 Hello everyone, welcome to NPTEL course on groundwater hydrology and management. This is week 4, lecture 5. Coming to the close of discussing the hydrological components for groundwater analysis, we understood the major components in this lecture, this week's lecture and we will look at some more important aspects of the component that we saw, especially the conductivity. So hydrologic conductivity has a lot of variations, which means a range was expressed in the detailed data set that we share from the book and most of these books have a similar range and so if you check with other aspects of the ranges would be similar. Most of these data are collected in the lab and measured, so more or less we can use it across the world for any system. So as I promised, we'll do some comparison for gravel of hydraulic conductivity at annual scales. So look, we have a gravel at around 10 power minus 1 meters per second and we also compare it with clay with very, very less around 10 power minus 9 centimeter per second. So we have two values for hydraulic conductivity and we have taken the mid average for gravel around 1 centimeter per second here and then 10 power minus 9 centimeter per second. Let's see what that equates to, if we convert it to an hourly, as I said you have to convert it to hourly, then daily, then annual. So to convert that, you can do it on your calculator or you can just quickly run it through Google. So 1 centimeter per second, 2 kilometer per year, please look at how I've typed it, centimeter slash second, two kilometer slash year and once typed it, the automatically Google will give you the calculator and convert it. So you have the one value I put is just one, but you can put 10, 5 depending on the value you have in your measurements. So for now let's take one, we have taken it from the table. So 1 centimeter per second equals to 350 kilometers per calendar here. So that's how much groundwater would travel from a particular location to another location. So HA to HB, the two wells, it would travel around estimating the velocity between the wells. We could estimate it to be around 315.36, the hydraulic conductivity per year. Let's compare that to clay. We had 1 centimeter second power, 10 power minus 9, so that is you have eight zeros and a one, two millimeters per year. If you convert that, that is not even in kilometers. So we forget the kilometers, we're not going to go to kilometers, we're just going to millimeters. So not even one millimeter per calendar year, the water will move. Millimeter is very small, but even that distance it doesn't move. So that is how the difference is in nature. And so when you go to a soil and a location with clay structures and soil, please understand the water moves very, very slow. So if you're depleting the aquifer, the recharge will happen very slow. And so you need to warn the farmers that you're not just going to get water every year at the same rate, it will come low. Whereas in a gravelly system it travels fast. So that is why the mountain water you could reach in the springs and waterfall because water enters these gravel and it quickly comes to the springs and waterfalls. Just think about it, 315 kilometers per calendar year is the hydraulic conductivity as a rate. So this, if you have a unit, for example, Q is the velocity, is equals to K times del H by del L and if del H, dH by dL is a unit difference, you have one. So if you're taking a unit difference and the distance between the locations was one. So that one will go off and your Q is absolutely equal to your K. And that is how you could estimate the velocity of a unit in your soil. So that unit is very, very important and it gives you around 315 kilometers per year. So that's how much faster water can flow through in a year in a gravel system, but in a clay system, it is very, very slow. Not only this, so why was the range present and also what are the differences in the hydraulic conductivity? Let's look at a typical case. So we have a heterogeneity in the system and anionisotropy in the system. When I say system, it is the soil or the rock matrix. Rocks are heterogeneous and anionisotropic, same with soils. Let's see what does that mean? What do you mean by heterogeneity and anionisotropy? So let's take a soil sample. We're taking a soil sample at a particular location and the K, it could be permeability or hydraulic conductivity. Let's take hydraulic conductivity here is Kx in the x direction and Kz in the z direction. Why am I not taking y? Because x and y are almost same. So this is how the plane is. This is your z plane and this is your x plane. Your y plane will go here. So your x and y can be represented by two x. I'm just showing you in a tilted fashion. So this is your z plane and this is your xy plane. It is lateral in direction. For those who want, I could just draw it quickly so that you could see. So this is your xy plane which is horizontal or lateral in groundwater flow whereas your z is on the vertical. So z is very important for groundwater hydrology because gravity acts on it. xy is when your gravity pulls the water but then more lateral movement happens, you do slope and other reasons. Okay, so just to simplify, your x can be equal to ky. So your x and y could be the same velocity or hydraulic conductivity or permeability. So we'll just take two planes. One is the z plane and then the xy plane. Moving on, let's take one example. One soil taken at xy location and that is kx in the hydraulic conductivity x plane and in the z plane it is kz. In another location, location 2, x1, y1 is here and x2, y2 is here. You have kx and kz and at the two locations the kx is the same as kx. kx1 is equal to kx2. Same kz1 is equal to kz2. So which means the medium is homogeneous and isotropic which means at the same location the values are same and when you move to another location also the values are same because kx is equal to kz. Okay, so in one location the hydraulic conductivity is the same in x plane and your yz plane which is isotropic same in the direction and when you move to a different location homogeneous it is the same kx1 is equal to kx2 and kx1 is also equal to kz1 because of isotropy. Okay, so now moving to homogeneous and anisotropy. So here at one location okay let's say x1, y1 you have kx which is not equal to kz. Okay kx is not equal to kz so it is anisotropic. So in different planes the k value is different. So that is not concerning the isotropy so it is anisotropic. But then when you go to a different location your kx are the same okay kx in the location 2 is the same as location 1 so kx, kx are the same but same kz is also present kz2 is equal to kz1. Okay, so both kz values are the same as kx values however kx is not equal to kz which means it is homogeneous so between locations it is the same but within the location within the location it is not the same. So kx is not equal to kz within the location so it is