- [Geoffrey] So, to start off with, let's look at some basic theory of these two measurements and how they actually see the world, see the formation. So to begin with, the NMR. NMR, Nuclear Magnetic Resonance is affected by the rock properties themselves, by the fluid properties, and by the interaction between the two, the rock and the fluids. The rock properties, of course, the porosity gives the overall signal size. But we also get some measurements of the texture of the rock, or pore size distribution. And we also get effects from different mineralogy, of how the signals from the fluids interact with the surface of the rocks. Part of the NMR signal also comes from the bulk fluid properties themselves, the bulk relaxation and diffusivity, and, of course, the fluid saturation and how those two fluids interact with each other. So, we have a rock fluid interaction relating to surface relaxivity, and also the wettability of the fluids, which fluids are actually in contact with the rock. That results in the basic NMR combination equation where the measurement that we see, the T2 measurement, is a combination of fluid properties, the surface interaction, the surface to volume ratio, and also the diffusivity and some tool parameters, the experiment parameters of our NMR measurements. Resistivity, in a similar sort of way, is also dependent on the rock properties. The overall porosity, essentially the water-filled porosity, is primarily what we're seeing with resistivity logs. The pore system, the connectivity, cementation, et cetera, also affects the way the current flows through the rocks. The different fluid properties. Again, conductivity is the one that we need in order to be able to see the fluids, so we don't directly really see hydrocarbons at all with resistivity data. And then we've got the fluid rock interaction again either from, for instance, the clays, in particular, have a surface interaction, different clay conductivities and surface layers. And also the wettability, whether it's the conductive or the non-conductive fluids that are actually in contact with the rock surface. So that results in the basic resistivity equation. You may recognize this. This is essentially Archie's equation, but written in a similar way that matches the NMR there. That what we're measuring, the resistivity, is a function here of the saturations, the porosity and texture, and the fluid content, the water resistivity, plus extra clay terms in other equations which we'll come onto later. The basic NMR signal interpretation consists of a decay, which we get from a series of electromagnetic pulses. Where that hits the axis, we get porosity, and then the rate of decay determines some of the other properties that we're gonna use the NMR for. We deconvolve that using a multi-exponential decomposition of some sort, into what, for a single fluid in the pore space, is essentially like a histogram of pore sizes. From very small pores, the clay-bound pore spaces, intermediate pores with the capillary-bound fluids, and the larger pores which are your hydrocarbon storage capacity, or your potential hydrocarbon storage capacity. So there are various ways then of partitioning that data either using simple cutoffs or more complex methods. And we tend partition into clay-bound water, irreducible water, and movable water, and I'm starting with water here. So then we can add hydrocarbons into the pore space, and we get an overprint of a different T2 distribution, which is related to the type of hydrocarbon. Lower T2 values for heavier hydrocarbons, much higher T2 values for lighter hydrocarbons. Also depending on the individual tool type, whether it's a gradient or non-gradient tool of course. So the combination is what we see on the logs, the hydrocarbons main modifier, the water spectrum slightly, as well as showing an individual position on the T2 related to the hydrocarbon type. So if we look at the position of the different signals we see from NMR. Essentially, for the wetting phase, and for the moment I'm going to assume that that is water, a water-wet rock, the wetting phase is what is controlled by the surface interaction and the pore size. So for larger pores we see higher T2 values. As we get smaller and smaller pores, we get decreasing T2 values as there is more of a surface to volume ratio to have a bigger effect on the data, decreasing the T2. For the non-wetting phase, generally the hydrocarbon type, the position of the peak that we see in the T2 distribution is much more affected by the bulk properties of the fluid. So, for a fixed-gradient here, the light oil will be at a much higher T2 as we go to intermediate oils, to heavy oils, and in fact, very heavy oils and tar may actually go below what we can measure with the typical wireline or LWD-NMR tools. Although you may still be able to measure that in the lab with a far higher signal-to-noise of equipment. In contrast, we have the resistivity equations. I hope everybody listening is familiar with Mr. Gustavo Archie, who in 1942 first put the resistivity equations together to actually understand what resistivity meant in the formation. He put together the components of the formation factor. Formation factor being a property of the rock, which relates the porosity of the rock and the water resistivity of the rock to the resistivity you actually measure of that water-filled, 100% water-filled rock to start with. If we then put some hydrocarbons into the rock, we change the resistivity. Archie introduced the concept of the resistivity index, which was the ratio of the resistivity of the mixed-fluids-filled rock to the water-filled rock. And if we put those two components together, we get Mr. Archie's famous equation, which allows us to combine the resistivity logs with porosity measurements, water resistivities, and actually calculate the volume of water in the rock. So it's an indirect measurement, really, based on the resistivity and combining in other logs when you're using resistivity data. So here's Mr. Archie's equation in 1942. Now, the petrophysicists listening may notice something missing there, or may think there's something missing. In fact, Archie never included this a factor. That was about 10 years later that that got included as an empirical better fit to the laboratory data that Winsauer was using. And there's still debates today, in fact, about whether a should really be there. And then, lots of other people complicated the equations. Simandoux added some clay terms on the end. Then, for instance, the Indonesian equation converted to V shale volumes. And many other people provided lots of different equations. There are now dozens of possible ways of interpreting resistivity data. It can sometimes be difficult to know which one to use. It's certainly not an easy choice. Generally, the equations were derived as empirical solutions to fit local reservoir data. Those local reservoirs, you need to know if they were derived for laminar or dispersed clays, dispersed equations such as Waxman-Smits, for instance. Generally, they were for high or low salinity formation waters. And some are derived for total or effective porosity. So you really need to know what you're doing to pick the correct resistivity interpretation equation. And you may get some of the parameters wrong, so by combining resistivity with, for instance, NMR, it helps reduce the uncertainties in the overall interpretation. NMR responses are based on direct fluid volumetrics. We can look at the ratio of the bound fluids to the movable fluids, the volumetrics of each of them. And I'm looking here at bound water as being both the clay-bound and the capillary-bound water. In the following slides, you will see we're not separating them out, we're just considering all the bound water volume. And it is, generally speaking, all water. Movable fluids, the movable component, which could either be water or hydrocarbons. So we're distinguishing here the bound fluids, the movable fluids, which is your potential hydrocarbon storage. I'm working essentially in a total-porosity system. Resistivity sees the formation of it differently. Resistivity really only sees conductive fluids. It doesn't directly see the hydrocarbons at all. The hydrocarbons have the same response as the matrix in most cases. So resistivity-based fluid volumes are based on the conductive fluid volume. We multiply the saturation we calculate by the porosity, and that will give us a water volume. And then we can subtract the water volume from the total porosity, or the total water saturation. Multiply that by the porosity, and we get, by default in a way, the bit that's missing is, in fact, the hydrocarbon volumes from resistivity data. We don't directly measure that volume at all with resistivity data.