 So we have seen the overall energy scenario, we have also looked at different ways in which we can do the energy economics calculations for projects. Now we are going to look at energy resources. So when we talk about energy resources, there are some questions which you may want to think about. We have heard, you might have heard the term peak oil. So what is this term peak oil? Do we believe in peak oil, peak coal, peak natural gas? We all know and we have seen in our overall energy balance where we look at India or we look at the world that predominantly today our energy use is based on fossil fuels. So the question that we want to ask is, are fossil fuels depletable? Will their consumption decline? How soon will they decline? How long will the fossil fuels last? And so this is some of the things that we will consider. We will, when we talk about resources, resources can be energy resources can be stocks or flows and in the initial part we are going to talk about resources which are stocks. Stocks means that they will be, they can be stored, they can be transported and then you have an estimate of how much we have, how much we have in terms of the resource and how long, how much are we using annually. So we want to get an estimate of how long that fuel would last. So if you see there is this interesting quote from the Saudi Arabian oil minister who said that the stone age didn't end for lack of stone and the oil age will end long before the world runs out of oil. So the estimation, the earlier calculations were where we would try to see how much stock is there, at what rate are we using that stock and estimate how much time it will take. And what has been said here is that it is all about dynamics, prices, substitutes and it is not necessarily about these estimates. However, it is still worthwhile to see traditionally we have these concept of the geological resources and reserves, how do we characterize it, how do we estimate how much time it will last if we have a certain consumption rate. So we have, this is the McKelvie diagram, this is the diagram which was used and this shows the, this is the basics by which we classify the resources. So typically what happens is when we talk about fossil fuels or we are looking at materials which are stocks, we look at some areas where we have done some extractions and we know that these are the, we have the, in the case of oil you will have a oil well dug and you will find that there is this percentage of concentration and it is viable to take the oil out. So that would be something where you have actually conducted explorations and we know that this is the kind of, in this situation we have the reserves. That means the reserves are known quantities and this could be which have been already measured. So this is called proven and then there is a second portion where you have done some sample wells and you know that the, that whole area has similar kinds of rock formation. So those will be called indicated and the third one is in similar areas and similar formulations we expect that though we have not done any exploration we think that it could be inferred that these will also have. So whenever we have these estimates it is given in terms of proven, indicated and inferred and the probability of occurrence is highest in the case of proven we have actually measured and quantified. So we are quite sure that this is existing, indicated with some lower probability and inferred with even a lower probability. So this is in terms of the resource. Now there are also other undiscovered, there is this whole set where there are other undiscovered resources and which are hypothetical, speculative and also in these there are two axis, one axis is in terms of the probability and the second one is in terms of the economics. So reserves which are easily extractable with higher concentrations, the cost of extraction would be much lower so they may be currently economic. As the technologies change things which were not economic earlier can become economic. So this, the between reserves there is this concept of reserves and resources, resources may be in known occurrences but they are currently not economic to extract. So resources is a slightly larger term which has a larger value and resources is. So this concept of resources and reserves is shown in this classification which is the McKelvie diagram and this is how it is plotted with the kind of increase as you go down, as you go up it is the more economic, the costs are lower and here this is the highest probability and lowest cost and then you go for lower probabilities on this side and you have higher cost going in this direction. So there are two kinds of beliefs about resources, one is that if we look at a finite amount of reserve which is there in the ground and if we look at a finite amount of reserve and we know that we have a particular kind of extraction pattern, we can estimate then how much time that extraction will occur. So if we have a finite reserve and we are talking of a stock, if we have a production in a particular year and we have t is a time and we have p and we say that okay, let the production be constant at the rate at which it is being consumed, then if we look at this area under the curve, this becomes the static, we define a static r by p ratio or the r by p ratio which is simply divide the total amount of known reserve and divide it by the production in a particular year assuming that it is constant, this will give us the number of years at which the resource will last at the current level at which we are consuming it. In many cases as we know the population grows exponentially and the requirement for many of the fossil fuels, coal, oil, natural gas has been growing exponentially. For instance, if you take the example numbers, if you look at in India 1970, we used about 70 million tons of coal and in 2012, we used 557 million tons of coal. So you can see very clearly that there is a exponential growth, so we are going to look at these following models, we will start with the static r by p ratio which I have already