Determination of Porosity

Determination of Porosity by Density Log

• The bulk density ρb of a formation can be written as a linear contribution of the density of the rock matrix ρma and the fluid density ρf , with each present is proportions (1- ф) and ф, respectively :

• In terms of Porosity:

• where: – ρb = the bulk density of the formation

– ρma = the density of the rock matrix

– ρf = the density of the fluids occupying the porosity– ф = the porosity of the rock.

Determination of Porosity by Neutron Logs

Determination of Porosity by Sonic Log

• The sonic log is commonly used to calculate the porosity of formations, however the values from the FDC and CNL logs are superior.

• It is useful in the following ways:– As a quality check on the FDC and CNL log

determinations.– As a robust method in boreholes of variable size

(since the sonic log is relatively insensitive to caving and wash-outs etc.).

– To calculate secondary porosity in carbonates.– To calculate fracture porosity.

The Wyllie Time Average Equation

• The velocity of elastic waves through a given lithology is a function of porosity.

• Wyllie proposed a simple mixing equation to describe this behaviour and called it the time average equation.

• It can be written in terms of velocity or ∆t:

• where ∆t is the transit time in the formation of interest, ∆tp is that through 100% of the pore fluid, and ∆tma is that through 100% of the rock matrix, ф is the porosity.

Identification of Lithologies

Neutron-Density Crossplots

• The neutron-density charts appear to be less affected by lithology than the others.

• Because of this, formulas have been defined to calculate porosity.

• where: φN = Neutron porosityφD = Density porosity

For gas bearing zoneOil- and water-bearing formations

Sonic-Neutron Crossplots

• Porosity values for the crossplots between the sonic log and neutron are as good as the density-neutron crossplots.

• However, if evaporites are present, porosities will be erroneous

M-N cross plot

• The M-N lithology plot can be used to estimate lithology from the combination of neutron-porosity, bulk-density, and interval-transit time measurements.

• Any three minerals which have unique M and N values can be used, although the most common mineral triads used are calcite-quartz-dolomite and calcite-dolomite-anhydrite.

• The parameter M is nothing more than the slope of the ∆t-ρb time average curve, which varies slightly between the three major lithologies due to the matrix endpoints.

• The neutron-density cross plot yields a similar slope, designated as N.