Robert C. Ransom



What are Archie’s Basic Relationships

The Graphical Model

What is Meant by the Plot of Rt versus Swtϕt

Summary of Equations

Parallel Resistivity Equations Used in Resistivity Interpretation

What is the Formation Resistivity Factor

The m Exponents

How is Exponent n Related to Exponent m

The a Coefficient

The Saturation Evaluation

Challenging Well-Log Examples

Observations and Conclusions from Figure 10 about Exponent n

Are There Limitations to Archie's Relationships Developed in this Model?




Symbols Defined



All Figures

About the Author

Table of Retrievable Contents:


This part will address two vintage well log examples, chosen because of their uniqueness and simplicity. All well bores in all well examples have been drilled with a fresh-water-based mud as verified by the SP curves. Figure 7 illustrates an oil-bearing bed in Well 1. Figure 8 illustrates the same oil-bearing bed in Well 2. It is not known which well was drilled first. There is no information about the reservoir beds in either example other than Well 1 produced much water and very little or no oil in a production test(s). The question is: Why does the bed in Well 1 not produce oil? Observe Figure 7 and Figure 8 during the following discussions.

Figure 7, Description of Well 1. This well has a significant resistive marker at the depth of 2516. The zone of interest is Zone A that lies between the depths of 2545 and 2620. This zone does contain oil. Zone A was tested over the marked intervals in the depth column and produced a large quantity of water and little to no oil. This bed, Zone A, exhibits a very distinctive annulus proving that there is both movable oil and movable water in the radial zone disturbed by invading drilling-mud filtrate. The deep resistivity curve suggests that Rt is 100 ohm-meters or greater and transitions to the predominantly water-bearing Zone B that lies between 2620 and 2629. In the predominantly water-bearing zone, Rt appears to be around 14 ohm-meters. Could this be R0? No other information is available. The question is: Why did a production test on Zone A recover a large amount of water from an apparently viable oil-bearing zone?

Figure 8, Description of Well 2. This well example is from the same stratum as Well 1 above. This well has the same marker as in Well 1 above, at 2536. The zone of interest is Zone A that lies between the depths of 2562 and 2596. This zone also contains oil. The SP currents are responding to the interference due to the presence of oil. In contrast to Well 1, Zone A in Well 2 does not exhibit an annulus. Why? The deep resistivity curve suggests Rt is around 100 ohm-meters and the bed transitions to Zone B that lies between 2596 and 2631 that appears to be wet with a resistivity of about 10 ohm-meters. Zone B transitions again to zone C that lies between 2631 and 2639 that appears to be even wetter with a resistivity of about 4 ohm-meters. Zone A at the upper part of this bed appears to contain oil. This bed in Well 2 provides more information than the equivalent bed in Well 1, however, the question still remains: Why was the large amount of water produced from what appears to be a viable oil-producing zone?

Channeling of water from the water-bearing zones B or C is not expected to be the answer, although it is a remote, but unlikely, possibility. But, it will be seen that there is another, more plausible possibility.

Information Derived from Logs from Wells 1 and 2: The calibration of the well logs on these two wells probably is not perfect, and there probably are inconsistencies between the two wells.

In Figure 7, Well 1, the gamma ray tool is very sensitive and shows some statistical variation. Zone A between 2545 and 2620 exhibits a very-well-developed annulus. The presence of an annulus means that there is both movable oil and movable water within the radial zone disturbed by invading drilling-mud filtrate. The radius of mud-filtrate invasion is shallow. The radius of invasion and resulting disturbance ends at the leading edge of the annulus. The Rt for this bed probably is in excess of 100 ohm-meters. The presence of mobile oil does not mean that the oil can be produced. It does mean, however, that the bed is very porous and permeable. With no other information to guide us, it might appear that Zone B between 2620 and 2629 is nearly 100% water saturated. If so, then R0 would be about 13 ohm-meters. The ratio of Rt / R0 of resistivity in the upper zone to that in the lower zone is about 10:1 and surely merits further investigation. The upper zone was tested over the depth intervals marked in the depth track and much water was recovered along with an insignificant amount of oil.

In Figure 8, Well 2, the zone of interest is Zone A between 2562 and 2596. The interesting thing in this zone is that there is no annulus. The hydrostatic pressure is great and mud-filtrate spurt-loss invades porous and permeable rock immediately as the drill bit penetrates the rock. Impermeable mud cake cannot develop on the face of the rock until the drill bit passes by and leaves the face of the rock open. An annulus then develops along with the creation of a filter cake that soon becomes an impermeable membrane, but begins to dissipate when the mud-filtrate no longer can invade the rock. Well 1 probably was logged with the resistivity tool immediately after drilling-mud circulation ceased and drill pipe was retrieved from the bore hole. The well, therefore, was logged while the annulus was still visible. After the mud circulation stopped and drill pipe was withdrawn from Well 2, the well operation probably incurred some delay before logging began. During that lull the annulus had time to dissipate before the well was logged. This behavior is not unique. Examples of this behavior have been observed by the author in “before” and “after” well logging sessions on numerous occasions, and are described in Ransom (1995). The dissipation of the annulus by the diffusion process is common in high-porosity, highly permeable reservoir beds, particularly where relative permeability to water is high compared with that to oil. In Zone A in Well 2, with the dissipation of the annulus and invaded zone, all resistivity curves read nearly the same and all are believed to approximate Rt . Has this zone and the upper zone in Well 1 been recently depleted and only oil at residual saturation remains? Why do these zones have such high resistivity and still produce only water?