discussed. We will look at the exponential growth model and then we will look at logistic growth curve where we take the fact that the area under the curve is bounded and yet there is a finite resource and then we will look at Adelman's model. Then this is the definition of the geological survey, the identified accumulation that can be extracted profitably under present economic conditions, that is the reserve and resources are the reserves plus all accumulations that may eventually become available, they may be today undiscovered but discovered but currently not technically or economically viable. So resource is greater than the reserve and if you see, I told you that we are going for an exponential growth rate for coal, it has been growing exponentially and if you see from the early years and this is the kind of growth. Just to give you an example, as we said, if we take 1970 and 2012, we can find out what is the growth rate, we can just take 557 divided by 70 and calculate the compound annual growth rate, now 70 to 2012 is 42 years and you will find that this G corresponds to roughly 5% or 0.05. In the recent past, you will find that coal has been growing at 6 to 7% per year. So the question is that if we think in terms of an exponential growth, then obviously instead of the static R by P ratio, the number of years for which the coal will last would be much lower and we can do that calculation. Just to give you a sense of it, if you look at the coal mines and the coal resources, you find that most of our coal, little bit in the central area and the significant proportion in the east, these are where the coal mines are there, there are some in the northeast, there is some lignite here in Tamil Nadu and some other things, but this is where the distribution of the coal is. So from the integrated energy policy document, this gives us a sense of what are the reserves which was there in 2003, 2004, you can see that the reserves were talking of 34000 million tons and the production was 414. If you divide these two, you get a R by P ratio of about 80, if we took proven plus indicated that R by P ratio goes up to 140. That means that at that level of production, this will last for about 140 years and similar things can be done for oil and natural gas. If you update these numbers, you can see that this is the number that you have in 2013-14 and we can calculate the R by P ratio for this. From the GSI, if you look at it, you will find that over the years, the proven reserves also keeps increasing and today if you see in the 2018 values, I think it is of the order of about 148000 million tons. So if you took 148000 million tons and if you look at this number of 148000 million tons and you divide that by the annual production, 148000 million tons of coal, annual production roughly about 600 million tons of coal, the number that we get static R by P ratio is about 200 years. So we have a reasonable amount of coal, though it is low grade coal and of course as we have seen there is a problem in terms of the CO2 emissions and so people we are talking about not using the coal. So we would like to see now if you have an exponential growth rate, how do we make this calculation? So that means we are talking of let us say that this is growing at 5%, then what will happen is in the first year we use P, next year we use P into 1 plus G and so on, P into 1 plus G raise to n. We want to find out n, the number of years in which the resource will get depleted. So that means here instead of that static we have P and this is Pt by T. So of course you know that area under the curve for an exponential curve is not bounded, but if we have a finite reserve then this is R and we want to find out what is the time when this gets sort of cut off, right. So we have already calculated if it was a static then it lasts for much longer. This is 246 years is what we had calculated. We want to now calculate what is this value, right. So in order to do that calculation we will take total reserve will be P, P1 plus G raise to n. So we can multiply this R into 1 plus G, it is simple actually it is just a geometric progression. So 1 plus G raise to n plus 1, we can take 2 minus 1 and we get R1 plus G minus R is equal to P1 plus G raise to n plus 1 minus P and this is nothing but RG is equal to P into 1 plus G raise to n plus 1 minus. So R by P is equal to 1 plus G raise to n plus 1 minus 1 by G. Now if you look at this we want to calculate n, this is what we want to calculate, we want to calculate n, we know R by P and we know G, we want to calculate n. So let us take this and all that we need to do is we take R by P into G is 1 plus G raise to n plus 1 minus 1, 1 plus G raise to n plus 1 is equal to 1 plus G into R by P, take natural logs on both sides. So we get n plus 1, ln 1 plus G is equal to ln 1 plus G into R by P. So n is equal to or n plus 1 is equal to ln 1 plus G into R by P divided by ln 1 plus G. Now let us just plug in the values for the numbers that we had, we calculated for India for coal that R by P ratio was about, was 246 and we said that let us consider a growth rate of 5 percent, we can of course take a higher growth rate. So we can suppose we take 5 percent then n plus 1 will be ln 1 plus 0.05 into 246 divided by ln 1.05, you can calculate this, it turns out to be ln, this is 2.59 by 0.049, it turns out to be 53, so n 52. So we of course, if we see the time which we are talking of in this is going to be lower than the time which we had calculated for the static R by P ratio. If we instead of 6, 5 percent if this was 6 percent then you will find that the life will, n will decrease and then turns out to be 47 years. So remember we talked about a static R by P ratio and we also talked about the ratio if we are going at an exponential growth rate. Now in actual practice what will happen is we expect that the pattern will not be exponential and suddenly coming to 0. So we expect this is similar to what Adelman had done but we have also, this has been also done by Hubbert who was a geologist and he proposed the method, it is called the Hubbert model.