anisotropic however if you take the same sample in a different location it is the same values in both the x and y direction or z direction so that is homogeneous. Now come to the next example so these are cases cases in the real world okay so you can have a homogeneous isotropic you can have a homogeneous anisotropic and now we're going to heterogeneous isotropic which means in a particular location okay the kx and kz are same so in location 1 kx is equals to kz in location 2 kx is equals to kz however your kx1 is not equal to kx2 okay in different locations the magnitude differs in your values however the within the location the values are same so within the location kx is equal to kz however in a different location kx1 is equals to is not equal to kx2 so that is heterogeneity but within the location it is the same so it is isotropic. Now we move to the more realistic version the heterogeneous anisotropic so which means within the location your hydraulic conductivity is different in different planes so kx is not equal to kz so you have to have two measurements at least and same when you go to another location your kx is not equal to kz okay so basically it is an isotropic and moreover the kx1 the measured value in kx at location 1 is not equal to kx2 so that is heterogeneous so in a real world this is the most abundant property it is heterogeneous and anisotropic which actually complicates the groundwater estimation it complicates the estimation of your hydrology and that is why you need more and more data for groundwater flow. Anisotropic is the direction dependent property so it is direction it is is it kx or kz and how it differs is the isotropic and anisotropic properties heterogeneity properties that varies from one point to another so it is this spatial property and it is at relevant scale okay so you need to understand that one is at the directions for a same location how within the direction it changes and homogeneous and heterogeneous are part of the the space how spatially it differs moving on so as I said therefore there is a need to solve Darcy's equation law at different points and take into account directionality you cannot assume that kx is equal to kz and also it is going to be the same as two locations but how much can you do is dependent on your time and the cost to do these estimates so you need to balance your cost and time with the heterogeneity and anisotropic conditions but in the real world please understand that anisotropy and heterogeneity is much much higher than homogeneous isotropy etc so only the beach maybe you could find homogeneous and isotropic conditions but even then are you going to study your water in the beach locations so you need to be very careful in where you are going to do these applications and understand the soil and hydraulic conductivity values do they differ or not moving on we are going to see the property that is more relevant more important is the heterogeneous anisotropy how do you solve it so in in the Darcy equation when we discussed last as we saw q is equals to minus k del h which is the gradient hydraulic gradient and if the hydraulic gradient is one your q is equal to your hydraulic conduct magnitude the direction is minus it goes the lowering direction so let's write it in terms of vector shorthand to represent flow in one direction so the flow in one direction is given as qx is equals to minus k dh by dx we're just expanding your gradient however we saw in the previous slide that it is heterogeneous and anisotropic which means from one location to the other location the values can change but within the location it differs as per the plane x y and z so in the normal very very simplistic version we say x and y are same okay so but however there is difference in the z so your x y plane you could take but z is definitely different because z is gravity and the process how water moves is different than the process how water moves on the horizontal version so then you have to expand in shorthand qx qz so q becomes qx now we are expanding it into two dimensions qx qz that is equals to minus kx x kx z kz x kz z and then you do the partial differential equations it can be written in short form as qx is equal to minus qxx del h by del x minus kx z dh by dx dz so all these are partial differentiators and you would know how to do this in the mathematical classes but more importantly you can have another one for qz and similar equations can be written but do we stop here no because it is a three-dimensional problem okay so in a three-dimensional world if you express it it becomes a huge matrix and you know how to solve it is by using matrix and differential equations hydraulic conductivity and permeability are tensors so you would have to calculate the component of kig of these tensors and that is a advanced groundwater hydrology class so since we are not going into the advanced level in this course it is a perspective and introduction course on groundwater and groundwater hydrology I'm just going to introduce the concept of what is the equation and how it varies in the different planes but solving it won't be part of the class if you think you're going to solve this by pen and paper it's going to be really really difficult at time consuming and how many times can you do because you if you want to study one hydrology groundwater equation per location per time it's okay but then you want to do it as a time series and you want to combine one location to the other and from there to the other and so this cannot be done by hand and that is why we do have groundwater models the most widely used model is modflow which is open source we will be introducing the model in the future lectures so with this I've covered most of the important hydrology components for the course let's do a quick recap so that we die all the lectures from both week three and week four to a common understanding of what we did so we introduced the hydrology components in terms of groundwater we studied how a water enters the system and goes into infiltration and percolation into different compartments we looked at the zone of aeration and zone of saturation and then we differentiated the aquifers based on is it open the surface to recharge as unconfined aquifers and then if there is a confining layer we said the aquifer within the confining layer to be a confined aquifer we also noted that the porosity is the most important factor to determine the groundwater storage and flow because that is the space which water occupies and water would reallocate itself between the pores to move okay so first infiltration gets the water inside and after that it starts to move through percolation and if the pore spaces are connected then more groundwater flow will occur porosity is a function of the soil or the rock material and we call it the matrix and how the soil particles are structured and in between how the pore space is there we also noted