- [Voiceover] Let's talk a little bit about lithology. Let's talk about it in more detail. We're going to focus on a density, neutron combination and a Rho matrix, U matrix. The Pe curve wasn't invented until about 1986, or something. So even though we can calculate from density, neutron acoustic devices of Rho matrix, delta T matrix cross plot, it isn't as good a differentiate as is the Rho matrix, U matrix plot. So we're gonna concentrate on Rho matrix, U matrix. This is kind of a summary where we got to the final bullet, it says sandstone, limestone, dolomite, and anhydrite each have distinct grain densities and also U matrix, which is the equivilant on the Pe log. They are very good, the combination of those two measurements, is a very good lithology differentiator. Pitfalls of using the density, neutron all by itself for lithology are gas effects will reduce the apparent grain densities. So you might think you're in a sandstone but you're not, you're in a gas-bearing limestone. And you might be in a limestone but you're not, you're in a gas-bearing dolomite. So that combination by itself doesn't sort out that problem for you. Also importantly, dolomite cemented sandstones will be misinterpreted as carbonates. You can't tell the difference between cherty dolomites and say a limestone-dolomite combination. We'll see that in a moment. Here is an example, courtesy of Lynn Watney from Kansas. On the left hand side is the density, neutron crossplot and then on the right hand side is the U matrix, Rho matrix. There's quartz, dolomite is down the bottom, calcite is on the upper left, and anhydrite is even further down to the right. You can see that there's a triangular solution to the quartz, dolomite, calcite combination but you could also set one up for calcite, dolomite, and anhydrite. You can see that this particular example is mostly limestone, a little bit of dolomite, and a little bit of quartz. The next one is from the Niobrara of Colorado and again you can see a similar kind of density, neutron pattern but now a little bit of a different distribution on the U matrix, Rho matrix. Much more dolomite in the sequence on the depth plot to the right and to the top. Then limestone, which is coming out of the bottom. On these depth plots we are making an attempt on the shale fraction to identify clay minerals. It's not easy, we're in the early stages of doing this because the clay mineral, petrophysical parameters are quite variable. But on the side logs in the shale intervals we are attempting to at least recognize clay mineral species. Here's an example, again from Lynn Watney in Kansas, and again you can see sort of a similar density, neutron pattern that we saw in all the other examples but now we can see categorically that this is not a limestone system, it is mostly a chert silica-bearing dolomite. It's very powerful in sorting out those kinds of etiologic combinations. Going back now to Archie's equation, which is the fundamental equation of all petrophysics. Water saturation related to Rw, water resistivity, total porosity and resistivity RT by theses exponents. N is the saturation exponent, m is the cementation exponent, and what we are looking for really isn't water saturation we're looking for what isn't water. So in all of petrophysics we calculate 1 minus Sw, assuming it's hydrocarbon saturation but it could be gas, oil, CO2, air, all sorts of things. Let's look at the very powerful graphical application of this that was invented by Pickett who was junior researcher working for Archie and I knew Pickett when he was at School of Mines. In fact, just in parenthesis, he turned down a prospective mine in Belize because of the Pickett plot. And he was right and I was wrong. Kind of interesting bit of history. Anyway, the way that this works is it's a graphical solution on a log-log plot. You choose the 100% water saturation mine, Sw is 100% and the slope of that line that you choose is equal to minus one over m and the extrapolation to 100% porosity is aRw. The way that we've done this also, that choice of the water saturation line is crucial. If you don't have any water in the system 100% wet, then this won't work and you have to judge using other methods. You might argue, why have I dilated the point in the bottom right, low porosity is below the 100% water saturation line. Why have I violated those? Well, there are two reasons. We know this reservoir pretty well, we know what Rw is, we know pretty much what m is, and also, more importantly, when you're interpreting these you should be relying more on the high porosity levels than the low porosity because the petrophysical calculations reliable. Pickett had a really good quick look, kind of application to this, that you might want to sort of note down. If the trend of data, in this case it's almost horizontal, if the trend of data is such that you could draw a line of about slope of two, just like we've got here, through it then I don't care what Rw is. Everything is at ISO saturation and you're either in water or you're at residual oil. If in fact you have a slope like this, where if you try to fit a line through it, you get an idiotic value for m, it means you've got hydrocarbons. So it's something to remember as sort of a quick look rule of thumb, is to have a look at these things. Here we have now changed n to greater than n, it's now n is 2.1, m is 1.9, and the green line that was vertical has now bent. If you flip back to the other, you can see that the saturation has infact now decreased, water saturation has decreased, not very much but it has decreased. The ISO saturation lines have moved up and towards the right. If you want to be an optimist, you use as low an Rw as you can and as low an m and n as you can. And if you're a pessimist, do the reverse. We tend to work in the effective porosity realm, effective porosity, effective water saturation. Some companies will work in the total porosity realm, total porosity, and total water saturation. Here's a suggestion by Dewan, who wrote the famous textbook, to calculate effective water saturation from total water saturation using the concept of Bound Water Saturation, contribution from the shales. You'll see some examples later on of SWE versus PhiE. I should say, we didn't talk about this, but in terms of saturation models in carbonates we tend to use Archie. The problem with Archie, especially in shaly sands, is that if there is a contribution of the shale, it reduces resistivity and you calculate saturates that are too high. There is a huge literature of adding to Archie and this is in fact part of it. This comes from the Dewan water model to try and correct. In carbonates, if you don't have very many clays, and also if you have water resistivities that are low or salinities of maybe 50,000 parts per million or greater, then Archie is the appropriate model to use. You don't have to worry about the problems of shaly sands. Permeability is not easy, there's no direct measurement petrophysically. Here is an equation that we use. It's modified on some classic work that Turk Timur did, sort of mimicking the Kozeny-Carman equation, suggesting that permeability is a function of porosity and irreducible water saturation. It won't work if you're not in irreducible water saturation, so what we do is to calculate the lower of Sw or from logs or Swi from the Buckles equation. If some of you haven't heard about the Buckles equation, he published in 1968 or so that PhiE times Swi is a constant and that constant varied because of rock type. Rock quality, from carbonates to sands and different kinds of carbonates and so on. This is an example of interpretation from the Niobrara. On the left hand side, is giving a statement of the fluids within the formation. The solid lines are core measured data. Core measured in blue is water saturation and magenta is oil. We are attempting to calculate differences between moved oil, which is in dark green, and unmoved oil in light green using detailed analysis of density, neutron responses. The next panel over is grain density and again, poor grain densities are shown. Not a very good correlation and it's probable because there's shale in this formation and the apparent grain densities coming out of density neutron cross plots are found spurious in shales. Next one over is the effective fluid volumes. Green is hydrocarbons, and dark blue is capillary-bound water and we're gonna tell you later on how we calculate that. Then right down the bottom, a little bit of light blue right there, that is either a different rock type or mobile water. If we relate over to the water cut, we put together a model to calculate water cut that is in fact based upon the ratio of light blue to dark blue. When there's a lot of dark blue, as in the upper part, there is no predicted water cut. We've taken that and published it into the relative permeability realm, to be able to then calculate water cut more vigorously than this. In oil, as it was, and also in gas reservoirs, to be able to calculate barrels of water per million cubic feet of gas. The vertical green bars are pay. The green means that it is satisfying porosity, shale, and water saturation cut offs. The red means that it is not satisfying water saturation, and there's a little bit of yellow right down the bottom that is indicating that it is not either satisfying the porosity cut off, it's only satisfying shale. Finally, permeability, using that transform we looked at and you can see it's a pretty good correlation with core measured permeability.