If the matrix composition remains constant over the formations under investigation, the basic measurement from the sonic, density, or neutron logs can be plotted directly vs. R_{t} with similar results. [4] This is possible because of the linear relationship between porosity and bulk density, sonic transit time, or neutron-hydrogen index response. 2. The transit time has been plotted against the induction resistivity for several levels. The northwesterly points define the 100% water saturation line. The transit-time value at the point where this line intersects the horizontal line of infinite resistivity is the matrix-transit time, t_{ma} In Fig. 2, t_{ma} is found to be approximately 47.5 ?s/ft (156 ?s/m). This corresponds to a matrix velocity of 21,000 ft/sec (6,400 m/s).

By knowing t_{ma}, a porosity scale, a scale of formation factor (e.g., from F = 1/? 2 ) can be easily derived. A vertical line drawn through F = 100 (or ? = 10) intersects the water line at R_{0} = 5 ohm•m; accordingly, R_{w} (= R_{0}/F) is 0.05 ohm•m.

The lines for other S_{w} values are straight lines, determined as previously described, radiating out from the R_{t} =?, t_{ma} = 47.5 pivot point.

## Having neutron logs, the latest intersection describes the fresh matrix-hydrogen list, otherwise visible matrix porosity

Density and neutron logs can be crossplotted against resistivity in a manner identical to the sonic logs. For density logs, the intersection of the 100% water line with the infinite-resistivity line yields the matrix-density value, ?_{ma}. Knowledge of matrix density or hydrogen index permits the ?_{B} or ?_{N} scale to be rescaled in ? and F units. With the F scale defined, R_{w} can be calculated as for the sonic-resistivity crossplot, and lines of constant water saturation can be constructed in a similar manner.

These resistivity-vs.-porosity crossplots require that formation water resistivity be constant over the interval plotted, that lithology be constant, that invasion not be deep, and that the measured-porosity log parameter (i.e., t, ?_{B}, or ?_{N}) can be linearly related to porosity. This last condition implies that the time-average transform for the conversion of t into porosity is appropriate.

The neutron-resistivity crossplot is not as satisfactory in gas-bearing formations as are the sonic- or density-resistivity crossplots. The apparent porosity measured by the neutron log in gas zones is often much too low. This results in overstated S_{w} values in gas zones. Indeed, in a gas zone, the neutron resistivity may indicate a porous gas-bearing zone to be near zero porosity and 100% water bearing. In contrast, the sonic- or density-resistivity tends to be slightly optimistic in gas zones (i.e., porosities may be slightly high and water saturations slightly low).

## Microresistivity versus. porosity crossplots

This method is particularly useful for older logs or cases in which the analyst has only a paper copy of the log. A resistivity-porosity plot can also be made using the values from a shallow-investigation resistivity log such as the microlaterolog, MSFL, or MCFL log. If the microresistivity log reads approximately R_{xo}, then a line through points of mud-filtrate-saturated formations (S_{xo} = 1) should have a slope related to R_{mf}. R_{mf} is an important parameter, and this check of its value by means of a sonic-microresistivity or density-microresistivity crossplot is often useful.

These plots are also valuable for improved determinations of matrix parameters (either t_{ma} or ?_{ma}), particularly in cases where the sonic-resistivity or density-resistivity plot does not give a clear answer because of hydrocarbon saturation. The F R_{mf} line should be easier to determine because S_{xo} is usually fairly high even in hydrocarbon-bearing formations.

Fig. 3 shows a resistivity-porosity plot in which both the deep induction reading and the microlaterolog at the same levels are plotted in a series of water-bearing formations. The porosity values were derived in this case from a neutron-density crossplot. The plots from the two logs define two trends corresponding respectively to S_{w} = 1 (using deep induction) and S_{xo} = 1 (using microlaterolog data). The points not in these trends best free hookup site Cardiff can be divided into two groups: