**Shaly Sands**

In a petrophysical sense shaly sands are clastic rocks with ‘excess conductivity’, that is a conductivity greater than the free water conductivity treated by the Archie’s equation. The Archie equation treats all rock conductivity as being due its free water so when Cw=0 then whole rock conductivity Ct=0. Archie accounts for this excess conductivity by assigning an extra water volume to the rock’s pore space causing it to report an Sw greater than the actual Sw. Archie is forced to report an extra water volume because it has nowhere else to put the excess conductivity.

The simplest way to think of this is with a Cw vs Co conductivity plot where shaly rock Co > 0, even if Cw=0.

Archie (1942) was aware that care should be exercised in applying his equation to more complicated cases; such as shaly sands. Waxman & Smits (1968) went on to quantify how to measure excess conductivity in the laboratory from the cation exchange capacity and Qv of reservoir cores and proposed an equation to treat this effect. Like many log analysis equations* the Waxman Smits equation is easiest to understand as a generalisation of the specific case of Archie, where shalyness, Qv = 0. If Qv = 0 then WS = Archie.

*Sw^n* = a.Rw / (Rt.Ø^m*)) . (1 / (1+(a.Rw.B.Qv/Sw)))*

* Sw = { Archie } x { Shaly bit } .. 1 if Qv = zero *

The shaly sand problem was and remains the most serious shortcoming of log analysis globally, despite the WS equation, its countless derivatives and other non-resistivity based solutions such as NMR, Dielectric, Sigma, Capillary pressure and of course direct Sw measurements from core.

* e.g. The Timur Coates permeability equation may also be thought of as a generalisation of the specific case of *k = f.(Ø),* by adding a qualifier to *Ø* and stating what portion of that *Ø* is movable.

water saturated Ro = a*Rw*Ø^-m.

*Under construction*