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. Rt 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, tma In Fig. 2, tma 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 tma, a porosity scale, places to hookup in Cedar Rapids 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 R0 = 5 ohm•m; accordingly, Rw (= R0/F) is 0.05 ohm•m.
The lines for other Sw values are straight lines, determined as previously described, radiating out from the Rt =?, tma = 47.5 pivot point.
For neutron logs, the latest intersection defines the fresh new matrix-hydrogen index, otherwise noticeable 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 ?Letter scale to be rescaled in ? and F units. With the F scale defined, Rw 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 Sw 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 compared to. 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 Rxo, then a line through points of mud-filtrate-saturated formations (Sxo = 1) should have a slope related to Rmf. Rmf 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 tma 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 Rmf line should be easier to determine because Sxo 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 Sw = 1 (using deep induction) and Sxo = 1 (using microlaterolog data). The points not in these trends can be divided into two groups:
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