- [Voiceover] 'Kay, so the basic interpretation is, first of all, you determine Vshale from gamma ray, SP, or density/neutron. You determine total porosity, effective porosity, by taking away from the total porosity, the Vshale contribution from the clay minerals that have porosity in the clay minerals. You determine formation resistivity, and then, a very powerful cross plot to compare resistivity with total porosity to interpret using the Archie relationship. 'Kay, Archie was a experimenter with Shell oil in the late 40's, and came up with this emperical relation, that is the absolute foundation of petrophysics. It's relating water saturation to the nth power, n is the saturation exponent, to Rw, which is water resistivity, to porosity, to a m power, which is the cementation exponent, times Rt. And so, the Archie equation is looking to get at water saturation, and then you assume that anything else in the porosity that is not water is hydrocarbons, oil or gas, or CO2, or nitrogen, or air, or something else. So, in petrophysics, we're only indirectly using Archie to get at oil saturation or gas saturation. 'Kay, the next diagram is a Pickett Plot, and this is a graphical solution to the Archie equation. On the vertical axis is porosity, logarithmic, on the x-axis is resistivity, logarithmic, and the data points are shown, and you, as the interpreter, choose what you believe to be aRw, water resistivity. If you have test data, you would at least consider that, but if you don't, you can get at it totally from logs. And then, you draw a line joining the points to the bottom right, and then you have made the assumption if that goes through what you consider to be aRw 100% water. Then, all the other data, by definition, have less than 100% water saturation. The vertical lines that you see, where it says n equals m, that is assuming if you stick it in vertically, that m is equal to n. If you think that there are differences, or have core data or something to show you, if you push it to the left, it means that you are assuming n is less than m. If you push it to the right, n is greater than m. And the concern is that this is highly interpretive, as I indicated for the gamma ray, you can essentially make things whatever you wish. And one of the problems is if you don't have water in the interval you're looking at, you don't know where that 100% water line is. And also, small changes on the logarithmic scale can make big differences in the numerics. So, again, it's a lot of skill and experience to interpret these things. If you want to be a pessimist, you make Rw as big as you can, and m and n as big as you can. If you're an optimist, you make Rw as low as you can, and n and m as low as you can. It's the most important petrophysical relationship of anything, it only applies to clean formation, and numerous adaptations including the dual water model that we use quite a bit attempt to correct for the excess conductivity of the clay minerals. There's probably 15 or 20 different models to try and incorporate that, basically adapting the Archie relationship to account for clay mineral conductivity. 'Kay, here's a fairly complicated picture. On the left, this is a clean formation analysis the standard one again from the Niobrara of Colorado. On the left side is shown all the raw data, gamma ray, porosity log, resistivity. The next one over is showing reservoir components, the yellow is matrix, in this case lime, calcites, limestone, or dolomitic lime. The little bit of grey on the left hand side is clay minerals, and the little bit of red on the right hand side is porosity. The next one over is water saturation. Cores in symbols, petrophysics in solid line, the green is oil, and the white stuff is in fact water. So, you can see here, that the water saturation coming out of cores is a little bit lower than coming out of logs, and we'll talk about that in just a moment. The next one over is bulk volumes of movable porosity that in the ping formation can contribute. Green is hydrocarbons, and they're very hard to see because the volumes are so small. There's a little bit of bulk volume of water, and again you can see the correlation with measured core porosity. The next one over is lithology, coming out of the U matrix of a matrix cross plot. The next one over is permeability, and it's a little difficult to see, but on the original you might be able to see it better. Quite often there's good correlation, but then, occasionally, you'll see points way over. It's a logarithmic scale, so occasionally you will see points that are three orders of magnitude bigger than what the petrophysical model would suggest. That probably is an indication of fractures, that is not being measured by the petrophysical analysis. Then, over on the right hand side is the Vshale model. The blue is the SP, and is totally useless, as you can see, doesn't work. The red is density neutron, the black is gamma ray, and you can see that the general trends of data are pretty close, and they agree quite well in the center towards the bottom, but not too well at the top. And I think most of us tend to accept the gamma ray.