-Going back now to Archie's equation, which is the fundamentalequation of all petrophysics. Water saturation relatedto 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 forreally isn't water saturation we're looking for what isn't water. So in all of petrophysicswe 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 whenhe was at School of Mines. In fact, just in parenthesis, he turned down aprospective 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 solutionon a log-log plot. You choose the 100% water saturation mine, Sw is 100% and the slope of that line that you choose is equalto minus one over m and the extrapolationto 100% porosity is aRw. The way that we've done this also, that choice of the watersaturation line is crucial. If you don't have any waterin 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 the100% water saturation line. Why have I violated those? Well, there are two reasons. We know this reservoir pretty well, we know what Rw is, weknow pretty much what m is, and also, more importantly, when you're interpreting these youshould be relying more on the high porosity levelsthan the low porosity because the petrophysicalcalculations 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 thiscase it's almost horizontal, if the trend of data is suchthat you could draw a line of about slope of two, justlike 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 changedn 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, watersaturation 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 theeffective porosity realm, effective porosity,effective water saturation. Some companies will work inthe total porosity realm, total porosity, andtotal water saturation. Here's a suggestion by Dewan, who wrote the famous textbook, to calculate effectivewater saturation from total water saturationusing the concept of Bound Water Saturation,contribution from the shales. You'll see some exampleslater on of SWE versus PhiE. I should say, we didn't talk about this, but in terms of saturationmodels in carbonates we tend to use Archie. The problem with Archie,especially in shaly sands, is that if there is acontribution of the shale, it reduces resistivity and you calculate saturates that are too high. There is a huge literatureof 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 youdon't have very many clays, and also if you have waterresistivities that are low or salinities of maybe 50,000parts per million or greater, then Archie is theappropriate model to use. You don't have to worry aboutthe 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 classicwork that Turk Timur did, sort of mimicking theKozeny-Carman equation, suggesting that permeability is a function of porosity and irreduciblewater saturation. It won't work if you're not inirreducible water saturation, so what we do is tocalculate the lower of Sw or from logs or Swi fromthe Buckles equation. If some of you haven't heardabout the Buckles equation, he published in 1968 or so that PhiE times Swi is a constant and that constant variedbecause of rock type. Rock quality, from carbonates to sands and different kinds ofcarbonates and so on. This is an example ofinterpretation 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 ofdensity, neutron responses. The next panel over is grain density and again, poor grain densities are shown. Not a very good correlationand 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 theeffective 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 modelto calculate water cut 146 00:07:04,800 --> 00:07:06,300 light blue to dark blue. When there's a lot of dark blue, as in the upper part, thereis 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, andalso 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 itis satisfying porosity, shale, and water saturation cut offs. The red means that it is notsatisfying water saturation, and there's a little bit ofyellow right down the bottom that is indicating that itis not either satisfying the 162 00:07:51,600 --> 00:07:55,133 Finally, permeability, usingthat transform we looked at and you can see it's apretty good correlation with core measured permeability.