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Resources and Reserve

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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. (Refer Slide Time: 00:34) 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 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 fuel 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 mean 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 fuels would last. (Refer Slide Time: 01:58) So, if you see, there is this interesting quote from the Saudi Arabian oil minister who said that the Stone Age did not 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 muchstock 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 this concept of 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? (Refer Slide Time: 02:45) So, we have this is the McKelvey diagram. This is the diagram which was used and this is shows, 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 we have the in the case of oil, you will have an 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 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 whole area has similar kinds of rock formations. So those will be called indicated and the third one is in similar areas, in similar formulations we expect that though we have not done any exploration, we think that it could be inferred that these will also help. (Refer Slide Time: 04:27) 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 measured and quantified, so we are quite sure that this is existing indicated with some lower probability and inferred with a, with even a lower probability. (Refer Slide Time: 05:07) 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 axes. One axis is in terms of the probability, and the second one is in terms of the economic. 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 are maybe known occurrences, but they are currently not economic to extract. So, resources are a slightly larger term which has a larger value and resources. (Refer Slide Time: 06:03) So, this concept of resources and reserves is shown in this classification, which is the McKelvey 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 in this, on this site and you have higher costs going in this direction. (Refer Slide Time: 06:28) So, there are two kinds of beliefs about resources. One is that if we look at a finite amount of reserves, 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 the extraction will occur. So, if we have a finite reserve and we are talking of a stock. (Refer Slide Time: 7:00) If we have a production in a particular year and we have t as time and we have P and we say that, 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 a static we define a static R by P ratio or the R by P ratio, which simply divides the total amount of known reserves 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 where the population grows exponentially and the requirement for many of the fossil fuels, coal or natural gas, has been growing exponentially. (Refer Slide Time: 08:27) 1970 70 MILLION TONNES 2012 557 MILLION TONNES For instance, if you take the example numbers, if you look at in India 1970, we use 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 exponential growth. (Refer Slide Time: 08:45) So, we are going to look at the 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 the logistic growth curve and where we take the fact that the area under the curve is bounded and yet there is a finite resource and then we look at Adelman’s model. (Refer Slide Time: 09:06) Again, this is the definition of the Geological Survey. The identified accumulation that can be extracted profitably under present economic conditions, that is the result and resources are the reserves, plus all accumulations that may eventually become available. They are, they may be today undiscovered but discovered but currently not technically or economically viable. (Refer Slide Time: 09:34) 1970 70 MILLION TONNES 2012 557 MILLION TONNES 557 70 =(1+g)42 g 5%(0.05) 6−7%/ year So, the resource is greater than the reserve and if you see, this is you, I told you that we are going for an exponential growth rate for coal. It is 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 you 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 exponential growth, then obviously that static R 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. (Refer Slide Time: 10:51) 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 significant proportion in the east. These are where the coal mines are there, there are some in the northeast, there are some lignite herein Tamil Nadu and some other. But this is where the distribution of the coal is. (Refer Slide Time: 11:16) Also, from the integrated energy policy document, this gives us a sense of what were the reserves which were there in 2003-4. You can see that the reserves were talking of 34000 million tons and the production was 414. If you divide these two, you get the 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 the, 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. (Refer Slide Time: 12:06) From the GSI if you look at it, you will find that over the years the proven reserves also keep increasing and today, if you see in 2018 values, I think it is of the order of about 148000 million tons. So, if we 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 we have an exponential growth rate, how do we make this calculation. So that means we are talking of let 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. The 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 you know, the 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 cutoff. So, we have already calculated if it was 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. (Refer Slide Time: 15:05) So, in order to do that calculation, we will take total reservation will be P, P 1 plus G raise to n so we can multiply this R into 1 plus g. The simple actually this is just a geometric progression. 