A model, or set of equations, for the resistivity response of formations with conductive minerals, such as shaly sands. The model is used to analyze core data and to calculate water saturation from resistivity and other logs. The conductive rock matrix model (CRMM) was proposed by W. Givens. The model treats the rock as two components in parallel: a conductive pore network with fluid that is free to move, and the remainder of the rock, which may have conductive minerals or immobile but conductive water. The model is not concerned with the origin of this conductivity, but gives it a resistivity, R_{m}. The two components are in parallel as follows:
1 / R_{t} = 1 / R_{p} + 1 / R_{m}
where R_{p} is the resistance of the free-fluid pore network and can be expressed in terms of the porosity and formation water resistivity by the Archie equation. The model was developed from core data, and can explain the observed variations of the porosity exponent with porosity and the saturation exponent with water saturation in shaly sands. For log analysis R_{m} needs to be related to parameters that can be measured by logs.
Reference:
Givens WW: Formation Factor, Resistivity Index and Related Equations Based upon a Conductive rock Matrix Model (CRMM), Transactions of the SPWLA 27^{th} Annual Logging Symposium, Houston, Texas, USA, June 9-13, 1986, paper P.