- So finally in summary, let's compare the Archie model, shown on the left, with the Geometrical Factor model, shown on the right. The Archie model is a power law in porosity. The Geometrical Factor model models the rock conductivity's product of the brine conductivity times the amount of brine times the geometrical distribution of the brine. If we include hydrocarbon bearing rocks into Archie's formulation then SW makes an appearance as a power. SW included in the Geometrical Factor theory is this SW times E. Now if I rearrange the terms then the SW is the fractional brine volume and the effective geometrical factor for the hydrocarbon bearing rock is a product in small E sub T so if we just use a simple beta for fractional brine volume and E sub T for the product of the geometrical factors, this is what we get. Now if I expand that equation in terms of the linear correlations to porosity and linear correlations to water saturation, you would notice that this equation is quadratic in water saturation, in other words if you multiply out the factors SW appears squared, so you can solve this equation for SW just using the quadratic formula and this is the result that you get, so this shows that the Geometrical Factor theory gives a complete theory for conductivity in Archie rocks whether they're brine saturated or hydrocarbon saturated, the comparable formula for Archie rocks is this SW is equal to the Nth root of all the stuff under the radical. We say in the paper that Archie will probably not be replaced by the geometrical factor theory as a practical matter because all of our computer programs are already well geared to Archie and there are plenty of Archie techniques that work and you can see also that the Archie formula for water saturation is quite a bit more compact than for the Geometrical Factor theory. The only disadvantages, it doesn't give you a way to interpret the rocks. So summing up, Archie's law is from an empirical observation. Hidden physics has been imputed to Archie's Law from the beginning. The adjustable parameters in Archie's Law are not understood to this day. We showed the data was scattered, can't be uniquely interpreted, and therefore Archie's Law is not a unique and inevitable inference from his data. We demonstrated a physics-based alternative, the Geometrical Factor theory. The Geometrical Factor theory has a priori physically interpretable adjustable parameters and we suggested connections to Geometrical Factor Theory to Percolation Theory which can be derived from first principals and we showed that relationships between well known, but little understood Archie extensions are a natural consequence of the Geometrical Factor Theory. Now I'd like to say before I leave, and this is a quote from the paper to someone up here, our intent is not Archie-bashing as criticism of Archie's model has been termed. We have utmost respect for Archie and his accomplishments. And we would like to use the opportunity, this presentation, to invite analysis and critiques and discussion of Archie's method. Finally, in the middle ages people used to argue about how many angels could dance on the head of a pin. Modern usage, that's the metaphor for wasting time. I would like to draw the parallel that we're wasting time arguing about the meaning of M and N and hey, we should use our time to better effect arguing about other things. Thank you.