The MID Plot

Part 12, Chapter 12: Lithology and Mineralogy

Learning objectives

Compute the apparent matrix density and transit time by stripping the fluid
Read lithology directly in grain density and matrix transit time
Explain why the apparent matrix needs an independent porosity
Use the gas and secondary-porosity departures as flags

Lithology in Real Units

The M-N plot identifies minerals with abstract ratios; the MID plot, for Matrix IDentification, does the same job in units you can read straight off a chart, the matrix grain density and the matrix transit time. You get them by stripping the fluid out of the density and the sonic with an independent porosity, the neutron-density crossplot value:

\rho_{maa} = \frac{\rho_b - \phi\,\rho_f}{1-\phi}, \qquad \Delta t_{maa} = \frac{\Delta t - \phi\,\Delta t_f}{1-\phi}.

A Two-Step Reading

Apparent matrix is a two-step calculation: first the porosity from the density and neutron, then the strip. Done right, every mineral lands at its true grain density and matrix transit time, quartz at (55.5, 2.65), limestone at (47.6, 2.71), dolomite at (43.5, 2.87), regardless of porosity, because the strip removes the fluid exactly. A binary mixture sits on the straight line between its endpoints, and its position gives the proportions.

When the Strip Lies

The strip is only as good as the porosity it uses. In gas the density-neutron porosity over-reads, the crossover from the earlier chapter, so the strip removes too much pore and the apparent matrix comes out too light, drifting toward low $\rho_{maa}$ . Secondary porosity, invisible to the sonic, leaves $\Delta t_{maa}$ too fast, drifting it toward the left. Each is a recognizable departure that flags a rock which is not the clean, liquid-filled mineral mixture the strip assumes, the same diagnostics the M-N plot carries in its own coordinates.

References

Schlumberger (2009). Log Interpretation Charts (chart CP-14). Schlumberger Educational Services.
Ellis, D. V. and Singer, J. M. (2007). Well Logging for Earth Scientists, 2nd ed. Springer.