A second zone in Well 2, Zone B, appears between 2596 and 2631. The radius of invasion is deeper in this zone than in Zone A because a lesser amount of oil is present and the relative permeability to water is higher. This zone has a resistivity of about 10 ohm-meters. This resistivity is not R0 because there is another zone below from 2631 to 2639 that shows even a lower resistivity. This bottom zone (Zone C) has a resistivity of about 4 ohm-meters and probably is R0 for both of the reservoir beds shown in Wells 1 and 2. If so, this makes the occurrence of all the water in the production tests that much more puzzling. Have the interesting top zones A in each well been depleted by recent emigration and now exhibit only residual oil? Then, what about Zone B between 2596 and 2631 in Well 2? This zone probably exhibits remnant oil after oil migrated out of the bed by natural means over geological time. This zone corresponds to Zone B between 2620 and 2629 in Well 1.

A depth marker in Well 1 appears at 2516. This marker could be compared with the correlative marker 2536 in Well 2 to help determine the depth relationship of one bed relative to the other and might help to explain any migration. But, the elevation of the depth datum is not known in either well so the true depth relationship between the A Zones cannot be determined. It remains that a quasi interpretation must be made in an effort to explain why neither zone of interest produces oil.

Deductive Interpretation: The potential oil-bearing beds in Wells 1 and 2 are found at shallow depths. Both porosity and effective permeability to water are expected to be high because of the lack of compactive overburden at the shallow depths of the beds of interest. This is supplemented with the reality that large amounts of water was recovered in the production test(s).

A second reason that the rock is thought to be very porous and highly permeable is because of the complete dissipation by diffusion of drilling-mud-filtrate in Zone A of Well 2. The porosity of Zone A in each well is expected to be higher than 25%, perhaps as high as 30%. Porosity of the bed and relative permeability to water are high and relative permeability to oil is low in this reservoir bed. Because of the expected good quality of the rock, the value of exponent m is believed to be low.

Resistivity R0 can be taken from zone C in Well 2, and is believed to be about 4 ohm-meters. Resistivity Rt in Zone A in Well 1 is in excess of 100 ohm-meters and in Well 2 is approximately 100 ohm-meters. It is possible that the difference in calibration betweenthe two logging tools would account for some of the difference in Rt values, but the more likely reason is the differences in Rwe and water-filled ϕne.

It is believed that oil might be at residual saturation in each Zone A, by emigration or by prior production from nearby wells. But what is the residual oil saturation value? It is not known, but could be 20%, 30%, 40%, 50%, maybe more.

The assumptions for any further calculations are: ϕt = 0.30, ϕne = 0.05, and m = 1.6. It should be noted that experienced analysts will agree that these assumptions are most favorable for the calculation and prediction of oil production.

The calculated Rw from zone C in Well 2 is about: 0.58

Questions inspired by these wells are:

a)  Should the prominent oil-bearing bed in either well be production tested?

b)  Should casing be set in either well?

c)  Is water channeling to the test depth from a location lower in the bed?

d)  Should attempts be made to isolate the tested depth interval in Well 1 and re-test?

e)  Should Zone A in Well 2 be tested?

f)  Can the water saturation be estimated?

Questions elicited here can be addressed with a certain amount of caution:

a)  To be absolutely certain that primary oil production is not viable, Well 1 probably should have been tested, as it was, but with the expectation that no oil would be recovered.

b)  No oil can be produced by primary production methods in either Zone A. No casing should be set in either well, unless enhanced oil recovery methods are entertained. Any method of recovery that can decrease the viscosity of the oil should be considered. If the viscosity of oil in Zone A can be reduced, whatever oil would be produced would have a very high water cut and the operator producing such oil would have to be prepared to handle the water produced.

c)  Water is not channeling from a lower level to Zones A or B in either well.

d)  No attempt should be made to isolate the test interval in Well 1 and re-test.

e)  Zone A in Well 2 should not be tested.

f)  What is the residual oil saturation in Zone A or B in either well? Because of the high resistivity and ample thickness in both Zones A, it is possible that enhanced oil recovery methods could be successful, but might not be economical. If considered viable and employed, perforations should be set high in the bed and withdrawal rate should be low to minimize coning by water. But, as it will be shown below, only the maximum calculated oil saturation can be predicted from these well logs and Figure 10. The actual oil saturation in any zone is speculative. It cannot be determined from these resistivity well logs alone. Other well logs and/or other disciplines should be employed.

A general conclusion is the reservoir bed is oil-wet because Rt in Zones A for both Well 1 and Well 2 have such high values in a rock where the assumed porosity is so high. Such resistivity values for Rt are 100 ohm-meters or more (and can be much higher in other oil-wet rocks) in the suspected oil-bearing zone when the probable R0 is only about 4 ohm-meters.

The relative permeability to water is much higher than the relative permeability to oil. This is corroborated by the large amount of water recovered in production tests.

Because the relative permeability to water and that to oil is significantly different, and because the mobility of water (is greater than the mobility of oil ( k0 / μ0 ) an annulus can form in Zone A of Well 1. Because the mobility of water is high, the time required for an annulus to develop or to dissipate is short as it was proposed for Well 2.

The reason why large amounts of water along with virtually no oil was produced during production test(s) in Zone A, Well 1, is believed to be because the mobility ( k /μ ) of water is so high and the mobility of oil is so low.

Because of the logic immediately above, the oil is expected to be very viscous, and the presence of oil is likely to reside at residual saturations in Zones A and B in both wells.

Because the proposed residual oil saturations in Zones B are lower than the oil saturations in Zones A, it is believed that the oil originally in place in both Zones B has been reduced by natural emigration over geologic time.



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