because permeability is a function of hydraulic conductivity, and if you use water as the liquid that goes through in your experiments, then row and new can be estimated, because you know the density of water you know the sample size has been divided into rocks, which is big big rocks under the soil profile and consolidated deposits which is above your rock profile. So you can have a cast limestone and on top of that a clean sand. Okay, so right now let's say that rocks are much much deeper in the profile and unconsolidated deposits are above. So let's say you have in this experiment I'm taking silt losses, okay, silt losses and you could see the hydraulic conductivity ranging from this line, okay, ranging from 10 power minus nine. It's normally given in meters per second. So let's say 10 power minus nine up until 10 power minus five again another 10 power minus four orders of magnitude. So it can be very very small hydraulic conductivity so it's very important to estimate it as accurate as possible. We will see in future lectures, how do you conduct a hydraulic conductivity experiment in the lab, how the initial equations were made. It's such a simple equation right q is equal to the discharge actually the discharge passes through the tube, and you have your hydraulic conductivity which is a function of your q times your by the area of cross section and the hydraulic head difference just to three parameters that's it. But your application of hydraulic conductivity has tremendous potential in groundwater hydrolysis. So we would look into that by going through how the instrumentation was set up and how you could understand from this table which hydraulic conductivity to use this I would conclude today's Thank you.