1 plus g raise to n plus 1, we can take 2 minutes 1 and we get R one plus g minus R is equal to P 1 plus g raise to n plus 1 minus P and this is nothing but R g is equal to P into 1 plus g raise to n plus 1 minus 1. So, R by P is equal to 1 plus g raise to n plus 1 minus 1 by g, 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. (Refer Slide Time: 16:35) g(RP )=(1+g)N +1−1 (1+g)N+1=1+g(RP ) (N+1) [ln ⁡(1+g)]=ln[1+g(RP )] N +1= ln[1+g(RP )] ⁡ln(1+g) (Refer Slide Time: 17:51) We calculated for India for coal that R by P ratio was about was 246. And we said that let us consider the growth rate of 5%. We can, of course, take a higher growth rate so we can, suppose we take 5% then N +1= ln (1+0.05×246) ln ⁡(1.05) ¿ 2.59 0.049 =53 N 52 6%N 47YEARS 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 5%, if this is for 6%, then you will find that life will n decrease and n 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 anexponential growth rate. Now, in actual practice, what will happen is we expect that the pattern will not be exponential and suddenly coming to 0. (Refer Slide Time: 19:26) So, we expect this is similar to what Adelman had done but we have also this has been also doneby Hubbert who was a geologist and he proposed the method, it is called the Hubbert model. (Refer Slide Time: 00:24) Let us look at the critic of the finite resource constraint and this is the critic which is given by an economics Adelman, he says the total mineral in the earth is an irrelevant non-binding constraint if expected, finding minus development costs exceed the expected net revenues, investment dries up and the industry disappears. Whatever is left in the ground is an unknown, probably unknowable, but surely unimportant geological fact of no economic interest. So, it is not just, the reserves that we are talking of, only when it is economic and if it is viable then only it will be extractable. So, this whole calculation of the this is a critic which says that the calculation of the reserves should not be necessary then it depends on the costs and we will define that. (Refer Slide Time: 01:10) But just historically when we look at it, the static R by P ratio, the exponential ratio is interesting to see. In the McKelvey’s paper, he talks about two different models of any resource and you have a close market where initially because of the economies of scale, the prices can go down and then and depletion results in higher prices and as a result of this, the demand rises while prices fall and then as the depletion goes up and then the production rate goes down. So, we expect a curve which will go through a maximum and come down and similar kind of thing is expected even in the case of an open market. (Refer Slide Time: 02:06) So, in all the cases, what we expect is that we will have a bell-shaped curve Pt versus t, we will start from 0. Go to a maximum and come down and this is similar, this is essentially similar to the initial analysis which was done by M. King Hubbert, M. King Hubbert way back in the 1950s, The 1960s was a geologist with the Geological Survey. This was a time when there was no concept of finite resources, and we were talking of coal and oil and gas being the main source where we are going to have a lot of innovation and development and growth and but he was the first person who talked in terms of a limit and a reserve and looked at this kind of a shape of the curve. (Refer Slide Time: 03:08) So, let us look at, we will upload for you the original paper and you can take a look at that. But his analysis showed, he made these kinds of plots with this was. So, if you see the plots, these plots all follow. This was the trend which was there in the till the 60s. We were looking at exponential growth in all the resources. So, where we look at this is the world production of coal and you can see it start from a small amount and then it is been growing is fluctuation, but it is been growing exponentially. (Refer Slide Time: 03:40) Similarly, the world production of oil, US production of crude oil and he postulated that the overall production trend for any exhaustible resource will follow this kind of a curve and then he said that let us take the total amount of reserves which is there which is called as skew infinity. (Refer Slide Time: 04:10) And if we take 0 to infinity of pt it. This will give us the total amount of cumulative amount of reserves that we have and the production rate at any point of time pt will be DQ, dQp by dt. This is the Qp is the cumulative production from time t is equal to 0, t is equal to 0, to some time t. So, it is the cumulative production and that cumulative production. When we look at that cumulative production the rate of the dQp by dt will be the production in the dt here. And what he did was this was in the period when we did not have the computers and the modelling capability. (Refer Slide Time: 05:22) And so, he took essentially looked at these world fossil fuel reserves and he plotted the production and used it on a graph paper where the area under the curve would be the reserve and he estimated, based on the recoverable reserves estimate with this production fitted a curve of this type. And this is what he had done for world coal. And he had done this for the US and he had done this for the world coal, world oil production. Interestingly, the projected the year in which the US. the oil will peak. And this is the whole concept, the beginning of this peak oil. And we projected it as happening in a particular year. And it happened within a few years of that. So, this is where his analysis in future showed that this is the kind of things. But this represents one of the earliest analysis where you have this limit. And today we can use this and we can plot a curve and we will do this. We will take this analysis, we will derive a curve for this and this will be like a logistic curve and we will see what is the year in which the peak occurs. (Refer Slide Time: 06:50) When we talk about oil, you will see that the oil that we have is. Some of it is offshore and about half is onshore and we have certain needs distributed in certain areas. We, of course, have relatively less amount of oil and production only met a small proportion of our total. So, the R by P ratio, if you take the R by P ratio or the R by C where if you take the oil consumption, the R by C ratio if you see it is small and we do not have oil for even more than a decade. If we are to meet the total consumption from the Indian resources. But of course, most of our oil comes in terms of imports. (Refer Slide Time: 07:36) Similarly, in the case of oil supply also you can see globally oil supply has been increasing. We can just take a look at some of the trends in prices of some of these fossil fuels. So, we look at the coal price trend. In the UK, you can see the price variations in Germany, price variations in natural gas. So, there are fluctuations in these and then not showing many trends there. Of course, some of them have increased and decreased and we will now try and replicate the analysis which the, which was done by Hubbert and we will try and do this in terms of the logistic growth curve.