that the pore space can have air water combination of both or none okay so none is in the lab conditions but most of the time it will be air and water in a dry situation it will be only air and in a wet flooded situation it will be only water when it is dry it is called dry soil where only air is present in the pore space and when it is full of water we call it saturated soil here we call it zone of aeration where air is there and water can come in by pushing the air out and then zone of saturation is two which is under the imaginary water table where water occupies the pore space then once we established that we wanted to see how the pore space can hold on to the water and what are the forces indicators of establishing this so we looked at specific yield wherein water enters a soil profile and gravity starts to act on it so how much is the drainable porosity was given by specific yield why is this important this is important because a plant can know how much pressure to exert to take the water a farmer can know how much he or she has to put a pump to exert the water and how much gravity actually keeps pulling down the water so in a gravel field you saw the specific yield to be very high which means water would just flush through the gravel banks and not much water is going to remain specific retention is the opposite of specific yield where it is a property of the soil to hold on to the water and this holding on to the water actually benefits the plants in a particular aspect if the specific retention is not too much okay so because this is the property of holding the water in your soil to visualize it we took the sponge in the kitchen washing dish example so you have a sponge and you squish it all the water is out it is a dry matrix now when you put water and soak it in water and lift it up the water will start to drip and that is specific yield acting on the drowning of the water out of the sponge through gravity and then what we did is when after gravity has exerted its force then some water is still present in the sponge which is called the specific retention specific retention should not be too much like in clay it clay can hold on to water long but that holding potential can also limit how much the plant can exert okay the plant can have some water that can be taken easily but if it is too tightly bound to the soil like in clay then the plant will not be able to grow then we looked at permeability and hydraulic conductivity permeability was also a function of the material of how water is allowed to permit to go through and it is also a measure of porosity and connected pores how well is the pore connected we looked at effective porosity and we looked at water velocity as a function of these permeability and effective porosity because the pore space can be at different spaces the big big spaces but if they are not connected then the water won't flow water will just get stored and be there and we wanted groundwater flow to occur right so from permeability we looked at another property which is also a function of the fluid not only the soil which is a solid particle we also looked at hydraulic conductivity wherein the medium or the soil or the rock matrix allows or conducts the water to flow as based on the properties of the fluid here the fluid is water so we used the viscosity and density of water to estimate hydraulic conductivity in soils so hydraulic conductivity is both a function of the soil and the liquid that is passing through the solid and for our rural applications and agricultural applications we took water as a fluid and based on that we had different values for hydraulic conductivity of water in these different soil parameters we looked at hydraulic conductivity in a three-dimensional space wherein you have your z x and y the x and y could be almost equal in the velocities and the magnitude however z can be different we looked at anisotropy and heterogeneity to be the major factors of making groundwater very complex just look at this in a surface hydrology perspective in surface hydrology you can quickly estimate is it going to be homogeneous or heterogeneous because the parameters are very less the stream bed you can look at okay water is going to flow in the river it is almost the same soil on the side so it is okay and is it isotropy there's no there's no big you know causes to stop the water oven like check dams and and large dams whereas in groundwater there are a lot of parameters that can impede the flow which can stop the flow and the impede is not the same at different points it is heterogeneous and anisotropic the the basic properties that actually allow the water to flow is complex in nature and we have looked at how it can be very very complex so the best way is to get a good fundamental understanding of these properties and the limitations of challenges in applying them in the real world at one point we also argue that we cannot afford both cost and time to take multiple samples along every location however we need to estimate and assume some things so most of the assumption would be at a range okay so yes we agree that it is heterogeneous but it is within the range and then we also said anisotropy yes and we have different values for kz and kx however we said between x and y it's almost the same so we said isotropic conditions for x and y homogeneous was dealt with very cautiously so you need to understand the soil type in different locations to estimate if it is homogeneous or heterogeneous so in a groundwater model you will actually dissect the differences in the layers and say is it homogeneous or heterogeneous and the model will calculate it we also looked at solving these equations once we established the variations in hydraulic conductivity we said okay it's not going to be a single one-dimensional problem or a two-dimensional problem it is a three-dimensional problem and we looked at the equations that will govern the three-dimensionality in Darcy's law we also found that it is not easy to to solve the equation on pen and paper maybe on one equation one location you can but for groundwater you need to estimate what is the hydraulic conductivity here and the q here Darcy's q and then what is it here what is it here to actually monitor the flow and for that you need a connectivity and a feedback from each of the q's and that is mostly done by models we also looked at water levels and hydraulic head how to estimate the hydraulic head and water from water levels and groundwater depth and from the hydraulic head and water levels you jump into the Darcy's law so with this we have almost finished most of the important components for groundwater hydrology in the coming weeks we will see how to use them and also we will go in deep for particular aquifers what are the parameters that are important so we will revisit some of these but the basic introductions have been done I will see you in the next class thank you