The M-N Plot

Part 12, Chapter 12: Lithology and Mineralogy

Learning objectives

Build the lithology ratios M and N from the three porosity tools
Explain why M and N are independent of porosity
Read a mineral mixture as a point on a tie-line between endpoints
Use the gas and secondary-porosity directions as diagnostics

Two Ratios That Forget Porosity

The photoelectric factor reads one mineral; to resolve a mixture you need more. The M-N plot crosses two lithology ratios built from all three porosity tools,

M = \frac{\Delta t_f - \Delta t}{\rho_b - \rho_f}\times 0.01, \qquad N = \frac{\phi_{Nf} - \phi_N}{\rho_b - \rho_f}.

Each is a difference over a difference, so the $(1-\phi)$ that scales every log response cancels top and bottom, and only the mineralogy is left.

Minerals Are Points, Mixtures Are Lines

Each pure mineral plots at a fixed point, quartz, calcite, and dolomite forming a tight triangle, and a binary mixture slides along the straight tie-line between its two endpoints. Porosity moves the point nowhere, which is the whole reason the plot exists. So a reading that lands between calcite and dolomite is a calcite-dolomite mix, and its position along the line gives the proportions with no porosity correction needed.

The Diagnostics

The plot earns its keep when a point falls off the mineral triangle. Gas, with its low density and low hydrogen, kicks the point up and to the right; secondary (vuggy) porosity, invisible to the sonic, lifts $M$ straight up; and shale drags the point down toward the clay corner. Each departure is a flag that the rock is not a clean mineral mixture. The next plots carry the same idea with different log pairs, and the chapter ends by solving the mixture algebraically.

References

Schlumberger (2009). Log Interpretation Charts (chart CP-8). Schlumberger Educational Services.
Asquith, G. and Krygowski, D. (2004). Basic Well Log Analysis, 2nd ed. AAPG Methods in Exploration 16.